Dilute Nitride Semiconductors

Dilute Nitride Semiconductors

Elsevier Internet Homepage - http://www.elsevier.com Consult the Elsevier homepage for full catalogue information on all books, major reference works, journals, electronic products and services. Elsevier Titles of Related Interest M. Henini & M. Razeghi Optoelectronic Devices: III Nitrides 0080444261, 2004 Professor M.O. Manasreh III-Nitride Semiconductors: Electrical, Structural and Defects Properties 0444506306, 2000 B.K. Meyer III-V Nitrides Semiconductors and Ceramics: from Material Growth to Device Applications 0444205187, 1998 Related Journals: Elsevier publishes a wide-ranging portfolio of high quality research journals, including papers detailing the research and development in III– N – V semiconductor alloys. A sample journal issue is available online by visiting the Elsevier web site (details at the top of this page). Leading titles include: Superlattices and Microstructures Physica E Physica B Microelectronics Journal Solid State Electronics Materials Science and Engineering: B Materials Science in Semiconductor Processing All journals are available online via ScienceDirect: www.sciencedirect.com To contact the Publisher Elsevier welcomes enquiries concerning publishing proposals: books, journal special issues, conference proceedings, etc. All formats and media can be considered. Should you have a publishing proposal you wish to discuss, please contact, without obligation, the publisher responsible for Elsevier’s Material Science programme:

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Dilute Nitride Semiconductors M. Henini School of Physics and Astronomy, University of Nottingham, UK

2005

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First edition 2005

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Preface The development of epitaxial growth technologies such as Molecular Beam Epitaxy (MBE) and Metal-Organic Chemical Vapour Epitaxy (MOCVD) has provided the possibility of producing very pure semiconductors and very well-defined layered structures known as Low Dimensional Structures (LDS). These structures, which display new physical phenomena, have led to a great improvement in our understanding of the basic physics of electrons and holes in semiconductors. Research on quantum wells (QWs), quantum dots (QDs), superlattices and heterostructures has rapidly expanded during the last few years due to their potential applications in novel devices and their many unique physical properties. The LDS technology is at the heart of many of the highest performance electronic and optoelectronic technologies being developed today. This is true not only in the research laboratories but also in the commercial marketplace. A brief assessment of the development of electronic and optoelectronic devices reveals the essential role played by compound semiconductor materials technology. This technology is highly sophisticated and the vision is of a new class of advanced semiconductor materials in which the band structure, for example, can be controlled by incorporating nitrogen in III –V semiconductors. The incorporation of small amounts of nitrogen, for example in III – V arsenides compound semiconductors, results in a decrease in the band gap such that it is possible to grow narrow band gap epilayers that exhibit optical emission in the technologically important 1.3 –1.55 mm wavelength range on GaAs substrates. After the proposal of GaInAsN as a material for long wavelength emission on GaAs by M. Kondow et al. (Jpn. J. Appl. Phys., 35 1273 1996), many laboratories are developing the technology of these materials due to the interest in its fundamental material physics and potential applications in QW and QD lasers. The investigation of dilute nitrides is revitalising semiconductor materials. These new materials offer device engineers new design opportunities for tailor-made new-generation electronic devices. Research in this strategically important area has already led to the demonstration of long-wavelength emission from QW laser devices, which are now commercially available using a (In,Ga)(As,N)/GaAs material system. In addition, novel dilute nitride-arsenide semiconductors QDs are expected to produce further extension of the lasing wavelength suitable for the optoelectronic communications industry. This book represents a timely and much needed attempt to bring together all the factors which are essential in dilute nitrides. The 18 chapters which make up this book give an account of the progress and challenges of III-N-V semiconductor alloys from their growth to device design and fabrication. It aims to convey important results and current ideas, and to provide an enjoyable account of a rapidly developing field. Moreover, the authors of this v

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Preface

book represent some of their own ongoing work. We trust that the publication of this book will contribute to the development of research and innovation in this exciting field of dilute nitrides. It is a pleasure to express special thanks and appreciation to the authors for their considerable efforts in contributing to this book. I would also like to acknowledge the assistance of the many individuals who donated their time to help make this a successful book. Special thanks go to all the people working at Elsevier for their invaluable help in the editorial process and for facilitating the rapid and accurate publication of this book. Mohamed Henini School of Physics and Astronomy University of Nottingham Nottingham, NG7 2RD, UK

Contents Preface

v

CHAPTER 1 MBE GROWTH AND CHARACTERIZATION OF LONG WAVELENGTH DILUTE NITRIDE III –V ALLOYS 1.1. Introduction 1.2. MBE Growth of Dilute III– V Nitrides 1.2.1 RF Nitrogen Plasma Source 1.2.2 Nitrogen Incorporation 1.2.3 Plasma Source Induced Ion Damage 1.2.4 Role of Sb as Surfactant in Metastable Growth 1.3. Dilute Nitride Characterization 1.3.1 Reflection High-Energy Electron Diffraction 1.3.2 High Resolution X-ray Diffraction 1.3.3 Photoluminescence 1.3.4 Secondary-ion Mass Spectrometry 1.3.5 Nuclear Reaction Analysis-Rutherford Backscattering 1.3.6 Cross-section Transmission Electron Microscopy 1.3.7 Cathodoluminescence 1.3.8 Photoreflectance, Electroreflectance and Absorption 1.3.9 Deep Level Transient Spectroscopy 1.3.9.1 Defects in MBE-grown GaNAs 1.3.10 X-ray Photoelectron Spectroscopy 1.4. Energy Band and Carrier Transport Properties 1.4.1 Doping Type 1.4.2 Electron and Hole Mobility 1.4.3 Carrier Lifetime 1.4.4 Diffusion Length 1.4.5 Effective Mass 1.4.6 Band Offsets 1.5. Annealing and N – In Nearest Neighbor Effects 1.6. Summary Acknowledgements References

vii

1 3 3 7 9 14 16 16 18 26 37 43 47 57 59 61 61 64 66 66 66 67 67 67 68 68 80 81 81

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CHAPTER 2 EPITAXIAL GROWTH OF DILUTE NITRIDES BY METAL-ORGANIC VAPOUR PHASE EPITAXY 2.1. Introduction 2.2. Epitaxial Growth of GaInAsN-based Structures 2.2.1 N Growth Precursors 2.2.2 Growth Conditions 2.2.2.1 Growth Temperature 2.2.2.2 Gas Phase Composition 2.2.2.3 Growth Rate 2.2.2.4 Growth Precursors 2.2.2.5 Growth Pressure 2.2.2.6 V/III Ratio 2.3. Long Wavelength GaAs-based Laser Performances 2.3.1 GaInAs Lasers up to 1.2 mm-Wavelength Range 2.3.2 GaInAsN Lasers up to 1.3 mm-Wavelength Range 2.3.3 GaInAsN Lasers Towards 1.5 mm-Wavelength Range 2.4. Conclusion Acknowledgements References CHAPTER 3 THE CHEMICAL BEAM EPITAXY OF DILUTE NITRIDE ALLOY SEMICONDUCTORS 3.1. Introduction to Dilute Nitride Semiconductors 3.2. The Chemical Beam Epitaxial/Metalorganic Molecular Beam Epitaxial (CBE/MOMBE) Growth Process 3.3. CBE of Dilute Nitride Semiconductors 3.4. Fundamental Studies of GaNxAs(12x) Band Structure 3.5. The Compositions and Properties of Dilute Nitrides Grown by CBE 3.5.1 Alkyl Source of Nitrogen 3.5.2 Plasma Nitrogen Source 3.5.3 Post-growth Annealing 3.6. CBE-grown Dilute Nitride Devices 3.6.1 Contacts 3.6.2 LEDs 3.6.3 GaInNAs Base Lasers 3.6.3.1 GaInNAs QW Laser Diodes 3.6.3.2 GaInNAs Quantum Dot Lasers

93 94 94 96 96 98 100 101 102 103 105 106 107 112 113 114 114

119 120 121 122 123 123 126 126 127 127 128 128 129 131

Contents 3.6.3.3 GaInNAs VCSELs 3.7. The Potential for Production CBE of Dilute Nitrides 3.8. Conclusions Acknowledgements References

CHAPTER 4 MOMBE GROWTH AND CHARACTERIZATION OF III –V-N COMPOUNDS AND APPLICATION TO InAs QUANTUM DOTS 4.1. Introduction 4.2. MOMBE Growth and Characterization of GaAsN 4.2.1 MOMBE Growth Method 4.2.2 N Incorporation and Lattice Relaxation 4.2.3 N Concentration Dependence of GaAsN Energy Gap 4.2.4 Reduced Temperature Dependence of GaAsN Energy Gap 4.3. Relation of In and N Incorporations in the Growth of GaInNAs 4.3.1 Observations of In and N Correlations in the Growth of GaInNAs 4.3.2 Observation of Enhanced N Incorporation with In Supply in MOMBE 4.3.3 Discussion on the Relation of In and N Incorporation in GaInNAs 4.4. Growth and Characterization of GaAsNSe New Alloy 4.5. Application of GaAsN to InAs Quantum Dots 4.5.1 Growth of InAs Quantum Dots 4.5.2 Strain Compensation by Burying InAs QDs with GaAsN 4.5.3 Red Shift of the Emission Wavelength of InAs Quantum Dots by Burying with GaAsN Layers 4.5.4 Improved Luminescence Efficiencies of InAs Quantum Dots by Burying with GaAsN Layers 4.6. Summary Acknowledgements References

CHAPTER 5 RECENT PROGRESS IN DILUTE NITRIDE QUANTUM DOTS 5.1. Self-organized Quantum Dots 5.1.1 A Brief Introduction to Quantum Dot Structures 5.1.2 Fabrication of Strained QDs by Self-organized Growth 5.1.3 Research Directions in Self-organized QDs

ix 131 132 133 133 133

137 138 138 138 141 143 145 145 145 147 148 149 149 150 151 153 154 154 154

157 157 157 159

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5.2.

Dilute Nitride Quantum Dots 5.2.1 Background 5.2.2 Prospects of Dilute Nitride QDs 5.3. Recent Experimental Progress in GaInNAS QDS 5.3.1 Self-organized Growth of GaInNAs QDs 5.3.2 Structural Properties of GaInNAs QDs 5.3.3 Growth Kinetics of GaInNAs QDs 5.3.4 Optical Properties of GaInNAs QDs 5.3.4.1 Effect of Nitrogen on Wavelength 5.3.4.2 Effect of Dot Size on Wavelength 5.3.4.3 Effect of Nitrogen on PL Intensity 5.3.5 Effect of Growth Temperature on GaInNAs QDs 5.3.6 Effect of Thermal Annealing on GaInNAs QDs 5.3.7 Effect of Intermediate Layer in GaInNAs QDs 5.3.8 Laser Diodes with GaInNAs QDs 5.4. Other Kinds of Dilute Nitride QDs 5.5. Summary and Future Challenges in Dilute Nitride QDs Acknowledgements References

159 159 160 161 161 163 165 165 165 166 167 168 168 169 170 173 173 174 174

CHAPTER 6 PHYSICS OF ISOELECTRONIC DOPANTS IN GaAs 6.1. Nitrogen Isoelectronic Impurities 6.2. The Failure of the Virtual Crystal Approximation 6.3. Prevalent Theoretical Models on Dilute Nitrides 6.3.1 The Band Anticrossing Model 6.3.2 Singularities in the Conduction Band Density of States 6.3.3 Symmetry-induced Splitting of the L-conduction Band 6.4. Electroreflectance Study of GaAsN 6.4.1 The Dependence of the Fundamental Band gap 6.4.2 The Broadening of E1 and E1 þ D1 6.4.3 The Origin of Eþ and Eþ þ D0 6.4.4 Another Unusual Transition Ep 6.5. Resonant Raman Scattering Study of Conduction Band States 6.5.1 LOG Intensity Resonance 6.5.2 LOG Width Resonance 6.6. Compatibility with other Experimental Results 6.7. A Complementary Alloy: GaAsBi 6.8. Summary

180 182 186 186 187 188 188 190 199 199 204 207 207 208 211 212 215

Contents 6.9. Conclusion References CHAPTER 7 MEASUREMENT OF CARRIER LOCALIZATION DEGREE, ELECTRON EFFECTIVE MASS, AND EXCITON SIZE IN InxGa12xAs12yNy Alloys 7.1. Introduction 7.2. Experimental 7.3. Single Carrier Localization in InxGa12xAs12yNy 7.4. Measurement of the Electron Effective Mass and Exciton Wave function Size 7.4.1 GaAs12yNy 7.4.2 InxGa12xAs12yNy 7.5. Conclusions Acknowledgements References

xi 217 218

223 225 225 230 232 244 247 248 248

CHAPTER 8 PROBING THE “UNUSUAL” BAND STRUCTURE OF DILUTE Ga(AsN) QUANTUM WELLS BY MAGNETO-TUNNELLING SPECTROSCOPY AND OTHER TECHNIQUES 8.1. Introduction 8.2. Resonant Tunnelling Diodes Based on Dilute Nitrides 8.3. Magneto-Tunnelling Spectroscopy to Probe the Conduction Band Structure of Dilute Nitrides 8.4. Electronic Properties: From the Very Dilute Regime (, 0.1%) to the Dilute Regime 8.5. Conduction in Dilute Nitrides and Future Prospects 8.6. Summary and Conclusions Acknowledgements References

264 269 274 275 275

CHAPTER 9 PHOTO- AND ELECTRO-REFLECTANCE OF III – V-N COMPOUNDS AND LOW DIMENSIONAL STRUCTURES 9.1. Principles of Electromodulation in Electro- and Photo-reflectance Spectroscopy 9.1.1 Line Shape Analysis 9.1.2 Experimental Details

280 282 284

253 255 259

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9.2. 9.3.

Band Structure of (Ga,In)(As,Sb,N) Bulk-like Layers (Ga,In)(As,Sb,N)-Based Quantum Well Structures 9.3.1 Theoretical Approach 9.3.2 Energy Level Structure of GaInNAs/GaAs QWs 9.3.2.1 Electron Effective Mass Determination 9.3.2.2 Conduction Band Offset Determination 9.3.3 Energy Level Structure of Step-Like GaInNAs/Ga(In)NAs/ GaAs QWs 9.3.4 Energy Level Structure of Sb Containing Ga(In)NAs/GaAs QWs 9.3.5 Broadening of PR Resonances 9.4. The Influence of Post-grown Annealing on GaInNAs Structures 9.4.1 Bulk Layers 9.4.2 Quantum Well Structures 9.5. Photoreflectance Investigation of the Exciton Binding Energy 9.6. Manifestation of the Carrier Localization Effect in Photoreflectance Spectroscopy References

CHAPTER 10 BAND ANTICROSSING AND RELATED ELECTRONIC STRUCTURE IN III-N-V ALLOYS 10.1. Introduction 10.2. Band Anticrossing Model 10.3. Experimental Evidence of Band Splitting and Anticrossing Characteristics 10.3.1 Synthesis of III-N-V Using Ion Implantation and Pulsed Laser Annealing 10.3.2 Optical Transitions Associated with the Split Conduction Band Edges 10.3.3 Effects of Pressure and Temperature 10.3.4 Effects of the Higher Conduction Band Minima 10.4. Novel Electronic and Transport Properties of III-N-V Alloys 10.4.1 Enhancement in Maximum Electron Concentration 10.4.2 Decrease in Electron Mobility 10.4.3 Mutual Passivation in III-N-V Alloys 10.5. Conclusions Acknowledgements References

285 293 294 296 299 301 302 305 307 309 309 311 316 319 321

325 327 332 332 334 336 340 343 343 347 348 353 354 354

Contents CHAPTER 11 A TIGHT-BINDING BASED ANALYSIS OF THE BAND ANTI-CROSSING MODEL AND ITS APPLICATION IN Ga(In)NAs ALLOYS 11.1. Introduction 11.2. Nitrogen Resonant States in Ordered GaNxAs12x Structures 11.3. Analytical Model for Quantum Well Confined State Energies and Dispersion 11.3.1 Confined State Energies 11.3.2 Effective Masses 11.4. Influence of Disorder on Nitrogen Resonant States, E2 and Eþ in GaNxAs12x 11.5. Conduction Band Structure and Effective Mass in Disordered GaNxAs12x 11.6. Alloy Scattering and Mobility in Dilute Nitride Alloys 11.7. Conclusions Acknowledgements References CHAPTER 12 ELECTRONIC STRUCTURE EVOLUTION OF DILUTE III –V NITRIDE ALLOYS 12.1. Introduction 12.2. Phenomenology of Dilute III – V Nitrides 12.3. Empirical Pseudopotential Methodology 12.3.1 Atomistic Geometries 12.3.1.1 Atomic and Structural Relaxation 12.3.1.2 Construction and Fitting of Atomic Pseudopotentials 12.3.1.3 Solving the Supercell Hamiltonian 12.4. Electronic Structure Evolution of Dilute Nitrides 12.4.1 Dilute Impurity Regime 12.4.2 Intermediate Regime 12.4.3 Conventional Alloy Regime 12.5. Summary of Electronic Structure Evolution 12.6. Phenomenology of Dilute Nitride Quaternaries 12.6.1 InyGa12y As12xNx 12.6.2 GaAs12x2yPyNx 12.7. Future Challenges of New Nitride Materials 12.7.1 InSb12xNx 12.7.2 GaAs12x2ySbxNy

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362 364 368 368 372 374 378 385 387 388 388

393 393 395 395 395 396 397 397 397 400 404 405 406 406 407 408 408 409

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12.8. Conclusions Acknowledgements References CHAPTER 13 THEORY OF NITROGEN –HYDROGEN COMPLEXES IN N-CONTAINING III– V ALLOYS 13.1. Introduction 13.2. Theoretical Methods 13.3. N – H Complexes in GaAsN Alloys 13.3.1 Structure and Energetics of Mono-hydrogen Complexes 13.3.2 Structure and Energetics of Di-hydrogen Complexes 13.3.3 Formation Energies and Stability of N – H Complexes 13.3.4 Transition Energies and H Passivation of N Electronic Effects 13.3.5 H Passivation of N Structural Effects 13.3.6 Formation Mechanism of N – Hp2 and N – 2HBC Complexes in p-type GaAsN 13.3.7 Vibrational Properties of N –H Complexes 13.4. Intrinsic N and H Impurities in GaP AND GaAs 13.5. N – H Complexes in InGaAsN 13.6. N – H Complexes in GaPN 13.7. Conclusions References CHAPTER 14 DISLOCATION-FREE III – V-N ALLOY LAYERS ON Si SUBSTRATES AND THEIR DEVICE APPLICATIONS 14.1. Introduction 14.2. Dislocation Generation Mechanisms in Lattice-mismatched Heteroepitaxy 14.3. Lattice-matched Heteroepitaxy of III –V-N Alloys on III– V Compound Semiconductors 14.4. Growth of Dislocation-free III – V-N Alloy Layers on Si Substrates 14.5. Device Applications 14.5.1 Double Heterostructure LED 14.5.2 III – V-N Alloy Lasers 14.5.3 Solar Cells 14.5.4 Opto-electronic Integrated Circuits

409 409 409

415 418 420 421 424 427 431 436 439 441 444 446 446 447 448

451 452 454 456 461 463 464 465 466

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14.6. Summary Acknowledgements References

467 468 468

CHAPTER 15 GaNAsSb ALLOY AND ITS POTENTIAL FOR DEVICE APPLICATIONS 15.1. Introduction 15.2. MBE of the GaNAsSb Alloy 15.3. Bands 15.4. Annealing Effect 15.5. Quinary Alloy 15.6. Long-wavelength GaAs-based Laser 15.7. HBT 15.8. Conclusions Acknowledgements References

471 472 475 478 482 485 488 491 492 492

CHAPTER 16 A COMPARATIVE LOOK AT 1.3 mm InGaAsN-BASED VCSELs FOR FIBER-OPTICAL COMMUNICATION SYSTEMS 16.1. Introduction: 0.85 mm versus 1.3 mm VCSELs 16.2. Approaches to Achieve 1.3 mm VCSELs 16.2.1 InP-Based Active Region 16.2.2 GaAs-Based Active Region 16.3. 1.3 mm VCSELs Based on InGaAsN 16.4. Outlook 16.5. Conclusion Acknowledgements References

495 497 497 498 499 502 503 503 503

CHAPTER 17 LONG-WAVELENGTH DILUTE NITRIDE –ANTIMONIDE LASERS 17.1. Introduction 17.1.1 Applications: The Driving Force for Long-wavelength Devices 17.1.2 Candidate Long-wavelength Materials Systems 17.2. Epitaxial Growth Systems: MOVPE and MBE 17.3. Ion Damage and Annealing Behavior 17.4. GaInNAsSb Edge-emitting Lasers

507 507 508 511 515 517

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Contents 17.4.1 17.4.2 17.4.3 17.4.4

Initial Results Pushing Beyond 1.3 mm Device Structures Laser Characterization 17.4.4.1 Temperature Dependence 17.4.4.2 Cavity Length Studies 17.4.4.3 Temperature Sensitivity 17.4.4.4 Above Threshold Parameters 17.4.4.5 Comparison of QW and Barrier Designs 17.5. Spontaneous Emission Studies 17.5.1 Features of the Spectrum 17.5.2 Fermi-level Pinning 17.5.3 Local Z-parameter 17.6. GaInNAsSb VCSELs 17.6.1 GaInNAsSb VCSEL Design 17.7. High Power Lasers Based on GaInNAs(Sb) 17.7.1 High-power Laser Design Issues 17.7.1.1 Catastrophic Optical Damage (COD) 17.7.1.2 Thermal Rollover 17.7.2 Current GaInNAs(Sb) Laser Results 17.8. Relative Intensity Noise 17.8.1 Definition of RIN 17.8.2 Theoretical Expression for RIN 17.8.3 Measurement of RIN 17.9. GaInNAsSb Electroabsorption Modulators and Saturable Absorbers 17.10. Laser Reliability 17.10.1 Constant Current Life-testing 17.10.2 Constant Power Life-testing 17.10.3 Accelerated Degradation 17.11. Summary Acknowledgements References

517 518 519 520 520 523 525 528 530 532 533 535 536 539 540 547 547 548 550 551 552 552 553 553 558 563 565 565 566 568 569 569

CHAPTER 18 APPLICATION OF DILUTE NITRIDE MATERIALS TO HETEROJUNCTION BIPOLAR TRANSISTORS 18.1. Introduction 18.2. Design Considerations for GaInNAs-based HBTs 18.3. Material Growth and Device Processing

579 585 591

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18.4. GaInNAs HBT Results 18.5. Circuit Applications for GaInNAs HBTs 18.6. Future Outlook Acknowledgements References

595 604 606 608 608

Index

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Dilute Nitride Semiconductors M. Henini (Ed.) q 2005 Elsevier Ltd. All rights reserved.

Chapter 1

MBE Growth and Characterization of Long Wavelength Dilute Nitride III –V Alloys J.S. Harris Jr., H. Yuen, S. Bank, M. Wistey, V. Lordi, T. Gugov, H. Bae and L. Goddard Solid State and Photonics Lab, Stanford University, Stanford, CA USA

1.1. INTRODUCTION

The level of research activity on GaInNAs and GaInNAsSb has increased dramatically since the discovery by Weyers et al. in 1992 and Kondow et al. in 1994 that the band gap of GaAs decreased rapidly with the addition of small atomic fractions of N [1 – 3]. This led very quickly to research on lattice or near-lattice-matched GaInNAs alloys as the addition of In not only provided a closer lattice match to GaAs, but also decreased the band gap, making GaInNAs useful for 1.3– 1.55 mm telecommunications applications [4]. The band gap versus lattice constant for the range of ternary and quaternary alloys lattice matched to GaAs and InP that are suitable for the 1.3 – 1.55 mm telecommunications wavelengths are illustrated in Figure 1.1, where the horizontal lines define band gap and wavelength and the vertical lines through GaAs and InP define lattice match. Before Kondow’s discovery, it was widely believed that InGaAsP lattice matched to InP was the only alloy series that could meet the telecommunications requirements. With the discovery that communications wavelength lasers could be fabricated on GaAs, a number of research groups initiated work on GaInNAs because of the tremendous processing advantages offered by GaAs over InP. The two most significant advantages are the larger refractive index difference for lattice matched alloys, enabling distributed Bragg reflecting (DBR) mirrors to be epitaxially grown with the quantum well (QW) active regions, and the highly selective oxidation of AIAs to form AlOx, which is used to provide current and optical confinement. We believe this will ultimately lead to integration of photonic crystal structures with lasers, detectors, optical amplifiers, etc. within a single alloy materials system, providing the foundation to fabricate truly revolutionary intergrated photonic circuit technology. The device applications and progress on the development of longwavelength lasers is reviewed in Chapters 15 –17. Research on GaInNAs has revealed several additional factors vis-a`-vis InGaAsP/InP that could prove decisive in the race to produce low cost, long-wavelength VCSELs and high power Raman pump lasers. First, for the same band gap material, the conduction band 1

2

Dilute Nitride Semiconductors

Figure 1.1. Band gap versus lattice constant for III-arsenide alloys showing lines of lattice match to GaAs for nitride–arsenide alloys and to InP for arsenide–phosphide alloys in the region applicable to long-wavelength fiber systems.

well is deeper [3,5,6], as described in Chapters 9 and 10 and the electron effective mass is larger, as [6,7] described in Chapters 7 and 8. This provides better confinement for electrons and a better match of the valence and conduction band densities of states, which leads to a higher T0 ; higher operating temperature, higher efficiency, and higher output power [5]. Second, most of the energy band engineering used to minimize heterojunction voltage drops use intermediate graded layers of AlxGa(12x)As or AlAs/GaAs superlattices, all of which are lattice matched to GaAs and do not require difficult compositional control over both column III and column V constituents in a quaternary layer, such as InGaAsP, to maintain lattice match [1]. Third, compositional control and uniformity of GaInNAs grown by molecular beam epitaxy (MBE) [8 – 14] is relatively easy compared to metalorganic vapor phase epitaxy (MOVPE) growth [15 –23] or to As/P control in InGaAsP [24,25]. This will translate into better yield and far easier scale up to larger wafers for lower cost. Fourth, VCSELs can be straightforwardly fabricated using the well-developed GaAs/AlAs mirror and AlAs oxidation for current and optical aperture confinement technologies. Fifth, GaInNAs on GaAs provides easy monolithic integration with GaAs electronics that will be essential to provide low-cost, high-speed integrated electrical drivers for direct laser modulation in high-speed networks. Because of the exciting potential and recent progress for GaInNAs, there have been a number of reviews [26 – 28], as well as Chapters 15 –17 of this volume, describing growth and fabrication of long-wavelength GaInNAs lasers. This alloy is a challenging material to grow because the end alloy constituents have different crystal structure: InGaN is wurtzite

MBE Growth and Characterization of Dilute Nitride III– V Alloys

3

(hexagonal) and InGaAs is zinc blende (cubic), which results in a large miscibility gap in the alloys. The equilibrium solubility of N in GaAs is very low, so growing useful material requires that growth be carried out under metastable conditions accessible only by MBE and MOVPE. To date, growth by MBE has proven far easier and the device results generally better and over a far greater range of wavelengths. However, even for MBE, there are very significant challenges to achieve good epitaxy and high optical quality material. One of those issues has been control of the growth parameters to achieve good material; one of the significant advances has been adding Sb to form a quinary alloy, GaInNAsSb. Although GaInNAs and G cxzaInNAsSb are relatively new, there has been significant progress made in understanding these alloys. For that reason, this chapter will focus specifically on the important issues and progress in MBE growth and characterization of GaInNAs (Sb), as well as their unusual and important properties for device applications.

1.2. MBE GROWTH OF DILUTE III –V NITRIDES

Dilute nitrides or dilute nitride –arsenides are very different III – V semiconductors, not only for their electronic properties, but also because of the very large range of miscibility gap in the alloys, the different crystal structure for the endpoint alloys (zinc blende for InGaAs or GaAsSb versus wurtzite for InGaN) and the methods by which they must be grown. Most ternary and quaternary semiconductors, such as AlGaAs and InGaAsP, have complete miscibility across the entire alloy range and can be grown by MBE using standard Knudsen effusion cells and thermal sublimator and cracker cells. Nitrogen in its standard state, N2, is an extremely stable molecule with a dissociation energy of 9.76 eV [29]. Injecting N2 into the MBE chamber would only lead to a very small amount of interstitially incorporated N2 and a cryopump full of N gas. In order to incorporate N into the lattice, one must create a more reactive form of N: atomic N. The dissociation energies for arsenic (3.96 eV) and phosphorous (5.03 eV) are small enough to enable cracking (i.e. As4, As2) using cells which have a high temperature zone and baffles to “crack” the molecules. Unfortunately, N has a bond much too strong for such standard ultrahigh vacuum cracking methods. Different sources of N must be considered and many have been used in the past including ammonia, hydrazine, radio frequency (rf) plasma, electron –cyclotron resonance plasma (ECR), and DC plasma sources. Because the plasma source is the largest difference between the dilute nitrides and other III– V alloys, we concentrate on the N source, ion damage from the source, N incorporation, the role of Sb as a surfactant in the control of metastability and N incorporation and MBE growth of the quinary alloy, GaInNAsSb. 1.2.1 RF Nitrogen Plasma Source The most successful method of obtaining reactive atomic N has been the use of a rf plasma source. Dissociated atomic and molecular radicals and ions are generated in the plasma

4

Dilute Nitride Semiconductors

and escape from a front aperture plate towards the substrate, depositing in substantial concentrations. Ions generated in the plasma can be accelerated by the rf fields and cause substantial substrate damage while radical neutrals should inflict little damage and incorporate on substitutional sites. There are many different parameters which control the plasma, including forward rf power, reflected rf power, the N gas flow rate, the number, size and configuration of holes in the front aperture. Unfortunately, there are very few analytical techniques which are available in MBE to measure the plasma properties and determine the ideal operating conditions directly. It is also not completely known which characteristics of the plasma are beneficial to high quality crystal growth and which contribute to detrimental defects. We chose a rf plasma over other options because of its low ion count and high atomic dissociation yield [30]. During the early history of GaInNAs, rf plasma cells normally used for growing GaN were adapted for use in growth of dilute nitride (a few atomic percent) alloys. Several companies now make rf plasma cells specifically for dilute nitride – arsenide growth including Veeco Applied-Epi [31], SVT Associates [32], Oxford Scientific [33], and Adon. Our group is most familiar with the SVT Associates rf plasma cell because of the circumstances surrounding available equipment during the early stages of GaInNAs growth. The SVT Associates cell was chosen at the time since it was the only model which had a removable pyrolytic boron nitride (PBN) front aperture plate in which the number, size, and orientation of holes could be modified to reduce the N flux as well as control the deposition behavior. This was particularly important initially since dilute nitride –arsenide growth was very new at the time and most N sources were used for high growth rates in GaN. Another advantage of the SVT Associates cell was the fully transparent back viewport which allowed for direct monitoring of the plasma glow. The operation of the rf plasma was optimized to maximize the generation of atomic N within the limits of stable plasma operation. The plasma conditions that maximize the amount of atomic N versus molecular N are determined using the emission spectrum of the plasma (see Figure 1.2). The amount of molecular N is determined from the ratio of the integrated intensity of the first set of bands at approximately 550, 580, and 650 nm to the integrated intensity in the bands at 740, 820, and 870 nm, which is proportional to the amount of atomic N present in the plasma [11]. Hence, the ratio of the integrated peak intensities due to atomic N transitions and the integrated peak intensities due to molecular N transitions is proportional to the relative amount of atomic versus molecular N in the plasma. The total intensity integrated from 550 to 950 nm is proportional to the total amount of excited N in the plasma. The amount of atomic and excited N in the plasma as function of (a) N flow, (b) plasma power, and (c) number and diameter of holes in the plasma source front cover plate. To optimize the plasma for maximum atomic N, we investigated how the ratio of atomic N versus molecular N varied in the plasma with N flow rate and plasma power. We observed that changes in gas flow and power did not produce linear

MBE Growth and Characterization of Dilute Nitride III– V Alloys

5

Figure 1.2. Measured fluorescence from N plasma source showing transitions for molecular N2 and atomic N. The ratio of the integrated intensity from these lines was used to optimize the plasma source operating conditions to maximize the atomic N ratio.

changes in atomic N and that the plasma changed modes with rather dramatic changes in output. Because the operating points for these mode changes were not particularly consistent and reproducible, we decided to operate the plasma source under constant conditions of power and gas flow where the source was very stable and the ratio of atomic N was near maximum. Not all plasma sources have such a viewport for plasma characterization; however, it also had its drawbacks. Monitoring the optical emission of the plasma in this configuration has limited utility. Only the back periphery of the glow is in reality being measured and this may not be representative of the active species emitted from the front aperture of the source. Also, the plasma is not completely confined by the PBN liner, which may change the rf environment and coupling to the plasma, thus sacrificing stable operation and reducing containment of N gas in the MBE chamber. Plasma stability during low N flow growth is one of the biggest problems for growth of dilute nitrides and is probably the greatest cause of differences not only between wafers grown in the same system, but particularly in comparisons between different groups who think they are growing under nominally identical conditions. Some of this is the result of short-term plasma instabilities in the source, others due to long-term changes in the source. A second issue is ion or electron damage to the epitaxial films from the plasma source, which is quite dependent upon the current operating region of the source. It is also dependent upon the use of charged particle deflecting plates at the source exit. Our experience with the stability issues of plasma sources is described in the remainder of this section and ion damage in the following section.

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Dilute Nitride Semiconductors

One of the major stability issues emanates from the fact that these sources were all originally designed for high growth rate GaN deposition. Source instability came in many different forms, including: difficulty maintaining a stable flow of injected gas at low flow rates, difficulty in igniting and maintaining a consistent plasma and its degradation over time, and difficulty in reproducibility due to thermal and power instability. The flow stability problem was one largely of system design due to rf coupling from the plasma power supply, matching network and source into the mass flow controller (MFC) which controls the flow of N gas. Improved rf shielding of the matching network and components, including the MFC, then enabled reliable control of very low and stable flow rates (as low as 0.1 sccm). The problem of igniting and maintaining the plasma is a degradation problem which gets worse with time. This manifests itself in requiring an increase in the flow rate necessary to ignite the plasma after several months of operation and in worst cases, the plasma would extinguish intermittently during growth. First, it appears that there is decomposition of the PBN crucible during operation, creating boron dust as well as plasma etching of the holes in the front aperture plate. The only solution to this problem is to replace the crucible when servicing the MBE system and to minimize the duration of plasma operation. Also, As contamination can be a problem in the crucible. During growth when the plasma cell is off, the cell is not heated and As can condense in or on the cell. This can either contaminate the inside of the cell which interferes with the plasma characteristics or coats the outside of the crucible which acts as an electromagnetic shield and reduces rf coupling into the plasma. In order to minimize this problem, a gate valve can be installed to isolate the cell from the rest of the chamber when N is not needed. Another stability problem is the time required for temperature and power to stabilize in the cell. This is a particular problem when growing laser structures as there is more N leakage or “blow by” around the shutter than for normal evaporative sources. This results in relatively heavy N “doping” when the source is operating, but with the shutter closed. We typically see mid-1019 cm23 levels of N in such films. This is a serious problem when growing AlGaAs as even minute quantities of N dramatically increase the trap density and non-radiative recombination rate. Our current solution to this problem is to run the cell for a period of time before the wafer is loaded and growth is started. This allows the cell to thermally stabilize before a growth starts. The source is then extinguished, but kept with below ignition rf power on to maintain the temperature while other non-N containing layers are grown and then ignited shortly before N containing alloys are grown. However, this is not always a viable solution and the blow by around the shutter is far worse when the plasma is ignited. These problems can be greatly reduced by using better shutter designs or completely eliminated by placing the source behind a differentially-pumped gate valve.

MBE Growth and Characterization of Dilute Nitride III– V Alloys

7

1.2.2 Nitrogen Incorporation Incorporation of N into GaAs is unlike crystal growth of most other III– V semiconductors. The kinetics of growth is different from that found for arsenides, phosphides, or antimonides in that the surface is not usually terminated or stabilized by one of the aforementioned group-V species. Nitrogen also does not compete in the same manner as other group Vs for the group-V lattice site. For example, there is no simple relation of composition for various As and P fluxes for a certain growth rate when growing arsenide – phosphides. The As and P compete for the group-V sites in complex ways which can also be altered by variables such as growth rate and substrate temperature. The material system requires many calibration samples beforehand to know the exact concentration obtained during growth. During dilute nitride– arsenide growth, N appears to be independent of the As flux and substrate temperature and is affected only by the group-III growth rate. It was decided to maintain constant plasma parameters while adjusting the group-III growth rate to ensure similar plasma conditions during deposition. Other groups control N incorporation by varying flow rate or rf power. However, as explained earlier, varying power or flow rate can greatly modify plasma characteristics and change material quality [34]. With constant rf power and N flow rate, the group-III growth rate was varied. It was found that the N concentration follows an inverse dependence to the group-III growth rate. This inverse linear dependence is valid to concentrations as high as 10%, at which N incorporation is difficult to analyze accurately due to phase segregation and relaxation [10]. A plot is shown in Figure 1.3 of a series of GaNAs samples grown at different growth rates [35].

Figure 1.3. Concentration of nitrogen in GaNAs as a function of group-III growth rate. Plasma conditions are 300 W forward power and 0.5 sccm N2 flow. Concentrations determined by HRXRD.

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Dilute Nitride Semiconductors

Figure 1.4. v=2u (004) scans of GaNAs samples grown at increasing temperatures showing N composition is virtually independent of temperature until the highest temperature (5758C).

The inverse linear dependence is due to the fact that all incident N (of the correct species) adsorbs onto the GaAs growth front with unity-like sticking and is then buried by additional Ga and As adatoms. Thus, the higher the group-III growth rate, the lower the amount of N found per volume of material. The N incorporation is also independent of substrate temperature up to temperatures close to normal GaAs growth temperatures of 5808C [36] as shown in Figure 1.4. At very high temperatures, phase segregation results and the incorporation kinetics are drastically altered. It was thought that there was unity sticking of N when growing Ga(In)NAs since the relationship between the inverse of the group-III growth rate and N concentration was linear. However, this was found not to be the case when Sb was introduced. The addition of Sb to GaNAs, forming GaNAsSb, had increased the amount of N under identical growth conditions [13,36,37]. This was surprising since this had disproved the theory that N had unity sticking when growing Ga(In)NAs. Antimony had somehow enhanced the N incorporation into the material leading to upwards of a 50– 60% increase in composition. The mechanism for the increased sticking of N in the material is not known. However, it is thought that the properties of Sb as a “reactive surfactant” [38,39] help promote the incorporation of N into GaAs. By reducing surface mobility and having strong interactions with the adsorbing species, it is possible that the Sb prevents any incoming N from desorbing back into the chamber. The behavior of the enhanced incorporation is also uncertain. Some studies have indicated that there is a relationship [13,37] between Sb and N concentration whereas others report the N concentration remains constant [36] for different values of Sb. The differences between the two findings may be due to different concentration regimes in which a certain saturation is required to enhance the N concentration or such that the Sb flux itself is more important than the resultant Sb concentration.

MBE Growth and Characterization of Dilute Nitride III– V Alloys 1.2.3

9

Plasma Source Induced Ion Damage

One of the most critical parameters for good optoelectronic devices is low non-radiative recombination. This has been one of the biggest challenges for all of the dilute nitrides because of the low growth temperature and requirement in MBE to use some type of plasma source to produce atomic N that is sufficiently reactive to be incorporated into the alloy. As a result of the low temperature growth and ion damage from the source, the luminescence properties of GaInNAs deteriorate incredibly rapidly with increasing N concentration [1,10, 11,40 –54]. We have undertaken a number of investigations of GaInNAs quantum wells to try to understand the luminescence problems. Thermal annealing increases the PL of GaInNAs QWs by 30 –75 £ over as-grown QWs as well as blue shifting the luminescence peak by 50– 80 nm. Typical PL spectra before and after annealing are illustrated in Figure 1.5 [10,11]. This effect has been extensively reviewed, although the causes have not been clearly elucidated. The increase in intensity is presumably due to both the out-diffusion of point defects and an increase in the crystalline quality of the quantum well material. The wavelength shift was long thought to be due to either or both N out-diffusion and group-III interdiffusion (Ga/In) [10,11,41 –45,55,56], however, this now appears to be largely due to local atomic rearrangement of the N nearest-neighbors (NN) from largely Ga in as-grown material to largely In in annealed material [57,58]. Section 1.5 reviews the new experimental results which support this conclusion. One of the suspected causes of the poor luminescence was ion or electron damage from the N plasma source as illustrated in Figure 1.6(a). Such damage was reported by Pan, Li and coworkers at the 2000 International MBE Conference [59 – 61], however, they were using a DC plasma source while almost all other MBE groups were using rf sources.

Figure 1.5. Photoluminescence of as-grown and annealed GaInNAsSb illustrating increased intensity, narrower linewidth and wavelength blue shift with increased anneal temperature.

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Dilute Nitride Semiconductors

Figure 1.6. (a) Schematic diagram of nitrogen plasma source and different species which are created (N2þ ion, N atom, electron) and their interaction at the surface, and (b) diagram illustrating bias plates at the output deflecting N2þ ions and electrons such that only neutral atomic N reaches the surface. (After Kovsh (2002) NAMBE Conf., Providence, RI, September 2002.)

We sought to see if any similar effect could be observed with the rf source by having bias deflection plates installed in our rf plasma source. These are simply parallel, metal plates on either side of the output beam of the plasma. If a bias is applied across the two plates, the electric field will drive positive ions in one direction and electrons in the opposite direction as illustrated in Figure 1.6(b). Negative ions are assumed to be negligible. Based upon Pan and Li’s results and thinking that a high bias would deflect all ions or electrons, we applied ^ 800 V bias to the plates and grew several QW structures and observed no improvement. In fact, if anything, we observed a slight decrease in PL from tested QW

MBE Growth and Characterization of Dilute Nitride III– V Alloys

11

Figure 1.7. Schematic diagram of the beam flux gauge being used as a Langmuir probe to measure the electron and N2þ ion currents emanating from the plasma source. The axis of the wafer holder is such that the beam flux gauge can be moved vertically to measure the ion and electron current vertical spatial distributions with and without bias on the source deflection plates.

structures with such high bias on the deflection plates. Hence, we grew QW structures for a 3-year period with no deflection plate bias. We have recently re-examined this result with more care by first measuring the ion and electron currents from the plasma source in the MBE system. One of the features of most MBE systems is that a nude ion gauge is mounted on the backside of the substrate holder to measure beam fluxes before growth. This is illustrated in Figure 1.7 where the sample is in the growth position at the top and the ion gauge facing the N source in the bottom. In this position, the beam flux monitor can be used as a Langmuir probe to measure the ion and electron currents which would impinge on the growing surface. We established that a significant number of ions and electrons were reaching the wafer as shown by the measured currents in the ion gauge as a function of filament bias in Figure 1.8 [62]. By then rotating the ion gauge up and down slightly and with different biases on the filament, one can produce a reasonable spatial map and energy distribution for both electrons and ions from the source. By measuring the location of peak electron current, we were able to demonstrate that small voltages physically deflect the ions and electrons to different locations, as shown in Figure 1.9. The solid line shows the suggested relation between the position of the peak ion flux (which is thermally broadened) and the voltage on the upper deflection plate. The lower deflection plate was grounded for this experiment. The deviation from the solid line from 2 20 to 2 308 was due to shadowing of the ion gauge collector wire by the thicker filament wire in front of it. The deviation to the right of þ 188 was due to blocking of the plasma beam by a protective bracket on the beam flux

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Dilute Nitride Semiconductors

Figure 1.8. Measured ion (negative bias on filament) and electron (positive bias on filament) currents from the plasma source under our normal operating conditions.

monitor. Also, the axis of motion of the ion gauge was vertical, but the axis of the deflection plates was about 458 from vertical, so the ion deflection has a horizontal component as well as a vertical one. At larger angles, this deflection could cause the ions to miss the gauge completely. These geometric complications prevented a simple quantification of the ion energy, but nevertheless indicate that complete deflection of ions from our plasma source does not require particularly high voltages.

Figure 1.9. Deflection of ions with applied bias on a single deflection plate.

MBE Growth and Characterization of Dilute Nitride III– V Alloys

13

In re-examining our earlier results with ^ 800 V applied to the deflection plates, for a 1600 V total bias, we believe that the high voltage bias may have encouraged sputtering of metal or adsorbed contaminants from the deflection plates onto the wafer, and may have also ionized additional N through a dc-enhanced plasma or field ionization of excited N2 radicals in front of the source exit. Another observation is that if the deflection plates are not equally and oppositely biased, then they can be used to provide a potential barrier to either electrons or positive ions. For example, if one deflection plate were biased to þ 30 V and the other to 2 10 V, there would be a net þ 10 V DC potential which would tend to repel ions. It should be noted that the repulsion is not necessarily one to one with applied voltage, i.e. a 1 V net potential would not necessarily be sufficient to repel ions with a 1 eV thermal energy, partly due to the finite size of the deflection plates, and partly due to the screening provided by the electrons. Because only one set of deflection plates is available in our system, the plasma is affected by the net potential on the deflection plates. This bias asymmetry can be used to further inhibit ion extraction from the plasma as a negative potential would extract additional positive ions from the plasma cell, and vice versa, assuming the plasma is in good electrical contact with the grounded pipe at the rear of the source, or in other words, the plasma is at a fixed potential [63]. Also, because electrons are believed to be less damaging than ions, a net positive bias should prevent the most damage to the wafer. We grew three samples, each with one 7 nm GaInNAsSb quantum well and a bias of þ 18, 0, or 2 40 V applied to one deflection plate for the respective samples. The other plate was grounded for all three samples. Figure 1.10 shows a clear improvement in

Figure 1.10. Photoluminescence (PL) for samples grown with different voltages applied to one deflection plate. The other plate was grounded. Note the higher luminescence over all annealing conditions, and the higher anneal temperatures reachable before the PL is quenched when using the deflection plates.

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Dilute Nitride Semiconductors

photoluminescence (PL) with applied deflection bias. At high anneal temperatures, the sample with þ 18 V deflection had more than 5 £ greater PL intensity, which corresponded to higher optical power and better material. At low pump powers, the relatively narrow PL linewidth was reduced even further by using deflection plates. For samples annealed at 7208C, the linewidth was reduced from 39 meV for no deflection to 37 meV or 35 meV, for positive or negative deflection, respectively. A PL linewidth of 32 meV was observed after 8008C anneal. The reason for the larger linewidth at net positive deflection biases is still unclear. It may be that þ 18 V was not quite sufficient to deflect ions, while the PL intensity of the 2 40 V sample was reduced due to some other cause. 1.2.4 Role of Sb as Surfactant in Metastable Growth Surfactants have played a crucial role in the development of high-quality epitaxial thin films. The term “surfactant” originated in chemistry and was used to describe “a substance that lowered the surface or interfacial tension of the medium in which it is dissolved” [64]. It mostly applied to substances which reduced the surface tension of liquids such as water. Early in thin film deposition, “surfactant” was adopted to mean any element which altered the growth mode of the film by lowering the surface free energy. For example, Sb was used to promote layer-by-layer growth of Ag on the (111) surface of an Ag substrate and Pb was used for the growth of Co on (111) Cu. Sb and Pb had suppressed the formation of islands or other 3D features during the metal deposition. The application of surfactants to semiconductor thin film growth was introduced by Copel. He showed that the usage of a single monolayer of As on Si could improve the growth of Ge on Si [65]. The growth of Ge on Si was difficult due to the large lattice mismatch, and thus strain, which existed between the two elements. Growth of Ge on Si generally begins in the Stranski – Krastanov (S– K) mode (layer by layer) for a few monolayers. However, the strain energy in the Ge film becomes large enough such that it is energetically favorable to form 3D islands. Continual growth with the 3D features leads to highly dislocated and defected material. By adding As, the layer changed the thermodynamics and kinetics of the growth by lowering the surface free energy and restricting the formation of 3D islands. The As also did not incorporate and continually segregated to the surface of the growth front. As acted as a surfactant for Ge on Si growth and thus enhanced the quality and thickness of the material grown. Many different elements have been used as surfactants in semiconductor growth including As, Bi, H, In, Sb, Sn, and Te [66]. Which element is most efficient depends upon the material grown. In general, surfactants affect the surface free energy of the semiconductor material. It is possible to obtain S– K growth of a film (substance B) on a substrate (substance A) if the surface free energies, g are such that gB , gA : However, if one desires to grow a superlattice or another sort of layered structure, one needs to grow B on A as well A on B. S – K growth of B on A is easily possible if gB , gA : The converse, growth of A on B, can be difficult since the surface free energy is increased upon

MBE Growth and Characterization of Dilute Nitride III– V Alloys

15

deposition of A on B. Consequences include islanding and the formation of 3D features, leading to defect creation. S – K growth of A on B is possible only if the situation gB . gA can be created. To lower the surface free energy, a surfactant can be deposited during growth and ensure S – K growth conditions. One theory in explaining how surfactants work in semiconductor growth was explained by Massies and Grandjean in 1993 and further described by Tournie et al. in 1995 [38,39]. They theorized that surfactants could be separated into two categories: reactive surfactants and non-reactive surfactants. Non-reactive surfactants were those used primarily in homoepitaxy in which strain did not play an important role in affecting the kinetics of growth. These elements floated upon the growth front and did not react with any of the actual growth species. Their function was simply to enhance the surface adatom diffusivity. Reactive surfactants were used mostly in heteroepitaxy in which strain did prevent S –K growth due to lattice mismatches. These elements also floated upon the surface but also tended to incorporate in dopant to dilute levels in the growing crystal. They reacted with the adsorbed species and reduced the surface diffusivity. It can be seen this is beneficial in growth of highly strained material because very good surface diffusivity could lead to clustering and islanding. On an atomistic scale, one can imagine the case for the non-reactive surfactant at the edge of a step. If an atom adsorbs on top of a layer, it will diffuse around on the surface until it finds the lowest energy position. When it arrives at the step edge (which is next to a lower level), it encounters a large energy barrier to drop down to the lower level because it must break extra bonds to traverse over the edge down to the layer. This prevents atoms from growing in an S –K mode and islands form. However, if a non-reacting atom sits at the step edge due to van der Waal forces, it can assist in S– K growth by eliminating the step energy barrier. An adsorbed atom approaching the step edge can easily move down to the lower level because the surfactant atom provides extra bonds for the adsorbed atom and thus extra bonds do not have to be broken. The surfactant atom, since it is non-reactive with the crystal, simply shifts over one atomic position and lets the adsorbed atom slip into place. This enhances the surface mobility. For the reactive case, the surfactant atom actually bonds into the crystal. However, when an adsorbed atom approaches the surfactant atom, it “grabs” or bonds with the surfactant atom and is either held in place or is buried in the layer beneath it. It is also possible that the surfactant atom, if buried, can switch places with an adsorbed atom on top of it. Since the surfactant atom is reactive, it is also possible it does not swap places or continue to float on the surface and becomes incorporated in the material. These actions reduce surface mobility. Sb has been used fairly widely as a surfactant in many different semiconductor alloys [67 – 77]. It is one of many elements which have been used, but primarily in III – V semiconductor growth. Since III – V growth usually involves heteroepitaxy, it is desired to have a surfactant which is reactive and does not provide electrical carrier dopants (such as column-IV elements). Isoelectronic surfactants (usually column-V) are preferred. Due to

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Dilute Nitride Semiconductors

electronegativities and bonding potentials, smaller atoms tend to be overly reactive and do not provide the surfactant-like effects which are desired. Sb and Bi are the usual candidates for III – V surfactant growth, where Sb is more popular due to economics and the number of past studies.

1.3. DILUTE NITRIDE CHARACTERIZATION

The dilute nitrides pose a number of very interesting and challenging characterization problems. First, the number of elements in the quaternary (GaInNAs) or quinary (GaInNAsSb) compounds produces a very large range of materials compositions, which produce the same band gap and lattice constant. Next, there are the huge differences in atomic mass and radii, and miscibility gaps with phase segregation and formation of micro-phases. Finally, there is uncertainty of the exact mechanisms for the large band gap changes with N composition. We describe a number of characterization techniques and results for the dilute nitrides, starting with reflection high-energy electron diffraction (RHEED) since it is used in situ during MBE growth and followed by X-ray diffraction (XRD) and photoluminescence (PL), which are done immediately after growth on every sample. The following sections then describe more difficult, but insightful measurements that are not performed on every sample, secondary ion mass spectroscopy (SIMS), cross-sectional transmission electron microscopy (XTEM), deep level transient spectroscopy (DLTS), electroreflectance (ER), and photoreflectance (PR) that are necessary to understand both the properties and quality of the material and provide feedback for growth as well as the fundamental properties that are essential to optimized design of lasers (described in Chapter 17). 1.3.1 Reflection High-Energy Electron Diffraction RHEED is an important in situ technique for MBE growth. It allows the grower to examine properties such as surface reconstruction, surface morphology, and growth rate. Although this tool is usually confined to examining oxide desorption from wafers before growth, it still has great utility when growing new materials such as the dilute nitride –arsenide– antimonides. By examining the RHEED patterns, one can determine whether or not adding Sb affects the surface morphology or quality during growth. It was known that surfactants were used to suppress Stranski –Krastanov growth by maintaining Frank –Van der Merwe conditions [65] and increase the critical thickness [78] in growth studies performed on Ge/Si systems. Various other surfactants have also been applied to III – V material systems as well including Sb [65,79]. Wang et al. added Sb to GaInNAs in an attempt to improve overall material quality. They used RHEED to examine the growth of the quantum well (QW) region with and without Sb. During growth, the RHEED pattern of GaInNAs had become partly spotty. This effect was even more pronounced with increasing N flux. Spotty RHEED is usually a sign of 3D morphology

MBE Growth and Characterization of Dilute Nitride III– V Alloys

17

Figure 1.11. RHEED showing the effects of adding antimony to GaInNAs (a) without antimony, (b) with antimony.

and is not desired in growing quantum well structures which requires atomically flat interfaces. However, adding Sb improved the surface morphology of the GaInNAs such that the surface remained 2D and the RHEED remained streaky throughout the growth as seen in Figure 1.11(a) and (b). Adding N to InGaAs should technically increase the critical thickness since N reduces the amount of lattice mismatch. However, 3D growth was observed for GaInNAs layers thinner than that predicted by Matthews and Blakeslee’s model for InGaAs of the corresponding composition [80]. They suspected that since N has a higher surface free energy than As, the surface kinetics were altered deleteriously. However, Sb has a lower surface free energy than As and thus prefers to “wet” the surface and suppress surface diffusion and island formation [81]. The same type of experiment was performed on GaNAs. Since the addition of Sb had improved the material quality of GaInNAs, it was thought the same could be said of GaNAs as well. It was seen that, although very faint, the RHEED pattern from GaNAs is

18

Dilute Nitride Semiconductors

streaky. Although not shown, the orthogonal [110] directions for GaNAs grown under typical growth conditions showed a 2 £ 4 reconstruction. When Sb was applied to form GaNAsSb, the RHEED pattern changed significantly. Instead of a streaky pattern, a spotty pattern emerged suggesting the surface quality was not as good as GaNAs. This result was slightly surprising since Sb had improved GaInNAs as seen above. Again in examining orthogonal [110] directions, the reconstruction here appeared to be 1 £ 4. From RHEED, it appears the growth surface of GaNAs is smoother than that of GaNAsSb. It is unclear as to why Sb did not improve the material quality in this case. In previous cases such as GaInNAs and InGaAs [82], the surfactant was applied to alloys with large lattice mismatches to GaAs. The mismatch found in GaNAsSb on GaAs is quite small [36] and this perhaps changes the surface growth kinetics. GaInNAs and InGaAs both contain indium, a relatively large atom. It is possible that In contributes enough strain to the surface such that Sb does not incorporate very easily and thus remains on the surface to reduce the surface free energy. In both cases of GaInNAs [81] and InGaAs [82], the composition of Sb is either very small or negligible. In GaNAsSb, where there is no In, Sb easily incorporates as much as 30 –40% [13]. It is unclear as to why GaNAsSb has worse surface morphology than GaNAs however. 1.3.2 High Resolution X-ray Diffraction One of the most useful techniques for analyzing epitaxial films is high resolution X-ray diffraction (HRXRD). Since the peaks in an X-ray diffraction pattern are directly related to the atomic distances, one may obtain information such as strain, film thickness, relaxation, and phase segregation. Although there can be some complications and complexities, HRXRD can also provide some compositional details rather quickly and nondestructively. The most common scan performed on HRXRD for epitaxially grown semiconductors is the v=2u scan of the (004) planes. Here, the diffraction vector is perfectly perpendicular to the surface and thus only measures components out-of-plane. There are several programs available on the market, as well as home-grown scripts, which can quickly simulate any epitaxial structure given the correct material property values and parameters. This is a useful tool so that one can easily determine whether or not the structure grown was the one which was desired. It is also useful for obtaining values such as layer thickness and composition by examining the features within the diffraction pattern. The process for obtaining such information will be described here since this is the basis for how all simulators process the information. Constructive interference of X-ray radiation occurs at certain angles of diffraction depending on the lattice spacing as given by Bragg’s Law: nl ¼ 2dhkl sin u

ð1:1Þ

where n is the order of the diffraction and can be any positive integer, l is the wavelength of the incident X-rays, u is the scattering angle, and dhkl is the spacing between the ðhklÞ planes.

MBE Growth and Characterization of Dilute Nitride III– V Alloys

19

For cubic crystals, dhkl is related to the lattice spacing a by the following relationship: 1 ðh2 þ k2 þ l2 Þ ¼ 2 dhkl a2

ð1:2Þ

When measuring fully relaxed, unstrained films, Bragg’s Law is sufficient for most analysis since the film relaxes to its equilibrium lattice parameter. For example, the (004) v=2u scan of a fully relaxed InGaAs film can give information on composition based on the lattice spacing dhkl and film thickness based on the width of the diffraction peak. For fully coherent films, a more complex analysis is needed. Strained GaNAs films grown on GaAs are tetragonally distorted such that the (004) plane spacings are different from its relaxed value. An example of a HRXRD pattern of GaNAs is shown in Figure 1.12. In a cubic crystal, the equilibrium unstrained lattice parameter, aeq ; can be calculated from the measured (004) lattice parameter a004 using the relationship:

sz ¼ 0 ¼ 2C12 1k þ C11 1’

ð1:3Þ

or solving for aeq :  aeq ¼

2C12 a þa C11 GaAs 004 2C12 1þ C11

 ð1:4Þ

˚ GaNAs QW on GaAs. Dynamical simulations using the strain of the Figure 1.12. v=2u (004) scan of a 200 A GaNAs QW peak indicate 2.7% N.

20

Dilute Nitride Semiconductors

where 1k is the in-plane strain for the unrelaxed film where 1k ¼

aGaAs 2 aeq aeq

ð1:5Þ

a004 2 aeq : aeq

ð1:6Þ

and 1’ is the out-of-plane strain in which 1’ ¼

The constant aGaAs is the lattice parameter for GaAs and sz is the strain in the out-of-plane direction. Parameters C11 and C12 are the stiffness coefficients for the film where the ratio 2C12 =C11 is approximately 0.9 for most III –V materials [83]. So for GaNAs, using the unstrained lattice parameter, the N concentration can be calculated using Vegard’s Law, which is valid in the dilute regime [84]. One must be careful in fully accepting the strain and compositional values using the described method. In order to obtain an accurate unstrained lattice parameter value, one has to assume there was no relaxation. If any relaxation has occurred, this would shift and possibly broaden the peak leading to incorrect results. One method to ensure relaxation has not occurred is using a reciprocal space map (RSM), which will be described later. Obtaining absolute N concentrations via X-ray diffraction simulation can only lead to erroneous results. The above calculations also assumed all atoms were located in substitutional sites. It has been reported that a significant amount of N is found on interstitial sites [85]. Since N is a small atom and the rf plasma itself can create highly energetic N species, it is not surprising that N is found on both interstitial and substitutional sites. The N found in the interstitial sites does not contribute to the strain as they would on substitutional sites. Since very little strain is added to the system from these atoms, HRXRD would not detect these atoms and would thus be ignored. Other methods such as RBS and SIMS are required to make a more accurate determination of N concentration. Another problem is the ambiguity in determining compositions of alloys with four or more elements. In a ternary compound, it is simple to analyze the change in lattice parameter, and thus strain, due to the addition of one element in the III– V semiconductor. However, once two elements are added, the source of the strain becomes more complex. For example in GaInNAs, there are an infinite number of combinations of In and N compositions which will give the same lattice parameter. One can obtain an estimate of the concentrations from past calibrations or general experience by giving a range in which In or N compositions can be in existence. The quinary GaInNAsSb is even more difficult to obtain a definite composition from HRXRD. SIMS in combination with RBS would be the best method of obtaining the composition for quaternary or quinary compounds. HRXRD is also useful for examining the amount of strain in a layer as well as the quality of this strained layer. GaInNAs QWs are typically grown near the critical thickness for dislocation formation. Because the N concentration is kept low to minimize localized

MBE Growth and Characterization of Dilute Nitride III– V Alloys

21

defects, a great deal of In is added to obtain the longest possible wavelength. By capping the amount of N to under 2%, the maximum amount of In able to be placed in a GaInNAs QW was 34– 35%, limiting the wavelength of devices to a maximum wavelength of 1.4 mm [86]. These layers were highly strained at 2%, but since the thickness was under the critical thickness, they did not relax. However, adding more In to GaInNAs in an attempt to reach the other important fiber wavelength of 1.55 mm had caused relaxation and also phase segregation in the QW. This can be seen in Figure 1.13 where the HRXRD signal for a GaInNAs sample with nominally 38% In shows no sharp diffraction features, Pendellosung fringes, and strain equivalent to layers with much less In indicating relaxation. Additional N could be added to provide strain compensation in the QW layer, however this would drastically degrade the optical quality of the material. Instead, Sb was added to the GaInNAs and GaNAs barriers in an effort to reduce or delay relaxation and improve overall material quality. The results were quite surprising. Sb had indeed improved the structural quality of the GaInNAs active region as can be seen in the HRXRD pattern with the reappearance of sharp diffraction peaks and Pendellosung fringes. Also, the strain in the QW was larger than that expected for completely unrelaxed

Figure 1.13. HRXRD of a series of GaInNAs(Sb) samples with increasing antimony flux. Adding antimony allows previously unachievable 38% In in GaInNAs. The strain increases up to a certain flux and then decreases due to increasing nitrogen incorporation.

22

Dilute Nitride Semiconductors

GaInNAs at that composition. It was apparent that a significant amount of Sb, 2%, had incorporated into the GaInNAs forming GaInNAsSb. What was most impressive with the addition of Sb was the ability to increase the strain to , 2.5%, beyond what was able to be achieved before without relaxation. The kinetics of relaxation was suppressed allowing for high-quality growth. Adding more Sb had continued to increase the strain without degradation to the material until the strain actually decreased with higher Sb fluxes as can be seen in the figure. This was due to the increased efficiency of N incorporation due to the presence of Sb as discussed earlier. Adding Sb to all layers containing N appeared to be a beneficial move in obtaining better material quality. However, as was seen in the case for RHEED, the addition of Sb to GaNAs did not have the same effects as it did with GaInNAs. From HRXRD, it was also observed that there are additional properties of GaNAs which are more beneficial than GaNAsSb as QW barriers for GaInNAs(Sb) [36]. Figure 1.14 shows the HRXRD (004) v=2u scans from four different GaNAs(Sb) SQW samples. The N compositions of the GaNAs samples were determined by dynamical simulation of the HRXRD spectra. Two different growth conditions were utilized to obtain the four different samples.

Figure 1.14. (004) v=2u HRXRD spectra showing amount of strain in the samples. (a) GaN0.029As0.873Sb0.098, (b) GaN0.034As0.867Sb0.099, (c) GaN0.019As0.981, (d) GaN0.027As0.973. (a) and (c) are grown under 1.3 mm device growth conditions. (b) and (d) are grown under 1.55 mm device growth conditions.

MBE Growth and Characterization of Dilute Nitride III– V Alloys

23

The compositions of GaNAs(Sb) used in the study were chosen to be similar to those used in 1.3 and 1.55 mm GaInNAsSb devices and are uniquely determined due to the restrictive nature of MBE. Since the MBE chamber has only one Ga cell, the flux is fixed during the entire growth and is preferentially set to obtain the proper GaInNAsSb QW composition. The N content is predetermined due to its inverse proportional relationship with the groupIII flux and the Sb flux is unchangeable since it is supplied by an unvalved cracker. These combined conditions do not allow the barrier compositions to be arbitrarily changed. As observed from the HRXRD scans, the GaNAsSb was either lattice matched to GaAs or was very slightly compressively strained for both compositions. This property is not advantageous when used with highly compressively strained GaInNAs(Sb) QW materials since the barriers would not provide any strain compensation for the active regions. However, both compositions of GaNAs showed an appreciable amount of tensile strain. The amount of strain found in GaN0.019As0.981 and GaN0.027As0.973 was 2 0.38 and 2 0.55%, respectively. From HRXRD, there does not appear to be much of an improvement or degradation of material quality upon addition of Sb to GaNAs for either set of growth conditions. From the Pendellosung fringes, the interfaces for all materials are of good quality. This could suggest that the GaNAs grown was already of excellent quality or there simply was no effect upon addition of Sb [36]. In an effort to examine some growth parameters of the growth of GaNAsSb, we varied the As to Ga flux ratio and substrate temperatures. Starting with the GaN0.029As0.873Sb0.098 QW sample (nominally the composition used as the barrier material for , 1.3 mm GaInNAs(Sb) QWs), the As overpressures and substrate temperatures were altered (independently) during the growth of the QW while everything else was held constant. Figure 1.15 shows that, from the (004) v=2u scans, as As overpressure increases from 15 £ to 30 £ , the strain in the GaNAsSb layer became less compressive. Since this is a quaternary system, it cannot be determined whether the decrease in compressive strain is due to a reduction in Sb concentration, an increase in N concentration, or a combination of both. SIMS is required and is discussed in the following sections. In all cases, the HRXRD scans did not show any degradation of material compared to the original 20 £ sample. In the substrate temperature study, the temperatures were varied from 425 to 5758C. Figure 1.16 shows that an increase in substrate temperature leads to a drastic change in strain from compressive to tensile. Similar to the As overpressure study, the exact cause of this cannot be determined strictly from HRXRD but is discussed in Section 1.3.4. Surprisingly, the crystalline quality of the samples appears to be quite good up to the highest temperature tested. We see Pendellosung fringes and no sign of phase segregation or relaxation. To confirm that the (004) v=2u scans were not missing any signs of relaxation or segregation; RSMs were taken of the (224) direction of GaNAsSb. RSMs show the in-plane and perpendicular components of diffraction and the lattice spacing of the material present. Figure 1.17 shows the RSM of GaNAsSb grown at 5758C. RSMs will be described in the next paragraph, but we will briefly

24

Dilute Nitride Semiconductors

Figure 1.15. (004) HRXRD scans showing a decrease in compressive strain with increasing arsenic overpressure in GaNAsSb QWs.

describe it here. If a material is grown coherently, there should be no diffraction peaks in the in-plane direction. It is seen in the figure that there are no major diffraction peaks in the in-plane direction away from the (224) GaAs peak. There is no sign of phase segregation or relaxation from the RSM. A more involved HRXRD measurement than the standard (004) scan v=2u is the RSM. A RSM is a series of 2u scans holding v constant. The v value is then increased

Figure 1.16. (004) HRXRD results from samples with increasing substrate temperature for GaNAsSb QWs.

MBE Growth and Characterization of Dilute Nitride III– V Alloys

25

Figure 1.17. RSM of a GaNAsSb/GaAs QW grown at 5758C. It is seen from the plot that the material has been grown coherently with no signs of phase segregation or relaxation.

incrementally such that a plot is obtained showing contours of diffracted intensity in reciprocal space. The beam diffraction path is also different such that an additional axis of diffraction is added. Without this third axis, the diffraction beam probe is a line which spans a finite amount in v: Since the probe is not a small dot, it will smear signals across in v; reducing the resolution of the map. With the third axis, fine diffraction features can be seen. This is very useful in examining any diffraction peaks which may not be obtained from the standard (004) v=2u scan including peaks which are found with in-plane components. RSMs are usually plotted with the out-of-plane ð00lÞ direction as the y-axis and the in-plane ðhk0Þ direction as the x-axis. The most common diffraction direction for RSMs is the (224) set of planes. As follows from diffraction theory and the rules which govern different crystallographic symmetries, these sets of planes give the highest diffraction intensity. If all layers are coherent on the substrate, the RSM will only show a “line” of diffraction with the same in-plane value but various out-of-plane values. This is actually very similar to the pattern one would get if the (004) v=2u scan were turned on its side and viewed from the top. However, any relaxation will generate diffraction intensities which will be found in different in-plane values as the substrate. Generally the relaxation is neither complete nor uniform so a smear of diffraction intensities will develop originating from the unrelaxed diffraction point. Depending if the layer was compressively or tensilely strained, the smear will be found on a path as shown in Figure 1.18. Figure 1.19(a) – (d) shows RSMs of GaNAs, GaNAsSb, GaInNAs, and GaInNAsSb, respectively. It is clear from the RSMs that no relaxation in any of the material has occurred since there are no components found in-plane not matching that of the GaAs substrate.

26

Dilute Nitride Semiconductors

Figure 1.18. Diagram showing the direction of relaxation for GaNAs when examining the (224) diffraction peaks.

1.3.3 Photoluminescence Photoluminescence (PL) is an extremely powerful, albeit relative, technique for assessing material quality. It is quite possibly the most useful technique when developing a new (direct band gap) material system. It is non-destructive and requires virtually no sample preparation or complex device structures. Moreover, variation of different parameters (e.g. temperature or pump power) can be used to obtain band offsets [87], identify various transitions [88 – 90], and even explore the structural quality of the material [89,91,92]. The time evolution of the PL signal can be used to accurately determine the Auger recombination coefficient in other material systems [93 – 95]. At the time of this writing, time-resolved PL measurements have not been reported for GaInNAsSb. In its simplest form, PL consists of an incident pump beam with photon energy larger than the band gap, optics to focus and collect the light, and a spectrometer and detector to measure the emission spectrum of the sample while filtering the pump beam. Typically a chopper and lock-in amplifier are used if a single detector is employed. If a detector array or CCD is used, the emission is averaged for many clock cycles to obtain sufficient signalto-noise ratio. Data collection and analysis are performed by computer. The main parameters of interest for room temperature PL (RT-PL) measurements are the wavelength of peak intensity, peak intensity, linewidth, and integrated intensity. The wavelength of peak intensity is of obvious interest as it is quite close to where lasing would occur with such an active layer. The other three figures of merit allow for a relative

MBE Growth and Characterization of Dilute Nitride III– V Alloys

27

Figure 1.19. RSMs of (224) diffraction peaks showing (a) GaNAs/GaAs QW-GaNAs is intensity above GaAs substrate peak, (b) GaNAsSb/GaAs QW-GaNAsSb is intensity above GaAs, (c) GaInNAs/GaAs QW-GaInNAs is intensity below GaAs, (d) GaInNAsSb/GaNAs QW-GaNAs barrier intensity is above GaAs and GaInNAsSb QW intensity is below GaAs.

28

Dilute Nitride Semiconductors

Figure 1.19. Continued.

comparison of material quality between samples. Peak intensity is an excellent indicator of the optical quality of the material. The lower the defect density, the stronger the peak PL signal. The peak intensity must be treated with some caution, however, as it is sensitive to layer structure (e.g. proximity to surface states). Conversely, the linewidth gives some information about defect density, but mainly broadening due to interface quality and alloy disorder. Closely spaced transitions may broaden the measured linewidth and the peaks must be carefully fitted to Gaussian or Lorentzian line shapes. An alternate approach is to

MBE Growth and Characterization of Dilute Nitride III– V Alloys

29

Figure 1.20. Photoluminescence (PL) intensity (triangles) and linewidth (squares) versus anneal temperature for a 1 min anneal of a single GaInNAsSb/GaNAs QW with peak luminescence at 1.5 mm.

reduce the pump power density until only the main transition is visible. The integrated intensity is somewhat intermediate between the peak intensity and linewidth cases as it depends upon both the height and width of the peak. In high quality samples, the three figures of merit generally track one another. One notable, but easily reconcilable exception to this rule is the annealing behavior of GaInNAs(Sb). Figure 1.20 shows the dramatic change in RT-PL peak intensity and linewidth with rapid thermal annealing (RTA) temperature for a 1 min anneal. The peak intensity increases dramatically with anneal temperature up to a certain point and then begins to degrade. Conversely, the linewidth shows a monotonic decrease with increasing temperature, over this range. At very high temperatures (not shown in figure) the linewidth also begins to broaden. The initial improvements in the peak intensity and linewidth at low temperatures are due to removal of non-radiative defects, and possibly some ordering. At higher temperatures, defects such as arsenic antisites have sufficient diffusivity that they may propagate from the surface into the active layer, thereby reducing the peak PL intensity. The QW structure continues to improve, as illustrated by the monotonic linewidth narrowing, despite the increasing defect density. At sufficiently high annealing temperatures, the linewidth begins to suffer as well. The temperature of the rollover depends upon the sample structure. Figure 1.20 was measured for a sample with a thin ˚ GaAs cap above the QW. Higher rollover temperatures are observed when an 500 A Al0.33Ga0.67As/GaAs cap or a thicker GaAs cap is employed because the Al0.33Ga0.67As or thicker cap serves to block defect propagation from the surface. This underscores the relative nature of the PL technique. Figure 1.21 shows a set of PL spectra that illustrate the extension of GaInNAs(Sb) from 1.3 to 1.55 mm through the addition of antimony [96]. To maintain strong luminescence, the

30

Dilute Nitride Semiconductors

Figure 1.21. Photoluminescence of GaInNAs(Sb) comparing the best 1.3 mm material grown without Sb and the dramatic improvement in PL at even longer wavelengths by adding Sb.

nitrogen content was nominally held to , 1.6%. The addition of antimony increased the nitrogen incorporation rate and the nitrogen content was , 2.5% at 1.55 mm [37]. The rightmost spectrum in Figure 1.21 was the highest intensity 1.3 mm PL sample grown thus far and consisted of 1.6% N and 31% In. A dramatic degradation in material quality was observed when the indium fraction was increased from 31 to 35%. Phase segregation was clear from the hazy appearance of the wafer after growth. By adding a small flux of Sb, the PL output shifted to 1.38 mm with little loss of efficiency. Increasing the Sb flux further during growth in sample, red shifted PL to 1.5 mm with peak emission still over 50% that of the best 1.3 mm sample. Finally, an additional increase in Sb flux extended the emission wavelength to 1.58 mm with only a slight reduction in peak intensity. The addition of antimony not only has allowed the extension of the wavelength, but most importantly, a tremendous improvement in material quality at wavelengths greater than 1.3 mm [81,97]. This was studied for GaInNAs(Sb)/GaNAs(Sb) at 1.3 mm in Ref. [88]. Ga0.70In0.30N0.016As0.984 and Ga0.68In0.32N0.012As0.64Sb0.024 QW samples, which showed PL peaks at 1.310 and 1.326 mm, respectively. The peak luminescence intensity was more than 40% larger for the GaInNAsSb sample. Moreover the blue shift with increasing anneal was seen to saturate more quickly in the GaInNAsSb sample as compared with the GaInNAs. The additional blue shift observed for annealing at temperatures beyond 7608C for 1 min was only 8 nm for the GaInNAsSb sample as compared to 20 nm for the GaInNAs. The linewidth was slightly larger, however, for

MBE Growth and Characterization of Dilute Nitride III– V Alloys

31

Figure 1.22. Room-temperature PL spectrum of a single GaInNAsSb QW, with a linewidth of 28.7 meV.

the antimony sample, 59.6 meV compared with 58.32 meV, likely due to increased alloy disorder due to the addition of antimony. The post-anneal linewidths of the samples in the above discussion were , 50 –60 meV at room temperature. By reducing plasma related damage, and further optimizing growth conditions as discussed in Section 1.2.3, the linewidth was reduced to , 28 meV and the peak intensity was improved , 9 £ , at substantially longer wavelengths [98]. An example ˚ PL spectrum of the improved material is shown in Figure 1.22. The sample is a single 75 A ˚ GaN0.025As0.975 Ga0.62In0.38N0.023As0.95Sb0.027 QW surrounded on either side by 220 A barriers with peak emission , 1.45 mm annealed at 8008C for 1 min. This linewidth is comparable to those reported for the lowest threshold 1.2 mm InGaAs lasers [99] and 1.5 mm InGaAsP/InP lasers [100]. The peak signal is , 9 £ higher than those reported in Ref. [96] and is largely due to the improved growth technology [35,101]. The line shape was also seen to depend upon temperature. The line shape was Lorentzian at very low temperatures (typically less than 10 – 50 K) and Gaussian at higher temperatures [90]. For many samples, the Gaussian line shape persisted to the lowest measurable temperature, indicating an unusually large exciton – phonon coupling in this material due to the high exciton mass, large exciton radius, and intrinsic lattice defects in the alloy. Asymmetry was also observed on the low energy side of the spectrum at low temperatures, as expected from line shape theory. At elevated temperatures, the asymmetry switched to the high energy side as the thermal distribution of carriers became significant. Temperature-dependent PL has been applied to examine the localization phenomena observed in GaInNAs [89,102]. Temperature-dependent PL did not show the characteristic S-shaped behavior of the transition energy with temperature observed in most of the earlier

32

Dilute Nitride Semiconductors

Ga(In)NAs samples reported in the literature [91,92,103,104], even for excitation densities as low as 1 W/cm2. The S-shaped behavior has been attributed to band-tail states that arise from local potential fluctuations due to non-uniformities in the nitrogen distribution [103]. These fluctuations provide confinement for excitons at reduced temperatures. The S-shape arises as the emission changes from mainly due to localized excitons (low temperatures) to that of a pure band-to-band transition (high temperatures). A rapid red shift in the band gap occurs from very low temperature up to , 50 K, followed by a similarly rapid blue shift up to , 100 K. For . 100 K, the luminescence is delocalized and the band gap shift with temperature obeys the traditional Varshni behavior (red shift with temperature). It was postulated that the degree of localization is directly linked to material quality, specifically the presence of non-radiative centers [92,103]. Indeed any improvements in optical quality, be it addition of antimony, post-growth anneal, or reduced ion damage during growth reduces these localization effects [89]. Even when no S-shape is observed, there still exists a significant difference between the measured data and the best Varshni fit at low temperatures (, 75 K) [91]. This energy difference, termed the localization energy, is directly related to the nitrogen content and inversely related to the material quality. With improvements in material quality, such as those reported by Misiewicz et al. [91], the S-shape has recently been suppressed, although some degree of localization still remains at low temperatures (, 70 K). This low temperature localization was found to be directly proportional to the nitrogen mole fraction. To quantify this effect, Misiewicz and co-workers have adopted the energy separation between the best Varshni fit and the measured data at 10 K [91]. Based upon the data reported, they predict a localization energy of 2.36 meV/%N for GaInNAs. The shift in the PL peak intensity with temperature is shown in Figure 1.23 for the GaInNAsSb QW sample of Figure 1.22. While no S-shaped curve was observed, a localization energy of 2.5 meV was required to properly fit to the Varshni model. This is, however, less than half the localization energy reported in Ref. [91] for GaInNAs films of comparable nitrogen content. This is further evidence of enhanced crystalline quality due to the addition of antimony and improvements in growth techniques. Additionally, GaInNAs QWs grown under similar conditions to those in Figure 1.22, but with PL peak around 1.3 mm, show similarly improved properties. Recent work [89] has shown the localization energy varies with anneal, and as-grown samples show somewhat larger localization. Moreover, the addition of antimony was found to reduce the localization energy, as expected from work on surfactant-mediated growth. For samples with identical nitrogen composition, 1.6%, the localization was reduced through the addition of antimony: the localization was greater than predicted by Misiewicz et al. [91] without antimony; with antimony, however, the localization energy was reduced below that predicted by Misiewicz. This indicates improved compositional homogeneity and optical quality through the introduction of antimony, consistent with cathodoluminescence (CL) measurements [89].

MBE Growth and Characterization of Dilute Nitride III– V Alloys

33

Figure 1.23. Varshni fit with temperature for an annealed GaInNAsSb/GaNAs sample containing 2.5% nitrogen in the QW. The localization energy was 2.51 meV and is substantially reduced as compared to the as-grown material.

It should be noted that the localization energy, and moreover the values of a and b in the Varshni equation, depend upon the excitation density. Shown in Figure 1.24 is the band gap shift with temperature taken under excitation densities ranging from 1 to 1000 W/cm2 for an as-grown GaInNAsSb sample with room temperature peak luminescence at 1.38 mm.

Figure 1.24. Band gap versus temperature for several decades of excitation density of an as-grown GaInNAsSb single QW sample emitting ,1.38 mm at room temperature. The red shift at low temperatures and the localization energy (inset) are reduced with increasing excitation density.

34

Dilute Nitride Semiconductors

S-shaped behavior has been reported in the literature for excitation densities ranging from , 5 to 1000 W/cm2, but was not observed. Several secondary features are evident, however. First, there is a red shift at low temperatures that is reduced with increasing excitation density. Second, there is a blue shift in the emission as the excitation density is increased, consistent with level filling. Third, there is a reduction in the localization energy, shown in the inset of Figure 1.24. This indicates the role of levels, likely defects, in the localization behavior. Increasing the excitation density effectively reduces the defect contribution to the luminescence behavior and, hence, the localization energy. GaInNAs samples show almost identical behavior with excitation density as GaInNAsSb. Line shape analysis was also employed to further understand the low temperature localization. The inset of Figure 1.25 shows the peak fitting results to the measured spectrum at 15 K for the GaInNAsSb sample of Figure 1.24. The spectrum is quite well fitted with three Gaussian peaks, but poorly for fewer Gaussian peaks or any number of Lorentzians. Figure 1.25 also shows the variation of each transition energy with temperature. The transition corresponding to the squares is the minimum transition energy, and is, therefore, attributed to the band gap. The transition shown as circles appears to correspond to a continuous distribution of states within the conduction band. This transition tracks the band gap with a constant separation proportional to the thermal energy, indicating a thermal distribution ðkTÞ: This rather broad peak may be due to thermal distribution of carriers, alloy fluctuations (nitrogen or indium), or some other defect(s). The third transition (triangles) lies within the band gap and is observed only at

Figure 1.25. Variation of the different transition energies with temperature for the GaInNAsSb sample of Figure 1.24. The inset shows the fit to the measured data at 15 K. The correlation coefficient is 0.99999 for three Gaussian line shapes but is substantially lower for fits employing one or two Gaussian peaks and worse when fitted with Lorentzians.

MBE Growth and Characterization of Dilute Nitride III– V Alloys

35

Figure 1.26. Variation of transition strength with excitation density at 15 K. Note the within-gap defect luminescence decreases less with excitation density than the band gap luminescence. The S-shape would likely be observed at an excitation density ,0.1 W/cm2 for this particular sample.

low temperatures. It is attributed to some within-gap defect levels, or band tail states. This defect level is seen to blue shift with increasing temperature, indicating a greater distribution near the conduction band edge, and may be responsible for the S-shape in PL versus temperature reported previously. If the luminescence of this transition were , 10 £ stronger in these samples, it would be of similar luminescence to the band gap. Figure 1.26 shows the peak intensity of the three peaks with excitation density at 15 K. It is observed that the within-gap defect level luminescence is less dependent upon excitation density than the band gap or above-gap transitions. As a result, it is likely the S-shape would be observed at an excitation density , 100 mW/cm2, where the transitions would be of comparable intensity. GaNAsSb was examined using PL to determine its quality as a material for GaInNAsSb QW barriers. Measurements were obtained from a GaN0.029As0.873Sb0.098 sample, the barrier material used in 1.3 mm GaInNAsSb QWs. The PL obtained from the as-grown GaN0.029As0.873Sb0.098 sample peaked at 1.316 mm, but was very weak in intensity. This was not surprising since GaInNAs(Sb) samples which have not been annealed generally have weak intensities. The sample was annealed at a series of temperatures between 720 and 8208C to study the effect upon the optical quality of the material. Similar to GaInNAs(Sb), annealing the PL samples led to a dramatic increase in PL intensity. As shown in Figure 1.27, the PL intensity increases with increasing annealing temperatures until it peaks at 7608C and decreases beyond this point. The PL peak wavelength also blue shifted with increasing anneal temperatures. Compared to the as-grown PL spectrum, the optimal anneal PL signal was 25 £ higher in intensity and was blue shifted 70 nm, which

36

Dilute Nitride Semiconductors

Figure 1.27. PL results from GaN0.029As0.873Sb0.098 sample. Filled dots show PL intensity. Empty dots show peak PL wavelength.

is slightly more than the blue shift found in GaInNAs(Sb). Although the blue shifting of the wavelength was expected and is seen in all nitride –arsenide samples, it is interesting to note that the wavelength essentially remains the same past the optimal 7608C annealing temperature. Unlike GaInNAs(Sb) samples, there is no indium in the GaNAsSb samples and thus the blue shifting of the PL wavelength upon annealing cannot be explained by In/ Ga/N rearrangement [105 – 107]. Sources of blue shifting likely include nitrogen outdiffusion, N/As/Sb rearrangement, and nitrogen de-clustering. When compared to typical GaInNAs(Sb) PL intensities, the GaNAsSb intensities are at least 25 £ lower. The low intensity in comparison to other nitride – arsenides could be due to poor optical quality material or poor band alignment in the active region design. It is unclear which reason dominates. One final point to note is the actual transition energy of the GaN0.034As0.867Sb0.099 sample in comparison with the QW material it surrounds in devices. If it is assumed that the PL peak wavelength gives a rough estimate of the band gap of the material, then it is seen that the band gap of the GaN0.034As0.867Sb0.099 is roughly 0.99 eV while the QW at 1.3 mm is 0.95 eV. With only 40 meV difference in band gap, there is very poor confinement of electrons and holes within the QW and it is possible that the alignment between the GaNAsSb and GaInNAsSb at 1.3 mm is not the desired type-I alignment. The substrate growth temperature of GaNAsSb was also studied with PL. As mentioned earlier in the chapter, increasing the substrate growth temperature had resulted in a large decrease in antimony incorporation while still maintaining coherent epitaxial growth. However, the PL results indicated a decrease in optical quality. As shown in Figure 1.28, with increasing substrate temperature, the PL spectra blue shifted as expected due to lower antimony concentration, but also decreased in intensity. There is also a large shoulder to the PL spectra for all three samples which was not found in the original substrate

MBE Growth and Characterization of Dilute Nitride III– V Alloys

37

Figure 1.28. PL spectra from GaN0.029As0.873Sb0.098 sample grown at different substrate temperatures. (a) þ1508C (5758C), (b) þ 1008C (5258C), (c) þ 508C (4758C). The small peak at 1400 nm is the water present in the testing environment.

temperature sample. This longer wavelength shoulder could be a result of microsegregation or a point defect of some kind which could not be observed easily in HRXRD. Since there could be areas of clustering of increased nitrogen concentration within the QW, it could lead to areas of luminescence in which the band gap is smaller, leading to luminescence of longer wavelength. If these regions occurred only inside the QWs, they would have no effect on the interfaces and thus would not affect or reduce the diffraction thickness oscillations. As evidenced by the poor PL results, GaNAsSb cannot be grown at high temperatures without a large decrease in optical quality of the material and thus, it is not a good choice for barriers around GaInNAsSb QWs. 1.3.4 Secondary-ion Mass Spectrometry Another widely used and powerful tool used in III– V growth analysis is SIMS depth profiling. A focused ion beam sputters atoms from the surface at a controlled rate such that the user is able to obtain compositional information with information about depth location as well. The secondary ions generated from this sputtering are collected and a depth profile is generated. When measuring N concentrations with SIMS, it does not form a negative atomic ion and thus GaN2 or CsNþ ions can be used when sputtering with a cesium ion beam. The GaN2 ion is generally produced with high yields and gives a good minimum detection limit during depth profiling. However, since this ion is dependent upon the Ga concentration as well, changes in the amount of Ga will affect the apparent N signal measured from GaN2. The CsNþ ion is immune to these effects, but the yield is much

38

Dilute Nitride Semiconductors

lower and thus the signal is much noisier. This increases the minimum detection limit as well as reduces the resolution of the measurement. SIMS is also greatly affected by matrix effects. The secondary ion yields generated are strongly dependent on the electronic properties, such as ionization energy, of the matrix. This problem can be eliminated by creating several known “standard” samples to calibrate the signals. In the case of GaInNAs(Sb) material, the N signal was calibrated using nuclear reaction analysisRutherford backscattering (NRA-RBS) and the Sb signal using particle induced X-ray emission-RBS (PIXE-RBS). RBS will be described in a later section. SIMS has been useful in helping to determine the effect and role of Sb when added to GaInNAs. Wang et al. introduced Sb as a surfactant using a standard effusion cell during GaInNAs growth in 1999. They had initially concluded that Sb did in fact act as a surfactant since the PL wavelength of their samples increased in intensity but remained at the same wavelength [81]. Negligible Sb incorporation was assumed from the data and also supported the general properties of surfactants. However, in a later paper, they used SIMS in a more careful examination of concentration and found that Sb had indeed been incorporated in the material in small quantities [108]. The SIMS data can be seen in Figure 1.29. Antimony was found in the QWs with compositions ranging from 0.4 to 1.0%. It was also noted that the amount of Sb found in the QWs was found to increase with each successive QW grown. To eliminate the fact that this could have been due to ion

Figure 1.29. SIMS showing compositions of a 10 QW sample of GaInNAsSb/GaAs PL sample. The indium and antimony profiles do not match.

MBE Growth and Characterization of Dilute Nitride III– V Alloys

39

roughening during sputtering, Auger spectrometry utilizing Zolar rotation was used. The results indicated this was not a sputtering artifact and thus was evidence of Sb segregation on the surface during growth [108]. It is also interesting to note the Sb peaks also do not match up with the In peaks or Ga dips delineating the location of the QWs. There appears to be a lag time in Sb incorporation when the shutter was supposedly opened and a continuation of Sb incorporation after the shutter was closed. Another group, Shimizu et al., also published using Sb as a surfactant during the growth of GaInNAs material, but were the first to also claim incorporation of up to 1.6% in the QW region [97]. These results were the first to indicate that Sb acts as a surfactant and incorporated species. SIMS was also performed on GaInNAsSb in which a different Sb source was used. Rather than the standard effusion cell which only sublimates Sb into mostly Sb4 tetramers, an unvalved Sb cracker was used to deposit Sb [85]. The cracker splits the sublimated tetramer into a combination of tetramers, dimers, or monomers depending on the cracker temperature and flux as shown in Figure 1.30. Operating at 8508C and at a beam equivalent pressure (BEP) of 7.8 £ 1028 Torr, the Sb exiting the cracker was , 100% Sb1 [29]. A SIMS depth profile of a triple GaInNAsSb QW sample with GaNAsSb barriers is shown in Figure 1.31 showing In, Sb, and N compositions. As mentioned earlier, the N and Sb concentrations were calibrated using NRA and PIXE-RBS. An increase in Sb for each QW, as was seen by Wang et al., was not seen in these samples. Conversely, the Sb concentration actually decreased with each QW and barrier grown. The exact reason is unknown although it was thought that this was due to different Sb species used during

Figure 1.30. Fraction of antimony species for different cracker temperatures for a BEP of 1 £ 1026 Torr. Triangles represent Sb1, bow-ties Sb2, and circles Sb4. The lines represent calculated values.

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Dilute Nitride Semiconductors

Figure 1.31. SIMS profile of a triple GaInNAsSb/GaNAsSb QW structure showing the indium (In), antimony (Sb), and nitrogen (N) depth profiles before and after annealing.

growth. However, upon closer examination of a single GaInNAsSb QW as shown in Figure 1.32, the trailing edge of the Sb signal on the surface side appears to drop-off much more slowly than that of N or In suggesting some Sb does in fact remain on the surface and continues to incorporate until the supply has been exhausted and/or completely

Figure 1.32. SIMS of a single GaInNAsSb/GaNAs QW showing the antimony and indium depth profiles. The antimony continues to incorporate after the shutter has closed.

MBE Growth and Characterization of Dilute Nitride III– V Alloys

41

desorbed. Antimony as high as 8 –9% was incorporated into the GaNAsSb barriers where the growth rate was slowest and 2.5% in the QWs where the growth rate was fastest. Nitrogen behaved similarly, incorporating more in the barriers than in the QWs due to the growth rate differences. The actual concentration varied inversely proportional to the growth rate as expected. Antimony was not as straightforward to examine. One could assume that the increased growth rate in the QW would lead to a decrease in incorporation by virtue of incorporation speeds. However, the Sb composition between the QW and barrier did not follow a linear dependence on the growth rate. If growth rate were the only contributing factor, the actual Sb concentration in the QW was , 54% lower than expected. Also, in GaAsSb growth, an increase in the Ga growth rate for a fixed As/Sb flux ratio leads to increased Sb incorporation [109]. These facts do not appear to apply to GaInNAsSb and thus indicates that the Sb incorporation in GaInNAsSb is greatly affected by different growth kinetics such as strain or the presence of another large atom such as In [85]. Also, the amount of Sb found in these samples in both the barriers and QW was much larger than previous studies using standard effusion cells suggesting that the monomer form of Sb is more reactive and has higher sticking coefficients than the large tetramer molecule. How this affects the material quality as well as growth kinetics is still being investigated. GaNAsSb samples were also examined by SIMS under different growth conditions. Figure 1.33 shows the SIMS depth profile for the GaN0.029As0.873Sb0.098 sample. An interesting feature to note in the SIMS depth profile is the top interface of the GaNAsSb layer. The N and Sb profiles do not end at the same location within the sample. This was

Figure 1.33. SIMS depth profile of GaN0.029As0.873Sb0.098 sample. Antimony incorporation continues 5– 7 nm after shutter has closed.

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Dilute Nitride Semiconductors

determined not to be a measurement or sputtering artifact, as it was repeatable within the same sample and was seen on all other samples measured with SIMS. Upon examination of the SIMS depth profile, it appears Sb continues to incorporate , 5 – 7 nm beyond the end of N incorporation. This segregation behavior was much more pronounced than that seen in GaInNAsSb. This growth artifact could be quite detrimental to devices since there is a thin layer of GaAsSb which could significantly change the originally intended band structure properties due to changes of both composition and strain. Growth conditions, specifically As overpressure and substrate temperature, were varied during GaNAsSb growth to examine the effects of altering these conditions. It is known that in mixed group-V materials, the relative fluxes of each group-V element play a large role in composition and growth kinetics. In GaInNAs, there was no significant effect on N incorporation by different As fluxes due to the “unity” sticking properties of N [10]. However in GaNAsSb, it is suspected that the As and Sb fluxes do indeed affect each other since they do not have the same sticking properties as N. It is also possible that a variation in Sb incorporation could affect the N composition. Starting with the original GaN0.029As0.873Sb0.098 sample, the effects of As overpressure on GaNAsSb, the original 20 £ As-toGa flux overpressure was varied between 15 £ , 25 £ , and 30 £ . All other growth conditions were held constant. HRXRD showed a decrease in compressive strain, however it was unclear if a decrease in Sb, an increase in N, or a combination of both was the cause of this change in strain. To determine the origin of the strain reduction, SIMS was performed to measure the composition. Figure 1.34 shows that the Sb concentration drops from 12 to 9% while the N concentration remains roughly constant as the As overpressure is increased from

Figure 1.34. Compositional results from SIMS of GaNAsSb QW samples growth with different arsenic overpressures.

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43

15 £ to 30 £ . This would explain the decrease in compressive strain with increasing As flux since a reduction in Sb would decrease the lattice constant of GaNAsSb. According to the SIMS data, the increase in As flux has a direct effect on the Sb incorporation rate but had no discernable effect on N incorporation (as seen in GaNAs). This decrease in Sb incorporation with increasing As flux is seen commonly in GaAsSb growth [109]. In addition, the change in Sb concentration had no effect on the N incorporation in agreement with previously obtained results [13,110]. The data also show enhanced N incorporation in the GaNAsSb. GaNAs grown under the same growth conditions yields 1.8% N, much lower than the observed 2.4–2.9% in GaNAsSb [36]. Changing the As overpressure only affects the Sb concentration and not the N concentration. The substrate temperature during GaNAsSb growth was also varied to examine the effects on crystal quality and composition. GaInNAs(Sb) was grown at 4258C to prevent phase segregation and relaxation. One of the driving factors in segregation in GaInNAs(Sb) is the clustering of In-rich areas. The GaNAsSb barriers were also grown at the same temperature since it was also thought the material would segregate. However, In is not present in this material and thus raised the possibility the material could be grown at a higher temperature. One problem with nitride –arsenide growth is the low substrate temperature. These low temperatures introduce defects in GaAs materials, such as As antisites and Ga vacancies. It is ideal to grow the material as close to 5808C as possible to minimize these defects, which may cause non-radiative recombination and reduce luminescence. A series of samples with structures and growth conditions identical those in the initial study were grown with varying substrate temperatures: þ 508C (4758C), þ 1008C (5258C), and þ 1508C (5758C). Another set of samples with no Sb (GaNAs) was also grown for comparison. With increasing temperature, HRXRD showed a shift from slightly compressive to slightly tensile strain. Again, due to the quaternary nature of the material, changes in composition were unknown. However, it was suspected that Sb was the main contributor since Sb tends to desorb more readily at higher growth temperatures. SIMS scans were taken of the GaNAsSb samples to measure composition and depth profiles. Figure 1.35 reveals a very large decrease in Sb concentration with increasing substrate temperature while the N concentration remains roughly constant. The loss of 8% Sb explains the large shift in the strain observed in HRXRD. Similar to the SIMS data from the As overpressure study, the N composition remained constant, even though the Sb concentration changed [36]. These high-temperature growth samples appeared to be promising since HRXRD scans had looked good and the compositions determined by SIMS suggested larger band gaps due to smaller amounts of Sb, but as will be seen later in the chapter, the PL results were very poor. 1.3.5 Nuclear Reaction Analysis-Rutherford Backscattering Another technique that is commonly used to quantify chemical composition in semiconductor films is RBS. A diagram of a typical RBS measurement setup is shown

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Figure 1.35. Compositional results from SIMS of GaNAs and GaNAsSb QW samples growth with different substrate temperatures.

in Figure 1.36. In RBS, an ion beam, usually helium, is accelerated toward the sample at high energies. A small fraction of the helium ions undergoes a direct collision with the atoms within a few microns from the surface and backscatter elastically. The energy of the detected ions backscattered from the sample depends on the energy lost traveling through the material and the energy lost as a result of the collision itself. The number of ions that backscatter from a particular element depends on both the concentration of the element and the effective size of the nucleus. This technique is particularly effective for “heavy” metal thin films on “light” substrates using 4Heþ þ ions. A heavy element will have a signal from high-energy backscattered ions separated from the lower energy backscattered helium ion signal from the substrate. As the ions escape from the film, they lose energy as they travel. The spread in energy between high-energy surface scattering and low energy ions escaping will give information on the thickness of the film. With a thin layer of a heavy element on a thick and light substrate, there would be a large separation between film and substrate peaks. However, for a film like GaNAs on a GaAs substrate, the lighter GaNAs film signal will be obscured by that from the substrate making analysis difficult. To measure N compositions accurately with greater sensitivity, a special form of RBS had to be used: NRA-RBS. Typical RBS experiments use helium ions with energies below 2.2 meV such that all ions scatter elastically. Ions with greater energies collide inelastically and increase the collision cross-section at specific resonant energies. At these energies, the ion is absorbed and re-emitted by the nucleus as opposed to being scattered by it. For these nuclear reactions, a variety of particles such as protons are emitted. For GaNAs analysis, a deuteron beam with an energy of 2.275 meV was used to

MBE Growth and Characterization of Dilute Nitride III– V Alloys

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Figure 1.36. Example of typical RBS experimental setup.

initiate the following nuclear reaction: 14

N þ deuteron ! 15 N þ proton:

By measuring the proton signal, parts per million sensitivity of N can be measured. Once a clear RBS spectrum is obtained, theoretical models can be simulated to obtain the best fit to determine the composition and physical structure of the sample. NRA-RBS was used to calibrate N measurements in SIMS to eliminate any matrix effects which invariably occur during ion sputtering. NRA-RBS, and RBS in general, cannot be used as the primary composition depth profiling tool for QW structures because it requires relatively thick layers (greater than 100 nm). QWs ranging only from 5 to 20 nm in thickness are too thin for RBS to obtain sufficient signal to make an accurate measurement. The thickness requirement puts a restraint as well on what compositions can be grown. Different compositions must be used such that the thick analysis layer does not relax during growth. RBS can also give useful structural information if a single-crystal sample is aligned such that ions channel down specific crystallographic directions. The ions are steered down rows of atoms reducing the backscattered yield from substitutionally located atoms. In this configuration, the beam is highly sensitive to non-substitutional sites and can quantify impurities such as atoms located in interstitial locations. To examine N interstitials in Ga(In)NAs(Sb) samples, 2Heþ ions were channeled down the [001] axis.

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Figure 1.37. NRA-RBS spectrum of a 150 nm GaInNAs film. The arrows point to the nitrogen peak for both channel and random crystal orientations.

Figure 1.37 shows the NRA-RBS results comparing channeled and random crystal orientations. The signal seen near channel 200 is drastically reduced in channeling orientations where interstitial sites are easily seen by the beam. High signals in this orientation indicate a significant presence of interstitial nitrogen. Other peaks near the N signal are surface contaminants such as carbon and oxygen which appear in both orientations. Table 1.1 summarizes the results from NRA-RBS ion channeling for GaNAs, GaInNAs, and GaInNAsSb before and after RTA. The values listed are the total N concentration and the percentage of that concentration which is found in interstitial sites. One can see with the new rf cell matching network, new front plate aperture, and new plasma operating conditions, the amount of interstitial N found in GaNAs has drastically reduced, improving the overall material quality. All materials with the new setup showed

Table 1.1. Total and interstitial nitrogen content in GaNAs, GaInNAs, and GaInNAsSb before and after annealing. The “previous design” samples were from the old rf cell configuration %N

Interstitial %N

GaNAs Annealed

2.4 2.0

5.8 8.3

GaInNAs (8% In) Annealed

2.4 2.4

3.7 4.2

GaInNAsSb (8% In, 7% Sb) Annealed

3.0 3.0

6.9 8.2

GaNAs (previous design) Annealed

3 3

26 16

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an increase in interstitial N during anneal and was most likely due to the sample being annealed in a N ambient [85]. SIMS measurements involving Sb also had to be calibrated by RBS. However, the similar cross-section sizes of In and Sb prevented the use of normal RBS. PIXE-RBS was required to distinguish between the two elements. In PIXE-RBS, the incident ion beam produces characteristic X-rays from the target elements. These X-rays are detected and a count is obtained giving composition. This technique is useful for heavy elements which have similar cross-sections. Once the calibration is obtained, SIMS measurements can be calibrated. 1.3.6 Cross-section Transmission Electron Microscopy We used high-resolution transmission electron microscopy (HRTEM) to structurally characterize GaInNAs and GaInNAsSb single and multiple quantum well samples. HRTEM is used in a novel way that allows us to map out the strain variations inside the quantum well layers. We believe that these strain variations, which are indicative of compositional fluctuations, are to blame for the broad emission spectra and high threshold currents of early lasers based on this material. In addition to the HRTEM method, we also use dark-field TEM (DFTEM) and energy-filtered TEM (EFTEM) to verify our findings from the high-resolution analysis. We investigated both GaInNAs and GaInNAsSb samples grown by MBE. All QWs had an 8 nm nominal thickness, with 20 nm barriers in between. GaInNAs samples had a nominal composition of 30% In and 1.6% N. GaInNAsSb samples had a nominal composition of 38% In, 2.0% N, and 2% Sb in the wells and 2.5% N in the GaNAs barriers. The substrate temperature was kept low during growth at around 4258C to prevent phase segregation. Cross-sectional TEM samples were prepared in the (110) orientation using the “sandwich” technique. All samples were examined in the as-grown condition (i.e. not annealed). Thinning was achieved by grinding and polishing followed by 5 keV Arþ ion milling at low angles to achieve electron transparency. A final polishing 1 keV low temperature ion milling was performed to achieve smooth surfaces. HRTEM lattice images of the QW area were obtained in an 800 kV, 0.15 nm resolution JEOL microscope and recorded on photographic plates. Dark-field images with the chemically sensitive (002) reflection and EFTEM images were obtained in a Philips CM200 FEG-TEM equipped with a 1024 £ 1024 pixel CCD camera and Gatan GIF analyzer. Strain maps were generated from the high-resolution lattice images using the DARIP program developed at the National Center for Electron Microscopy (NCEM) at the Lawrence Berkeley National Laboratory (LBNL) in Berkeley, California. DF and EFTEM images were analyzed with Gatan Digital Micrograph. Figure 1.38(a) shows a selection from a HRTEM lattice image of the quantum well area of a GaInNAs sample and Figure 1.38(b) is the corresponding strain map across the well. The image was taken in the [110] zone axis. Performing strain mapping analysis requires

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Figure 1.38. HRTEM image of the QW area of (a) a GaInNAs sample and (b) strain map across the well.

very high quality lattice images over large areas of the sample. Therefore, it is critical to perform a final very low energy (1 keV) ion polishing on the sample to achieve very smooth surfaces and large thin areas. Strain mapping is performed on the HRTEM images in several steps. First, the images are filtered to subtract the diffuse background intensity and make the peaks (which can be interpreted as the positions of the atoms) more defined. The DARIP program is used to identify and mark those peaks. Next, a lattice is defined by choosing several peaks and based on these selections, DARIP calculates a lattice which it locks to the peak positions. The data is extracted and a strain map, which is essentially a map of the lattice parameter over the selected area, is generated. Figure 1.38(b) shows this type of strain map for a single QW GaInNAs sample. The well clearly appears as a peak due to the fact that In increases the equilibrium lattice parameter; the higher the In concentration, the greater the lattice distortion. It can also be seen that the In concentration profile is very asymmetric. It consists of two bumps with the higher In concentration occurring near the top interface of the well, providing evidence that In segregates near the top of the well. This is very undesirable since there are effectively two different In compositions in the well, which would broaden the emission spectrum. The difference in the rear and leading edge compositions was estimated to be around 8%.

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Figure 1.39 shows the strain maps across the three QWs in (a) a GaInNAsSb sample and (b) a GaInNAsSb sample with identical composition but with 58C drop in the growth temperature for each successive well. The compositional profiles across the wells appear very uniform due to the Sb. The sample in Figure 1.39(a) exhibits tensile spikes at the bottom interface of the wells due to the opening of the Sb shutter which increases the incorporation of N. Figure 1.39(b) does not show these spikes which indicates that the temperature drop affects the interaction between Sb and N and results in decreased N

Figure 1.39. Strain maps across three-QW GaInNAsSb samples with (a) constant growth temperature and (b) 58C drop in growth temperature for each successive well.

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Figure 1.40. DF image with the (002) reflection of a GaInNAs sample with three QWs.

incorporation at the interface of the well. This should increase the carrier confinement in the well and result in more efficient recombination and increased luminescence efficiency. Figure 1.40 shows a dark-field image of a three QW GaInNAs sample taken with the chemically sensitive (002) reflection. The intensity of the (002) reflection has a square dependence on the difference between the composite structure factors of the group-III and group-V atoms and for the GaInNAs alloy is modeled as shown in Eqs. (1.1) – (1.3): I002 ¼ A2 ¼ k2 lfIII 2 fV l2

ð1:7Þ

fIII ¼ xðfIn 2 fGa Þ þ fGa

ð1:8Þ

where I002 is the (002) intensity, f designates the structure factors, x and y are the fractions of In and N, respectively, and k is a constant. In Figure 1.40, the wells show up as stripes clearly delineated by dark lines. These occur at the well interfaces because the combination of the fractions x and y is such that the reflection is completely extinguished. Within the wells, as the In concentration increases, the (002) reflection is no longer extinguished and the brightness is recovered. Figure 1.40 shows that the well interfaces for the GaInNAs sample are quite rough and the deterioration is greatest for the top well. This is in good agreement with Figure 1.38(b) where the strain map clearly evidenced the tendency of In to phase segregate in a GaInNAs sample. Figure 1.41 shows the DF images for the GaInNAsSb samples grown at (a) constant growth temperature and (b) with 58C growth temperature drop for successive wells. These images show much smoother interfaces compared to the GaInNAs sample in Figure 1.40 and confirm the strain map findings that Sb improves the compositional uniformity of

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Figure 1.41. DF images with the (002) reflection of three-QW GaInNAsSb samples with (a) constant growth temperature and (b) 58C drop in growth temperature for each successive well.

the material. In addition, comparison between the two images in Figure 1.41 reveals that the sample in (b) shows slightly smoother interfaces than the one in figure (a) which reinforces the idea that a slight reduction in the growth temperature for successive wells might be beneficial.

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Figure 1.42 shows the EFTEM images for (a) a three-QW GaInNAs sample and (b) a three-QW GaInNAsSb sample. These images are formed by selecting only the electrons that are scattered inelastically off the In atoms, so the wells where the In is concentrated, appear as very bright stripes. In Figure 1.42(a), the white arrows indicate non-uniformities in the contrast of the upper well which are indicative of In compositional fluctuations. This observation is in good agreement with the DF (002) images of the GaInNAs sample where

Figure 1.42. EFTEM images of (a) a three-QW GaInNAs sample and (b) a three-QW GaInNAsSb sample.

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the well interfaces appeared quite rough, although these non-uniformities appear less pronounced in the EFTEM image. Figure 1.42(b) shows that the presence of Sb improves the compositional uniformity as evidenced by the more uniform contrast in the EFTEM image. Figure 1.43 shows the strain maps across the three QWs in an annealed GaInNAsSb sample (a) and an annealed GaInNAsSb sample with identical composition but with 58C drop in the growth temperature for each successive well (b). The annealed profiles look

Figure 1.43. Strain maps across annealed three-QW GaInNAsSb samples with (a) constant growth temperature and (b) 58C drop in growth temperature for each successive well.

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Dilute Nitride Semiconductors

very similar to the ones for the unannealed samples in Figure 1.39. The uniformity is preserved but the tensile spikes observed in Figure 1.39(a) disappear. The similarity in profiles confirms that annealing has little effect on the In clustering behavior, rather its importance is in annealing-out point defects and plasma damage. Figure 1.44 shows the strain profiles for two annealed single QW GaInNAsSb samples. The sample in Figure 1.44(a) was grown under standard conditions with no voltage between the deflection plates in front of the N plasma cell. Figure 1.44(b) shows the strain profile for a sample with identical composition and grown under the same conditions but with voltage applied between the deflection plates. As seen in Figure 1.44, the sample that was grown with the deflection plates biased exhibits a more uniform profile. We believe

Figure 1.44. Strain maps across annealed single QW GaInNAsSb samples (a) with no deflection plates bias and (b) with deflection plates bias.

MBE Growth and Characterization of Dilute Nitride III– V Alloys

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that applying a bias to the deflection plates prevents some of the high-energy N or N2 ions or radicals from reaching the surface of the sample. These highly energetic radicals are believed to promote In clustering by imparting additional energy into the sample. By preventing them from reaching the surface, the severity of In clustering is reduced. Figure 1.45 shows the DF (002) images for the same two samples from Figure 1.44. The sample grown with the deflection plates under bias (Figure 1.45(b)) shows smoother

Figure 1.45. DF images with the (002) reflection of annealed single QW GaInNAsSb samples (a) with no deflection plates bias and (b) with deflection plates bias.

56

Dilute Nitride Semiconductors

interfaces which indicates less In segregation and/or N clustering. This is in good agreement with the strain maps in Figure 1.44. Figure 1.46 shows the DF (220) images for the same samples from Figures 1.44 and 1.45. The (220) reflection is sensitive to relaxation due to compositional variations. It is clearly seen that the sample grown with deflection plates (Figure 1.46(b)) has more uniform composition as evidenced by the more uniform contrast in the image. These results are again in good agreement with the strain maps and the DF (002) images.

Figure 1.46. DF images with the (220) reflection of annealed single QW GaInNAsSb samples (a) with no deflection plates bias and (b) with deflection plates bias.

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1.3.7 Cathodoluminescence CL is similar to PL in that it excites carriers such that emission occurs. The excitation source in CL uses a high energy electron beam rather than photons as in PL. When a beam of energetic electrons of energies above 1 keV hits a solid, , 10% of the electrons backscatter from the surface while the others penetrate into the material. While traveling in the material, the electrons quickly lose energy via impact ionization, generating electron – hole pairs. These electron –hole pairs which are close to the band gap energy thermally relax to the lowest energies in the conduction and valence bands. They then recombine and emit photons which are then detected. The CL process is much less efficient than PL since most of the energy imparted by the electrons is converted into phonons. The penetration depth of the primary electrons, Re ; depends on the incident electron energy beam, Eb ; as follows [111]:   0:052 1:75 Re ¼ ð1:9Þ Eb r where r is the material density in g/cm3. Thus, luminescence generated by the secondary carriers can be generated deeper within the sample by increasing the energy of the beam. CL is usually performed in a scanning electron microscope (SEM) so that the electron beam can be scanned and rastered to obtain a “map” of the luminescence which gives an indication of the homogeneity of the material. Unfortunately the luminescence efficiency is very low so the samples must be cooled in order to obtain a decent signal. Figure 1.47 shows the CL scans from InGaAs, GaInNAs, and GaInNAsSb measured at 4 K. The images were obtained by scanning the electron beam across the surface while recording the luminescence with a spectrometer set a specific wavelength. Figure 1.47(c) shows the CL from an InGaAs QW sample which has RT-PL at 980 nm. The homogeneity of the image is indicative of very homogenous material with a uniform band gap across all areas. A GaInNAs QW with 1300 nm RT-PL has a very spotty CL image with dark and light spots across the surface. The luminescence spectrum from the same GaInNAs sample obtained by scanning the sample while measuring the light in a spectrometer is displayed in Figure 1.48 and shows two peaks from the material which was unresolved in RT-PL. The GaInNAs CL image was taken with the spectrometer wavelength set at 1230 nm. There is a great deal of non-uniformity within the QW due to either clustering or phase segregation. Since there is a change in composition in different areas of the QW, the band gap fluctuates along the plane of the QW leading to different emission wavelengths. A GaInNAsSb QW with RT-PL at 1480 nm was then measured with CL and is shown in Figure 1.47(b). Compared to the GaInNAs sample, the In concentration was increased from 30 to 39%, the N content remained the same, and Sb with a BEP of 1.2 £ 1027 Torr was added. With the increased amount of strain from the addition of more In and Sb, it was thought that phase segregation would be more apparent. However, the CL image shows that the sample is more uniform suggesting a smaller degree of phase segregation or clustering. Some contrast and features still remain compared to the standard InGaAs sample, but

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Figure 1.47. CL scan of triple QW samples at 4 K: (a) annealed 1300 nm RT-PL GaInNAs, (b) annealed 1480 nm RT-PL GaInNAsSb, and (c) 980 nm RT-PL InGaAs.

Figure 1.48. CL spectrum for the GaInNAs QW sample, (b) in Figure 1.47.

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the overall homogeneity is improved compared to the GaInNAs sample when Sb is added. This agrees with the belief that Sb has a surfactant-like effect on the growth surface by reducing the surface mobility and reducing segregation. 1.3.8 Photoreflectance, Electroreflectance and Absorption PR and ER, and absorption spectroscopy are useful tools in the analysis of semiconductor properties such as the energy band structure, quantum well depths, and trap levels. In PR, a chopper-modulated laser beam is directed towards a semiconductor sample which absorbs the light, creates electron – hole pairs, and causes modulation of the surface electric field, manifested as a measured change (DR) in the reflectivity (R). A second probe beam, whose energy is scanned, is focused on the illuminated area to measure the spectral dependence of the change in reflectivity by using phase-sensitive detection. The final data set obtained is a plot of DR=R versus wavelength. The features in the PR spectra are related to the derivatives of the energy band transitions and thus give valuable information on the interband transitions of the sample. By using model-fitting procedures, one is able to determine important parameters such as heterojunction band offsets, band gaps, dopant levels, and internal electric fields [112,113]. ER is similar to PR except that rather than using a laser beam, the electric field in the sample is directly modulated using a variety of methods of applying voltage to the sample. A more detailed discussion of PR and ER can be found in Chapter 9 by Misiewicz and Kudrawiec. The absorption technique is a direct measurement of the attenuation spectra for amplified spontaneous emission in a laser structure after passing through an unpumped absorbing length of the laser waveguide. The method is described in more detail in Ref. [114]. Of key importance in dilute nitride semiconductor laser devices is the heterojunction band offsets between GaAs, the QW barriers, and the QWs themselves. Band offsets are very important in laser device design. One of the primary advantages of GaInNAs(Sb)/ GaAs devices over InGaAsP/InP devices is the higher T0 for the GaAs-based lasers due to improved electron confinement in the QW. There have been several studies on the band offsets of GaNAs and GaInNAs to GaAs, however there have not been any experimental measurements of these values for Sb-containing dilute nitrides [6,115 –118, 120]. It was unclear what effect adding Sb to GaNAs and GaInNAs has on the band offsets. Traditionally, the addition of Sb to GaAs mostly affects the valence band by pushing it upwards towards the conduction band and has a very small effect on the conduction band (also pushing it upwards). In the dilute nitrides, it was unclear if the Sb would mostly only affect the valence band or if there would be a more complex interaction of the valence band and conduction band due to effects such as the band anticrossing model proposed by Shan et al. [119]. To determine the band offsets of the GaNAsSb and GaInNAsSb layers, PR measurements were performed on GaInNAsSb/GaNAs/GaAs and GaNAsSb/GaAs QWs and the results were simulated. The GaInNAsSb/GaNAs/GaAs double stepped structure was used in

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the edge-emitting lasers which operated at 1.5 mm and the VCSELs at 1.46 mm. The general structure and compositions of the active regions in each of those devices are 20 nm GaAs, 8 nm GaN0.027As0.973, 20 nm Ga0.61In0.39N0.023As0.957Sb0.02, 8 nm GaN0.027As0.973, and 20 nm GaAs. Simulation of the PR results was difficult due to the ambiguity in several parameters in the dilute nitride alloy. The band offset between GaNAs and GaAs is still a debatable subject as some groups report a slight type-II offset with the GaNAs valence band below that of GaAs while others report a type-I offset with the GaNAs valence band slightly above that of GaAs [120,121]. Most of the reduction in band gap occurs at the conduction band. Figure 1.49 shows the rough estimates of the band structure for the GaInNAsSb/ GaNAs/GaAs structure. The Qc for the GaInNAsSb/GaNAs heterojunction is , 0.8 and GaInNAsSb/GaAs is , 0.9. For GaInNAs/GaAs measurements, it was found that Qc was , 0.7. The GaInNAsSb alloy in the composition regime which was studied was found to have a larger electron well than GaInNAs. Most of the reduction in band gap by addition of Sb occurred in the conduction band, a somewhat surprising result as Sb normally affects the valence band. Final measurements are still under analysis. GaNAsSb/GaAs QWs were also measured and simulated. It was observed that Sb mostly affected the valence band (as in GaAs) while N still mostly affected the conduction band. Knowledge of the GaNAsSb band offset is important since we have used it in the past as QW barrier material for the GaInNAsSb QWs, but PL measurements indicated the band gap of GaNAsSb was much smaller than anticipated [36]. With the raising of the valence band, there existed a situation in which the GaInNAsSb/GaNAsSb QW region was of type II in nature.

Figure 1.49.

Schematic drawing illustrating the energy band structure for a GaInNAsSb QW with GaNAs/GaAs barriers.

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Polarization resolved absorption measurements were performed at 358C on the edgeemitting laser described in Chapter 17: a 7.8 nm Ga0.62In0.38N0.023As0.950Sb0.027 SQW inside 22 nm GaN0.025As0.975 barriers embedded in a GaAs waveguide and annealed at 8008C for 1 min. By matching the energy level spacings of the various transitions to finite quantum well theory, we determined EgQW ¼ 815 ^ 7 meV, meQW ¼ 0.113 ^ 0.024 m0, QW ¼ 0.35 ^ 0.09 m0, DEc ¼ 164 ^ 5 meV, DEvHH ¼ 159 ^ 12 meV. However, due mhh to the tensile strain induced valence band splitting, the efective valence band barrier height is only 115 ^ 6 meV (EgBarrier ¼ 1094 ^ 5 meV). With the smaller effective barrier height, there will be significant hole leakage into the barriers since the thermionic emission lifetimes for holes could be less than 7 ps at room temparature assuming there is efficient scattering from the heavy to light hole bands at the QW/barrier interfaces. We find excellent agreement with the PR data conducted on an unannealed sample after acounting for the annealing blueshift. The QW and barrier bandgaps are blueshifted by 32 and 84 meV, respectively, and the electron and heavy hole barrier heights are 20 and 32 meV higher after annealing. The annealing blueshift is definitely larger ( < 2.5 £) for the GaNAs barriers than the GaInNAsSb QW. Thus, annealing improves device performance not only by improving material quality, but also by increasing the carrier confinement in the QW [114]. 1.3.9 Deep Level Transient Spectroscopy Deep level transient spectroscopy (DLTS) is an extremely powerful technique for quantitatively characterizing not only the defect density of semiconductor layers, but also the nature of the defect(s) including capture cross-section, activation energy, and spatial distribution. The capacitance of a metal/semiconductor junction is monitored as the junction is pulsed with injected carriers. The junction capacitance or voltage provides a measure of the trap emission rate, which is dependent upon the energy depth of the trap (i.e. the thermionic escape time). The DLTS spectrum is obtained by repeating this measurement over a wide range of temperatures. Peak heights are proportional to the trap density and the temperature dependence gives the energy level of the defect. The role of hydrogen-related defects in GaInNAs is presented in Chapter 3 by Amore Bonapasta and Fillippone. The focus of this section will be on the observation and quantification of defects in Ga(In)NAs layers. To remain consistent with published reports, the nomenclature from each was retained. DLTS work on GaInNAs alloys can be divided into two distinct groups: low Ncontent GaNAs and lattice-matched GaInNAs. The two are expected to be somewhat different in terms of N-related defects as strain plays an important role in defect incorporation [122]. 1.3.9.1 Defects in MBE-grown GaNAs. Much of the early work on characterizing deep levels in the dilute nitrides was performed on GaNAs (, 3%) owing to the relatively low strain that allows sufficient layer thickness for DLTS measurements.

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Hole Traps in p-GaNAs. Traps in p-type (unintentionally doped) GaNAs have been studied in Ref. [55]. Nitrogen related defects give rise to electron traps [123] and do not create any hole traps. Several traps were found and denoted HK1 – HK5. HK1 (0.16 eV) behaves similarly to defects observed in particle-irradiated surfaces [55]. The density was postulated to be a defect due to an alteration in growth process in the presence of a plasma (operating with shutter closed). HK1 was found to be highest at the GaNAs/GaAs interface. HK2 (0.39 eV) and HK5 (0.69 eV) are GaAs (Ga on an As site) traps and are most prevalent at the GaAs/GaNAs interface. HK3 (0.35 eV) is associated with copper impurities from the N cell. The capture cross-section was found to be relatively large, , 10214 cm22. HK4 (0.45 –0.55 eV) is also associated with N cell operation due to iron impurities with a capture cross-section , 10215 cm22. Hole deep levels are almost completely removed upon anneal except for HK1 (unchanged) and, to some degree, HK2 (density reduced by 3 £). It was postulated that deep donors in the upper half of the band gap must exist to fully account for the defect density in GaNAs. Electron Traps in n-GaNAs. The same authors examined Si-doped GaNAs to identify any N related defects [124]. Distinct compositional fluctuations were observed in the depth profiles and the defect density was found to be much increased with N content. Further study revealed two traps with locations, independent of composition, at 0.8 and 1.1 eV above the valence band edge [122]. The defects can be traced back to defects observed for e2-irradiated GaAs. These defects were found to have a threshold energy , 10 eV which is consistent with the ion energy associated with a sparse plasma, such as the rf N plasma cell used in the growth. It is likely that deflection plates reduce these defects directly [62,124]. The defect with 0.8 eV activation energy was tentatively associated with the (N – N)As split interstitial [123]. The defect density increased dramatically with N% from 4 £ 1015 cm23 for , 0.1% N to 1.3 £ 1017 cm23 for 0.5% N [122]. The capture cross-section was found to have a low capture cross-section , 10217 cm2, making it a relatively inefficient trap [123]. The 1.1 eV defect was uniformly distributed within the GaNAs and was attributed to the (N –As)As split interstitial. This defect is resistant to anneal and lies within the conduction band for . 2.5% N. The capture cross-section was also found to be large, , 10215 – 10214 cm2 and could serve as an extremely efficient trap. It is postulated that this defect explains why low threshold GaInNAs(Sb)/GaNAs lasers have been demonstrated by MBE for barrier compositions , 1% but performance is typically degraded when the N mole fraction exceeds , 2%. Both the (N –As)As and (N– N)As defects have been theoretically predicted to introduce compressive strain and, from strain consideration alone, are energetically favorable to form in tensilely strained GaNAs [121]. The (N – As)As defect introduces greater compressive strain than (N –N)As and is more favorable to form for reducing the tensile strain. Moreover, the 0.8 eV peak was seen to increase with increasing layer thickness, consistent with formation driven, in part, by increasing tensile strain. The (N – N)As defect has been

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predicted to trap both holes and electrons; however the measured capture cross-section was quite low. Zhang et al. also predicted the presence of AsGa – NAs defects as well which have also been reported [125]. This defect was found to be removed upon anneal [119]. Defects in MOCVD-grown GaInNAs. DLTS work on GaInNAs has focused primarily upon lattice-matched materials with band gap , 1 eV that are desirable for next generation solar cells. This work is reviewed in detail in Ref. [126]. The broad nature of DLTS peaks in lattice-matched GaInNAs, as compared to the narrow peaks observed in strained GaNAs samples, is not understood but serves to complicate analysis. This was attributed to a continuous distribution of defects within the band gap [127]. Defects in p-type GaInNAs. Several hole traps were observed at 0.1, 0.23, and 0.48 eV above the valence band edge and an additional midgap trap that disappeared upon anneal [128]. The concentrations after anneal were estimated to be 3.5 £ 1014, 3.8 £ 1014, and 8.2 £ 1014 cm23. The 0.48 eV peak was not reduced by anneal indicating that it may be a limiting factor in solar cell efficiency. Defects in n-type GaInNAs. Sn-doped GaInNAs samples yielded four electron traps and a minority hole trap that was observed under forward bias [127]. The activation energies for E1 –E4 were determined to be 0.2, 0.36, 0.34, and 0.82 eV, respectively, below the conduction band. The activation energy of the hole trap, H1, was 0.71 eV. The appearance of both E2 and H1 upon anneal suggests they are the same defect. As the defects were not observed in p-type material this defect is potentially specific to Sn-doped GaInNAs. E1 and E3 were dramatically reduced upon anneal, however, E4 remained. Due to the similar activation energy, E1 is possibly the (N –N)As split interstitial. Dark I– V measurements with temperature performed on annealed material yielded an activation energy of 0.35 eV, correlating it to the E2/H1 defect. Defects in MBE GaInNAs. Lattice-matched MBE-grown material was also examined, and only annealed results were presented. The p-type material, as for MOCVD GaInNAs was undoped [129]. Two main hole traps were reported in the p-type samples, one at 0.38 eV (H30 ) and one at 0.51 eV (H40 ). No evidence of minority traps was found. In the n-type (Sidoped) sample, a shallow distribution of defects, E10 , a deep electron trap (0.56 eV) and a deep hole trap (0.71 eV) were observed. Comparison Between MBE and MOCVD GaInNAs. Experiments by NREL on highquality material grown by MBE and MOCVD have allowed for a comparison of the two techniques. Unique features to each technique can be ruled out as the root causes of the low diffusion length and high recombination common to all GaInNAs. Poor diffusion length limits the potential use of GaInNAs for high efficiency solar cell operation. The main differences observed between MBE and MOCVD material are the H50 defect in MBE material, likely (N – As)As, and the E2/H1 feature in MOCVD material. The shoulder on

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the high temperature side of the N-related electron trap only occurs in MOCVD material. It is interesting to note that In was found to have no effect on the deep level spectra for either technique, indicating behavior is purely N related. As a side note, MOCVD shows higher carbon and hydrogen content, however similar performance between the two techniques indicates this is not the main cause of low diffusion length and non-radiative recombination in GaInNAs. However, the presence of hydrogen has been found to be detrimental to device performance, as will be shown next. Ga vacancies (VGa) have been recently attributed to the anomaly in MOCVD material and this is discussed in the next section [130]. Positron Annihilation Studies. Evidence of gallium vacancies, caused by N – H complexes, was found by positron annihilation [130,131]. This work is consistent with Janotti et al. [132] who showed that hydrogen enhances the formation of VGa in GaNAs. Positron annihilation measurements confirmed the presence of more VGa in material grown by MOCVD than by MBE [131]. The addition of an atomic hydrogen flux (2 £ 1025 Torr) during MBE growth showed an enhancement in VGa, confirming the role of both hydrogen and N in the formation of this defect. This may explain higher p-type background of MOCVD material as the defect is acceptor-like. Additionally, this difference between MOCVD and MBE explains observations of VGa in GaInNAs grown by gas-source MBE by Li et al. [133]. This may be the root cause for their observation of Ga –In intermixing as a mechanism causing the blue shift in GaInNAs with anneal [134]. Similar effects have been found to occur in solid-source MBE as well when a surface SiN cap is sputtered [135]. The sputtering introduces VGa that promote Ga –In intermixing that blue shifts the luminescence further. 1.3.10 X-ray Photoelectron Spectroscopy X-ray photoelectron spectroscopy (XPS) is also called electron spectroscopy for chemical analysis (ESCA) depending on who is speaking. However, the name ESCA highlights the primary importance of this technique: the analysis of elements in the material. The basis for XPS (and the other photoemission methods) is the photoelectric effect. A photon incident on an atom will interact with an atomic orbital electron and transfer its energy. If the photon has enough energy, it can cause the electron from an atom to be ejected with a kinetic energy defined by KE ¼ hn 2 EB ð1:10Þ where n is the frequency of the photon and EB is the binding energy of the electron to the atom. Most of the time, XPS is used for the determination of the chemical makeup of a material. However, with more detailed analysis, band offsets may be extracted from the data. The XPS method of measuring heterojunction band offsets is theoretically simple. In actual practice, the measurement is rather difficult due to the small shifts that need to be detected. The important quantities that need to be measured or determined are shown in

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Figure 1.50. Diagram of a heterojunction made from semiconductors “A” and “B” with relevant quantities for measuring the band lineup by XPS.

Figure 1.50. Referring to the figure, one set of values that must be measured by XPS is the difference between a reference core level and the valence band in a bulk sample, ECL 2 EV. This must be done for each semiconductor that makes up the heterojunction. The difference between the reference core level and the valence band is a function only of the material and not of the heterojunction. This provides a value with which one can compare any energy shifts due to band offsets. The quantities that are dependent upon the heterojunction are the valence band and core level offsets. The last measurement that must A B be made by XPS is DECL ¼ ECL 2 ECL : If there were no band offset, DECL should be zero. However, the presence of a band offset causes the core levels to shift due to the fact that the Fermi level of the heterojunction semiconductors must line up to the same value. With, A B DECL ; ECL 2 EVA ; ECL 2 EVB one can determine the valence band offset using the following equation: B A DEV ¼ DECL þ ðECL 2 EVB Þ 2 ðECL 2 EVA Þ ¼ EVA 2 EVB :

ð1:11Þ

In order to determine the conduction band offset, DEC, which is often of more interest than the valence band offset, one simply uses the following relation: .

DEG ¼ EGA 2 EGB ¼ DEC þ DEV

ð1:12Þ

Theoretically, when two purely intrinsic semiconductors are joined together, there should be no band bending because there are no excess concentrations of electrons or holes. However, it is nearly impossible to grow purely intrinsic semiconductors due to defects

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such as impurities and lattice defects. This results in semiconductors which are very slightly p or n-type and thus small levels of band bending result. If one were to measure the DECL of the two semiconductors relatively far from the interface (greater than the Debye length), an incorrect measurement of DECL would be obtained. However, one side of the ˚ ). This thickness is much less than the heterojunction must be extremely thin (, 20 A total thickness in which band bending occurs and thus any measurements made are of the actual band offset.

1.4. ENERGY BAND AND CARRIER TRANSPORT PROPERTIES

1.4.1 Doping Type In keeping with the theoretical predictions of Zhang, material grown by both MBE and MOCVD is p-type as-grown [122,127]. For MOCVD material, the background carrier density ranges from 3 £ 1016 to 1 £ 1017 cm23, although 5 £ 1015 cm23 has recently been reported in high mobility lattice-matched GaInNAs [127,137]. Interestingly, type conversion has been observed with anneal [138]. Samples shifted to n-type , 1017 cm23, which was attributed to N –H (donor) defects that form upon anneal. MBE-grown material shows approximately the same as-grown hole background [130]. 1.4.2 Electron and Hole Mobility It is expected that mobility should be lower in Ga(In)NAs due to strong alloy scattering and the enhanced electron effective mass. The enhanced effective mass was predicted in Ref. [139] to reduce the electron mobility. However, the band anticrossing effects should not alter the valence band structure appreciably. Since reduced mobility of both electrons and holes has been observed, alloy or impurity scattering is likely the dominant effect governing mobility. In practice, the high trap density also serves to limit both hole and electron mobilities. Fahy and O’Reilly recently calculated, through S-matrix and band anticrossing methods, the maximum electron mobility for GaNAs to be , 1000 cm2/V s [140]. In addition to the increased effective mass, the anticrossing model introduces a second order perturbation to the Born approximation. The perturbation is negligible in typical III – V alloys but is an order of magnitude greater in the dilute nitrides. The calculated values are in reasonable agreement with the highest figure reported for GaInNAs [137]. Electron mobility is higher in GaInNAs than predicted for GaNAs, as expected. Typical mobility values are 300 and 150 cm2/V s for electrons and holes, respectively for GaInNAs [127]. A strong (non-linear) degradation of hole mobility was observed with increasing N mole fraction for both MBE and MOCVD-grown GaNAs [131]. Similarly, researchers at CNRS found a precipitous drop in AlGaAs/GaNAs 2D electron gas mobility with increasing N content [141]. Interestingly, for 0.6% N in the channel, the mobility was

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constant with temperature from 300 to 100 K, before a precipitous drop at , 100 K. This is contrary to typical AlGaAs/GaAs 2-DEGs and what was observed for the very low N concentrations (, 0.02%) where the mobility increases dramatically saturating , 77 K. This drop is likely correlated with the localization phenomena observed in the band gap shift of GaInNAs with temperature [103]. Maximum reported values for annealed material grown by MOCVD are 2000 cm2/V s for electrons (, 1 £ 1017 cm23 tellurium) and 200 cm2/V s for holes (nominally undoped) [137]. The carbon and oxygen levels of this material were quite low, below the 1 £ 1016 cm23 detection limit of SIMS. 1.4.3 Carrier Lifetime The carrier lifetime is quite low in the dilute nitrides, as expected for material with high defect density. At the present time, it is unclear whether this is due to intrinsic defects or if improvements can be expected. Regardless, the carrier lifetime is an extremely important parameter for solar cells and lasers. Room temperature lifetimes , 1 ns have been reported for GaN0.01As0.99 [127]. Persistent photoconductivity was also observed, consistent with the presence of deep levels [142]. TR-PL mechanisms were investigated in Ga0.63In0.37NxAs12x. The room temperature carrier lifetime was seen to increase for 0:02% # x # 2:3% and to decrease above that [103]. The lifetime was , 1 ns throughout the sample set. Lattice-matched structures appear to suffer from particularly low carrier lifetimes, including measured lifetimes , 0.4 –0.6 ns for annealed 1 eV material [131]. The lifetimes are consistent between MBE and MOCVD. It is possible that the weak (if any) compressive strain allows the preferential formation of split interstitial: (N– N)As or (N –As)As. This is discussed more thoroughly in the DLTS section. 1.4.4 Diffusion Length The diffusion length is proportional to the square root of the mobility and carrier lifetime. From the previous discussion, poor diffusion lengths are expected for GaInNAs. Hole diffusion lengths of 0.9 mm have been reported for MOCVD-grown GaInNAs, but electron diffusion lengths are quite low [127]. MBE-grown GaInNAs was found to have a higher electron diffusion length (0.5 mm) [143]. The low diffusion length has application to lasers as etching through the QW layer improves beam quality and does not degrade the threshold current density or external efficiency appreciably [144]. 1.4.5 Effective Mass No area of GaInNAs research has seen such a divergent set of reported values as the electron effective mass, mpe : Initial reports were consistent with the extremely large mass originally predicted by band anticrossing but were caused by assorted problems ranging from poor material quality to the assumption of a parabolic conduction band. It appears as though most techniques have converged upon mpe , 0.08– 0.1m0 for GaInNAs, , 30 –40% larger than for GaAs [6,115,141,145– 147]. Pan et al. measured

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mpe of Ga0.7In0.3NxAs12x with photovoltaic and PL measurements [115]. A slightly sub-linear variation in mpe was observed from 0.053 to 0.09m0 as the N content was increased from 0 to 1%. Similar values , 0.073m0 were obtained for low N content (0.02%) AlGaAs/GaNAs 2-DEG structures [141]. Skierbiszweski found it possible to calculate the effective mass directly from PL measurements, without any assumptions regarding band offsets due to band anticrossing [146]. Measurements showed an increase in mpe to 0.12m0 with the addition of 3% N into GaAs. Aside from strain effects and second-order conduction – valence band mixing effects, no fundamental differences in the hole effective mass are expected from the band anticrossing model. Poor hole mobility is likely due more to strong alloy scattering and traps than changes in the effective mass. 1.4.6 Band Offsets Similar to effective mass, much work has been performed to determine the band offsets of Ga(In)NAs/GaAs, as it is extremely important for device applications. Indeed, it is the most important parameter governing the temperature stability of GaInNAs(Sb) lasers. For GaNAs/GaAs, the valence band was found to be weakly type-I over the range of N compositions (N # 3%) studied [120]. The valence band offset for 3% N was measured with C –V techniques to be 11 ^ 2 meV. It is expected from band anticrossing and strain arguments that the light hole band should be weakly type-I while the heavy hole band is weakly type-II. This, in part, explains why other techniques (PL, PR, and photoemission, etc.) have shown such a variation. In such cases, C –V is the most reliable technique for determining band offsets. Other techniques such as optically detected cyclotron resonance (OCDR) showed similar results [148]. The situation is different for GaInNAs/GaAs, and an appreciable valence band offset is expected. This allows accurate measurement with other techniques. Indeed, the band discontinuities have been found to be , 80% in the conduction band and 20% in the valence band, 80:20, for typical 1.3 mm range GaInNAs QWs [6]. Band offset measurements of GaAsSb with GaAs show that band gap reduction takes place primarily in the valence band up to , 40% Sb [149]. Consequently, it is believed that the valence band offset for GaInNAsSb/GaNAs should improve hole confinement. This was found not to be the case as the hole offset has been found to be 250 –280 meV — less than for GaInNAs/GaAs at 1.3 mm — form XPS, PR, and PL measurements [150].

1.5. ANNEALING AND N– In NEAREST NEIGHBOR EFFECTS

Annealing behavior in both GaInNAs and GaInNAsSb has a completely unique behavior [1,10,11,105,106,134,151 –163] compared to all similar III – V semiconductor alloys: there is a dramatic increase (30 – 75 £) in PL efficiency and a significant blue shift (50 – 100 nm)

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in wavelength which was illustrated in Figures 1.4 and 1.20. Also refer to Section 1.3.3 for additional details. There have been a very large number of studies of this annealing behavior and the initial hypothesis was that the blue shift was due to either In [134,151,164] or N [1,11,37] outdiffusion from the quantum wells. We have carried out a substantial investigation of this phenomenon and the annealing behavior appears to be a unique property of alloys with both In and N content. Annealing of InGaAs QWs in GaAs produces absolutely no change in either PL intensity or wavelength. Annealing GaNAs QWs in GaAs produces a small (2 – 4 £) increase in PL intensity and very little wavelength shift and neither exhibits any discernible difference in PL linewidth or lattice constant from HRXRD [35 –37,165]. However, the situation is entirely different for both GaInNAs and GaInNAsSb QWs on GaAs. Both QWs show similar increases in PL intensity and blue shift, however, no change is observed in lattice constant from XRD [35,36,165– 167]. As-grown GaInNAsSb tends to show a higher PL intensity than as-grown GaInNAs, and a subsequently smaller increase in intensity after annealing. The similarity of blue shift among many investigators and materials grown by different techniques and annealed under a variety of conditions suggested that there was possibly some very localized change occurring in the material under annealing to form a more equilibrated and homogeneous alloy. Theoretical predictions discussed in Refs. [106,107, 168,169] suggested that the localized unit cell would decrease in energy if N was surrounded by 2, 3, or 4 In atoms in its tetrahedral site. The bond strength of Ga –N is much greater than that of In – N, hence a very real possibility is that because of the low growth temperature, the alloy grows with N being predominantly surrounded by Ga nearest neighbors, but during anneal, In and Ga locally exchange lattice sites, resulting in an increase in band gap of the GaInNAs or GaInNAsSb QWs, but without any change in the QW composition, QW width or average lattice constant. Measurement of the local N environment is possible, but quite challenging. Several groups have reported results using Fourier transform infrared (FTIR) absorption spectroscopy [154,156,170], photoreflectance [107], X-ray absorption near edge fine structure (XANES) spectroscopy [105,106, 171], and extended X-ray absorption fine structure (EXAFS) spectroscopy [105,106,155]. All these measurements require great care in sample preparation, measurement and particularly in interpretation because some can be done on thin, strained QWs, while others require thicker films which will be lattice relaxed. Clearly if strain is playing a role in the annealing behavior, one must use thin strained QWs identical to those used in lasers and PL studies of annealing rather than thicker, lattice relaxed layers. Alt et al. [154] used FTIR spectroscopy to study the chemical environment of N atoms in thick GaInNAs films grown by solid source MBE. An absorption band at 471 cm21 was attributed to the local vibrational mode (LVM) of the isolated substitutional N atom. The position of the LVM in GaNAs was also found at 471 cm21, so the feature was concluded to correspond to a nearest neighbor (NN) configuration with four Ga atoms

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surrounding N. The expected peak positions for other NN configurations were estimated from the positions of similar absorption features from GaAs and InAs model compounds, but IR absorbance features in the expected bands were not observed for GaInNAs samples, even for material annealed in situ up to 7508C for 10 min. Thus, the authors concluded that their MBE material contained only N – Ga bonds, regardless of annealing conditions. Kurtz et al. [156] also used FTIR spectroscopy to study the local environment around N in 10 mm-thick GaInNAs films, but for MOCVD-grown material. This group also observed an absorption band around 470 cm21 (the exact position depended on bond strain), which they attributed to the Ga – N stretching mode. However, after annealing at 600– 7008C for 100 min, a peak appeared at , 487 cm21, which was believed to indicate the formation of N –Ga3In bonds. The samples used in this study contained only 2.5% In (and 0.2% N), which probably limited the formation of higher In-coordinated N sites. Some experiments were performed on material with up to 6% In and 2% N, but the spectral features were broadened in those cases. The FTIR results of Kitatani et al. [170] for gas-source MBE-grown Ga0.95In0.05N0.02As0.98 are similar to those reported by Kurtz et al. The Ga –N stretch at , 469 cm21 was found to dominate the absorbance in as-grown material, while a peak at 489 cm21 was found to gradually increase in magnitude as the samples were annealed up to 6508C for 1 h in the MBE chamber under AsH3 flow. The total absorbance was found to remain constant throughout the experiments, indicating a gradual transition between the two states without loss of N. The authors did not directly attribute the 489 cm21 peak to a N – Ga3In state, but instead conjectured that annealing had shortened some of the Ga – N bonds. In addition, Klar et al. [107] published a study using PR and tight-binding calculations on the fine structure of the band gap of MOVPE-grown GaInNAs due to NN configurations of the isovalent N. In this study, PR spectra taken at 80 K for QWs with appreciable fractions of both In (30%) and N (1%) showed a series of fairly distinct peaks attributed to the different N – In NN configurations. Arsenic-stabilized annealing up to 7258C for 60 min was found to shift the distribution of peaks from low In-coordinated to high In-coordinated states as the band gap increased. The peak positions were correlated with tight-binding calculations of a splitting of the band gap (mostly in the conduction band) due to the different NN configurations. Our group carried out a series of N K-edge XANES and In K-edge EXAFS measurements to directly examine changes in the tetrahedral NN configurations in GaInNAs upon annealing [106,171]. X-ray absorption spectroscopy generally measures the partial local density of states of a core electron excitation, which is sensitive to the chemical environment around the excited atom [172]. The samples were grown by solid source MBE [10,11] with compositions of , Ga0.7In0.3N0.03As0.97. Nitrogen K-edge XANES spectra were taken in fluorescence from both as-grown and annealed samples at beam line 4.0.2 of the Advanced Light Source in Berkeley, CA [173] using a highresolution superconducting tunnel junction X-ray detector operated at 0.1 K [174].

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Figure 1.51. Tetrahedral lattice site for N in GaInNAs alloy illustrating the most likely bonding configuration in a random 30% In alloy with 1-In NN and 3-Ga NNs (GaInNAs(1)).

In K-edge EXAFS spectra were measured at beam line BL01B1 of SPring-8 in Japan using a liquid N2-cooled Ge detector. Our annealing conditions are 1 – 3 min in a rapid thermal annealer with a N2 ambient and GaAs proximity cap for temperatures ranging between 600 and 9008C, with the optimum generally near 8208C. Since GaInNAs is nominally a zinc-blende random alloy, each N atom sits in the center of a tetrahedron, surrounded by a total of four Ga and/or In atoms, as shown in Figure 1.51. If the arrangement of atoms in the alloy were random on the proper lattice sites, then the probability distribution for finding a given number of In atoms surrounding any group-V atom is shown in Figure 1.52, for 30% In. The notation “GaInNAs(n)” will be used heretofore to denote a model crystal with n In NNs around each N atom (i.e. GaInNAs(0) indicates a crystal where every N atom is bonded to four Ga NN atoms) [106].

Figure 1.52. The probability of finding a given number of In nearest neighbors to a Group V lattice site for a 30% In random alloy.

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Figure 1.53. Calculated variation of lattice constant and total energy of Ga0.69In0.31N0.03As0.97 as a function of the N chemical environment.

The XAS experiments were motivated by atomic relaxation simulations that showed a decrease in total energy by . 10 kcal/mol when two or more In atoms are bonded to N, as shown in Figure 1.53 [106]. The decrease in chemical energy with increasing number of N – In bonds is due to overall decrease in individual bond strains, since the longer N –In bond is stretched less from equilibrium than the N –Ga bond. Furthermore, we performed ab initio band structure calculations that show an increase in band gap of , 150 meV as the In coordination is increased from GaInNAs(0) to the thermodynamically favored GaInNAs(3), consistent with the observed PL blue shift after annealing. ˚ -thick GaInNAs samples, both The N K-edge XANES spectra taken from 3000 A as-grown and annealed, as well as from a GaNAs reference sample, are shown in Figure 1.54.

Figure 1.54. Measured N K-edge XANES spectra from 3000 A thich-film GaInNAs samples, before and after annealing.

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The spectra exhibit a shift of 0.2–0.3 eV when In is added to GaNAs and an additional 0.1–0.2 eV after annealing the GaInNAs. Increasing the number of N–In bonds was calculated by density functional theory to shift the N K-edge to lower energies monotonically by ,0.07 eV per In atom. By comparing the magnitudes of the measured and calculated shifts in the N K-edge XANES spectra, the as-grown material was determined to be a nearly random alloy and the observed spectral shifts are consistent with a distribution of bonds dominated by GaInNAs(1) before annealing and GaInNAs(3) after annealing. This result is consistent with expectations, since the low-temperature MBE growth promotes kinetically dominated (random) epitaxy, while the high temperature annealing drives the material toward thermodynamic equilibrium (highly In-coordinated N). Kim and Zunger [169] used Monte Carlo simulations also to predict a thermodynamic preference for N–In3Ga1 clusters in GaInNAs, in agreement with our calculations and measurements, although they did not consider the effects of annealing or high In content. ˚ ) GaInNAs In addition, we performed N K-edge XANES measurements on thin (100 A samples to examine the effect of strain on NN bonding [90,171]. Representative spectra are shown in Figure 1.55. These data were also analyzed by using theoretical calculations of the expected spectrum shift versus N –In coordination, while accounting for strain; the results are summarized in Figure 1.56. We find that strain neither affects the NN bonding in as-grown material nor the behavior upon annealing. For both thick-film and quantum well samples, the as-grown material is nearly random and after annealing the bonding shifts to higher In coordinations. In addition to N K-edge XANES, we also measured the NN radial distribution function (RDF) around In using In K-edge EXAFS (and taking Fourier transforms of the acquired ˚ GaInNAs quantum spectra). Spectra were measured for both as-grown and annealed 80 A well samples. The RDFs for both as-grown and annealed material show a dominant In – As ˚ and a smaller shoulder at shorter bond lengths. The shoulder corresponds to peak at 2.25 A the In – N bond, whose precise length is shown by simulations to depend on the number of

˚ thin-films of GaInNAs. Figure 1.55. Nitrogen K-edge XANES spectra taken from as-grown and annealed 100 A

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Figure 1.56. Measured spectrum shifts of N K-edge XANES (symbols), relative to GaNAs, plotted on theoretical curves showing the dependence on N –In NN bonding. Arrows indicate transitions from as-grown to annealed material.

In atoms bonded to N. The experiments were fit to simulations of the RDFs by assuming that annealing drives the material from a distribution with mostly GaInNAs(1) to mostly GaInNAs(3). The In –N shoulder in the RDF becomes more prominent after annealing because the number of In –N bonds increases and also because the peak radius shifts further from the center of the overwhelming In – As peak. There is an excellent match between the simulation and experiment, and again we conclude that annealing increases the degree of N –In bonding. Additionally, recent X-ray emission and absorption measurements by Strocov et al. [175] generally showed results similar to ours. They further showed that the optical efficiency of the material is improved for samples with large In concentrations, which favor the formation of high N – In coordinations. They attribute the increase in optical efficiency to a charge accumulation at the valence band maximum with increasing N –In bonding, consistent with our own density functional theory calculations of the local density of states and orbital projected band structure of GaInNAs [176]. Thus, our XAS experiments, and also the results of others using quite different techniques on a variety of different samples, combined with the theoretical predictions of our density functional theory calculations, provide a conclusive framework for understanding the spectral blue shift with annealing in GaInNAs and GaInNAsSb. The relative low temperature of MBE growth does not provide enough energy for deposited atoms to find the lowest energy configuration, and a random alloy results. Thermal annealing drives the material toward equilibrium with high N – In coordination, which also corresponds to a higher band gap state. Material grown by MOVPE at higher temperatures appears to have greater concentrations of N –In bonds after growth than the random configuration, but the final annealed product is expected (and observed) to be similar to the result found for MBE material.

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As described at the beginning of this section, other mechanisms for the band gap blue shift have been proposed, such as N or In out-diffusion; however, at least for MBE material grown in our lab, the effects of these other mechanisms have been diminished by optimized growth procedures (for example, the use of an optimized N cell aperture that essentially eliminates incorporation of N interstitials). For our optimized material, the local Ga/In site exchange surrounding N is the dominant mechanism for the spectral blue shift after annealing. With this mechanistic understanding of the blue shift, we were able to perform optical spectroscopic experiments to study the nitrogen NN states quantitatively and determine the distribution of the NN states as the material was annealed. This study was performed using a combination of photoluminescence (PL) and electroreflectance (ER) spectroscopy [90]. PL is essentially a ground state spectroscopy since the energetic carriers generated by the excitation laser quickly thermalize to the bottom of the bands before recombining radiatively. In QW samples, the density of states at the band edges is very high and so band-filling effects from high excitation densities are relatively minimal. Nevertheless, the presence of NN excited states in PL has been detected for GaInNAsSb samples taken at room temperature and using high excitation density (. 20 kW/cm2), as shown in Figure 1.57 [90]. Peak fitting of the PL spectra for a series of annealed samples (as-grown, and annealed 7608C for 1 min, 8008C for 1 min, and 8008C for 3 min) yielded a set of exactly five peaks common among the spectra, separated by 17– 20 meV. These peaks were identified as a splitting of the first heavy hole to first electron transition by the five N – In NN configurations, since the light hole transition in this material occurs more than 100 meV higher in energy. The vertical lines in Figure 1.57 denote the positions of these peak fits, and the labels denote the number of In atoms bonded to N for each state. Furthermore, as the annealing was continued, the wavelength blue shift saturated while

Figure 1.57. Photoluminescence spectra taken from a series of differently annealed GaInNAsSb samples at room temperature, with N –In NN peak positions indicated by vertical lines.

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the intensity continued to increase, suggesting an equilibrium was reached in the NN distribution, while healing of non-radiative defects continued. ER spectroscopy is a technique better suited to examining excited states, as it uses a scanned-energy probe beam and modulation of electric field in the material to effectively measure a derivative of the absorption spectrum. Excellent overviews of the technique can be found in several references [112,113]. Essentially, phase-sensitive detection is used to measure the change in reflectivity of the sample as a small AC voltage is applied across the QWs. The AC voltage induces a modulation of electric field across the QWs, which leads to variations in band gap and linewidth through the quantum confined Stark effect [177]. The resulting modulated reflectivity is proportional to the real part of derivatives of the complex dielectric function with respect to band gap and linewidth. A sample ER spectrum taken from the as-grown GaInNAsSb sample of Figure 1.57 is shown in Figure 1.58. Analysis of the spectrum requires an assumption of the oscillator line shape in the dielectric function [178]. Often, Lorentzian line shapes are used for such analysis [179,180], but our measurements of PL, electroluminescence, and absorption indicate a Gaussian line shape at room temperature. A Gaussian line shape in the dielectric function leads to a line shape in the ER spectrum involving the confluent hypergeometric function [181]. The proper choice of line shape and our use of an experimental configuration that ensures a homogeneous electric field in the QWs are essential for quantitative analysis of the spectra. The ER spectra are fit to the theoretical line shape to determine the energy, phase, and amplitude of the transitions. The data for GaInNAsSb were not well fit to a single transition, but fit extremely well to multiple transitions which agreed (without assumption) to the energy and linewidth of the peak fits in PL shown in Figure 1.57. The arrows in Figure 1.58 show the energies of the fit

Figure 1.58. Sample measured ER spectrum from as-grown GaInNAsSb at room temperature (symbols), with overlaid multiple oscillator fit. Arrows indicate the energy positions of the oscillators.

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transitions. In this sample, the four transitions with lowest energy correspond to first heavy hole to electron transitions split by the four lowest energy N –In NN states (N coordinated to 0 –3 In atoms). The two transitions with highest energy in Figure 1.58 correspond to a combination of second heavy hole to electron and first light hole to electron transitions, showing the large energy separation between these higher order transitions and the ground state transition. This large energy separation is absolutely required for the analysis here, to avoid complications from overlapping states of different character. The especially significant result of this analysis is that the relative amplitudes of the NN transitions can be used to directly determine the distribution of NN states in the material, since the states have approximately the same intrinsic matrix element. The extracted distributions are plotted in Figure 1.59 for the variously annealed GaInNAsSb samples from Figure 1.57. Also plotted in Figure 1.59 is the calculated distribution for a random alloy of the same composition (stars and dashed line). We clearly see the quantitative agreement between the measured NN bonding distribution of the as-grown MBE GaInNAs(Sb) material and the calculated random distribution, as well as the evolution of the NN bonding toward high ($ 2) – In coordinations. We also notice the especially rapid depletion of the statistically most favored states (N –In0Ga4 and N – In1Ga3) in favor of the thermodynamically preferred ones (N –In2þGa22), during the early stages of annealing. Nearest-neighbor rearrangement can only explain part of the blue shift due to anneal. It is noteworthy that the blue shift of GaInNAs cannot be fitted by either a single or double exponential with temperature, which strongly suggests that three or more different physical effects of comparable magnitude are present. The source of the remaining blue

Figure 1.59. Distributions of N –In NN in variously annealed GaInNAsSb samples, determined from ER amplitudes.

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shift has been the subject of controversy and heated discussion, but four principal candidates exist: N diffusion and/or removal from the QW, Ga – In interdiffusion at the QW boundary (thereby decreasing the quantum confinement), and localized depressions in band gap due to either N clusters or point defects, either of which might be removable with anneal. We will explore each of these in some detail below. Nitrogen out-diffusion from the QW was demonstrated by performing SIMS on early samples at Stanford [182] and elsewhere [183]. Although these results were called into question due to the frequent run-to-run variations common with SIMS, there was a consistent decrease in N signal after annealing, as shown in Figure 1.60(a). Also, the SIMS signal from other elements such as In or Sb (not shown) did agree from run to run. Furthermore, when using GaNAs barriers around the QW, SIMS clearly showed different rates of N loss in GaInNAs QWs as compared to the GaNAs barriers, as shown in Figure 1.60(b). The GaNAs barriers also decreased the blue shift with anneal, which is consistent with maintaining N in the QW. This N out-diffusion decreased in more recent material which contains less N interstitials, and other groups reported finding no outdiffusion whatsoever [135], leading to some controversy. A similar controversy has centered around whether there was interdiffusion of group-III elements at the QW boundary. If In is able to diffuse out of the quantum well, then the well becomes wider and shallower, leading to a strong blue shift due to the decreased quantum confinement. Some researchers found about 1 nm of In out-diffusion from the QWs with TEM [135], while Stanford material never did show such interdiffusion to within measurable limits of TEM (approximately 1 –2 monolayers). Although In rode the surface for 3– 4 monolayers during growth, and the QWs were rough to begin with, the “softness” or grading of the QW interfaces did not change with anneal according to TEM [11]. A blue shift from QW intermixing presents a long-term reliability problem for VCSELs and edge emitting lasers due to the endless shift in wavelength and reduction of carrier confinement.

Figure 1.60. SIMS profiles of N concentration in pre and post-annealed GaInNAs/GaAs QWs (left) and GaInNAs/GaNAs QWs (right). A decrease in N interstitial out-diffusion is apparent from the QWs with GaNAs barriers.

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The resolution of the discrepancy between groups appears to be the recognition of the effect of vacancies in the crystal. Sputtering SiO2 onto the surface of GaAs creates Ga vacancies, and subsequent annealing allows those vacancies to propagate to the underlying QW and promote rearrangement. Although this mechanism has been known in industry for many years [56], it has only recently been demonstrated and explained in GaInNAs [136]. GaInNAs growth generally starts with a layer of GaAs under normal growth conditions, but then the temperature of the substrate is reduced 100 –1808C in order to stabilize it at temperatures appropriate for GaInNAs. This results in a layer of low temperature grown GaAs before the quantum well(s). There is a similar layer of LT-GaAs after the quantum well(s), as the substrate is ramped back up to normal GaAs growth temperatures. Khreis has reported that InGaAs grown at low temperatures has a high concentration of point defects, and these defects were responsible for In –Ga interdiffusion at the QW interfaces, causing a larger blue shift with anneal [184]. For MOCVD and gas source MBE, Ga vacancies are generated by a N – H complex during growth [132]. For solid source MBE, the defect density near the QWs is critically related to the duration and temperature of the adjacent, low temperature GaAs layers, as well as the quality of GaNAs barriers, if present. So the Ga – In interdiffusion is almost wholly dependent upon poor growth conditions outside of the QW, and even post-growth processing, and the best quality material in PL or low threshold lasers should demonstrate the least blue shift with anneal. Indeed, as mentioned in Section 1.3.3, the highest quality material from several groups does not show as much shift with anneal. Section 1.3.3 also discusses temperature dependent PL measurements that indicate a possible correlation between carrier localization and damage. Although N dramatically decreases the band gap of the material, it also brings a host of associated defects such as As antisites AsGa, split interstitials (N– N)As, vacancies, and other point defects. (See, for example, Ref. [123,124] for a list of many possible defects, with citations.) Identifying and removing the sources of these defects has proven to be crucial to the development of our 1.5 mm edge emitters and the VCSELs presented in Chapter 17. There is one additional type of defect worth mentioning: the N – H complex. Although hydrogen has been reported to improve surface morphology [185], A. Ptak at the National Renewable Energy Lab has found [132] that the concentrations of Ga vacancies, VGa, closely follow the concentrations of hydrogen in the structure. These vacancies are theoretically unfavorable in solid-source epitaxy [133], but are prevalent in material grown by MOCVD [186] and by gas-source MBE [187]. These vacancies are only partially removed by anneal. The correlation between vacancies and hydrogen concentration suggests that a N – H complex is responsible for the Ga defects. The N – H complex should be a shallow acceptor, and removal of hydrogen by anneal can even cause p-type as-grown material to change to n-type material after anneal [138]. These complexes

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suggest that hydrogen may be responsible for the reliability problems with MOCVDgrown lasers, whereas MBE-grown lasers have been demonstrated with an extrapolated lifetime of decades [188]. It is fairly likely that early studies of material parameters, such as effective mass and band gap, were unwittingly misled by the effects of these vacancies. Even today, care should be taken to distinguish the effect of widespread defects from inherent material properties of dilute nitrides, because these defects—and others which are not removed by anneal—greatly complicate the analysis. Of the five blue shift mechanisms mentioned above (“healable” point defects, NN rearrangement, N diffusion or removal, Ga –In interdiffusion, and N clusters), only the last three can contribute to a continuing blue shift as the wafer is progressively annealed. Nearest-neighbor rearrangement and the breakup of N dimers are, in principle, processes which run to completion after a certain amount of time or temperature, and only those are sources of blue shift that saturates with temperature/time. Additionally, only NN rearrangement is associated with an intrinsic property of the material, rather than extrinsic defects introduced by varying growth conditions.

1.6. SUMMARY

The discovery of 1.3 – 1.6 mm active quantum well material that can be grown on GaAs to capitalize on the superior AlAs/GaAs materials and processing technology has been a real breakthrough and has fueled a complete re-evaluation of long-wavelength lasers. We believe that GaInNAsSb on GaAs will become the foundation technology that will enable low cost, wide bandwidth MAN/LAN/SAN networks, optical switching and routers. Dilute nitride GaInNAsSb grown epitaxially on GaAs can produce active quantum well regions that cover the full 1.2– 1.6 mm wavelength region with a single alloy material system. This not only greatly simplifies processing, but enables incorporation of the tremendous processing advantage of oxidized AlAs to form high index contrast photonic crystal structures as well as the existing AlAs/GaAs DBR mirror and VCSEL manufacturing technology. This will become an enabling technology not only for longwavelength lasers, but advanced photonic integrated circuits which will be key to ultimately realize the dramatic cost reductions necessary to make access to high-speed networks universally available. The major challenge for GaInNAs(Sb) has been to understand the differences of the dilute nitrides compared to other III– V alloys and to produce low threshold lasers at any desired wavelength between 1.3 and 1.6 mm. The most recent results incorporating Sb to form a quinary alloy, GaInNAsSb appear to overcome many of the prior problems with phase segregation. We believe that GaInNAsSb will be the active gain material of choice because it has significantly higher gain for VCSELs, is closer to the existing QW technologies than InAs QDs, and has fundamental energy band advantages

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over its other competitors. GaInNAsSb also has an inherent lateral uniformity advantage over other active QW materials choices, but this has only been realized so far by solid-source MBE. As illustrated from the TEM strain maps, there are still challenges for vertical uniformity. However, recent improvements based upon these observations suggest that with proper feedback and control during QW growth, these problems can be overcome by MBE. While MBE has been utilized for production of very low cost, edge emitting CD-lasers, it has not been utilized in the production of VCSELs, although it has been the tool of choice for most of the research and development of VCSELs. The newest versions of production MBE systems, with their greater versatility in number of liquid metal sources, could easily change the role of MBE. As described in this chapter, not only is the large wafer capability advantageous, but — most importantly for VCSELs — the vertical configuration allows for eight or even 10 column III metal sources, enabling very simple step grading of the mirrors and higher growth rates without oval defects. This advances eliminate the greatest challenges that have faced VCSEL production by MBE. When combined with the significantly easier growth of GaInNAsSb by MBE, they will likely make MBE the choice for production of both VCSELs and high power edge emitting lasers. Progress has been rapid and the future for this materials system and the potential for its inclusion as a major part of the optical networks is indeed bright.

ACKNOWLEDGEMENTS

The work at Stanford has been the result of efforts by a number of graduate students, including; Wonill Ha, Vincent Gambin, Sylvia Spruytte, Chris Coldren, Mike Larson, Evan Pickett, postdocs Dr Kerstin Volz and Dr Seongsin Kim and Dr Danielle Chamberlin of Agilent Technologies.

REFERENCES [1] Harris, J.S., Jr. (2002) GaInNAs long-wavelength lasers: progress and challenges. Semicond. Sci. Technol., 17, 880– 891. [2] Kaiser, P. (2001) Photonic network trends and impact on optical components. 2001 Digest of LEOS Summer Topical Meetings: WDM Components, Keystone, CO, July 30, 2001, pp. 3 – 4, private communication. [3] Weyers, M., Sato, M. & Ando, H. (1992) Jpn. J. Appl. Phys. Part 2, 31, 853. [4] Kondow, M., Uomi, K., Niwa, A., Kitatani, T., Watahiki, S. & Yazawa, Y. (1996) GaInNAs: a novel material for long-wavelength-range laser diodes with excellent high-temperature performance. Jpn. J. Appl. Phys., 35, 1273– 1275. [5] Kondow, M., Nakatsuka, S., Kitatani, T., Yazawa, Y. & Okai, M. (1996) Room-temperature continuous-wave operation of GaInNAs/GaAs laser diode. Electron. Lett., 32, 2244– 2245.

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[114] Goddard, L.L., Bank, S.R., Wistey, M.A., Yuen, H.B., Rao, Z.L. & Harris, J.S. (2005) Recombination, gain, band structure, efficiency, and reliability of 1.5 mm GaInNAsSb/GaAs lasers. J. Appl. Phys., in press. [115] Pan, Z., Li, L.H., Lin, Y.W., Sun, B.Q., Jiang, D.S. & Ge, W.K. (2001) Conduction band offset and electron effective mass in GaInNAs/GaAs quantum-well structures with low nitrogen concentration. Appl. Phys. Lett., 78, 2217– 2219. [116] Tu, C.W. (2001) III – N– V low-band gap nitrides and their device applications. J. Phys.: Condens. Matter, 13, 7169–7182. [117] Luo, X.D., Xu, Z.Y., Pan, Z., Li, L.H., Lin, Y.W. & Ge, W.K. (2001) Optical properties and band lineup in GaNxAs12x/GaAs single quantum wells. J. Infrared Millimeter Waves, 20, 25 – 29. [118] Hader, J., Koch, S.W., Moloney, J.V. & O’Reilly, E.P. (2000) Influence of the valence-band offset on gain and absorption in GaNAs/GaAs quantum well lasers. Appl. Phys. Lett., 76, 3685 –3687. [119] Wu, J., Shan, W., Walukiewicz, W., Yu, K.M., Ager, J.W., III, Haller, E.E., Xin, H.P. & Tu, C.W. (2001) Effect of band anticrossing on the optical transitions in GaAsN/GaAs multiple quantum wells. Phys. Rev. B, 64 085320/1 – 3. [120] Krispin, P., Spruytte, S.G., Harris, J.S. & Ploog, K.H. (2000) Electrical depth profile of p-type GaAs/Ga(As,N)/GaAs heterostructures determined by capacitance – voltage measurements. J. Appl. Phys., 88, 4153– 4158. [121] Sun, B.Q., Jiang, D.S., Pan, Z., Li, L.H. & Wu, R.H. (2001) Optical transitions and type-II band lineup of MBE-grown GaNAs/GaAs single-quantum-well structures. J. Cryst. Growth, 227– 228, 501–505. [122] Zhang, S.B. & Wei, S.H. (2001) Nitrogen solubility and induced defect complexes in epitaxial GaAs:N. Phys. Rev. Lett., 86, 1789– 1792. [123] Krispin, P., Gambin, V., Harris, J.S. & Ploog, K.H. (2003) Nitrogen-related electron traps in Ga(As,N) layers ( % 3% N). J. Appl. Phys., 93, 6095– 6099. [124] Krispin, P., Gambin, V., Harris, J.S. & Ploog, K.H. (2002) Ga(As,N) layers in the dilute N limit studied by depth-resolved capacitance spectroscopy. Appl. Phys. Lett., 81, 3987 –3989. [125] Wistey, M.A., Bank, S.R., Yuen, H.B., Lordi, V. & Harris, J.S. Redshift from plasma-related defects in GaInNAs(Sb), Appl. Phys. Lett., submitted for publication. [126] Thinh, N.Q., Buyanova, I.A., Hai, P.N., Chen, W.M., Xin, H.P. & Tu, C.W. (2001) Signature of an intrinsic point defect in GaNxAs12x. Phys. Rev. B, 63, 033203. [127] Geisz, J.F. & Friedman, D.J. (2002) III – N– V semiconductors for solar photovoltaic applications. Semicond. Sci. Technol., 17, 769– 777. [128] Kaplar, R.J., Arehart, A.R., Ringel, S.A., Allerman, A.A., Sieg, R.M. & Kurtz, S.R. (2001) Deep levels and their impact on generation current in Sn-doped InGaAsN. J. Appl. Phys., 90, 3405 –3408. [129] Kurtz, S.R., Allerman, A.A., Jones, E.D., Gee, J.M., Banas, J.J. & Hammons, B.E. (1999) InGaAsN solar cells with 1.0 eV band gap, lattice matched to GaAs. Appl. Phys. Lett., 74, 729– 731. [130] Kaplar, R.J., Ringel, S.A., Kurtz, S.R., Klem, J.F. & Allerman, A.A. (2002) Deep-level defects in InGaAsN grown by molecular-beam epitaxy. Appl. Phys. Lett., 80, 4777– 4779. [131] Ptak, A.J., Johnston, S.W., Kurtz, S., Friedman, D.J. & Metzger, W.K. (2003) A comparison of MBE- and MOCVD-grown GaInNAs. J. Cryst. Growth, 251, 392–398.

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[132] Ptak, A.J., Kurtz, S., Weber, M.H. & Lynn, K.G. (2003) Positron annihilation study of vacancies in GaInNAs, North American Molecular Beam Epitaxy Conference, October 2003, Keystone, Colorado. [133] Janotti, A., Wei, S.H., Zhang, S.B., Kurtz, S. & Van de Walle, C.G. (2003) Interactions between nitrogen, hydrogen, and gallium vacancies in GaAs12xNx alloys. Phys. Rev. B, 67, 161201. [134] Li, W., Pessa, M., Ahlgren, T. & Decker, J. (2001) Origin of improved luminescence efficiency after annealing of Ga(In)NAs materials grown by molecular-beam epitaxy. Appl. Phys. Lett., 79, 1094– 1096. [135] Peng, C.S., Li, W., Jouhti, T., Pavelescu, E.M. & Pessa, M. (2003) A study and control of lattice sites of n and In/Ga interdiffusion in dilute nitride quantum wells. J. Cryst. Growth, 251, 378– 382. [136] Macaluso, R., Sun, H.D., Dawson, M.D., Robert, F., Bryce, A.C., Marsh, J.H. & Riechert, H. (2003) Selective modification of band gap in GaInNAs/GaAs structures by quantum-well intermixing. Appl. Phys. Lett., 82, 4259– 4261. [137] Volz, K., Koch, J., Kunert, B. & Stolz, W. (2003) Doping behaviour of Si, Te, Zn and Mg in lattice-matched (GaIn)(NAs)/GaAs bulk films. J. Cryst. Growth, 248, 451– 456. [138] Kurtz, S., Geisz, J.F., Friedman, D.J., Metzger, W.K., King, R.R. & Karam, N.H. (2004) Annealing-induced-type conversion of GaInNAs. J. Appl. Phys., 95, 2505– 2508. [139] Skierbiszewski, C., Perlin, P., Wisniewski, P., Suski, T., Walukiewicz, W., Shan, W., Ager, J.W., Haller, E.E., Geisz, J.F. & Friedman, D.J. (1999) Effect of nitrogen-induced modification of the conduction band structure on electron transport in GaAsN alloys. Phys. Status Solidi B, 216, 135– 139. [140] Fahy, S. & O’Reilly, E.P. (2003) Intrinsic limits on electron mobility in dilute nitride semiconductors. Appl. Phys. Lett., 83, 3731– 3733. [141] Mouillet, R., de Vaulchier, L.A., Deleporte, E., Guldner, Y., Travers, L. & Harmand, J.C. (2003) Role of nitrogen in the mobility drop of electrons in modulation-doped GaAsN/ AlGaAs heterostructures. Solid State Commun., 126, 333– 337. [142] Ahrenkiel, R.K., Johnston, S.W., Keyes, B.M. & Friedman, D.J. (2000) Transport properties of GaAs12xNx thin films grown by metalorganic chemical vapor deposition. Appl. Phys. Lett., 77, 3794– 3796. [143] Kurtz, S.R., Klem, J.F., Allerman, A.A., Sieg, R.M., Seager, C.H. & Jones, E.D. (2002) Minority carrier diffusion and defects in InGaAsN grown by molecular beam epitaxy. Appl. Phys. Lett., 80, 1379– 1381. [144] Kovsh, A.R., Wang, J.S., Hsiao, R.S., Chen, L.P., Livshits, D.A., Lin, G., Ustinov, V.M. & Chi, J.Y. (2003) High-power (200 mW) singlemode operation of InGaAsN/GaAs ridge waveguide lasers with wavelength around 1.3 mm. Electron. Lett., 39, 1726– 1728. [145] Kondow, M., Fujisaki, S., Shirakata, S., Ikari, T. & Kitatani, T. (2003) Electron effective mass of Ga0.7In0.3NxAs12x, 2003 International Symposium on Compound Semiconductors, San Diego, CA, pp. 76 – 77. [146] Skierbiszewski, C. (2002) Experimental studies of the conduction-band structure of GaInNAs alloys. Semicond. Sci. Technol., 17, 803– 814. [147] Heroux, J.B., Yang, X. & Wang, W.I. (2002) Photoreflectance spectroscopy of strained (In)GaAsN/GaAs multiple quantum wells. J. Appl. Phys., 92, 4361–4366. [148] Buyanova, I.A., Pozina, G., Hai, P.N., Chen, W.M., Xin, H.P. & Tu, C.W. (2000) Type I band alignment in the GaNAs/GaAs quantum wells. Phys. Rev. B, 63 033303/1 – 4.

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[149] Teissier, R., Sicault, D., Harmand, J.C., Ungaro, G., Le Roux, G. & Largeau, L. (2001) Temperature-dependent valence band offset and band-gap energies of pseudomorphic GaAsSb on GaAs. J. Appl. Phys., 89, 5473– 5477. [150] Kudrawiec, R., Yuen, H.B., Ryczko, K., Bank, S.R., Wistey, M.A., Bae, H.P., Harris, J.S. & Misciewicz, J. (2004) Photoreflectance and photoluminescence investigations of a step-like GaInNAsSb/GaAsN/GaAs quantum well tailored at 1.5 mm: the energy level structure and the Stokes shift. J. Appl. Phys., submitted. [151] Pavelescu, E.M., Jouhti, T., Peng, C.S., Li, W., Konttinen, J., Dumitrescu, M., Laukkanen, P. & Pessa, M. (2002) Enhanced optical performances of strain-compensated 1.3-mm GaInNAs/ GaNAs/GaAs quantum-well structures. J. Cryst. Growth, 241, 31 –38. [152] Albrecht, M., Grillo, V., Remmele, T., Strunk, H.P., Egorov, A.Yu, Dumitras, Gh., Riechert, H., Kaschner, A., Heitz, R. & Hoffmann, A. (2002) Effect of annealing on the In and N distribution in InGaAsN quantum wells. Appl. Phys. Lett., 81, 2719–2721. [153] Chauveau, J.M., Trampert, A., Pinault, M.A., Tournie, E., Du, K. & Ploog, K.H. (2003) Correlations between structural and optical properties of GaInNAs quantum wells grown by MBE. J. Cryst. Growth, 251, 383– 387. [154] Alt, H.Ch., Egorov, A.Yu., Riechert, H., Wiedemann, B., Meyer, J.D., Michelmann, R.W. & Bethge, K. (2001) Local vibrational mode absorption of nitrogen in GaAsN and InGaAsN layers grown by molecular beam epitaxy. Physica B, 302– 303, 282– 290. [155] Ciatto, G., Boscherini, F., D’Acapito, F., Mobilio, S., Baldassari, G., Polimeni, H.v.H., Capizzi, M., Gollub, D. & Forchel, A. (2003) Atomic ordering in (InGa)(AsN) quantum wells: an In K-edge X-ray absorption investigation. Nucl. Instrum. Methods Phys. Res., Sect. B, 200, 34 – 39. [156] Kurtz, S., Webb, J., Gedvilas, L., Friedman, D., Geisz, J. & Olson, J. (2001) Structural changes during annealing of GaInAsN. Appl. Phys. Lett., 78, 748– 750. [157] Spruytte, S., Wampler, W., Krispin, P., Coldren, C., Larson, M., Ploog, K. & Harris, J.S. (2001) Incorporation of nitrogen in nitride – arsenides: origin of improved luminescence efficiency after anneal. J. Appl. Phys., 89, 4401– 4406. [158] Buyanova, I.A., Pozina, G., Hai, P.N., Thinh, N.Q., Bergman, J.P., Chen, W.M., Xin, H.P. & Tu, C.W. (2000) Mechanism for rapid thermal annealing improvements in undoped GaNxAs12x/GaAs structures grown by molecular beam epitaxy. Appl. Phys. Lett., 77, 2325 –2327. [159] Kageyama, T., Miyamoto, T., Makino, S., Koyama, F. & Iga, K. (1999) Thermal annealing of GaInNAs/GaAs quantum wells grown by chemical beam epitaxy and its effect on photoluminescence. Jpn. J. Appl. Phys., 38, L298– L300. [160] Kitatani, T., Nakahara, K., Kondow, M., Uomi, K. & Tanaka, T. (2000) Mechanism analysis of improved GaInNAs optical properties through thermal annealing. J. Cryst. Growth, 209, 345– 349. [161] Pornarico, A., Lomascolo, M., Cingolani, R., Egorov, A.Yu. & Riechert, H. (2002) Effects of thermal annealing on the optical properties of InGaNAs/GaAs multiple quantum wells. Semicond. Sci. Technol., 17, 145– 149. [162] Xin, H.P., Kavanagh, K.L., Kondow, M. & Tu, C.W. (1999) Effects of rapid thermal annealing on GaInNAs/GaAs multiple quantum wells. J. Cryst. Growth, 201– 202, 419– 422. [163] Makino, S., Miyamoto, T., Kageyama, T., Ikenaga, Y., Arai, M., Koyama, F. & Iga, K. (2001) Composition dependence of thermal annealing effect on 1.3 mm GaInNAs/GaAs

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[182] Spruytte, S.G.B., Wistey, M.A., Larson, M.C., Coldren, C.W., Garrett, H. & Harris, J.S. (2001) 1.3 micron opto-electronic devices on GaAs using group III nitride arsenides. Proc. SPIE, 4286, 22 – 33. [183] Bosker, G., Stolwijk, N.A., Thordson, J.V., Sodervall, U. & Andersson, T.G. (1998) Diffusion of nitrogen from a buried doping layer in gallium arsenide revealing the prominent role of As interstitials. Phys. Rev. Lett., 81, 3443– 3446. [184] Khreis, O.M., Gillin, W.P. & Homewood, K.P. (1997) Interdiffusion: a probe of vacancy diffusion in III – V materials. Phys. Rev. B, 55, 15813– 15818. [185] Ohmae, A., Matsumoto, N., Kawabe, M. & Okada, Y. (2002) Effects of atomic hydrogen on the growth of Ga(In)NAs by RF-molecular beam epitaxy. Phys. Status Solidi C, 1, 175– 178. [186] Toivonen, J., Hakkarainen, T., Sopanen, M., Lipsanen, H., Oila, J. & Saarinen, K. (2003) Observation of defect complexes containing Ga vacancies in GaAsN. Appl. Phys. Lett., 82, 40 – 42. [187] Li, W., Pessa, M., Ahlgren, T. & Decker, J. (2001) Origin of improved luminescence efficiency after annealing of Ga(In)NAs materials grown by molecular beam epitaxy. Appl. Phys. Lett., 79, 1094– 1096. [188] Prakash, S.R., Chirovsky, L.M.F., Naone, R.L., Galt, D., Kisker, D.W. & Jackson, A.W. (2003) Reliability of 1.3 micron VCSELs for metro area networks. Proc. SPIE, 4994, 44 –54.

Dilute Nitride Semiconductors M. Henini (Ed.) q 2005 Elsevier Ltd. All rights reserved.

Chapter 2

Epitaxial Growth of Dilute Nitrides by Metal-Organic Vapour Phase Epitaxy F. Alexandre ALCATEL CIT, OPTOþ , Route de Nozay, F-91461 Marcoussis, France

2.1. INTRODUCTION

The development during the 1990s of the dilute nitride semiconductor family has opened a new opportunity to largely extend the band gap engineering capabilities of III– V semiconductor compounds. Dilute nitrides, formed by alloying small amount of nitrogen into arsenide or phosphide, are a new class of semiconductor compounds with specific material properties. The most remarkable physical characteristic is the strong band gap bowing which has been experimentally observed for some of the dilute group-III nitride compounds such as Ga(In)AsN [1,2], GaPN [3] and InPN [4]. This unusual property has been attributed to the repulsive interaction between a specific narrow band of localised N states and the conduction band of the host crystal [5]. As a consequence, the introduction of a low N-content in Ga(In)As(P) induces a large reduction of both the band gap and the lattice parameter. Such behaviour has first opened a new interesting pathway to potentially cover the strategic 1.3– 1.55 mm emission wavelength range for telecommunication application using the GaInAsN alloy grown on GaAs instead of the conventional GaInAsP alloy grown on InP substrate. The main interest of this alternative semiconductor system is based on an increased conduction band offset of the GaInAsN/GaAs heterostructure as compared with InP-based heterostructures [2], which leads to a more efficient electron confinement, especially at high temperature. Therefore, the thermal stability of these long wavelength lasers is expected to be improved with higher values of the T0 characteristic and with a higher maximum operating temperature than common InP-based lasers. On the other hand, GaInAsN active layer can be monolithically combined with high reflectivity GaAs/AlAs Bragg mirrors, making this material system also attractive for the realisation of long wavelength vertical-cavity surface emitting lasers (VCSELs). Finally, this new development of long wavelength lasers on GaAs substrate can fully take advantages of the well-matured GaAs technology and of higher fabrication yield thanks to the largest size of available GaAs substrates (6 – 8 in.) as compared with InP (4 –6 in.). In addition, the expected removal of the thermoelectric cooler used to stabilise the laser can also be 93

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an important step towards the realisation of low-cost emitters for optical communication and interconnection systems. The GaInAsN alloy can also be grown on InP substrates in order to extend the emission wavelength range as compared with conventional GaInAsP alloy. Thus, the whole C- and L-band emission can be covered using tensile strained GaInAsN/(Ga)In(As)P quantum wells (QWs) while the emission wavelength range can be further extended far into the infrared, using compressive strained QWs structure [6,7]. However, the growth of optoelectronic devices based on GaInAsN material has been a new challenge for the epitaxy research field due to the divergent properties of arsenides and nitrides. Indeed, GaAs12yNy is an alloy composed of group V elements with large ˚ for As as compared with 1.2 A ˚ for N) as well as in differences in ionic radii (0.75 A electro-negativity values [8]. Also, the crystal structure of the binary parent compounds of this alloy is of zinc-blende structure for GaAs and of zinc-blende or wurtzite structure for GaN, which can be the origin of a miscibility gap with phase separation. Also, the equilibrium solubility of nitrogen in GaAs is known to be extremely low [9]. This new epitaxy challenge requires for a suitable growth technique to choose an appropriate N-based growth precursor and to optimise specific growth conditions of N-containing alloys. Due to the N solubility limitations, growth techniques far from the thermodynamical equilibrium have been preferred such as solid or gaseous molecular beam epitaxy (SSMBE, GSMBE), chemical beam epitaxy (CBE) or metal-organic vapour phase epitaxy (MOVPE). So far, the most important improvements in N-containing material quality as well as in laser performances have been mainly obtained by MBE while MOVPE-grown structures appeared to be a step behind [10]. However, there is a large interest to determine if MOVPE, which is the mainstream for the current production of InP-based lasers for telecommunication applications, can also be efficient to grow high performance long wavelength GaInAsN-based lasers. This chapter reviews, from our own experimental results as well as from the recent results of the literature, the specific features of the MOVPE epitaxial growth of dilute nitrides as compared with MBE and the improved performances of GaAs-based long wavelength lasers as compared with the state of the art of InP-based lasers.

2.2. EPITAXIAL GROWTH OF GaInAsN-BASED STRUCTURES

2.2.1 N Growth Precursors The choice of an appropriate N growth precursor can be done among a large variety of available N-containing chemical compounds (Table 2.1). The requirements for an efficient N source suited to MOVPE process are: (i) a high vapour pressure (. 10 Torr) at room temperature, (ii) a low pyrolysis temperature (, 4008C) combined to a good stability at ambient temperature and (iii) excellent properties in terms of purity and safety of use.

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Table 2.1. Properties of N growth precursors for MOVPE technique [13,15,16,80] N growth precursor

Chemical formula

Ammonia Hydrazine (Hy) Monomethylhydrazine (MMHy) Dimethylhydrazine (DMHy) Tertiarybutylhydrazine (tbHy) Phenylhydrazine (PhHy) Tertiarybutylamine (t-BuNH2) Nitrogen trifluoride

NH3 H2N–NH2 CH3HN –N(CH3)2 H2N –N(CH3)2 t Bu(H)N–NH2 C6H5HN –NH2 (CH3)3C–NH2 NF3

Vapour pressure (Torr at 208C) .760 9.2 50 130 48 0.04 254 .760

E (bond) (kcal/mol) 110 (N –H) 71 (N –N) 59 (N –N)

Strong C– N

The simplest molecules such as nitrogen (N2) or ammonia (NH3) have a high thermal stability and cannot be used in the case of a low growth temperature regime except using a plasma-cracked gas source. This approach has been initially performed in the first report by Weyers and Sato [11] of the MOVPE growth of GaAsN, but this plasma source can be only operated at very low growth pressure. So, such a plasma source operating at RF or microwave frequency range is more conveniently used in MBE technique under vacuum [12]. More complex molecules offer the advantage of a much lower pyrolysis temperature, which is compatible with the standard growth temperature of III – V alloys in vapour phase epitaxy techniques. Such precursors can be chosen among the family of hydrazine (Hy) which is a very reactive and toxic product [13] and of its methyl-substituted compounds such as monomethylhydrazine (MMHy) [14], dimethylhydrazine (DMHy) [15], tertiarybutylhydrazine (tbHy) [16] and phenylhydrazine [17]. Such species are carbonfree molecules with a weak N – N bond strength. Another family is that of the alkylamine compounds such as the tertiarybutylamine (tbAm) [13], which are based on a high N – C bond strength. Unsymmetrical dimethylhydrazine (u-DMHy) is one of the N precursors fitting most of the required source specifications. DMHy is a liquid source at room temperature with a sufficient vapour pressure of 130 Torr [18]. As compared with hydrazine molecule, two methyl groups replace two hydrogen atoms which make the molecule less stable and less reactive. Thus, a low dissociation temperature of DMHy of 4208C has been reported [19]. So, up to now, this N precursor is the most commonly used in epitaxial techniques using all-gaseous sources such as MOVPE and CBE. However, this chemical compound is highly hygroscopic and advanced purification techniques have been addressed to reduce the water content which has been identified as the major impurity of this precursor [20]. More recently, a new alternative N source, NF3, has been evaluated for the MOVPE growth of GaAsN, comparatively to other N precursors [21]. It has been demonstrated that NF3 is a more efficient N source as compared with DMHy, resulting in a higher N

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incorporation in GaAs while using lower N precursor concentration in the gas phase [22]. However, on the contrary of all the other sources detailed above, NF3 is an oxidiser. So, its use in a strongly reducing hydrogen-based growth atmosphere that is typical of MOVPE process presents some hazards that must be taken into account [23]. 2.2.2 Growth Conditions The growth of high quality N-containing III –V alloys is not straightforward. So, a general growth strategy in order to optimise the growth conditions of such alloys grown on GaAs substrate is: (i) to study the N incorporation in GaAs, (ii) to design a highly strained GaInAs/GaAs QW and to optimise its growth conditions in order to get the maximum wavelength around 1.2 mm achievable without strain relaxation, and (iii) to incorporate into the GaInAs well, the minimum N-content required to achieve the 1.3 mm emission and above up to 1.55 mm if possible, thanks to the combined decreases of the band gap and lattice parameter on N-content. Typical values to attain 1.3 mm emission are In and N concentrations around 0.35 and 0.01, respectively. In both cases of MOVPE- and MBE-grown Ga(In)AsN epilayers, a strong deviation in the optimised growth conditions has been observed in comparison with the standard growth parameters of conventional III– V alloys. This is discussed in the following and is depicted in Table 2.2 in which the MOVPE growth parameters (growth temperature, growth pressure, growth rate and V/III ratio) and conditions (group III and V precursors) of Ga(In)AsN are compared with the conditions typically used for the growth of cladding layers (GaAlAs or GaInP) of a GaAs-based laser structure. Our own investigations of the MOVPE growth of GaInAsN have allowed to define these advanced conditions, which are also compared in Table 2.2 to the conditions that we have initially used in a previous work [24]. 2.2.2.1 Growth Temperature. One of the most important evolutions of growth parameter of dilute nitrides is the decrease in the growth temperature T to a value around 470 –5308C for MOVPE-grown material [25] as compared with the standard Table 2.2. MOVPE optimised growth parameters of Ga(In)AsN materials as compared with initial growth conditions (see text) and to standard conditions used for the growth of GaAlAs

Growth temperature (8C) Growth pressure (Torr) Growth rate (mm/h) V/III ratio Group III precursors Group V precursor

Advanced Ga(In)AsN growth conditions

Standard Ga(In)AsN growth conditions

Standard GaAlAs growth conditions

530 100 0.15 High TEGa, TMIn TBAs, DMHy

530 750 .1 Low TMGa, TMIn AsH3, DMHy

.650 .1 TMAl, TMGa AsH3

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growth temperature above 6508C for arsenide or phosphide compounds. A similar tendency has also been observed for MBE-grown dilute nitrides with an optimised growth temperature around 430– 4708C lower than the standard growth temperature of N-free alloys above 5008C [26]. Such a difference is firstly due to a strong reduction of more than two orders of magnitude of the N incorporation rate specifically in MOVPE-grown GaAs using DMHy as N precursor while increasing T from 530 to 6508C. This is illustrated in Figure 2.1 showing the Arrhenius plot of nitrogen concentration versus the growth temperature. On the contrary, in the low temperature regime (500 – 5308C), the N incorporation appears to be constant and to be controlled only by the fractional flow of DMHy. Such a behaviour in the high T range has also been reported in the case of CBEgrown GaAsN using MMHz precursor, but with a slightly reduced activation energy [27]. On the contrary, this effect has not been encountered so drastically, in the case of MBEgrown GaAsN layers using the atomic N precursor [28,29]. This suggests that the origin of the decrease of the N incorporation rate on T is certainly the desorption of volatile N-containing species from the surface. Furthermore, this desorption effect can be reduced by increasing the V/III ratio, as shown in Figure 2.1 from our experimental data or by increasing the growth rate, as reported by Ho¨hnsdorf et al. [30]. An additional origin of this N-content drop with increasing T can also be the increased pyrolysis efficiency of AsH3 if used as the group-V precursor. However, this alternative cause is not predominant since such a similar T dependence of N concentration has also been reported in the case of the use of TBAs [31]. In MBE-grown layers, the low growth temperature of nitrided alloys is required in order to avoid a transition from smooth two-dimensional (2D) to rough three-dimensional (3D) growth mode, which could be induced by the presence of nitrogen above 4808C [32].

Figure 2.1. Temperature dependence of the nitrogen incorporation in GaAs12yNy grown by atmospheric pressure MOVPE using low and high V/III ratio.

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Furthermore, in both techniques, a narrow optimised T range has also been deduced from the characterisation of a GaInAsN/GaAs MQW structure by high-resolution X-ray diffraction (HR-XRD) [30] or by photoluminescence (PL) [10]. Finally, another reason to use a low temperature for the growth of strained GaInAsN/GaAs QWs is that the net strain in these wells is very high (typically higher than 2%), and it is known that metastable layers beyond the equilibrium critical thickness can be produced at low growth temperature. 2.2.2.2 Gas Phase Composition. The typical relationship between the group V vapour phase and solid composition in the case of the MOVPE growth of GaAs12yNy alloy is shown in Figure 2.2 for two different values of growth temperature (530 and 6008C) and of growth pressure (750 and 100 Torr). The gas phase composition is determined as the ratio of DMHy flow to the total group V flows (AsH3 þ DMHy) while the N solid composition y in the layer is determined from high-resolution X-ray diffraction (HR-XRD) or secondary ion mass spectrometry (SIMS) measurements. As it can be seen, the strong under-linearity of this relationship demonstrates a very low N incorporation efficiency in GaAs even at low T; since a N-content of a few per cent requires a DMHy gas phase composition in excess of 50%. The slight increase of N solid composition obtained by reducing the growth pressure to 100 Torr is related to a lower decomposition efficiency of AsH3, especially at low growth temperature, favouring the N incorporation. Recently, it has been observed that the N incorporation behaviour is strongly related to the N growth

Figure 2.2. Dependence of the nitrogen content in GaAs12yNy on the DMHy gas phase composition (DMHy flow relative to the total [DMHy þ AsH3] group V flows) for two different growth temperatures (530 and 6008C) and growth pressures (750 and 100 Torr). Nitrogen concentration is determined from XRD characterisations (filled symbols) or from SIMS measurements (open symbols) [99].

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precursor nature and that higher N incorporation efficiency can be obtained using Hy or NF3 sources despite their specific use conditions [22]. The N incorporation is also found to be strongly alloy composition dependent in the case of MOVPE-grown epilayers, using DMHy source. This is depicted in Figure 2.3, where a severe reduction of N concentration can be observed in GaInAs versus the In composition, as also reported in several publications [33,34]. On the contrary, we have observed a two times higher N concentration in GaAlAs as compared with GaAs even in the cases of a low Al composition and a high T growth. Such an effect can be related to the higher bond strength between Al and N than between Ga or In and N atoms. A similar behaviour has been reported for N incorporation into GaAlAs grown by CBE or by MBE [35,36]. However, no significant influence of In on the N incorporation efficiency has been observed, for layers grown by MOVPE using the alternative NF3 source or by MBE using the N plasma source [37]. This suggests that the low efficiency of DMHy in the presence of In is rather related to the desorption of incompletely dissociated N-based radicals from the In-rich surface. Another growth feature of dilute nitrides is the material quality degradation when GaInAsN is continuously grown on GaAlAs layer or after previous GaAlAs growth within the same reactor. This results in a surface roughness and in a very low PL intensity of GaInAsN layers. A first cause of such behaviour is a reduced surface mobility of N atoms on an Al-based semiconductor surface, due to the high cohesive bond strength between Al and N atoms as already reported in the case of MBE-grown structures [38]. However, this effect is more severe in the case of MOVPE-grown structures for which the recovery of PL efficiency is obtained after several growth runs within the same reactor. In that case, oxygen incorporation in GaInAsN related to a memory effect of Al remained inside the

Figure 2.3. Dependence of N concentration in MOVPE-grown Ga12xInxAs12yNy and Ga12xAlxAs12yNy alloys on In or Al composition, respectively. The lines serve as guide for the eye [99].

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reactor or to Al-based complex segregated toward the layer surface is suspected [39]. Different solutions have been proposed in order to reduce the impact of this growth limitation such as optimised GaAlAs growth conditions [40], growth interruption without or with reactor purge and reactor transfer between the growth of Al- and N-containing structures [41]. Another radical approach is the use of GaInP cladding layers or barriers in place of GaAlAs layers. 2.2.2.3 Growth Rate. The dependence of N incorporation in GaAs on the growth rate has been reported to be quite opposite in MOVPE and MBE techniques. Thus, as the growth rate is lowered, the N-content decreases in the case of MOVPE-grown layers using DMHy source and it increases for MBE- or CBE-grown alloys using atomic N [30,42], as shown in Figure 2.4. Such opposite behaviours can be explained by an increased desorption of N-based species from the layer surface in the first case and by a constant N incorporation rate like for a doping element in the second one. The slight difference of slopes on Figure 2.4 between our own atmospheric-pressure MOVPE data and the lowpressure MOVPE data of Ho¨hnsdorf et al. [30] is probably related to the different growth pressure. A low growth rate is also a key point in the optimisation of the MOVPE process, as initially reported by Kawaguchi et al. [43]. Indeed, as shown in Figure 2.5, we have observed a strong improvement of the 1.23 mm PL emission of a GaInAsN/GaAs single QW while decreasing the alloy growth rate from a typical value of 1 mm/h down to 0.15 mm/h. Thus, an increase of two orders of magnitude of the PL intensity at room temperature as well as a two times decrease of the full width at half maximum (FWHM) of the emission peak are obtained. This leads to PL properties quite similar to those of

Figure 2.4. Dependence of N concentration in GaAs12yNy on the growth rate for MOVPE- and MBE-grown layers (this work and [30,42,99]).

Epitaxial Growth of Dilute Nitrides by Metal-Organic Vapour Phase Epitaxy 101

Figure 2.5. RT–PL spectra of GaInAsN/GaAs QWs grown at 0.15 mm/h (bold line) as compared with 1 mm/h (dotted line). The PL spectrum of a GaInAs/GaAs QW (dashed line) is also shown as a reference [99].

a reference N-free GaInAs QW (Figure 2.5). We think that the low growth rate can be helpful to compensate the reduced surface mobility of N at low temperature and to favour the desorption of H from the surface. Indeed, both interstitial atoms and N –H complex have been identified as possible origin of the non-radiative centres observed in Ga(In)AsN material [25,44]. More recently, a detailed study of Kurtz et al. has shown that increased PL lifetimes and lower background C contamination of GaAsN layers with low N-content (0.2%) grown using TMGa can be obtained by decreasing the growth rate [45]. In that case, the reduced lifetime may be caused by non-radiative recombination from centres associated with both nitrogen and carbon. 2.2.2.4 Growth Precursors. The low growth temperature as well as the very rich DMHy gas phase composition required for the MOVPE growth of N-containing alloys lead to a preferential choice of group III and group V precursors. Indeed, using the conventional TMGa source, the growth rate of Ga(In)As is found to be T dependent in the range 5308C and below due to incomplete decomposition of TMGa molecules. This is not the case of TEGa, which offers the combined advantages of lower pyrolysis temperature and of reduced carbon incorporation in GaAs grown at such a low temperature [45,46]. For similar reasons, tertiarybutylarsine (TBAs) will be preferred as group V precursor in place of the conventional hydride source AsH3. Indeed, this alternative low temperature cracking precursor is better suited for low temperature growth with a higher efficiency in use. We have observed that switching from AsH3 to TBAs offers a more reproducible control of the group V gas phase composition and consequently of the Ga(In)AsN alloy composition because the TBAs decomposition is total in the low growth temperature range on the contrary of AsH3.

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2.2.2.5 Growth Pressure. The optimisation of the GaInAsN MOVPE growth is found to be extremely tedious due to a strong cross-coupling between growth conditions and DMHy flow. For example, as illustrated in Figure 2.6a, we have observed that the PL emission wavelength of GaInAsN/GaAs single QW grown at atmospheric pressure (750 Torr) decreases rather surprisingly with increasing DMHy flow, all other growth parameters being kept constant. Thanks to the extraction of the QW parameters from the HR-XRD and PL characterisations, we can attribute this unexpected evolution to a strong reduction of both the In-content and the QW thickness, as shown in Figure 2.7. In the simplest case of GaAsN ternary alloy, we have also measured a decrease of the growth rate on DMHy flow rate. Such behaviour is most likely related to gas-phase pre-reactions between DMHy and group III precursors such as TEGa and TMIn, probably leading to the formation of volatile adducts [18]. One way to reduce such parasitic reactions is to decrease the growth pressure. This results in a lower probability of collisions and interactions between molecules. Indeed, by performing the MOVPE growth of similar GaInAsN QW at a reduced pressure (100 Torr), we have well obtained in that case the expected increase of the PL emission wavelength on the DMHy flow (Figure 2.6b). The extraction of QW characteristics confirms a reduced In-content variation combined to a similar QW thickness decrease on DMHy flow at low pressure MOVPE process as compared with atmospheric pressure. However, we have to notice that at a pressure of 100 Torr, the In-content is not stable but on the contrary, it is slightly increased by flowing DMHy. This shows that a lower pressure does not remove completely interactions between DMHy and group III precursors, but it only modifies the balance of conflicting parasitic reactions. As a consequence, it could be possible to set the pressure at an intermediate value, which exactly compensates the evolution of In-content due to DMHy-based interactions.

Figure 2.6. Evolution of the RT–PL emission wavelength of GaInAs(N) QW on the DMHy gas phase composition for MOVPE growth performed at atmospheric pressure (a) or reduced pressure (b). The lines serve as guide for the eye [99].

Epitaxial Growth of Dilute Nitrides by Metal-Organic Vapour Phase Epitaxy 103

Figure 2.7. Dependence of In composition (filled symbols) and thickness (open symbols) of GaInAsN/GaAs QW on DMHy injected flow rate. The QW characteristics are extracted from XRD and PL characterisations.

Such parasitic reactions at high injected DMHy flow rates are also highly dependent on both the growth reactor and the gas manifold design. From this point of view, a dedicated gas line for the injection of DMHy separated from the lines for group III and group V precursors is preferred in order to avoid otherwise parasitic pre-reactions starting in a common feed line. 2.2.2.6 V/III Ratio. Finally, we have observed that the V/III ratio is also an important MOVPE growth parameter strongly influencing the material quality of low nitrogen content alloys. This is illustrated in Figure 2.8, which demonstrates that the RT – PL properties of single GaInAsN/GaAs QWs versus their emission wavelength are drastically improved in terms of higher PL intensity and lower FWHM when increasing the V/III ratio. Similar observations have also been reported by Asplund et al. [47] with, additionally, a lower thermal sensitivity of the PL emission wavelength on growth temperature by applying a very large V/III ratio. This last improvement of the GaInAsN growth process can be related to the lower thermal dependence of the N concentration in GaAsN that we have observed by increasing V/III ratio (Figure 2.1). In fact, as previously discussed, a very rich DMHy gas phase composition is required to attain a long wavelength emission of GaInAsN QWs. This can be achieved by increasing the DMHy flow rate as well as by reducing the As precursor injected flow. However, in this last case, the As/III ratio can become too low to stabilise the surface of a GaInAsN alloy, which remains mainly an arsenide compound in the range of group-V composition explored for long emission wavelengths. So, a too low V/III ratio leads to a degradation of PL properties of GaInAsN QWs.

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Figure 2.8. Dependence of RT–PL intensity of GaInAsN/GaAs SQW on emission wavelength with increasing V/III ratio [99].

In summary, the MOVPE growth of high quality dilute nitrides requires very specific growth conditions far away from those of GaAs or InP-based conventional semiconductor alloys. Moreover, the growth control is not straightforward since the GaInAsN alloy group-III and group-V compositions as well as the growth rate are dependent on growth temperature and gas phase composition. Despite the high level required for the growth control, we have achieved a rather good reproducibility from run to run during about a 1-month period of the PL emission wavelength of a GaInAsN/GaAs QW epitaxial structure as a reference with a total dispersion of ^ 10 nm (Figure 2.9). Furthermore, the

Figure 2.9. Run-to-run dispersion of RT–PL wavelength emission of GaInAsN/GaAs SQW grown using the same conditions during about 1-month period [99].

Epitaxial Growth of Dilute Nitrides by Metal-Organic Vapour Phase Epitaxy 105 GaInAsN growth uniformity that we have obtained using AIXTRON equipment (AIX200) corresponds to a PL wavelength dispersion of ^ 3 nm on 2 in. epiwafers. 2.3. LONG WAVELENGTH GaAs-BASED LASER PERFORMANCES

Based on these optimised MOVPE growth conditions, GaInAsN has been applied to the realisation of GaAs-based edge-emitting lasers with emission wavelength higher than 1.1 mm. The typical laser structure grown on (100)-oriented n-GaAs substrate is a separate confinement double heterostructure (Figure 2.10) formed by a strained GaInAs(N) QW surrounded on each side by two 150 nm thick GaAs barriers for the electron confinement and by two 1.5 mm thick Ga0.7Al0.3As cladding layers for the optical confinement. The Albased laser structure was usually grown in three steps with growth interruptions in the GaAs waveguide layers (shown as broken lines in Figure 2.10), in order to minimise surface contamination. The first growth interruption is required to avoid the degradation of the PL efficiency of GaInAsN QW when grown on structures including Al-containing layers, as discussed previously. The second growth interruption is only useful to characterise the active layer prior to the regrowth of the top cladding layer at high temperature (7008C). Indeed, this step is equivalent to a post-growth thermal annealing of GaInAsN which leads to an enhanced PL intensity of the active layer combined to a blue shift of the emission wavelength [48]. An alternative to GaAlAs confinement layers is GaInP which offers several benefits, such as the high etching selectivity between phosphide and arsenide or the low oxygen contamination of this Al-free material, which are helpful for the realisation of ridge lasers or of buried lasers, respectively.

Figure 2.10. Schematic cross-section of typical GaInAsN/GaAs SQW laser structure.

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2.3.1 GaInAs Lasers up to 1.2 mm-Wavelength Range First of all, the characterisation of highly strained GaInAs QW lasers grown on GaAs substrate is of interest as a reference for the further evaluation of GaInAsN lasers. An additional interest is to validate the specific growth conditions optimised for N-containing alloys and used in a similar way, for the GaInAs active layer. Broad-area (BA) lasers with a 100 mm width and a cavity length in the range 300 to 1200 mm have first been fabricated to evaluate the laser performances of GaInAs QW laser structures with either GaAlAs or GaInP cladding layers. For a lasing wavelength around 1.18 mm at pulsed conditions, the typical threshold current density Jth is as low as 150 A/cm2 for the lasers with 900 mm cavity length ðLÞ and 92 A/cm2 for infinite cavity length as deduced from the Jth curve against 1=L reported in Figure 2.11. The external efficiency is 0.28 W/A. Both Al-based and Al-free laser structures lead to similar performances. A further investigation of laser properties has been performed on 2 mm wide ridge waveguide lasers defined by chemical etching. Continuous wave operation at room temperature of the ridge lasers without facet coating has been obtained with a threshold current as low as 7 mA and an external efficiency per facet as high as 0.34 W/A for a 300 mm cavity length. The maximum power is above 60 mW. The threshold current is below 25 mA at 858C and the external efficiency does not depend drastically on the temperature. The best results are obtained for 600 mm long devices, for which the decrease of efficiency with temperature is only 0.5 dB in the range (25 – 858C). For comparison, lowest variations for InGaAsP lasers are close to 1.5 dB [49]. As deduced from the inverse efficiency versus cavity length, an internal efficiency of 0.6 and a loss as small as 2.6 cm21 have been measured on Al-free lasers. These results for as-cleaved devices are very competitive with regard to the best results obtained with InGaAsP materials. Furthermore,

Figure 2.11. Threshold current density under pulsed operation versus the inverse of the cavity length of GaInAs SQW BA lasers with GaAlAs and GaInP cladding layers.

Epitaxial Growth of Dilute Nitrides by Metal-Organic Vapour Phase Epitaxy 107 a high T0 value as high as 160 K has been measured on GaInAs lasers emitting close to 1.2 mm confirming already the interest of the GaAs-based material over InP-based materials, for which T0 varies between 50 and 70 K. The longest wavelength achieved with the N-free GaInAs QW grown on GaAs substrate is 1.24 mm from PL emission [50] and 1.23 mm for edge-emitting lasers [51] or 1.26 mm for a surface-emitting laser using extensive gain detuning [52]. In all cases the In concentration in the well is increased beyond 40%. This corresponds to a very high compressive strain on GaAs close to 3%. So, specific growth conditions are required in order to avoid the transition from 2D to 3D growth mode by reducing the migration length of In atoms on the surface. This can be achieved by lowering the growth temperature or by increasing the growth rate and/or the V/III ratio [53]. More recently, the growth of highly strained GaInAs QW has been investigated by MBE assisted by the presence of an adequate surfactant element such as Sb. This experimental approach results to significantly increase the critical thickness of the well prior to the relaxation of strain and to delay the formation of misfit dislocations. By this way, the PL emission wavelength has been extended to 1.27 mm, but no laser emission has been reported up to now at such a long wavelength with a N-free alloy on GaAs substrate [54]. 2.3.2 GaInAsN Lasers up to 1.3 mm-Wavelength Range To extend the emission wavelength of GaAs-based lasers and to assess the device quality of N-containing material, BA lasers made of a single GaInAsN/GaAs QW initially combined with GaAlAs cladding layers have been fabricated and characterised. The threshold current density of lasers emitting at 1.24 mm as a function of the cavity length is displayed in Figure 2.12. This figure compares the performances of lasers realised using

Figure 2.12. Comparison of threshold current density of 1.24 mm GaInAsN QW BA lasers versus the inverse of cavity length L for laser structures grown using advanced growth conditions (GC) and standard conditions.

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the advanced MOVPE growth conditions, as defined in the previous section (Table 2.2), to those of lasers grown using conventional conditions, as reported in a previous study [55]. As shown in this figure, a decrease of the threshold current by a factor of 5 is obtained by reducing the GaInAsN growth rate from 1 mm/h down to 0.15 mm/h and by using a high V/III flow ratio. These laser performance improvements are also in agreement with the amelioration of PL characteristics of GaInAsN QWs, as reported in Figures 2.5 and 2.8. We have obtained, by this way, a laser emission up to 1.27 mm at room temperature with a threshold current density as low as 530 A/cm2 for a cavity length of 1220 mm. The result of our optimisation of the MOVPE growth conditions that we have specifically defined for GaInAsN material can also be clearly seen in Figure 2.13, which shows the dependence of the threshold current density of several BA lasers as a function of the emission wavelength. This figure also summarises the data reported in the literature about GaInAsN QW BA lasers (cavity length in the range 700– 1200 mm) grown by MOVPE and MBE. The large scattering of Jth values from several years of publications is certainly representative of large efforts devoted to the improvement of material quality thanks to very specific optimised growth conditions, which have been determined in narrow ranges, whatever the

Figure 2.13. Comparison of threshold current densities as a function of the lasing wavelength for GaInAs(N)/GaAs QW BA lasers grown by MOVPE using the advanced MOVPE growth conditions (ad. GC) and standard conditions (st. GC) defined in this work. This figure also compiles the data reported by several laboratories: RICOH [81,82], T.I.T [58,83], KTH [84,85], Univ. Philipps [86], Univ. Wisconsin [59], AGILENT [87], SUMITOMO [88], NANOPLUS [26,70,89], INFINEON [60,90,91], FURUKAWA [77,92], LPN [72], Univ. Tampere [93], Univ. Princeton [94], Univ. Colombia [95], Univ. Stanford [71,96]. The cavity length is in the range 700 –1200 mm. Typical data of GaInAsP/InP MQW lasers (OPTO þ ) are included as a reference. Filled symbols refer to MOVPE-grown structures while open symbols correspond to MBE grown lasers.

Epitaxial Growth of Dilute Nitrides by Metal-Organic Vapour Phase Epitaxy 109 growth technique is. In fact, the progress of GaInAsN laser performances during about one decade of published results as reported in Figure 2.14 in the case of GaInAsN-based lasers emitting around 1.3 mm has been delayed for device structures grown by MOVPE as compared with MBE. Initially, very high Jth values in excess of 10 kA/cm2 were obtained for a laser structure made of a GaInAsN bulk active layer lattice matched to GaAs for which a high N-content around 4% is required [56,57]. Then, a remarkable Jth reduction has been further obtained using a strained QW laser structure as a result of a N-content decrease to about 1%. This dependence of Jth on the N-content in the active region is also at the origin of the continuous increase of the threshold current with the laser emission wavelength, as observed in Figure 2.13. This general tendency can be correlated to the degradation in material quality with increasing N concentration as already observed from the photoluminescence properties of GaInAsN QWs. However, the gap initially observed between the poor performances of MOVPE-grown GaInAsN-based lasers and the best results achieved using MBE is now suppressed (Figure 2.14). Indeed, our present MOVPE data as well as the most recent published MOVPE results of several laboratories [58,59] lead to threshold current densities well below 1 kA/cm2 with a record value of 0.23 kA/ cm2 at wavelengths around 1.3 mm, which are comparable to the best data reported so far with MBE [60,61]. Finally, such laser performance data of this new GaInAsN/GaAs

Figure 2.14. Evolution on the last decade period of the threshold current density of GaInAsN BA lasers (1.25–1.35 mm emission wavelength range) grown by MOVPE (filled dark or grey symbols) and by MBE (open symbols). The initial data refer to laser structure with bulk active layer while further results correspond to QW laser structures. Additional data to Figure 2.13 correspond to references of RICOH [57,97] and HITACHI [98].

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semiconductor system compare favourably with the performances of the well-matured InGaAsP/InP system which are also included in Figure 2.13, from our own data. However, one stringent difference between lasers in both material systems is the number of QWs required to obtain a given optical power which is lower for GaInAsN-based lasers as compared with GaInAsP-based lasers. This may be related to a difference of material gain as it has been deduced from the analysis of laser parameters [62]. We have measured the external efficiency of 2 mm wide ridge Al-based GaInAsN SQW lasers emitting at 1.285 mm at room temperature. Efficiencies as high as 0.4 W/A/facet and 0.24 W/A have been measured at 20 and 808C, respectively. Separate measurements on laser bars confirmed that this high efficiency is symmetric on both facets and that it is not due to an asymmetry occurring in the laser and resulting in the power being emitted on only one side. For high reflection coated lasers on the rear side using Si/SiO2 dielectric Bragg mirrors with a reflectivity of 96%, a record efficiency of 0.68 W/A was measured at 208C, this efficiency being still of 0.55 W/A at 808C. The drop of efficiency shown in Figure 2.15 between 20 and 808C is only of 0.9 dB and the equivalent characteristic temperature T1 of the thermal dependence of the external efficiency is as high as 286 K. Such laser efficiency performances are, to our knowledge, among the best reported to date for 1.3 mm lasers. We have also processed and characterised narrow-stripe ridge lasers from an Al-free laser epiwafer. The active layer is formed of a single GaInAsN/GaAsN QW embedded in a GaAs waveguide and sandwiched by 1.5 mm thick GaInP cladding layers. The 2.5 mm wide ridge geometry defined by wet chemical etching is depicted in the inset of Figure 2.16. The laser performances under continuous operation (cw) were measured on 600 mm long lasers with an as-cleaved output facet and a high reflection coated facet (95%).

Figure 2.15. Plot of efficiency and emission wavelength versus temperature of a 2 mm wide GaInAsN laser stripe with high reflection coated/as-cleaved facets (L ¼ 600 mm).

Epitaxial Growth of Dilute Nitrides by Metal-Organic Vapour Phase Epitaxy 111

Figure 2.16. Temperature dependence (15–858C) of L – I curves under cw operation of 600 £ 2.5 mm2 laser emitting around 1.3 mm with high reflection coated/as-cleaved facets. The inset shows the cross-sectional SEM view of Al-free GaInAsN/GaAsN QW laser ridge.

The PðIÞ characteristics versus temperature in the range 15 – 858C are shown in Figure 2.16. Threshold current as low as 19 mA and external efficiency of 0.33 W/A have been measured at room temperature. This threshold current of cw operating Al-free GaAs-based lasers emitting at 1.3 mm and grown by MOVPE compares favourably to the best reported results so far for Al-based lasers grown by MBE [63]. Lowest threshold current of 11 mA at 1.28 mm has also been reported by INFINEON in the case of an oxide-confined laser stripe [64]. Another important feature to examine is the evolution of laser characteristics at increased operating temperatures since GaInAsN-based lasers are expected to yield clear improvements in this respect. In the case of the 1.3 mm Al-based and Al-free lasers described just above, we have derived from the temperature dependence in the range 20 –858C of threshold current densities of 600 mm long BA lasers under pulsed operation, T0 characteristics higher than 110 K. Surprisingly, a lower T0 value of 86 K has been measured for the same wafer on narrow-stripe ridge lasers under continuous lasing operation as shown in Figure 2.16. However, such high T0 values are already higher than the state of the art of GaInAsP-based lasers at the same wavelength. Despite a large

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dispersion of T0 values reported in the literature, high T0 values up to 158 K have been obtained for ridge lasers [61]. This result confirms the expected breakthrough brought by GaInAsN materials for high temperature operation. Yet, these T0 values are far beyond GaInAsP ðT0 , 75 KÞ [65] and GaAlInAs ðT0 , 120 KÞ [66] material capabilities. As initially reported by Kondow et al. [67], the temperature dependence of the emission wavelength of GaInAsN-based lasers is found to be lower as compared with GaInAsP-based lasers. As shown in Figure 2.15, the lasing wavelength shift against temperature that we have measured for the laser emitting at 1.285 mm at room temperature is 0.36 nm/K. This value as well as the values reported by several authors [68,94,95] at different wavelength are much lower than the typical value around 0.8 nm/K obtained on GaInAsP lasers [67]. This characteristic is similar to the reduced thermal variation of the band gap of N-containing alloys as compared with N-free compounds [69]. Therefore, GaInAsN lasers offer better lasing wavelength stability as compared with GaInAsP/InP Fabry – Perot laser diodes. Such a property is an advantage for the design of high temperature DFB lasers and for the realisation of wavelength division multiplexing (WDM) optical fibre communication systems, which are very important to increase the transport capacity. 2.3.3 GaInAsN Lasers Towards 1.5 mm-Wavelength Range The extension of the emission wavelength of GaAs-based lasers above 1.3 mm has been reported in a few publications. The threshold current density is found to be increased to values around 2 kA/cm2 for lasers emitting up to 1.4 mm, grown both by MOVPE [86] and MBE [89,94]. Longer lasing emission wavelengths around 1.5 mm have been obtained by several groups using MBE [70 – 72] and up to now, there are, as evidenced in Figure 2.13, no reported results for MOVPE-grown lasers in this wavelength range of interest for optical fibre telecommunication applications. In fact, this very large wavelength range extension is obtained by increasing the N-content beyond 1%. So, this present limitation of MOVPE process is certainly related, in that case, to the very low incorporation efficiency of N in GaInAs using DMHy and to the severe dependence of the N incorporation on In-content. The development of alternative N sources such as NF3 [22] with a reduced dependence of N incorporation efficiency on the growth conditions and on In concentration will probably open new pathways to attain 1.5 mm emission wavelength of GaInAsN lasers grown by MOVPE. For the 1.5 mm edge-emitting lasers achieved by MBE, a drastic increase of the threshold current density to values in excess of 10 kA/cm2 and a decrease of the external efficiency to 0.1 W/A were initially obtained at such a long wavelength [73]. This degradation of laser performances is most likely due to an increasing defect density related to the high N-content of GaInAsN material. However, further optimisations have been done in the laser structure design. Indeed, thanks to the large reduction of both the lattice parameter and the band gap of GaInAsN

Epitaxial Growth of Dilute Nitrides by Metal-Organic Vapour Phase Epitaxy 113 with N-content, the long emission wavelength range can be alternatively attained with a lower N concentration combined with a higher In concentration. From this point of view, the use of Sb acting as a surfactant during the MBE growth of highly strained GaInAs(N) QWs has enabled higher In incorporation while maintaining 2D growth [54,92]. The incorporation of Sb in Ga(In)As can also help to red-shift the wavelength thanks to the reduction of GaAsSb band gap on Sb content [74,75]. Thus, a record Jth value of 1.1 kA/cm2 for laser emitting at 1.49 mm has been reported using optimised Sb-assisted MBE growth [71]. However, this approach has not been, up to now, so extensively investigated using MOVPE [76] and has not been applied to the realisation of long wavelength emitting GaAs-based lasers. Finally, GaInAsN wells can be advantageously inserted between barriers formed either with low band gap Ga(In)AsN [77] or with high band gap Ga(In)AsP alloys [78,79]. Indeed, the use of low band gap barrier leads to the possibility of reducing the nitrogen content while red-shifting the emission wavelength thanks to a reduced quantisation effect. Additionally, such barriers can also reduce the overall strain of the active region because the QWs with high In-content are compressively strained while these alternative barriers can be tensilely strained. 2.4. CONCLUSION

It has been established from our experimental results that the optimum MOVPE growth conditions of GaInAsN QWs are further away from standard parameters. Thus, a lowpressure MOVPE process combined with low growth temperature and growth rate, as well as the choice of specific low cracking temperature group-V and III precursors such as DMHy, TBAs and TEGa are essential to achieve GaInAsN material suitable for laser devices. Indeed, we have shown that such optimised conditions result in a drastic improvement of both PL properties and of lasing performances of structures based on a GaInAsN/GaAs QW. By this way, we could achieve lasing at 1.27 mm with a threshold current density as low as 540 A/cm2 for a cavity length of 900 mm. Such lasing performances as well as the most recent results of the literature for MOVPE-grown GaInAsN-based laser structures are now similar to the data reported for MBE-grown material. So, the MOVPE process, which is presently the mainstream in the industrial production of InP-based lasers for telecommunication applications, is on the way to be also useful for the realisation of long wavelength GaAs-based lasers. Furthermore, the device performances discussed in this review prove that this new GaInAsN/GaAs semiconductor system can compete with the conventional GaInAsP/InP system. When comparing the highest published record values, 1.3 mm GaAs-based edge-emitting lasers show superior performances as compared with InP-based devices, both in terms of efficiency and robustness to temperature. Work has still to be done to take advantage of this material for high bit rate performances. The next challenge under progress is also to extend GaAs-based lasers to the further 1.55 mm fibre-optic wavelength range.

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ACKNOWLEDGEMENTS

It is a great pleasure to acknowledge many collaborators without whom much of this work would not have been possible, including E. Gouardes, O. Gauthier-Lafaye, N. Bouadma, G. Hallais, F. Martin, L. Roux, A. Vuong and V. Colson. I also greatly appreciate the expertise of B. Thedrez, B. Fernier, L. Goldstein, J.L. Gentner, P. Pagnod-Rossiaux, A. Mereuta and A. Ougazzaden for many helpful discussions.

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Dilute Nitride Semiconductors M. Henini (Ed.) q 2005 Elsevier Ltd. All rights reserved.

Chapter 3

The Chemical Beam Epitaxy of Dilute Nitride Alloy Semiconductors Jessica O. Maclean QinetiQ Ltd, Malvern Technology Centre, St. Andrew’s Road, Malvern WR14 3PS, UK

3.1. INTRODUCTION TO DILUTE NITRIDE SEMICONDUCTORS

The dilute nitride semiconductors were first grown epitaxially in the 1990s [1 –3] and represent a relatively new family of III –V compound semiconductors with unusual physical properties and potential technological importance. In general terms, the alloying of a “conventional” III – V semiconductor binary (i.e. one of Al, Ga, In with one of As, Sb) with a few per cent (, 10%) of the same Group III pure nitride may give a single crystal ternary with a significantly narrower band gap than would be expected. For example, gallium arsenide (GaAs) alloyed with a few per cent of gallium nitride (GaN) to give single crystal GaNx Asð12xÞ has a band gap which decreases with nitrogen (N) composition as x increases, at a rate of approximately 150 meV decrease per 1% nitrogen [4]. The general origin of this negative band bowing and other associated effects is considered to be the existence of nitrogen-related localised states near the conduction band edge which result from the large size and electronegativity differences between the nitrogen and the host anion [5]. The potential semiconductor device applications of the dilute nitrides stem from the decrease in the fundamental band gap and the associated increase in the effective mass of the electrons. In order to lattice match the dilute nitride alloy to the rest of the epitaxial device structure, a quaternary dilute nitride alloy is more often used than a ternary. The reduction in the lattice parameter by nitrogen is then balanced by the co-incorporation of an atom of larger atomic radius, such as In or Sb. Thus, studies of quaternaries such as epitaxial GaInNAs and GaNAsSb are more common than those of ternary dilute nitrides. The compositional analysis of these alloys is complex, especially given that nitrogen content is challenging to measure quantitatively. To date there have been very few reports of a quaternary composition with no net strain because it is difficult to incorporate sufficient nitrogen in substitutional lattice sites. Therefore, the dilute nitride epilayer thicknesses employed in dilute nitride devices are limited by critical thickness considerations. Growth on single crystal substrates of GaAs and Si is important because these wafers are of high quality and are available in large areas at relatively low cost. The compound in 119

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the dilute nitride family which is of most technological interest currently is gallium indium nitride arsenide (GaInNAs). Those compositions of GaInNAs which are fairly closely lattice matched to GaAs and which have a direct band gap in the range of telecommunications wavelengths (1.25 – 1.65 mm) are required for vertical cavity surface emitting lasers (VCSELs) and edge-emitting lasers for use in local- and metro-area (LAN, MAN) communications networks. The alloy Ga(12x)InxNyAs(12y) is exactly lattice matched to GaAs when y ¼ 0:35x and is required in this form for thick epilayers as the third junction in next-generation solar cells [6]. In terms of lattice-matched structures on silicon, it may be possible to grow optical devices based on GaNAs quantum wells (QWs) in GaP barriers [3]. The quinternary GaInNAsSb has shown some benefits in heterointerface quality with respect to GaInNAs and has reached longer wavelengths in MBE-grown QWs [7]. The introduction of InNSb multiple QWs to InSb-based lightemitting diode (LED) and detector structures has shown promise for extending the wavelength of III– V-based emitters and detectors [8,9]. In terms of electronic devices, such as heterojunction bipolar transistors (HBTs) and heterojunction field effect transistors (HFETs), the main advantages arise in terms of increased design flexibility as a result of greater freedoms in band gap engineering and lattice matching [10].

3.2. THE CHEMICAL BEAM EPITAXIAL/METALORGANIC MOLECULAR BEAM EPITAXIAL (CBE/MOMBE) GROWTH PROCESS

This review aims to summarise published achievements and future potential for progress in the growth of dilute nitride alloys using the chemical beam epitaxy (CBE) technique. This technique uses Group III metalorganic precursors and Group V hydrides or metalorganics as sources. CBE is also known as metalorganic molecular beam epitaxy (MOMBE) by some, although others make the distinction that MOMBE uses Group III metalorganic precursors with elemental Group V sources. There are currently relatively few reports of dilute nitride epitaxy by MOMBE and the references here are almost exclusively CBE related. CBE growth proceeds, in general, without the use of a carrier gas, unlike metalorganic vapour phase epitaxy (MOVPE). The total chamber pressure is low, in the range 1 £ 1027 – 5 £ 1024 mbar (of the order of 0.01 –50 Pa), the higher pressure range usually consisting largely of hydrogen from the high-temperature cracking of hydrides. Precursor flows are in the molecular flow (UHV) regime and hence there are no reactions between precursor molecules in the gas phase. The use of in situ analytical techniques requiring an electron/ion beam probe, such as reflection high energy electron diffraction (RHEED), is therefore possible. The CBE growth process proceeds by the adsorption and decomposition of the precursor molecules on the wafer surface. Chemisorbed species then react to form

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Group III and Group V adatoms, mediated by surface catalysis, and decomposition byproducts are desorbed. The chemistry of both the precursors and the wafer surface therefore influences the growth process, in addition to the growth conditions (such as substrate temperature, V/III ratio and growth rate). As a result of the complexity of the CBE growth process, selective area epitaxy (SAE) may take place in which, under a restricted range of growth conditions, selected areas on the wafer patterned with certain mask types may remain completely free of deposited material during growth. The high pressures and temperatures of MOVPE cause gas-phase collisions and reactions. In general, the window of appropriate MOVPE growth conditions for SAE is rather narrower than for SAE by CBE. SAE has not been achieved below 6008C by MOVPE [11]. SAE may be exploited for on-wafer integration of different device structures [12 – 14], and hence integration of different device types side by side with low optical/electrical losses.

3.3. CBE OF DILUTE NITRIDE SEMICONDUCTORS

The large differences in both anionic radii and in electronegativity between nitrogen and the other Group V anions are often cited as causes of a miscibility gap in dilute nitride alloy systems. It is, at present, unclear which alloy compositions are genuinely inaccessible to the various epitaxial growth techniques. The predictions of one model of GaInNAs growth by Molecular Beam Epitaxy (MBE) [15], using the law of mass action, suggest that incorporation of active nitrogen species at high growth rates can be unity below 4808C and that the ratio of Ga to In does not affect this incorporation factor. However, for nitrogen contents exceeding 10%, growth rates of , 0.05 ML (monolayer) s21 were predicted to be necessary and pure GaN growth was predicted to be feasible for growth rates approaching zero! The model was verified experimentally for Ga0.75In0.25NxAs(12x) compositions with up to 3% nitrogen. The UHV nature of the CBE process allows for the use of either a plasma source or an alkyl (or hydride) source of active nitrogen (precursor compounds of non-metals, such as nitrogen, are frequently referred to as “alkyl” precursors). The choice of a suitable precursor for CBE involves consideration of a number of its physical and chemical properties. The source stability, and hence decomposition temperature, must be as low as possible, consistent with the simple transport of its vapour into the growth chamber. The vapour pressure as a function of temperature must be appropriate for the gas handling of the reactor and matched to the growth rates achievable from the other precursors. The source materials must be as free as possible from oxygen contamination since any contamination will arrive at the growth surface. Finally, an analysis of any additional hazards in the use of the precursor must be made and appropriate precautions taken. Beyond this, the suitability of a nitrogen alkyl for the growth of dilute nitrides depends on the efficiency of nitrogen incorporation. This is difficult to predict and needs

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Table 3.1. Summary of the properties of the alkyl precursors used for the CBE growth of dilute nitrides Nitrogen precursor name and abbreviation Dimethylhydrazine, DMHy Monomethylhydrazine, MMHy Ammonia, NH3

Chemical formula

Decomposition temperature (8C)

(CH3)2N2H2

350 [18]

206 (258C)

0.5

90 [4]

57.0 (258C)

0.2

CH3N2H3 NH3

1000 [30]

Vapour pressure at room temperature (mbar)

8.75 £ 103 (218C)

Toxicity—threshold limit value (ppm)

25

experimental verification. Nitrogen atoms may be incorporated at interstitial rather than substitutional lattice sites so that, ideally, substitutional nitrogen incorporation is to be maximised but interstitial nitrogen incorporation is to be minimised—a complex growth process indeed! The efficiency of nitrogen incorporation influences the overall pressure regime of the growth process since high flow pressures of nitrogen alkyl will be required if the incorporation efficiency is low. Modifications to the gas handling aspects of the reactor design may be necessary, particularly in the case of process scale-up. This is also the case for plasma sources of nitrogen. It is significant that the first 1.55 mm GaInNAs laser diode was grown by MBE using a differentially pumped nitrogen plasma source [16]. Table 3.1 compares the properties of the nitrogen precursors which have been repeatedly used for the CBE of dilute nitrides. Both alkyl precursors, monomethylhydrazine (MMHy) and dimethylhydrazine (DMHy), have high vapour pressures at room temperature compared with other CBE precursors and they are therefore used in conjunction with a cooled, temperature-controlled bath. Ammonia is thermally very stable and therefore has to be decomposed using a high-temperature gas inlet rather than at the wafer surface. However, partial decomposition is required to release active nitrogen because complete decomposition will produce stable N2.

3.4. FUNDAMENTAL STUDIES OF GaNxAs(12x) BAND STRUCTURE

The mechanism by which N-related states delocalise with increasing N content, x, and incorporate into the extended states of the dilute nitride alloy’s conduction band is controversial. An established mechanism would allow calculation of the composition- and pressure-dependencies of the band gap, Eg ; and the effective electronic mass, mpe : The first experimental evidence for the selective delocalisation of N-pair states in GaNxAs(12x) via band-mixing processes was obtained using CBE-grown GaNxAs(12x)/GaAs multiple QW structures [17]. The photoluminescence (PL) spectra of the samples under high pressure

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were studied in order to distinguish between excitonic states bound to specific N-related centres and localised excitons trapped in a quasi-continuum of fluctuation states. Changes corresponding to selective delocalisation were observed in the spectra for specific resonant states. Distinct differences were observed in the PL spectra for unannealed samples with fully substitutional N contents of 0.25 and 0.4% [18]. This indicated that this is the compositional range within which localised states begin to mix into the conduction band continuum. The excitonic features were clearly resolved suggesting that sample quality was high. This behaviour is qualitatively consistent with theoretical studies of conduction band formation in GaNxAs(12x) dilute alloys that use a full-hybridisation approach to treat incorporation of N-pair (cluster) states [19].

3.5. THE COMPOSITIONS AND PROPERTIES OF DILUTE NITRIDES GROWN BY CBE

There are good reasons to attempt the growth of dilute nitride alloys by CBE. Nitrogen incorporation is found to increase with reduction in growth temperature for all growth techniques and CBE growth temperatures for epitaxial III –V’s of optoelectronic quality are generally somewhat lower than for MBE and MOVPE. Thus, overall epitaxial quality may not need to be significantly compromised in order to incorporate nitrogen. The V:III ratios used for CBE are usually similar to those used in MBE and are significantly lower than those used in MOVPE. Thus, consumption of high purity nitrogen alkyl is expected to be more moderate than in the MOVPE case. In the first few years of work on dilute nitride alloys, it proved difficult to incorporate more than 3% N into GaAs and more than 1% N into GaInNAs using all III –V growth techniques. Nevertheless, a number of reports indicated that CBE growth may access relatively high N contents in dilute nitrides. 3.5.1 Alkyl Source of Nitrogen Fully substitutional N contents of 7(^ 2)% in GaNxAs(12x) were confirmed by comparing measurements of the lattice parameter of fully strained samples with the chemical concentration deduced by secondary ion mass spectrometry (SIMS) [18]. The nitrogen alkyl was 1,1-dimethylhydrazine, used with cracked arsine and triethylgallium (TEGa), at a growth temperature of 490(^ 5)8C. Nitrogen incorporation in GaNxAs(12x) was also compared for two different sources of arsenic, As2 from cracked arsine and As from triisodimethylaminoarsenic (TDMAAs) (see Figure 3.1). At low flow pressures of DMHy, giving dopant-level nitrogen, incorporation was similar. For % levels of nitrogen, incorporation was less efficient when using TDMAAs than As2. This may be the result of mechanistic factors at the growth surface. The first report also of Al0.3Ga0.7NxAs(12x) growth showed that N was readily incorporated into the Al-containing alloy, achieving

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Figure 3.1. Nitrogen concentration as measured by SIMS against flow pressure of dimethylhydrazine (DMHy) for GaNxAs(12x), Al0.3Ga0.7As(N) and In0.15Ga0.85As(N), scaled for constant Group III growth rate of 0.5 mm h21.

% levels of N with approximately 1/10th of the flow pressure of DMHy as compared with incorporation into pure GaAs. Incorporation of N into Ga0.85In0.15As was less efficient than into GaAs under the Group III-limited growth conditions used, but nevertheless % levels of N were achieved. Careful SIMS measurements of unintentional hydrogen concentrations in all the samples (Al0.3Ga0.7NxAs(12x), GaNxAs(12x), Ga0.85In0.15NxAs(12x)) showed that the hydrogen (H) concentration was around 10% of the N concentration (see Figure 3.2). Since the different alloys were grown under differing growth conditions this finding strongly suggests that the unintentional hydrogen concentration is associated with N incorporation. This may show that the N originates from the – NH2 end of the DMHy molecule. It was found that CBE growth of Ga0.571In0.429NxAs(12x) incorporated more N than growth of GaNxAs(12x) under the same conditions [20]. Whereas growth under a MMHy flux of 6.6 £ 1023 mbar gave 2.2% N in GaNAs, the N content in Ga0.571In0.429NxAs(12x) grown with the same alkyl flux was 9%! In order to investigate whether this enhancement

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Figure 3.2. Hydrogen concentration in GaNxAs(12x) and 15% InGaAs(N) and 30% AlGaAs(N) (grown using cracked AsH3) plotted as a function of the nitrogen concentration, as measured by SIMS.

was caused by a surface effect, a further experiment was carried out which compared the N content of GaNxAs(12x) grown with and without intermittent surface coverage of In atoms (beam equivalent pressure of 7.9 £ 1025 mbar for 5 s). A high growth temperature (5758C) was chosen to ensure that the In atoms desorbed from the surface. With 6.6 £ 1023 mbar MMHy, and with no triethylindium (TEIn) supply, 1.36% N incorporated into GaNxAs(12x). The periodic (every 10 min) supply of TEIn increased this to 4.37%! Clearly, the presence of In at the surface was enhancing the incorporation of N, possibly by favouring the release of active N species from MMHy. A significant breakthrough was the first report of 1.55 mm, room-temperature PL from GaInNAs QWs grown by CBE. A multiple QW GaInNAs/GaAs sample, grown at 5208C using TEGa, TEIn, TDMAAs and MMHy showed PL at 1.55 mm with a composition, analysed by XRD of 20.4% In and 5.5% N [21]. After annealing at 6508C for 3 min under flowing N2, the PL intensity was nearly 8000 times weaker than a similar Ga0.796In0.204As/GaAs sample. By keeping all growth parameters unchanged and growing a series of samples with different TEIn fluxes, under Group V flux-limited growth

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conditions, the band gap reduced by more than would be predicted from the In content increase alone, thus showing that the increased In flux was enhancing the N incorporation. 3.5.2 Plasma Nitrogen Source In the use of a plasma source of N radicals for CBE it was found that N composition was inversely proportional to the growth rate indicating that the active species have a constant sticking coefficient [22]. The benefits of optimising the nitrogen rf plasma operating conditions were clearly demonstrated in a study of the optical quality of CBE-grown GaNAs and GaInNAs QWs [23]. Optical spectroscopy of the plasma species showed that an increase in the active nitrogen peaks correlated with an increase in the nitrogen content of the epitaxial GaNAs. The optical quality as measured by the PL intensity and full-width at half-maximum (FWHM) improved with the use of low conductance settings to the radical beam cell. Still further improvement was obtained with the use of an ion trap to deflect energetic ions away from the growth surface. This was demonstrated by comparing the ratio of PL peak intensity to the PL excitation power for as-grown and annealed MQW GaNAs/GaAs samples containing 0.9% nitrogen. The gradient of a log – log plot was used to measure the amount of non-radiative recombination, with a gradient of 1 corresponding to a purely radiative process and a gradient of 2 corresponding to a purely non-radiative process. A decrease in gradient by around 2 –5% was observed for both pre- and postannealed MQW GaNAs and GaInNAs samples (0.2% nitrogen) when grown with the ion trap suggesting that there was some decrease in non-radiative processes. Furthermore, those samples grown with an ion trap showed an improvement in PL intensity on annealing, by a factor of around 3, for a wider range of annealing conditions than for those grown without ion trap and subsequently annealed. 3.5.3 Post-growth Annealing In order to maximise photoluminescence efficiency from the GaInNAs QWs, it is found that a short anneal (of duration between 20 s and a few minutes) at high temperature (between 600 and 8508C) after the growth of the QWs is necessary. This enhances the PL integrated intensity by a factor of 3 –100. A study which aimed to optimise the post-growth annealing of CBE-grown GaInNAs QWs (grown using an rf plasma source, cracked AsH3, TEGa and trimethylindium, TMIn) investigated a range of annealing temperatures (550 – 7008C) and annealing times [24]. When annealing at 7008C, a rapid increase in the maximum PL intensity was observed after only 30 s, but samples annealed at this temperature for 45 min no longer showed any PL at all. Annealing at lower temperatures achieved similar maximum PL intensities as the times were lengthened. Optimal annealing of 45 min at 6008C was chosen as a procedure least sensitive to variations in temperature ramp rate. For all compositions of QW, which before annealing emitted around 1.3 mm, the final wavelength was blueshifted by 70 nm.

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The threshold currents of lasers processed from similar QWs increased by a factor of around 3 as the N content increased from 0.95 to 1.35%. A new approach to annealing was taken with the use of strain-mediated GaInNAs QWs grown by CBE (using an rf plasma source, cracked AsH3, TEGa and In metal) [25]. Highly strained (þ 1.9%) Ga0.7In0.3N0.01As0.99 QWs were grown at 4608C using 1 ML of a lessstrained composition between each QW and GaAs barrier. Annealing at 6008C for 10 min under an arsenic beam was carried out after the growth of each QW in a double QW structure. It was found that PL intensity was maximised when the strain in the intermediate layer was between 0 and 1.5%. Thus, no intermediate layer was necessary for high PL intensity, although the wavelength was slightly shorter (1.22 mm) as compared with the use of a Ga0.8In0.2As (þ 1.5% strained) barrier (1.23 mm). The use of a separate annealing step immediately after the growth of a QW gave 15 times higher PL intensity than the same procedure applied post-growth to the whole structure.

3.6. CBE-GROWN DILUTE NITRIDE DEVICES

3.6.1 Contacts Essential for devices with low drive currents are low resistance contacts to the active device layers. Epitaxial semiconductors with high carrier concentrations are often used between metallic contacts and the device layers. High carrier concentrations are routinely achievable by CBE in the standard III –V alloys, for example, as-grown high p-type electrical concentrations of 7 £ 1019 cm23 in GaAs using carbon tetrabromide (CBr4) as the dopant precursor [26] and n-type electrical concentrations of 1 £ 1019 cm23 in GaAs using tetraethyltin (TESn) [27]. The use of heavily doped InGaAs layers grown on GaAs device structures can reduce parasitic resistances by up to an order of magnitude relative to having the contacts directly on GaAs. With the same aim, electron cyclotron resonance (ECR) MOMBE, using nitrogen and TMIn, has been used to develop InN contacts for GaN devices [28]. A new dilute nitride alloy suitable for high n-type contact layers has recently been grown by CBE using a Group VI precursor, ditertiarybutylselenide (DtBSe) [29]. Contacts of gallium nitride arsenide selenide (GaNAsSe) containing up to 15% Se and up to 9% N were grown using TEGa, TDMAAs and MMHy resulting in an alloy with a band gap as low as 1.03 eV. Without any need for contact alloying by annealing, the Au/GaAsNSe contacts had a specific contact resistance of 4.5 £ 1024 V cm22 and a sheet resistance of 22 V A21. The room temperature electron concentration was 1 £ 1020 cm23 and the electron mobility was surprisingly high at 500 cm2 V21 s21. This contrasts with the much lower p-type background of 4 £ 1017 cm23 and mobility of 80 cm2 V21 s21 for the intrinsic GaNAs material. The high mobility of the electrons in the GaNAsSe suggests that unintentional background impurities and/or intrinsic defects in the alloy are low.

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In addition to the interesting effect of the DtBSe on the carrier mobility of the dilute nitride, this precursor also enhanced the incorporation of nitrogen from MMHy in the growing dilute nitride as deduced from the analysis of lattice parameter measurements. The GaAsNSe band gap dependence on composition is to be determined. It may be that the larger selenium atom, similarly to the In atom, favours the incorporation of the small nitrogen atom at the surface since this lowers the surface strain energy, as has been suggested for the CBE growth of GaInNAs [20,30]. However, in the bulk the GaNAsSe is tensilely strained on GaAs since Ga2Se3 has a lattice constant of 0.5429 nm in the zinc blende crystallographic structure (GaAs 0.5653 nm). 3.6.2 LEDs The same team has gone on to demonstrate the bright, broad band PL of GaNAsSe/GaAs superlattices centred around 1.5 –1.6 mm with up to 2.2% N [31]. The improvement in the luminescence intensity with respect to GaNAs was attributed to an increase in radiative recombination rate as a result of the high electron concentration in the conduction band. A study of the PL intensity as a function of temperature showed a broad band (FWHM 110 – 140 meV) luminescence which decreased in intensity by a factor of 100 on increasing the temperature from 19 to 300 K. The temperature dependence of the PL of the superlattice was reduced by sandwiching it between compressively strained superlattices of GaAsSb/ GaAs, reducing the average strain from around 2 0.9 to 2 0.08%. On raising the temperature from 19 to 300 K, the peak PL intensity fell to just 20% of its low-temperature value. Thus, the new dilute nitride alloy GaNAsSe was demonstrated to have applications as both an optical and an electronic material. 3.6.3 GaInNAs Base Lasers The negative band-bowing of the GaAs –GaN alloy system makes it possible to extend the wavelength of optoelectronic devices on GaAs beyond the 1.2 mm possible with InGaAs QWs in GaAs barriers. The large (with respect to kT) conduction band offset of GaInNAs QWs in GaAs barriers [32] and the nitrogen-related reduction of the temperature sensitivity of the band gap (in comparison to GaInAs) result in high predicted laser characteristic temperatures. The commercial drive for the large volume manufacture of directly modulated, uncooled edge-emitting lasers and VCSELs in the communications waveband arises from the need for low-cost optical amplifiers and optical interconnects suitable for use in LAN and MAN optical-fibre-based networks. In order to maximise luminescence efficiency from the GaInNAs-QW-based laser diodes, it is found that a short anneal (of duration between 20 s and a few minutes) at high temperature (between 600 and 8508C) after the growth of the QWs is necessary. The optimum annealing process is composition dependent. High-temperature anneals within the reactor (in situ) or in a separate rapid thermal annealing chamber (ex situ) may require the protection of the sample surface from loss of Group V elements. When the growth of

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a subsequent upper cladding layer takes place at a higher temperature than the active region, the further ex situ anneal of the dilute nitride QWs may be reduced in temperature and/or duration. The post-growth anneal also has the effect of shifting the PL to shorter wavelengths, by about 70 nm [24], further increasing the challenge of fabricating longer wavelength (. 1.3 mm) devices. The possible explanations for this blueshift include outdiffusion from the QW, of In and/or N atoms, change in the QW shape or redistribution of the N atoms’ nearest neighbours. The processes which occur during annealing will depend, to a large extent, on the initial crystalline quality and on the compositions of the QW and its barriers, and the resulting strain in the structure. It is generally found that the PL intensity decays rapidly for GaInNAs compositions beyond 1.3 mm whether the longer wavelengths are achieved by increased In or increased N compositions. It is clear that, for all III – V epitaxial techniques, the as-grown crystal quality of GaInNAs requires improvement. Indeed, if the as-grown dilute nitride quality were improved, the post-growth anneal may possibly be unnecessary. Growth of the complete laser structure by CBE at relatively low growth temperatures (including high quality AlGaAs) would preserve any strain in-built to the QWs and barriers. For this reason, there has recently been renewed interest in the growth of GaAs/AlAs superlattices for reflector stacks by CBE [33]. For future progress, it is essential to understand why the threshold current of GaInNAs lasers increases dramatically with increase in the wavelength. Greater understanding of the source of non-radiative centres in these materials is needed and methods need to be developed for the removal of such centres. In CBE growth, the precursors can potentially be sources of non-radiative centres, such as oxygen, given the fact that precursor molecules arrive unimpeded at the growth surface. Improvement of TMIn source purity has been correlated with longer PL non-radiative lifetimes and has enabled the growth of very low threshold current InGaAs QW lasers by CBE [34]. Quantitative measurement of unintentional oxygen incorporation into AlGaNAs using SIMS has shown that DMHy can be a source of oxygen-containing species [35]. Nitrogen was found to readily incorporate into AlGaAs and up to % levels of N by CBE [18]. By quantitatively comparing different batches of DMHy, improvements to its purification route have been made. 3.6.3.1 GaInNAs QW Laser Diodes. A summary of some of the key CBE-grown GaInNAs QW laser parameters is given in Table 3.2. The first report of CBE-grown GaInNAs QW lasers described devices with a CBE-grown waveguide core containing two GaInNAs QWs in GaAs barriers and MOVPE-grown AlGaAs-based cladding regions (for reasons of source availability) [36]. An rf plasma source of nitrogen, TMIn, TEGa and AsH3 was used for the QWs and growth proceeded at 4808C and 1.7 mm h21. Growth of the upper cladding took place by MOVPE at 6708C and no further annealing of the active region is explicitly mentioned. These devices, with QW compositions having 35 – 37%

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Table 3.2. Summary of measured parameters of CBE-grown GaInNAs QW lasers by Kageyama et al. Lasing wavelength, l (mm)

%N

%In

Tgr (8C)

1.19

0.3

36

470

2.6

1.4

1.7

34

470

1.3 1.27 1.23 1.2

0.95 0.5 0.3 0.3

34 37 37 35

470 480 480 480

7.6 10.6 2.2 2.99 1.36 0.96

J (kA cm22)

Cavity length (mm)

Slope efficiency, h (WA21)

(VCSEL, area 9.1 mm £ 8.8 mm) 1 1080 ,700 780 800 750

Characteristic temperature, T0 (K)

Ref.

0.23

–

[42]

0.096

94

[37]

– – – –

– – – 270 (0– 508C), 138 (50–808C)

[24] [36] [36] [36]

In and 0.3 –0.5% nitrogen, showed lasing wavelengths ranging from 1.2 to 1.27 mm. The threshold currents for as-cleaved devices were fairly high (960 A cm22 at 1.2 mm for a 750 mm cavity) when pulsed every 1 ms with a 0.1% duty cycle, and increased further with increasing nitrogen composition for longer wavelength. The laser characteristic temperatures, T0 ; were notably high at 270 K. The high threshold currents may have been due, in part, to the three-stage growth process employed since the samples were air exposed twice in order to grow the lower and upper cladding by MOVPE. Possible interfacial contamination is also suggested by the results from similarly grown 35% InGaAs QW lasers which also showed high threshold currents (660 A cm22). For comparison, very low threshold current CBE-grown 980 nm InGaAs 2QW broad area lasers also using AlGaAs cladding regions showed an infinite length threshold current density, J1 ; of 160 A cm22 [35]. Nevertheless, this first report was significant in that it confirmed that GaInNAs QWs of sufficient quality for lasing action could be grown by CBE and also that these devices had good temperature characteristics. Progress to longer (1.4 mm) wavelength lasers has been made more recently [37]. It was found that the PL intensity of GaInNAs was very sensitive to the growth temperature. The growth temperature range for PL emission from a given GaInNAs composition decreased as the N content increased. This finding is in agreement with earlier observations of GaInNAs growth temperature sensitivity [18]. The precursor combination chosen limited the minimum growth temperature to 4708C. The N content was 1.7% and the In content was 34% with a well width of 8 nm. In situ annealing for 45 min under AsH3 was performed at 6008C. A ridge waveguide laser 7 mm wide and 1080 mm long emitted at 1.4 mm for a threshold current density of 10.6 kA cm22 under pulsed operation (1 ms at 1 kHz). The characteristic temperature was estimated to be 94 K and the wavelength change as a function of temperature was 0.40 nm K21. A summary of the team’s results

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at various wavelengths is given in Table 3.2. The earlier work on both the optimisation of the rf plasma source [23] and the annealing procedure [24] appears to be an important step towards demonstrating longer wavelength laser devices. 3.6.3.2 GaInNAs Quantum Dot Lasers. The same team tested the first CBE-grown GaInNAs quantum dot (QD) lasers and measured a lasing wavelength of 1.02 mm (equivalent to a 1.1 mm wavelength at 300 K) for a threshold current density, of 1.9 kA cm22 at 77 K, under pulsed operation (1% duty cycle) [38]. The lower cladding was grown by MOVPE so that there was one air exposure within the structure. The QDs were grown at 5008C using an rf source of N2, TMIn and TEGa with hydrogen carrier gas and by cracking AsH3 at 10008C. The 8 MLs deposited to create the dots resulted in an areal dot density of 1.2 £ 1011 cm22 and a wide dot size distribution. The average dot diameter was 30 nm and the height was 4 nm. A comparison of the dot density and size distribution with InGaAs dots suggested that the GaInNAs dot density was higher and the lateral size smaller for up to 1% nitrogen, whereas for 1.5% nitrogen the dot density decreased and the size increased. These observations indicate the significant effect of nitrogen at the GaInAs growth surface. The GaInNAs QD laser device results illustrate the potential feasibility of longer wavelength GaInNAs QD lasers, which are expected, when optimised, to have very low threshold currents, as a result of the sharp density of states of the QDs and the more similar electron and hole masses in this quaternary system [2]. Indeed, 1.24 mm InGaAs QD lasers recently grown by MOVPE have shown a threshold current of 7.2 A cm22 per QD layer in 10-layer 65% InGaAs QD lasers after optimising the annealing process and hence the strain distribution [39]. Further studies of QD morphology under different CBE growth conditions have incorporated up to 2% nitrogen and showed that growth at 5408C with 2% nitrogen gives quantum-wire-like islands [40]. 3.6.3.3 GaInNAs VCSELs. Dilute nitride 1.3 mm VCSELs are attractive for optical interconnects in optical fibre networks of up to a few kilometres reach because of their temperature stability and resulting low cooling requirement. Furthermore, device processing is greatly simplified, with respect to indium phosphide-based VCSELs, by the use of GaAs/AlAs mirror stacks, for definition of the stop band, which can be grown monolithically with the active region and to which standard device processes may be applied. Lateral confinement can be simply achieved using lateral oxidation of AlAs leading to high modal purity operation. A characteristic of GaInNAs QWs as the optically active material in 1.3 mm VCSELs is the wide operating temperature range observed for the device. Temperature ranges of operation are typically quite limited for VCSELs because a close match between the Fabry –Perot cavity mode and the gain peak is needed

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to obtain low threshold current and high power devices. This situation cannot normally be maintained over a wide temperature range because the gain peak varies much faster than the cavity mode dip in reflectivity. GaInNAs VCSELs grown by MOVPE were found to have an impressively wide operating range from 30 to 388 K [41]. This was explained by analysing the modulated reflectance signal as a function of temperature and as a function of angle for the structures. Three different QW ground state transitions were revealed to be present. The broadening of the temperature dependence of the gain was explained to arise from the different band gaps associated with alternative stable lattice sites for the N atom. Thus, it is an intrinsic material property of GaInNAs which results in a broad band gain useful for lasers and amplifiers in general, and for resonant cavity devices in particular. GaInNAs/GaAs VCSELs with the l-cavity grown by CBE have shown continuous wave (CW) operation at 1185 nm giving a maximum of 1 mW in multimode operation and around 0.4 mW when operating in single mode, under electrical pumping [42]. The QWs contained 0.3% N and 36% In. The threshold current density was 2.6 kA cm22 and the slope efficiency was 0.23 W A21. An output power of 4 mW was obtained when pulsed. The VCSEL linewidth was as low as 0.2 nm and high single transverse mode output was observed with side-mode suppression ratios of 25– 30 dB. This performance compares very favourably with the first electrically pumped MBEgrown VCSEL beyond 1.2 mm (1.294 mm) which, for a threshold current density of 4 kA cm22, gave single mode output power of 60 mW [43]. In fact, at that time, the CBE-grown VCSEL showed the highest output power for a similar threshold current density.

3.7. THE POTENTIAL FOR PRODUCTION CBE OF DILUTE NITRIDES

The scaling-up of the CBE process for volume epiwafer production has potential in terms of the quality of epitaxy and quantity of epiwafers [44]. CBE reactor running costs are predicted to be modest because the power requirements of the gas cells and liquid nitrogen consumption by the cryopanel are low, and no carrier gas is required. The total growth rate may be high—for example, up to 14 mm h21 have been recorded for GaAs growth [45]—and may be straightforwardly varied during a growth run. Device yields are high resulting from high cross-wafer uniformity and low defect density [46]. The environmental impact is low. With appropriate gas inlet design, the precursors may be consumed highly efficiently leaving few metal deposits on the chamber walls. Simple byproducts of precursor decomposition (e.g. ethane, hydrogen, nitrogen) are exhausted. The potential for the production-scale CBE of dilute nitride epiwafers may depend on the relative maturity of the competing nitrogen source technologies. A large-area plasma

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source for growth across a multiwafer platen has been developed for the production MBE growth of dilute nitrides [47]. The cross-wafer wavelength variation was 13 nm before post-growth annealing for a 1.29 mm wavelength GaInNAs composition. A high purity, efficiently incorporating alkyl source of nitrogen would be of significant benefit to production MOVPE since, in general, the MOVPE of dilute nitrides has required very high nitrogen precursor flows. If the cost of the nitrogen alkyl were to make dilute nitride MOVPE uneconomical and the uniformity of large-area plasma sources were unacceptable, there might be an opportunity for the large-scale CBE process, using all alkyl and hydride precursors.

3.8. CONCLUSIONS

We have seen that dilute nitride alloys may be grown by CBE/MOMBE and we have highlighted those reports which demonstrate both the existing level of achievement and the potential for further development. It is clear that significant progress has been made, in spite of the much smaller number of research groups involved in the development of CBE compared with those involved in MBE/MOVPE. Perhaps the advantages of the CBE technique itself go some way towards explaining the relatively quick progress. Undoubtedly, the reproducible and responsive control of the Group V fluxes is essential in the growth of dilute nitride devices. Photoluminescence at 1.55 mm has been demonstrated in QWs of GaInNAs, crucially, without the need for the incorporation of Sb and without strain-reducing barriers. Edgeemitting lasers and VCSELs operating near and beyond 1.3 mm have been demonstrated with comparable performance to MBE- and MOVPE-grown devices.

ACKNOWLEDGEMENTS

This work was supported by Technology Group 7 of the Corporate Research Programme of the UK Ministry of Defence.

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[3] Kondow, M., Uomi, K., Kitatani, T., Watahiki, S. & Yazawa, Y. (1996) Extremely large N content (up to 10%) in GaNAs grown by gas-source molecular beam epitaxy. J. Cryst. Growth, 164, 175–179. [4] Uesugi, K. & Suemune, I. (1997) Band gap energy of GaNAs alloys grown on (001) GaAs by metalorganic molecular beam epitaxy. Jpn. J. Appl. Phys., 36, L1572– L1575. [5] Hjalmarson, H.P., Vogl, P., Wolford, D.J. & Dow, J.D. (1980) Theory of substitutional deep traps in covalent semiconductors. Phys. Rev. Lett., 44, 810. [6] Friedman, D.J., Geisz, J.F., Kurtz, S.R. & Olson, J.M. (1998) 1-eV solar cells with GaInNAs active layer. J. Cryst. Growth, 195, 409– 415. [7] Ha, W., Gambin, V., Wistey, M., Yuen, H., Kim, S. & Harris, J., Jr. (2002) Long wavelength GaInNAs(Sb) lasers on GaAs, Proceedings of the 14th Indium Phosphide and Related Materials Conference, May 12– 16, Stockholm, Sweden, ISSN 1092-8669, pp. 381– 384. [8] Johnson, A.D., Bennett, R.H., Newey, J., Pryce, G.J., Williams, G.M., Burke, T.M., Jones, J.C. & Keir, A.M. (2000) InNxSb12x light emitting diodes grown by MBE. Mater. Res. Soc. Symp. Proc., 607, 28. [9] Ashley, T., Burke, T.M., Pryce, G.J., Adams, A.R., Andreev, A., Murdin, B.N., O’Reilly, E.P. & Pidgeon, C.R. (2003) InSb(12x)Nx growth and devices. Solid-State Electron., 47, 387– 394. [10] Welty, R.J., Xin, H., Tu, C.W. & Asbeck, P.M. (2004) Minority carrier transport properties of GaInNAs heterojunction bipolar transistors with 2% nitrogen. J. Appl. Phys., 95 (1), 327–333. [11] Abernathy, C.R. (1993) Growth of III –V materials by metalorganic molecular beam epitaxy. J. Vac. Sci. Technol. A, 11 (4), 869– 875. [12] Yang, L., Sudbo, A.S., Tsang, W.T., Garbinski, P.A. & Camarda, R.M. (1990) Monolithically integrated InGaAs/InP MSM-FET photoreceiver prepared by chemical beam epitaxy. IEEE Photon. Technol. Lett., 2 (1), 59 – 62. [13] Balmer, R.S., Martin, T., Kane, M.J., Maclean, J.O., Whitaker, T.J., Ayling, S.G., Calcott, P.D.J., Houlton, M., Newey, J.P. & O’Mahoney, S.J. (2000) Integrated laser/waveguide by shadow-masked selective area epitaxy using chemical beam epitaxy. J. Cryst. Growth, 209, 486– 491. [14] Balmer, R.S., Heaton, J.M., Maclean, J.O., Ayling, S.G., Newey, J.P., Houlton, M., Calcott, P.D.J., Wight, D.R. & Martin, T. (2003) Vertically tapered epilayers for low-loss waveguide/ fiber coupling achieved in a single epitaxial growth run. J. Lightwave Technol., 21 (1), 211– 217. [15] Odnoblyudov, V.A., Yu Egorov, A., Kovsh, A.R., Zhukov, A.E., Maleev, N.A., Semenova, E.S. & Usitnov, V.M. (2001) Thermodynamic analysis of the MBE growth of GaInAsN. Semicond. Sci. Technol., 16, 831– 835. [16] Fischer, M., Reinhardt, M. & Forchel, A. (2000) GaInNAs/GaAs laser diodes operating at 1.52 microns. Electron. Lett., 36 (14), 1208– 1209. [17] Weinstein, B.A., Stambach, S.R., Ritter, T.M., Maclean, J.O. & Wallis, D.J. (2003) Evidence for selective delocalisation of N-pair states in dilute GaAs(12x)Nx. Phys. Rev. B, 68, 035336. [18] Maclean, J.O., Wallis, D.J., Martin, T., Houlton, M.R. & Simons, A.J. (2001) Nitrogen incorporation into GaAs(N), AlGaAs(N) and InGaAs(N) by chemical beam epitaxy (CBE) using 1,1-dimethylhydrazine. J. Cryst. Growth, 231 (1 – 2), 31– 40. [19] Kent, P.R.C. & Zunger, A. (2001) Evolution of III – V nitride alloy electronic structure: the localised to delocalised transition. Phys. Rev. Lett., 86, 2613– 2616. [20] Moorooka, N., Uesugi, K. & Suemune, I. (1999) Role of indium on nitrogen incorporation in GaNAs grown by metalorganic molecular beam epitaxy. Jpn. J. Appl. Phys., 38 (11B), L1309 – L1311. Pt 2.

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[21] Zhou, W., Uesugi, K. & Suemune, I. (2003) 1.55 micron emission from GaInNAs with indiuminduced increase of N concentration. Appl. Phys. Lett., 83 (10), 1992– 1994. [22] Miyamoto, T., Takeuchi, K., Kageyama, T., Koyama, F. & Iga, K. (1999) Chemical beam epitaxy of GaInNAs/GaAs quantum wells and its optical absorption property. J. Cryst. Growth, 197, 67 – 72. [23] Kageyama, T., Miyamoto, T., Makino, S., Koyama, F. & Iga, K. (2000) Optical quality of GaNAs and GaInNAs and its dependence on RF cell condition in chemical beam epitaxy. J. Cryst. Growth, 209, 350– 354. [24] Makino, S., Miyamoto, T., Kageyama, T., Ikenaga, Y., Arai, M., Koyama, F. & Iga, K. (2001) Composition dependence of thermal annealing effect on 1.3 micron GaInNAs/ GaAs QW lasers grown by chemical beam epitaxy. Jpn. J. Appl. Phys., 40 (11B), L1211– L1213. Pt 2. [25] Kitatani, T., Kondow, M. & Tanaka, T. (2000) Effects of thermal annealing procedure and a strained intermediate layer on a highly-strained GaInNAs/GaAs double-quantum-well structure. J. Cryst. Growth, 221, 491– 495. [26] Hamm, R.A., Chandrasekhar, S., Lunardi, L. & Geva, M. (1995) Characteristics of carbondoped InGaAs using carbontetrabromide by metalorganic molecular beam epitaxy. J. Cryst. Growth, 148 (1). [27] Weyers, M., Musolf, J., Marx, D., Kohl, A. & Balk, P. (1990) Gaseous dopant sources in MOMBE/CBE. J. Cryst. Growth, 105, 383–392. [28] Abernathy, C.R., Pearton, S.J., Ren, F. & Wisk, P.W. (1993) Growth of InN for ohmic contact formation by electron cyclotron resonance metalorganic molecular-beam epitaxy. J. Vac. Sci. Technol. B, 11 (2), 179– 182. [29] Uesugi, K. & Suemune, I. (2001) Highly conductive GaAsNSe alloys grown on GaAs and their nonalloyed ohmic properties. Appl. Phys. Lett., 79 (20), 3284– 3286. [30] Leys, M.R., Buda, M., Silov, A.Yu., Vonk, H. & Wolter, J.H. (2000) Growth of InGaAsN/InP structures by chemical beam epitaxy, Proceedings of IEEE/LEOS Symposium, Benelux Chapter, Delft, pp. 203– 206. [31] Uesugi, K. & Suemune, I. (2003) Metalorganic molecular-beam epitaxy and characterisation of GaAsNSe/GaAs superlattices emitting around 1.5 mm wavelength. Appl. Phys. Lett., 82 (6), 898– 900. [32] Miyamoto, T., Takeuchi, K., Kageyama, T., Koyama, F. & Iga, K. (1999) Chemical beam epitaxy of GaInNAs/GaAs quantum wells and its optical absorption property. J. Cryst. Growth, 197, 67 – 72. [33] Shi, B.Q., Kondow, M. & Tu, C.W. (2000) Chemical beam epitaxy of AlAs using novel groupV precursors. J. Cryst. Growth, 216, 80 – 86. [34] Maclean, J.O., Martin, T., Houlton, M., Calcott, P.D.J., Ayling, S.G., Rushworth, S.A. & Smith, L.M. (2002) Quantitative comparison of trimethylindium sources and assessment of their suitability for low threshold 980 nm InGaAs/GaAs lasers grown by chemical beam epitaxy. Appl. Phys. Lett., 80 (6), 914– 916. [35] Maclean, J.O., Simons, A.J., Houlton, M.R., Martin, T. & Birbeck, J. (2002) Calibration of SIMS measurements of unintentional oxygen concentrations in Al0.3Ga0.7NxAs(12x) and assessment of the purity of dimethylhydrazine, Proceedings of Indium Phosphide and Related Materials, Stockholm, Sweden, ISSN 1092-8669, pp. 261– 263. [36] Kageyama, T., Miyamoto, T., Makino, S., Nishiyama, N., Koyama, F. & Iga, K. (2000) High temperature operation up to 1708C of GaInNAs – GaAs quantum-well lasers grown by chemical beam epitaxy. IEEE Photon. Technol. Lett., 12 (1), 10 – 12.

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[37] Ikenaga, Y., Miyamoto, T., Makino, S., Kageyama, T., Arai, M., Koyama, F. & Iga, K. (2002) 1.4 micron GaInNAs/GaAs quantum well laser grown by chemical beam epitaxy. Jpn. J. Appl. Phys., 41 (2A), 664– 665. Pt 1. [38] Makino, S., Miyamoto, T., Kageyama, T., Nishiyama, N., Koyama, F. & Iga, K. (2000) GaInNAs/GaAs quantum dots grown by chemical beam epitaxy. J. Cryst. Growth, 221, 561– 565. [39] Kaiander, I.N., Sellin, R.L., Kettler, T., Ledentsov, N.N., Bimberg, D., Zakharov, N.D. & Werner, P. (2004) 1.24 micron InGaAs/GaAs quantum dot laser grown by metalorganic chemical vapour deposition using tertiarybutylarsine. Appl. Phys. Lett., 84 (16), 2992– 2994. [40] Makino, S., Miyamoto, T., Ohta, M., Kageyama, T., Ikenaga, Y., Koyama, F. & Iga, K. (2003) Growth characteristics of GaInNAs/GaAs quantum dots by chemical beam epitaxy. J. Cryst. Growth, 251, 372– 377. [41] Choulis, S.A., Hosea, T.J.C., Klar, P.J., Hofmann, M. & Stolz, W. (2001) Influence of varying N-environments on the properties of (GaIn)(NAs) vertical-cavity surface-emitting lasers. Appl. Phys. Lett., 79 (26), 4277– 4279. [42] Kageyama, T., Miyamoto, T., Makino, S., Ikenaga, Y., Nishiyama, N., Matsutani, A., Koyama, F. & Iga, K. (2001) Room temperature continuous wave operation of GaInNAs/GaAs VCSEL’s grown by chemical beam epitaxy with output power exceeding 1 mW. Electron. Lett., 37 (4), 225– 226. [43] Choquette, K.D., Klem, J.F., Fischer, A.J., Allerman, A.A., Fritz, I.J., Kurtz, S.R., Breiland, W.G., Sieg, R., Geib, K.M., Scott, J.W. & Naone, R.L. (2000) Room temperature continuous wave InGaAsN quantum well vertical cavity lasers emitting at 1.3 microns. Electron. Lett., 36 (16), 1388– 1390. [44] Freundlich, A., Newman, F., Vilela, M.F., Monier, C., Aguilar, L. & Street, S. (2000) Development of GaAs space solar cells by high growth rate MOMBE/CBE. J. Cryst. Growth, 209, 481–485. [45] Benchimol, J.L., Juhel, M., Petitjean, M. & Ancillotti, M. (1995) High growth rate of III –V compounds by free carrier gas chemical beam epitaxy. J. Vac. Sci. Technol., B13, 55. [46] Koch, T.L., Corvini, P.J., Koren, U. & Tsang, W.T. (1988) Wavelength uniformity of 1.3 mm GaInAsP/InP distributed Bragg reflector lasers with hybrid beam/vapour epitaxial growth. Electron. Lett., 24 (13), 822– 824. [47] Malis, O., Liu, W.K., Gmachl, C., Fastenau, J.M., Joel, A., Gong, P., Bland, S.W. & Moshegov, N. (2003) MBE development of dilute nitrides for commercial long-wavelength laser applications. J. Cryst. Growth, 251, 432– 436.

Dilute Nitride Semiconductors M. Henini (Ed.) q 2005 Elsevier Ltd. All rights reserved.

Chapter 4

MOMBE Growth and Characterization of III –V-N Compounds and Application to InAs Quantum Dots Ikuo Suemune, Katsuhiro Uesugi and Sasikala Ganapathy Research Institute for Electronic Science, Hokkaido University, Sapporo, Japan

ABSTRACT

This chapter deals with mainly two topics. One is the metalorganic molecular-beam epitaxy (MOMBE) of III –V-N compounds such as GaAsN, GaInNAs, and GaAsNSe. The relation of the In and N incorporations is known to depend on the growth techniques and this topic will be discussed to give some unified understanding. The other is the discussion on the more general physics-oriented special features of III –VN compounds such as the temperature dependence of the GaAsN energy gap and the strain compensation of InAs quantum dots by combining with GaAsN. 4.1. INTRODUCTION

III –V-N compounds such as GaAsN were found to have extremely large band gap bowing [1]. This gave us a breakthrough to realize long-wavelength semiconductor lasers on GaAs substrates [2], which can introduce higher potential barriers to confine carriers to active layers and to prevent current overflow in comparison to commercial InGaAsP semiconductor lasers. Metalorganic vapor-phase epitaxy (MOVPE) has been the major mass-production technique of semiconductor lasers. However, it has not been an easy task to realize III– V-N-based semiconductor lasers with the wavelength longer than 1.3 mm by MOVPE [3]. Metalorganic molecular-beam epitaxy (MOMBE) dealt with in this chapter can employ precursors, in principle, common with those used in MOVPE. The only difference is the absence of the carrier gas and the higher vacuum in MOMBE and this makes it possible to utilize equipments for in situ monitoring the surface reactions. The information thus acquired with MOMBE can be transferred to MOVPE to solve the problems for the mass production of the III –V-N-based semiconductor lasers. In this chapter, MOMBE growth of GaAsN [4], GaInNAs [5], and GaAsNSe [6] alloys is discussed. The nitrogen (N) concentration in GaAsN was estimated from X-ray 137

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diffraction (XRD) measurements and the detailed discussion on how to evaluate and eliminate the strain effect is given [7]. The observation of the reduced temperature dependence of the GaAsN energy gap [8] is discussed with the band anti-crossing (BAC) model [9]. The growth of GaInNAs and GaAsNSe alloys showed mutual interactions between In –N and N – Se, respectively, which enhanced N incorporation. This made it possible to realize the long-wavelength emission of 1.55 mm in both the alloys. GaAsN alloys grown on GaAs substrates are under tensile strain because of the smaller atomic radius of N atoms. The combination of the tensile-strained GaAsN with compressively strained InAs quantum dots (QDs) grown on GaAs substrates is shown to be effective to realize long-wavelength emission up to 1.55 mm with higher radiative quantum efficiencies [10]. It is shown that the overall strain compensation is important to improve the quantum efficiencies in both the GaAsNSe [11] and InAs QDs [12] cases.

4.2. MOMBE GROWTH AND CHARACTERIZATION OF GaAsN

In this section, growth and structural characterization of GaAsN are discussed. The relation of the N concentration and the energy gap is examined precisely. The observation of the reduced temperature dependence of GaAsN energy gaps and the related physics is discussed with the BAC model. 4.2.1 MOMBE Growth Method GaAs (001) substrates were inserted into a vacuum chamber and were thermally cleaned at the substrate temperature of 6008C with the simultaneous supply of tris-dimethylaminoarsenic (TDMAAs). All the metalorganic precursors used in the present MOMBE were supplied without any carrier gas and without thermal cracking. TDMAAs has the capability to remove surface oxides and the clear As-stabilized 2 £ 4 pattern was observed with reflection high-energy electron diffraction (RHEED) after cleaning. A thin GaAs buffer layer was grown at the same temperature by supplying triethylgallium (TEGa) and TDMAAs. GaAsN layers were grown at the temperature range of 540– 6008C with the additional supply of monomethylhydrazine (MMHy). The N concentrations in the grown GaAsN layers were reduced for the higher growth temperature due to the higher desorption rate of the N precursors from the growth surfaces. 4.2.2 N Incorporation and Lattice Relaxation The N concentrations in the grown GaAsN layers were estimated with XRD measurements of the lattice parameters. It is well known that coherently strained layers generally exhibit different lattice parameters perpendicular ða’ Þ and parallel ðak Þ to the surfaces. The first assumption to examine these lattice parameters is the coherent growth of the layers. This examination is possible with the measurement of asymmetric reflection such as (115). The angle c between the (001) plane and the (115) plane is

MOMBE Growth and Characterization of III –V-N Compounds

139

pffiffi given by c ¼ tan21 ð 2a’ =5ak Þ [7]. Therefore, the angle c is different between the GaAs substrate (115) plane and the coherently strained GaAsN layer (115) plane and the difference is given by pffiffi pffiffi Dc ¼ tan21 ð 2=5Þ 2 tan21 ð 2a’ =5ak Þ: ð4:1Þ To examine this deviation of the (115) reflection planes, a ð2u 2 uÞ vs. u offset angle ðDvÞ mapping around the (115) diffraction peaks was measured on GaAsN/GaAs samples. One example is shown in Figure 4.1. The Dv separation of the GaAsN and GaAs (115) diffraction peaks corresponds to the tilt angle Dc and was 0.0488 in this case. From the Bragg angle of the GaAsN (115) peak shown in Figure 4.1, the lattice spacing ˚ . Similarly from the Bragg of the GaAsN (115) plane d115 is estimated to be 1.0848 A angle of the GaAsN (004) peak with a separate measurement, a’ for the GaAsN layer is ˚ . The lattice parameters are related in the following form: estimated to be 5.6356 A 2 1=d115 ¼ 2=a2k þ 25=a2’ :

ð4:2Þ

˚ in this case. This is in good The lattice parameter ak is calculated to be 5.6517 A agreement with the lattice constant of GaAs and this shows that the GaAsN layer is coherently grown on the GaAs substrate. The elastic deformation of the grown layers is expressed by a’ ¼ ak þ ½ðC11 þ 2C12 Þ=C11 ða0 2 ak Þ;

ð4:3Þ

where C11 and C12 are the elastic constants of GaAsN layers, which will be given by the interpolation of the values for GaAs and cubic GaN [13]. The N concentration x is estimated from the lattice constant a0 of the cubic GaAsN assuming Vegard’s law, a0 ¼ xaGaN þ ð1 2 xÞaGaAs ;

ð4:4Þ

Figure 4.1. Two-dimensional mapping of X-ray diffraction to demonstrate lattice distortion of (115) reflection plane.

140

Dilute Nitride Semiconductors

Figure 4.2. (a) Measured lattice parameters parallel and perpendicular to the surface. (b) Estimated variation of the angle c between (001) and (115) planes with lattice strain.

˚ . The estimated lattice where aGaN is the lattice constant of cubic GaN and is given by 4.50 A parameters a’ and ak as well as the tilt angle Dc were plotted in Figure 4.2 for several GaAsN samples against the N concentration. The solid lines are for the coherently strained case calculated from Eq. (4.3) and the measured samples are shown to satisfy this condition. It will be useful to show how such coherent growth conditions are satisfied for the grown layer thicknesses. The results are summarized in Figure 4.3. The filled circles are

104 Coherent Partially relaxed Calculated

Layer Thickness (nm)

36% 10%

44%

103

38%

102

GaAsN on GaAs 101 0

1

2

3

4

5

Nitrogen Concentration in GaAsN (%) Figure 4.3. Measured N concentration dependence of the lattice relaxation and the comparison with the calculated critical thickness.

MOMBE Growth and Characterization of III –V-N Compounds

141

the samples which follow the above-discussed coherent growth condition. The partial lattice relaxation is quantified by defining the following relaxation ratio of the lattice parameters parallel to GaAs substrate surfaces, R ¼ ðak 2 aGaAs Þ=ða0 2 aGaAs Þ; and the numerical values are given in Figure 4.3. The solid line is the critical thickness calculated with the Matthews and Blakeslee model [14]. The experimentally observed critical thicknesses for lattice relaxation are slightly thicker than the model calculation. 4.2.3 N Concentration Dependence of GaAsN Energy Gap In addition to the above examination of the N concentration in the GaAsN samples, the band gap energies of GaAsN layers were estimated with Fourier-transform absorption spectroscopy measurements at 300 K. The measured N concentration dependence of the band gap energy is shown by the filled circles in Figure 4.4. All of these samples were coherently grown on (001) GaAs substrates. Almost all the other reports [1,15,16] align on the same line except for those grown on GaP substrates [17]. The dielectric model calculation [18] can fit the measurements below the N concentration of , 1%, but the deviation becomes more and more serious with the increase of the N concentrations. The first-principle supercell model calculation [19] shows the large substrate dependence, but the agreement with the measurements is still moderate. This will be due to the problem of how to depict the random distribution of the N atoms in GaAsN alloys. In addition to the large band gap bowing in GaAsN, additional excited states in the higher energy were observed and were blue-shifted for the higher N concentrations [20,21]. This additional feature as well as the band gap bowing was successfully explained with a simple phenomenological model, the so-called BAC model [20]. This model considers the interaction of the extended conduction-band state with localized N states. When the extended state in the conduction band and the N localized state are given with

Figure 4.4. Relation of N concentration in GaAsN and energy gap.

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Dilute Nitride Semiconductors

the energies of EM and EN ; respectively, the coupling between the two states is described by the following matrix equation:    E 2 EM VMN   ð4:5Þ  ¼ 0:   V E 2 EN  MN VMN is the matrix element describing the coupling effect. Under the assumption of low N concentrations in the group-V sublattice sites, VMN is given by CMN x1=2 ; where CMN is the constant and x is the N concentration in the III– V-N alloy. By solving this equation, the subband energies are given by E^ ¼

2 EN þ EM ^ ½ðEN 2 EM Þ2 þ 4VMN 1=2 ; 2

ð4:6Þ

where Eþ and E2 correspond to the excited and ground states in the III –V-N alloy. The fitting parameters in this model are limited to two, that is, EN and CMN ; which were determined as EN ¼ EM þ 0:23 eV ¼ 1:65 eV and CMN ¼ 2:5 eV for GaAsN with additional pressure dependence measurements [20]. Figure 4.5 summarizes the reported N concentration dependence of the ground state and the excited states [7,20,21]. The solid lines are the Eþ and E2 state energies calculated from Eq. (4.6). The nice fits for both states will be evident in Figure 4.5. Following this BAC model, the large band gap bowing in GaAsN is interpreted to be the increase of the energy repulsion of the coupled states

2.1 2 1.9

Energy (eV)

1.8 1.7

Calculated

1.6

W. Walukiewicz etal

1.5

J.D. Perkins etal

Measured at RT

1.4 1.3 1.2 1.1 1 0.9 0

1

2

3

4

5

N Concentration in GaAsN (%) Figure 4.5. Measured excited and ground states in GaAsN and the fits with the band anti-crossing model.

MOMBE Growth and Characterization of III –V-N Compounds

143

when the coupling between the conduction-band extended state and the N localized state is enhanced with the increase of the N concentration. 4.2.4 Reduced Temperature Dependence of GaAsN Energy Gap Increase of the information communication traffic demands more and more communication capacities in optical-fiber communication networks, and wavelength-division multiplexing with higher communication capacities is being developed. Higher temperature stability of the lasing wavelengths in long-wavelength semiconductor laser sources is a highly requested feature for such an application. From the viewpoint of materials, the main factor responsible for the temperature variation of the emission wavelength is the temperature dependence of the semiconductor energy gap. In this relation, the temperature dependence of the absorption edge in GaAsN was found substantially reduced with the increase of the N concentration [8]. The results are summarized in Figure 4.6 and the measured temperature dependence of the absorption edge for several samples is shown by the open circles. Comparison of the GaAs data with the other GaAsN data will clearly show that the temperature dependence of the absorption edge energy is reduced in GaAsN alloys.

1.6 Calculated GaAs

Measured

1.5

Absorption Edge (eV)

GaAsN 1.4 N=0.34% 1.3 N=1.22% 1.2 N=2.7% 1.1 N=3.76% 1 0

50

100

150

200

250

300

Temperature (K) Figure 4.6. Fit of the measured temperature dependence of GaAsN energy gap with band anti-crossing model.

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Dilute Nitride Semiconductors

This special feature of the GaAsN alloys was analyzed with the BAC model. The modification of the model given in Section 4.2.3 is only to introduce the temperature dependence of the GaAs energy gap, which is given by the well-known Varshni relation: Eg ðTÞ ¼ 1:512 2 aT 2 =ðT þ bÞ ; EM ðTÞ;

ð4:7Þ

where the constants a and b are fitted as a ¼ 5:6 £ 1024 eV/K and b ¼ 146 K [8]. The other fitting parameters were left unchanged, i.e. EN ¼ 1:65 eV and CMN ¼ 2:5 eV: The study of pressure-induced change of GaInNAs fundamental band gaps showed that the pressure dependence of the N localized state was one order of magnitude weaker than that of GaInAs conduction-band edge [20]. This was attributed to the localized nature of the N state. Based on this information on the stability of the N localized state, the temperatureindependent constant energy level was assumed for the N state. The measurements of the absorption edge shown in Figure 4.6 for GaAs and the GaAsN samples with the N concentrations of 0.34, 1.22, 2.7 and 3.76% were compared with the BAC model calculations. The solid lines are the lower-band E2 state energies calculated for each case. The overall temperature dependences are well reproduced with the BAC model. To clarify the temperature dependence more quantitatively, the measured energy differences between 24 and 297 K were plotted against the N concentration in GaAsN and are plotted in Figure 4.7. The solid line is the BAC model calculation and gives a reasonable fit to the measurements. This shows that the temperature dependence of

Energy Difference ( 24K and 297K) (meV)

120 GaAsN 100 80 60 40 Calculated

20

Measured 0 0

1 2 3 N Concentration in GaAsN (%)

4

Figure 4.7. Temperature-induced energy gap change between 24 and 297 K and comparison with band anticrossing model calculation.

MOMBE Growth and Characterization of III –V-N Compounds

145

the band gap energy is reduced up to 40% of that in GaAs with the increase of the N concentration in GaAsN. 4.3. RELATION OF In AND N INCORPORATIONS IN THE GROWTH OF GaInNAs

In this section, the growth issue of GaInNAs quaternary alloys is discussed. Especially, the growth technique dependence of the In and N incorporations in GaInNAs will be summarized and the physical origin of this dependence will be discussed. It is shown that the enhanced N incorporation in GaInNAs with MOMBE makes it possible to realize 1.55-mm wavelength emission from GaInNAs-based heterostructures. 4.3.1 Observations of In and N Correlations in the Growth of GaInNAs GaInNAs alloys are capable of lattice matching to GaAs substrates and have been the main alloy semiconductors for the development of long-wavelength semiconductor lasers on GaAs substrates. GaInNAs has been grown by solid-source molecular-beam epitaxy (MBE) with N radical sources for the N incorporation. With this MBE technique, N concentrations are reported to be not affected by the In incorporation [22]. However, in MOVPE of GaInNAs, the increase of the In concentration is reported to reduce the N incorporation [23]. This problem in MOVPE has made it difficult to realize GaInNAsbased semiconductor lasers with the emission wavelength longer than 1.3 mm with MOVPE. In the present MOMBE, the opposite trend between In and N incorporations was observed. After the description of the MOMBE growth of GaInNAs and the related findings, the growth technique dependence will be discussed. 4.3.2 Observation of Enhanced N Incorporation with In Supply in MOMBE The role of In on the surface kinetics or the effect of the In segregation during the growth of GaAsN was studied with 30-s growth interruptions every 50-nm-thick growth of GaAsN [24]. Two sequences were compared at the substrate temperature of 5758C: One is with 5-s triethyl indium (TEIn) supply after every growth interruptions and before the growth of GaAsN. Therefore, In will be present on the growth surfaces during the GaAsN growth. The other is essentially the same sequence but without any TEIn supply. The GaAsN sample grown following the latter sequence showed the N concentration of 1.36%, while it was increased up to 4.37% in the GaAsN sample grown with the former sequence. The In incorporation in the grown layer during the former growth sequence was estimated following the former growth sequence but without the MMHy supply, which resulted in the remaining In concentration of 0.68%. This very low In concentration in the GaAsN layer will be too low to account for the increase of the N concentration from 1.36 to 4.37% with the In – N “bulk” effect, and this enhancement of the N incorporation will be attributed to In-oriented surface-kinetics-based phenomenon.

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Dilute Nitride Semiconductors

To confirm the enhancement of the N incorporation with the supply of TEIn on the growing surface, the relation of the In and N concentrations in the grown GaInNAs layers was quantitatively studied. GaInNAs/GaAs multiple quantum well (MQW) structures were adopted to keep the coherent growth condition, which will be more readily satisfied by reducing each layer thickness against the variation of the In and N concentrations in each layer. The lattice constants of Ga12yInyNxAs12x layers were measured following the method described in Section 4.2.2, which are expressed as aGaInNAs ¼ ð1 2 xÞð1 2 yÞaGaAs þ ð1 2 xÞyaInAs þ xð1 2 yÞaGaN þ xyaInN ;

ð4:8Þ

where the lattice constants of cubic GaN and InN, GaAs, and InAs are given as 4.50, 4.98, ˚ , respectively [13]. 5.65325, and 6.0583 A GaInNAs/GaAs MQW structures were grown at 5208C by keeping the supplies of TEGa, TDMAAs, and MMHy constant at 1 £ 1024, 1 £ 1023, and 3.2 £ 1023 Torr, respectively, and by changing the TEIn supply in the range of 0 –1.15 £ 1024 Torr. The GaInNAs well layer thicknesses were in the range of 6.8 –7.2 nm, which were estimated from the XRD superlattice (SL) satellite peaks. Photoluminescence (PL) spectra were measured on the series of MQW samples and the observed PL peaks are plotted with the filled circles in Figure 4.8. In spite of the constant MMHy supply, the substantial red shift of the PL peaks was observed with the increase of the TEIn supply, which will not be 1.1

Photon Energy (eV)

1.05 1 0.95 0.9

GaInNAs/GaAs MQW Measured

0.85 0.8 0.75 0.2

Calc. Model II (In fixed to GaInAs case) Calc Model I (N fixed to GaNAs case)

0.4

0.6

0.8

1

1.2

TEIn B. E. Pressure (x10−4 Torr) Figure 4.8. Enhanced red shift of the emission wavelength observed from GaInNAs alloy with the increase of TEIn precursor supply under the simultaneous constant MMHy supply. Two model calculations were compared to the measurements.

MOMBE Growth and Characterization of III –V-N Compounds

147

0.06 GaInNAs/GaAs MQW N Concentration in GaInNAs

0.055

Estimated Fitted

0.05 y(N) = y0+A*exp(B*x(In)) y0 = 0.03

0.045

A = 0.002 B = 12

0.04 0.035 0.03 0

0.05 0.1 0.15 0.2 In Concentration in GaInNAs

0.25

Figure 4.9. Relation of the In and N concentrations in the GaInNAs alloys studied in Figure 4.8.

accounted for only by the increase of the In concentration and suggests the increase of the N concentration. The energy gap of the GaInNAs alloy is calculated by replacing EM for GaAs in Eq. (4.6) with EM ðyÞ for Ga12yInyAs. With the additional information on band offsets and the effective masses [5], the transition energies in the GaInNAs/GaAs MQW can be calculated. In these calculations, both Eqs. (4.6) and (4.8) depend only on the N and In concentrations, x and y, respectively. Therefore, the x and y values will be uniquely determined self-consistently with numerical calculations. A simpler calculation method will be to assume two extreme cases: One is to assume the N concentration in the GaInNAs alloy to be fixed to that of the GaNAs case grown without the TEIn supply, which will be designated as Model I. The other is to assume the In concentration of the GaInNAs alloy the same as that of GaInAs grown without the MMHy supply, designated as Model II. The comparison of the two models in Figure 4.8 clearly shows that the Model II gives a nice fit to the measurements, that is, the In concentration is not influenced by the presence of N and the N incorporation is enhanced by the presence of In on the growing surfaces. Based on this finding, the relation of the N and In concentrations in the GaInNAs alloys was determined as shown in Figure 4.9. The solid line is the fit to the measurements shown by the filled circles, and the N concentration was found to increase exponentially with the increase of the In concentration. 4.3.3 Discussion on the Relation of In and N Incorporation in GaInNAs Concerning the relation of the In and N incorporations in GaInNAs alloys, one may argue the difference of the bond strengths, that is, more stable Ga – N bonds relative to In – N

148

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ones. This viewpoint may lead to the discussion that the In coverage of the growing surface will prevent the formation of stable Ga – N bonds and therefore enhance N desorption [23]. However, the strain consideration completely changes the viewpoint: Kim and Zunger showed with finite-temperature Monte Carlo simulation that In –N and Ga – As bonds are more preferable to reduce the strain in GaInNAs alloy system [25]. This may explain the change of atomic configurations from N –Ga4 to NInGa3 in GaInNAs, i.e. the change from N –Ga bonds to N – In bonds after thermal annealing, which was observed with the Fourier-transform infrared spectrum measurements [26]. The strain issue is also involved in the surface processes. Zhang and Zunger theoretically explained the reason why the N solubility in III –V is much larger than that expected under the thermal equilibrium. They showed that surface reconstructions enhance the solubility of N so that the sub-surface compressive strain induced with the surface reconstructions is reduced by the incorporation of N atoms with smaller atomic radii [27]. The enhanced N incorporation observed with the In supply in MOMBE discussed in Section 4.3.2 will be reasonable if we follow these strain-based considerations. In MOVPE growth of GaInNAs, where the decrease of the N concentration for the increase of the In concentration was observed, AsH3 has been used for the As source in most cases [23,28]. This suggests the influence of hydrogen on the reduced N incorporation. The MOMBE growth discussed in this chapter employs TDMAAs, which does not have the direct As – H bonds. MOVPE growth of GaInNAs with tertiarybutylarsine (TBA) exhibited more complex behavior concerning the In – N relations [29]. Therefore, concerning the problem with MOVPE, the AsH3 source will most probably be attributed as the main factor. It is noted that the N source, MMHy, used in the MOMBE or dimethylhydrazine (DMHy) more frequently used in MOVPE also has the direct N –H bonds in the precursors. However, it was shown with thermodynamical calculations that the chemical reactivity of H in hydrazine is much lower than that of NH3 [30]. This suggests that H in MMHy does not change the essential point of the present discussions.

4.4. GROWTH AND CHARACTERIZATION OF GaAsNSe NEW ALLOY

Through donor doping studies in GaAsN, a new GaAsNSe alloy was found [6]. This is an alloy of GaAsN and Ga2Se3 in the zinc blende structure [31]. This GaAsNSe alloy showed very high electron concentration up to , 1020 cm23 and this made nonalloyed ohmic contacts possible [32]. The N incorporation in this alloy was enhanced with the increase of the Se concentration and the long-wavelength emission at 1.55 mm or beyond was easily observed [6]. The characteristic feature of its luminescence is the broad spectrum covering the whole optical-fiber communication wavelengths from 1.3 to 1.6 mm. Luminescence intensities observed from earlier GaAsNSe/GaAs SL were quenched above

MOMBE Growth and Characterization of III –V-N Compounds

149

200 K. However, the strain compensation by sandwiching the tensile-strained GaAsNSe/ GaAs SL with slightly compressively strained GaAsN/GaAsSb SLs dramatically improved the luminescence efficiency at room temperature, and the integrated PL intensity at room temperature remained , 20% of that observed at low temperature [11]. This broad-band luminescence covering the whole optical-fiber communication wavelength as well as the high luminescence efficiency may find some new applications for optical-fiber communications.

4.5. APPLICATION OF GaAsN TO InAs QUANTUM DOTS

III –V-N compound semiconductors opened the capability to realize long-wavelength MQW semiconductor lasers with higher temperature stability on GaAs substrates. Laser performances will be improved further with the introduction of QD structures in the wavelength range of 1.3 and 1.55 mm. QDs most extensively studied so far are InAs QDs self-assembled with the Stranski – Krastanow (SK) growth mode. This naturally induces residual compressive strains inside the QDs. In case InAs QDs are not buried, these compressive strains inside the QDs are relieved and the long-wavelength emission up to 1.5 mm is possible [33]. However, burying these QDs to increase radiative-emission quantum efficiencies for practical applications tends to accumulate the net compressive strain and the resultant blue shift of the emission wavelength makes it difficult to apply to optical-fiber communication systems. It will be shown that burying InAs QDs with tensilestrained III – V-N compounds such as GaAsN can solve these problems and is shown to be effective to improve luminescence quantum efficiencies. 4.5.1 Growth of InAs Quantum Dots InAs QDs were grown on (001) GaAs substrates by MOMBE. The precursors used are the same as described in the previous sections. After oxide desorption from GaAs substrate surfaces, 100-nm-thick GaAs buffer layers were grown at 5508C. The substrate temperature was then lowered to 4008C and 2.0 monolayers (ML) of InAs were deposited with a pulsed supply of TEIn together with continuous supply of TDMAAs at a growth rate of 0.1 ML/s. In situ RHEED observation showed the transition from the twodimensional to three-dimensional growth mode, which confirms the Stranski –Krastanow growth mode. After the growth of the first stack of InAs QDs, a 10-nm-thick GaAsN layer with a different N concentration was grown at the same temperature. A 10-nm-thick GaAs buffer layer was additionally grown for the growth of the next stack of InAs QDs. The N concentrations in the GaAsN layers were estimated with the procedure described in Section 4.2.2. Figure 4.10 shows the 500 nm £ 500 nm atomic force microscope (AFM) image of the self-assembled InAs QDs grown on a GaAs (001) substrate. The mean diameter and height

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Dilute Nitride Semiconductors

Figure 4.10. AFM image of InAs quantum dots grown by MOMBE.

of the QDs were 25 and 3 nm, respectively. Very high dot density of 9 £ 1010 cm22 was observed. 4.5.2 Strain Compensation by Burying InAs QDs with GaAsN Figure 4.11(a) and (b) shows the typical example of the cross-sectional transmission electron microscope (TEM) images of two stacks of InAs QDs buried with GaAsN with different N concentrations. With the lower N concentration of 0.5% in the GaAsN burying layer shown in Figure 4.11(a), the strain field around the InAs dots will be evident from the following three findings: (i) The presence of the clear fringes induced by the lattice distortion around the InAs dots. (ii) The dots in the upper layer are slightly larger than

Figure 4.11. TEM cross-sectional view of InAs quantum dots buried with GaAsN alloys: (a) N ¼ 0.5%; (b) N ¼ 0.7%.

MOMBE Growth and Characterization of III –V-N Compounds

151

those in the lower layer due to the penetration of the strain field to the upper layer. (iii) The dots are vertically aligned with the strain field penetrating into the adjacent upper layer. The InAs QDs buried with GaAsN with the higher N concentration of 0.7% are shown in Figure 4.11(b) and exhibited much reduced strain field from the findings: (i) The lattice distortion around the InAs QDs is much reduced. (ii) The dot sizes in the two stacks of layers are similar and no strain effect from the lower layer is evident. (iii) The vertical alignment of the dots is loosened and some dots are missing in the upper layer. These results demonstrate the role of the tensile-strained GaAsN layer as the strain compensating layer (SCL) on compressively strained InAs QDs. 4.5.3 Red Shift of the Emission Wavelength of InAs Quantum Dots by Burying with GaAsN Layers InAs QDs buried with GaAsN SCL showed more distinct sub-peaks originating from QD discrete energy states in the observed PL spectra in comparison to those buried with GaAs layers [10]. This demonstrates the SCL effect to improve the uniformity of the buried QDs. The temperature dependence of the PL sub-peak energies also showed clear dependence on the burying layers. The ground-state emission from the InAs QDs buried with GaAs exhibited an S-shaped temperature dependence, which is explained by carrier localization in inhomogeneously broadened disordered systems [34]. This will be due to the spatial distribution of strain around QDs, which induces the change of the QD sizes in the neighboring stacks as well as the strain-induced spatial variation of the energy gap. On the other hand, the PL sub-peaks observed from InAs QDs buried with the GaAsN SCL showed monotonous and more uniform temperature dependences. One of the most distinct features of the InAs QDs buried with the GaAsN SCL is the red shift in their emission photon energies with the increase of the N concentration. The measured data are shown in Figure 4.12 by the filled circles. These measurements show that 1.55-mm wavelength (0.8-eV photon energy) emission from InAs QDs grown on GaAs is possible by burying them with GaAsN SCLs with the N concentration of 2.7%. It is noted that the diffusion of N into the InAs QDs will not be the dominant factor for this red shift from the following two reasons: N atoms induce extremely large strain fields around them due to their small atomic radii and the random distributions of the limited number of N atoms in InAs QDs will induce inhomogeneous broadening, which is contradictory to the above observations of well-defined QD-state sub-peaks. The other reason is based on an additional examination of intentional N purging on InAs QDs, which may induce N diffusion into InAs dots. This intentional N purging induced the red shift of the transition energies but was not as large as is given in Figure 4.12, and the turn-over to blue shifts was observed with the prolonged N purging. Therefore, the other physical origins should be involved in the observed red shift. One possibility may be the reduced band offsets due to the reduced energy gap of the GaAsN barriers, and the N concentration dependence of the GaAsN energy gap is plotted

152

Dilute Nitride Semiconductors 1.5 Measured PL peak InAs QW Transition Energy (eV)

1.4 1.3

Eg (GaAsN)

1.2 1.1 1 n=2

0.9

n=1

0.8

Eg (In 0.75 Ga 0.25 As)

0.7 0

0.5

1 1.5 2 2.5 N Concentration in GaNAs (%)

3

Figure 4.12. Emission wavelength of InAs quantum dots vs. the N concentration in the burying GaAsN layers. Measurements at 20 K are shown by the filled circles. The solid lines are simulation of the transition energy considering the strain compensation.

in Figure 4.12. Since the band offsets in GaAs/InAs/GaAsN heterostructures are mostly localized in the conduction bands, the reduction of the GaAsN energy gap will mainly reduce the conduction-band offset. A simple energy-state calculation indicated that the shift of the quantum state energies, especially the ground state energy, by the modification of the band offsets is much smaller than the observations shown in Figure 4.12. It is noted that the observed red shift of the emission energies from the InAs QDs was even larger than that of the GaAsN energy gap! Inclusion of the narrowing of the InAs energy gap itself is inevitable to account for this “huge” red shift. Then the remaining physical factor should be the strain effect. Saito et al. observed the emission at the photon energy of 0.8 eV from InAs QDs open to air [33]. They observed swift blue shift of the InAs QDs emission with the increase of the burying GaAs layer thickness, and they attributed the origin to the compressive strain induced from the GaAs burying layers. Following these findings, the red shift of the transition energies shown in Figure 4.12 is interpreted to be the reduction of the compressive strain by burying with tensile-strained GaAsN SCLs. To examine this possibility, the transition energy was calculated with a simple model. The main assumptions for this calculation are the following: (i) The InAs QDs grown on a GaAs substrate and buried with the GaAsN SCL were approximated with a simple asymmetric GaAsN/InAs/GaAs quantum well with an effective well thickness to account for the lateral electronic confinements. From the better fits of the calculated n ¼ 1 and n ¼ 2 sub-band transition energies to the measured PL sub-peaks for

MOMBE Growth and Characterization of III –V-N Compounds

153

the GaAs/InAs/GaAs case (with N ¼ 0%), the effective well thickness was set to 2 nm. (ii) InAs is known to have a large nonparabolicity in the conduction band and the energydependent effective electron mass was introduced based on the k·p theory. (iii) The inclusion of 25% of Ga was assumed in the well layer to fit the measurements for the GaAs/InAs/GaAs case (with N ¼ 0%), which gave , 220 meV blue shift of the transition energies. (iv) The strain dependence of the In(Ga)As energy gap was introduced via the deformation potentials [35]. The nice fitting shown in Figure 4.12 was possible by assuming that the strain in the InAs QDs was reduced depending on the spatial average in one period of the InAs/GaAsN stack. The verification of this final assumption needs more exact calculation of the strain field. What can be concluded here is that the quantitative explanation of the observed red shift is possible by considering the strain reduction in InAs QDs. 4.5.4 Improved Luminescence Efficiencies of InAs Quantum Dots by Burying with GaAsN Layers III –V-N alloy semiconductors usually suffer degradations of their crystalline quality with the increase of the N concentration. An exceptional case is shown here with the application of the GaAsN alloys to InAs QDs. Integrated PL intensities observed from InAs QDs buried with the GaAsN SCLs are plotted against the N concentrations in the GaAsN SCLs as is shown in Figure 4.13(a). The PL efficiency was improved with the increase of the N concentration, and the improvement up to five times was observed compared with the sample buried with GaAs. This demonstrates that the degradation of GaAsN crystalline quality is not necessarily an intrinsic problem. Thermal activation energies estimated from the Arrhenius plots of the integrated PL intensities showed the corresponding tendency [12]: They showed nice agreements with (a) 6 Integrated PL Intensity (arb. units)

5 4 3 2 1 20 K 0

0 0.5 1 1.5 2 2.5 3 N Concentration in GaNAs SCL (%)

Average Strain in InAs/GaNAs (%)

(b) 0.4 InAs QDs / GaNAs SCL

0.3

InAs (2ML) /GaNAs SCL on GaAs

0.2 0.1 0 −0.1 −0.2

0 0.5 1 1.5 2 2.5 3 N Concentration in GaNAs (%)

Figure 4.13. (a) PL emission efficiency of InAs quantum dots vs. the N concentration in the GaAsN burying layers. (b) The corresponding average strain in one period of the stacked layers is shown.

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Dilute Nitride Semiconductors

the quantum state energy differences observed in InAs QDs PL spectra buried with the GaAsN SCLs. The PL quenching mechanism in this case was the usual thermionic emission over the potential barriers. However, the thermal activation energies estimated from the InAs QDs buried with GaAs were lower than the quantum state energy differences in the PL spectra, suggesting the presence of additional defect levels which quench the PL efficiencies. These differences demonstrate that the strain compensation of the compressive strain induced by the InAs QDs with the tensile strain of the GaAsN SCL is effective for the improvement of the luminescence properties. An explanation of the characteristic shown in Figure 4.13(a) was tried from the viewpoint of strain compensation. The strain averaged in one period of the InAs QDs/ GaAsN SCL was calculated by considering the effective volume ratio between InAs and GaAsN as well as the lattice mismatch. As shown in Figure 4.13(b), the average compressive strain induced by the InAs “effective layer” is compensated with the increase of the N concentration in the GaAsN SCL. The average strain is reduced to zero near the N concentration of 2.1%, which will be a reasonable correspondence with the maximum improvement of the PL efficiency at , 1.5% of the N concentration in the GaAsN SCL. 4.6. SUMMARY

MOMBE growth of GaAsN, GaInNAs, and GaAsNSe was discussed. Enhanced N incorporation with the increase of the In concentration will be an intrinsic nature originating from the strain issue. The capability to realize 1.55-mm emission from GaInNAs and GaAsNSe alloys and InAs QDs buried with GaAsN was demonstrated. Intrinsic physical features such as the lower temperature dependence of the energy gap in III– V-N semiconductors were also discussed. ACKNOWLEDGEMENTS

The authors wish to thank the important contributions from Dr Xiqing Zhang for the detailed optical characterization of the InAs QDs, Dr Wei Zhou for the GaInNAs studies, Prof. Tae-Yeon Seong for the TEM observations, Dr Wladek Walukiewicz for the discussion on the BAC model, and Dr Hidekazu Kumano for the assistance on optical characterization of the III– V-N materials. REFERENCES [1] Weyers, M., Sato, M. & Ando, H. (1992) Jpn. J. Appl. Phys., 31, L853 Part 2. [2] Kondow, M., Kitatani, T., Nakahara, K. & Tanaka, T. (1999) Jpn. J. Appl. Phys., 38, L1355.

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[3] Ellmers, C., Ho¨hnsdorf, F., Koch, J., Agert, C., Leu, S., Karaiskaj, D., Hofmann, M., Stolz, W. & Ru¨hle, W.W. (1999) Appl. Phys. Lett., 74, 2271. [4] Uesugi, K. & Suemune, I. (1998) J. Cryst. Growth, 189/190, 490. [5] Zhou, W., Uesugi, K. & Suemune, I. (2003) Appl. Phys. Lett., 83, 1992. [6] Uesugi, K. & Suemune, I. (2001) Appl. Phys. Lett., 79, 3284. [7] Uesugi, K., Morooka, N. & Suemune, I. (1999) Appl. Phys. Lett., 74, 1254. [8] Uesugi, K., Suemune, I., Hasegawa, T., Akutagawa, T. & Nakamura, T. (2000) Appl. Phys. Lett., 76, 1285. [9] Suemune, I., Uesugi, K. & Walukiewicz, W. (2000) Appl. Phys. Lett., 77, 3021. [10] Ganapathy, S., Zhang, X.Q., Suemune, I., Uesugi, K., Kim, B.-J. & Seong, T.-Y. (2003) Jpn. J. Appl. Phys., 42, 5598 Part 1. [11] Uesugi, K., Suemune, I., Machida, H. & Shimoyama, N. (2003) Appl. Phys. Lett., 82, 898. [12] Zhang, X.Q., Ganapathy, S., Suemune, I., Kumano, H., Uesugi, K., Nabetani, Y. & Matsumoto, T. (2003) Appl. Phys. Lett., 83, 4524. [13] Vurgaftman, I., Meyer, J.R. & Ram-Mohan, L.R. (2001) J. Appl. Phys., 89, 5815. [14] Matthews, J.W. & Blakeslee, A.E. (1974) J. Cryst. Growth, 27, 118. [15] Kondow, M., Uomi, K., Hosomi, K. & Mozume, T. (1994) Jpn. J. Appl. Phys., 33, L1056 Part 2. [16] Ougazzaden, A., Le Bellego, Y., Rao, E.V.K., Juhel, M., Leprince, L. & Patriarche, G. (1997) Appl. Phys. Lett., 70, 2861. [17] Bi, W.G. & Tu, C.W. (1997) Appl. Phys. Lett., 70, 1608. [18] Sakai, S., Ueta, Y. & Terauchi, Y. (1993) Jpn. J. Appl. Phys., 32, 4413 Part 1. [19] Bellaiche, L., Wei, S.H. & Zunger, A. (1997) Appl. Phys. Lett., 70, 3558. [20] Shan, W., Walukiewicz, W., Ager, J.W., III, Haller, E.E., Geisz, J.F., Friedman, D.J., Olson, J.M. & Kurtz, S.R. (1999) Phys. Rev. Lett., 82, 1221. [21] Perkins, J.D., Mascarenhas, A., Zhang, Y., Geisz, J.F., Friedman, D.J., Olson, J.M. & Kurtz, S.R. (1999) Phys. Rev. Lett., 82, 3312. [22] Tournie, E., Pinault, M.-A., Vezian, S., Massies, J. & Tottereau, O. (2000) Appl. Phys. Lett., 77, 2189. [23] Friedman, D.J., Geisz, J.F., Kurtz, S.R., Olson, J.M. & Reedy, R. (1998) J. Cryst. Growth, 195, 438. [24] Morooka, N., Uesugi, K. & Suemune, I. (1999) Jpn. J. Appl. Phys., 38, L1309. [25] Kim, K. & Zunger, A. (2001) Phys. Rev. Lett., 86, 2609. [26] Kurtz, S., Webb, J., Gedvilas, L., Friedman, D., Geisz, J., Olson, J., King, R., Joslin, D. & Karam, N. (2001) Appl. Phys. Lett., 78, 748. [27] Zhang, S.B. & Zunger, A. (1997) Appl. Phys. Lett., 71, 677. [28] Bhat, R., Caneau, C., Salamanca-Riba, L., Bi, W. & Tu, C. (1998) J. Cryst. Growth, 195, 427. [29] Hakkarainen, T., Toivonen, J., Sopanen, M. & Lipsanen, H. (2002) J. Cryst. Growth, 234, 631. [30] Koukitu, A., Kumagai, Y., Kubota, N. & Seki, H. (1999) Phys. Stat. Sol. (b), 216, 707. [31] Palmer, J.E., Saitoh, T., Yodo, T. & Tamura, M. (1993) J. Appl. Phys., 74, 7211. [32] Uesugi, K. & Suemune, I. (2001) Appl. Phys. Lett., 79, 3284. [33] Saito, H., Nishi, K. & Sugou, S. (1998) Appl. Phys. Lett., 73, 2742. [34] Grenouillet, L., Bru-Chevallier, C., Guillot, G., Gilet, P., Duvaut, P., Vannuffel, C., Million, A. & Chenevas-Paule, A. (2000) Appl. Phys. Lett., 76, 2241. [35] Van de Walle, C.G. (1989) Phys. Rev. B, 39, 1871.

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Dilute Nitride Semiconductors M. Henini (Ed.) q 2005 Elsevier Ltd. All rights reserved.

Chapter 5

Recent Progress in Dilute Nitride Quantum Dots S.F. Yoona,b, Z.Z. Suna and K.C. Yewa a

Compound Semiconductor Materials and Devices Group, Microelectronics Center, School of Electrical and Electronic Engineering, Nanyang Technological University, Nanyang Avenue, Singapore, Singapore 639798 b Singapore-MIT Alliance (SMA), Nanyang Technological University, Nanyang Avenue, Singapore, Singapore 639798

5.1. SELF-ORGANIZED QUANTUM DOTS

5.1.1 A Brief Introduction to Quantum Dot Structures It is well known that three-dimensional (3D) quantum confinement in quantum dot (QD) structures gives rise to discrete energy levels, leading to a d-like function in the density of states. This essential characteristic results in some attractive potential applications of semiconductor QD structures. For example, it had been theoretically predicted that QD lasers could exhibit high characteristic temperature ðT0 Þ [1], high optical gain, and low threshold current density [2]. These theoretical advantages usually require the QD ensembles to have good size uniformity, which otherwise may result in the density of states losing its d-like function characteristic and assuming a behavior similar to that in bulk materials [3] (as shown in Figure 5.1). To achieve the advantages of quantum confinement, which are determined by parameters associated with the energy band structure, the fabricated QD size has to be commonly below 50 nm in all three dimensions. While it is possible that such nanometer dimensions are achievable using advanced techniques such as electron beam lithography, micro-structural defects induced by post-processing steps could greatly degrade the optical quality of the QDs. To obtain high-density, defect-free QD nanostructures, selforganized growth is currently one of the most prevalent methods, especially for applications in optoelectronic devices. 5.1.2 Fabrication of Strained QDs by Self-organized Growth Self-organized growth of QDs is based on Stranski – Krastanow (SK) growth mode of strained epilayers. Under the SK growth mode, in minimizing the total surface energy and strain energy, the strained layer maintains two-dimensional (2D) planar growth below the critical thickness and evolves to 3D island growth above the critical thickness [4]. The key attribute of this growth mode is that defect-free nanometer-sized islands could form within a small range above the critical thickness, under certain well-controlled growth conditions. 157

158

Dilute Nitride Semiconductors

Figure 5.1. Variation of density of state of QDs ensemble with the increase of the size inhomogeneous distribution. The ratio of standard deviation to the average size of QDs ensemble is signed by percent number. The density-of-state curves of QW and bulk material are also plotted for comparison.

Obviously, such growth of strained islands under the SK growth mode is an extension of the 2D growth of strained quantum well (QW). As described below, there are two important advantages that accompany the occurrence of these 3D islands. Firstly, it is known that the 3D quantum-confined structures can be formed relatively easily when the islands are capped vertically and surrounded laterally by a high band gap material. These are known as “self-organized” or “self-assembled” QDs. The selforganized growth mechanism has proven to be effective for fabricating defect-free QD nanostructures. So far, self-organized QDs have been fabricated successfully in a number of semiconductor material systems such as GeSi/Si [5 – 7], In(Ga)As/(Al)GaAs [8 –10], InAlAs/AlGaAs [11,12], InP/InGaP [13,14], In(Ga,Al)As/InAlAs/InP [15 –18], InAs/ InGaAs/InP [19], InAs/InGaAsP/InP [20,21], GaSb/GaAs [22], PbSe/PbEuTe [23], etc. Amongst these, the In(Ga)As/GaAs QD system is probably the most widely studied, and novel devices such as QD lasers [24,25] and QD infrared photodetectors [26] have been demonstrated. Secondly, the height of the self-organized QDs must exceed the critical thickness of the material system. Hence, the emission wavelength of the QDs is commonly greater than that of the corresponding strained QW at thickness equal to or lower than the critical thickness. This is because QDs exhibit relatively weak quantum confinement in the vertical dimension compared to the QW, and generally the lateral quantum confinement of QDs does not overwhelm the difference in vertical quantum confinement between the QD

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and QW. This can be exploited to extend the emission wavelength, which was previously unachievable by tuning the wavelength of strained QW structures. Considerable success on 1.3 mm lasers [27] based on In(Ga)As QDs has been made, and this serves as an important scientific platform from which more advanced studies on self-organized growth of QDs based on new material systems can be developed. On the other hand, self-organized formation of QDs poses certain difficulty from a growth control standpoint. This is because formation of defect-free QDs is only achievable within strict growth process latitude beyond which dislocations will begin to form due to strain relaxation. Furthermore, the properties of strained QDs are very sensitive to material and interface conditions. In addition, the control of QD size uniformity is an important issue to be addressed for self-organized growth. It is known that relative good QD size uniformity could only be achieved under strict growth conditions. Typical size fluctuation of an ensemble of QDs is more than 10%, an effect which is generally exhibited by the spectrally broad photoluminescence (PL) linewidth and observed by atomic force microscopy (AFM) and transmission electron microscopy (TEM) measurements. Because self-organized QD formation is a process of certain randomicity, it is natural that the process will result in a certain amount of inhomogeneity, which is not accidental [28]. For this reason, generally the threshold current density of QD lasers is still higher than expected. 5.1.3 Research Directions in Self-organized QDs Current research efforts in self-organized QDs are focused in several major directions: (i) exploring fundamental physical phenomena in low-dimensional nanostructures using comprehensive optical and surface sensitive characterization techniques, including in situ tools for observing early stage QD surface nucleation; (ii) designing and demonstrating new applications in microelectronic and optoelectronic devices with QD structures; (iii) improving QD size and position uniformity to achieve more repeatable device performance that approaches the behavior of ideal QD systems; (iv) extending the emission wavelength for optoelectronic applications based on selforganized QDs. Current studies on QDs based on dilute nitride materials are mainly focused on the last issue in the above list. 5.2. DILUTE NITRIDE QUANTUM DOTS

5.2.1 Background In recent years, there has been considerable attention devoted to achieve long wavelength lasers (1.3 and 1.55 mm for optical communication) on GaAs substrate. This motivation

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is driven primarily by the lower cost of GaAs substrate compared to InP substrate, and compatibility with GaAs/AlAs distributed Bragg reflectors, making it an attractive option for GaAs-based vertical cavity surface emitting laser (VCSEL) [29]. Present success is so far limited generally to two methods: one involving the use of self-assembled In(Ga)As QD structures and another involving QW structures based on dilute nitrides such as GaInNAs. As a relatively new material system, narrow band gap dilute nitride alloys, such as GaAsN and GaInNAs, have attracted strong interests [30,31]. The large difference in electronegativity and lattice constant between GaAs and GaN results in large optical bowing coefficient [32,33] and significant band gap reduction following incorporation of small N concentration in the material. Moreover, in the GaInNAs/GaAs system, reduction in the GaInNAs band gap contributes to a large conduction band offset. Furthermore, incorporating N in GaInAs can compensate for the compressive strain due to In, and result in GaInNAs lattice-matched to GaAs substrate. For these reasons, the GaInNAs/GaAs system is finding promising applications in 1.3– 1.55 mm laser diodes with good hightemperature performance [30]. GaInNAs laser diodes emitting at 1.3 mm with T0 of 270 K [34], low threshold current density of 220 A/cm2 [35], and operational lifetime of over 1000 h [36] have been reported. Electrically pumped GaInNAs VCSELs based on GaAs substrates were also reported [37]. Solar cells [38], resonant cavity enhanced photodetectors [39], and heterojunction bipolar transistors [40] employing the GaInNAs material system have shown improved performance. Recently, following efforts to push the emission wavelength of GaInNAs/GaAs higher to 1.55 mm, room temperature (RT) lasing at 1.52 mm from GaInNAs QW with 5% N has been reported [41,42]. Long-wavelength lasers based on InGaAs/GaAs QDs on GaAs substrate have been investigated over the last decade. Realization of 1.3 mm GaAs-based InAs QD lasers including VCSELs has also been reported [43]. To extend the QD emission wavelength, techniques such as stacked structures [44], alternate layer deposition [45 –47], and strain reducing barrier layers [48] have been investigated. Recently, RT continuous wave (CW) lasing at 1.51 mm has been demonstrated using stacked InAs/InGaAs QDs confined by metamorphic InGaAs– InGaAlAs layers grown on GaAs [49]. 5.2.2 Prospects of Dilute Nitride QDs Following significant research progress in dilute nitride materials and InGaAs/GaAs selforganized QDs, studies on GaInNAs QDs on GaAs substrate have intensified. Generally regarded as an intermediate between GaInNAs QW and InGaAs QD structures, GaInNAs QD lasers based on GaAs substrate have the potential for application in the 1.3 –1.55 mm telecommunication wavelength. Compared to GaInNAs QW, the advantage of using GaInNAs QDs is the expectation to achieve the same long wavelength emission with relatively lower N content, an effect

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assisted by the wavelength extension ability of the 3D strained islands. The high N content needed for long wavelength emission in GaInNAs QW lasers deteriorates the optical characteristics of the material and limits the device performance. It is hoped that the lower N content in GaInNAs QDs will help alleviate this problem without compromising device performance. Compared to GaInAs QDs, the advantage of using GaInNAs QDs is the expectation to achieve the same long wavelength emission with wider control latitude of the growth conditions, emission wavelength, and QD structures, assisted by the effects of N incorporation.

5.3. RECENT EXPERIMENTAL PROGRESS IN GaInNAS QDS

5.3.1 Self-organized Growth of GaInNAs QDs Sopanen et al. [50] first reported the fabrication of GaInNAs QDs by self-organization using gas-source molecular beam epitaxy (GSMBE). Following that, there have been numerous reports on self-organized growth of GaInNAs QDs using GSMBE [51 – 54], solid-source molecular beam epitaxy (SSMBE) [55 – 61], chemical beam epitaxy (CBE) [62 – 68], and metalorganic vapor phase epitaxy (MOVPE) [69 – 72]. The formation of GaInNAs QDs has been extensively confirmed to follow the conventional SK growth mode. The transition from 2D to 3D growth mode was observed through change from streaky to spotty pattern in the reflection high-energy electron diffraction (RHEED) trace. Furthermore, AFM observation of change in surface morphology of samples with different GaInNAs monolayer (ML) thickness confirms the nucleation of QDs after a certain number of MLs. The existence of GaInNAs dots in capped samples was also observed by TEM. Figure 5.2 shows the AFM images of the surface morphology of Ga0.6In0.4N0.01As0.99 QD samples of different thicknesses from 3 to 6 ML grown by SSMBE at 0.5 ML/s and As4/Ga beam equivalent pressure (BEP) ratio of 18. As shown in Figure 5.2(a), the surface appears to be atomically flat at 3 ML thickness, with root mean square (RMS) roughness of , 0.4 nm. When the GaInNAs thickness is increased to 4 ML, low density (, 1.8 £ 1010 cm22) dots began to form as shown in Figure 5.2(b), indicating initiation of the self-organized QD formation process. At GaInNAs thickness of 6 ML, dense dots with sheet density of , 6 £ 1010 cm22 can be seen from the AFM image in Figure 5.2(c). The dots have average height of , 5 nm and lateral diameter of , 33 nm with relatively homogenous distribution. Further increase in thickness to 7 ML and beyond results in coalescence of the dots leading to significant surface roughening (RMS surface roughness . 2 nm). Figure 5.2(d) and (e) shows the cross-sectional TEM images of 4.5 ML-thick Ga0.6In0.4N0.01As0.99 QDs and 5 ML-thick Ga0.5In0.5N0.01As0.99 QDs multilayer samples, respectively. The images show coherent dot profile with aspect ratio of , 0.1. This is in good agreement with the AFM measurements, in terms of dot size.

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Figure 5.2. AFM images of (a) 3 ML-thick, (b) 4 ML-thick, and (c) 6 ML-thick Ga0.6In0.4N0.01As0.99 QD samples. Cross-sectional TEM images of (d) 4.5 ML-thick Ga0.6In0.4N0.01As0.99 QDs and (e) 5 ML-thick Ga0.5In0.5N0.01As0.99 QDs multilayer.

The critical thickness is an important parameter governing the self-organized growth kinetics. Using in situ RHEED observation, the transition time to change from 2D to 3D growth mode can be used to estimate the value of critical thickness. Critical thickness values of 3 and 2.5 ML have been reported for GSMBE-grown Ga0.3In0.7N0.04As0.96 and InN0.02As0.98 QDs, respectively [50]. For MOVPE-grown Ga0.4In0.6(N)As QDs [69], critical thickness value of 3 ML has been reported. Figure 5.3 shows the variation in critical thickness for SSMBE-grown GaInNAs QDs of different In compositions (30 – 100%) as function of N composition (0 –1.5%). It can be seen that the GaInNAs critical thickness decreased drastically from 10– 15 to , 1 nm as the In composition is increased from 30 to 100%. This is because the GaInNAs-to-GaAs layer strain is mainly determined by the In composition at low

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Figure 5.3. The variation in critical thickness for SSMBE-grown GaInNAs QDs with different In and N compositions, estimated from RHEED observations.

N content. For GaInNAs samples of the same In composition, the dependence of critical thickness on N composition shows obvious fluctuations with respect to theoretical expectation. In general, the critical thickness required for spontaneous SK island formation is inversely proportional to square of the misfit of the strained layer [73,74]. This is represented by dotted lines in the figure. It can be seen that the experimental data are quite different from theoretical expectations. A possible reason for such deviation is the non-uniformity in composition or strain in the GaInNAs layer, which will be discussed further in the following section. Furthermore, it was found that the fluctuation of critical thickness is less significant in GaInNAs at higher In composition. This could suggest that the non-uniformity in composition or strain caused by N incorporation plays a relatively weaker role compared to the strain effects at high In composition. 5.3.2 Structural Properties of GaInNAs QDs Depending on growth conditions [50,61,63,66,69], GaInNAs QD density can reach levels as high as 1010 – 1011 cm22 with average dot height in the range of 2– 16 nm and dot lateral diameter in the range of 20– 45 nm. Thickness and material composition are basic parameters, which impact the QD structural properties. Figure 5.4 shows the dot density and average dot height of GaInNAs QDs grown by SSMBE, as a function of thickness at different In compositions [75]. As expected, increasing the surface coverage results in greater dot density and dot height. Moreover, for GaInNAs of high In composition, highdensity dots can be formed at relatively lower surface coverage. Besides smaller critical

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Figure 5.4. (a) Dot density and (b) average dot height measured by AFM as a function of GaInNAs surface coverage. The In composition was varied from 30 to 100%. The N composition was 0.4% for the sample with 70% In and ,1% for all other samples. The lines serve as guide for the eye.

thickness in GaInNAs at high In composition, another possible reason for this observation is the strong local strain caused by N incorporation. This enhances the formation of strained dots, especially in GaInNAs of high In composition [78]. The incorporation of N has a complicated influence on the QD size and density. Some experiments have suggested that low N incorporation results in smaller GaInNAs QD size and much higher dot density compared to InGaAs QDs grown under identical conditions [50,62,69]. However, this behavioral trend may not be true at N composition . 1%, where there are reports of dot coalescence resulting in low-density, large-sized incoherent GaInNAs dots [50,62,65]. On the contrary, some experiments on InNAs QDs [51] and GaInNAs QDs [54] grown by GSMBE have shown that the introduction of N induces a reduction in dot density and an increase in dot sizes. As far as QD size uniformity is concerned, experiments have shown that the growth kinetics governing GaInNAs and InGaAs QD formation are significantly different [50,51].

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5.3.3 Growth Kinetics of GaInNAs QDs Present results have shown that compared to InGaAs QDs, the formation of GaInNAs QDs poses some additional complexity. Firstly, in big miscibility gap mixed group V nitride – arsenide systems [76,77] such as GaInNAs, the incorporation of N tends to give rise to phase separation in the material, leading to fluctuation in the N distribution. Secondly, N incorporation compensates the compressive strain in the GaInNAs layer and results in smaller average strain, whereas the local strain around the N atom could be large due to the small atomic radius of N. Thirdly, the N atom may change the surface potential due to its strong bonds. This could affect the atomic migration length at the growth surface. Moreover, In – N atomic interactions may give rise to locally In-rich regions. A combination of these factors could affect the QD nucleation kinetics, strain conditions, and QD coalescence. This may account for the different effects on critical thickness for dot formation, and influence the size and density of the GaInNAs QDs. It is highly possible that one or a combination of above factors takes place as early as deposition of the wetting layer prior to QD nucleation. Xin et al. [78,79] have reported the presence of lateral undulations in composition and strain in Ga0.7In0.3N0.02As0.98/GaAs QW structures grown by GSMBE. The lateral undulations are more significant in GaInNAs QWs compared to GaInAs QWs, an effect that could arise from the local strain resulting from N incorporation. Volovik et al. [56] have reported that even for the GaInNAs QW with low In composition (25%), the TEM images revealed pronounced corrugation at the upper interface and formation of nanodomains. This effect is a likely outcome of QW phase separation into In-rich and In-poor regions. Chalker et al. [80] have reported the existence of a continuous nitride intermediate layer at the interface between the GaAs buffer layer and GaInNAs layer in GaInNAs/GaAs QW samples analyzed by energy dispersive X-ray and high-resolution scanning TEM measurements. This polar nitrogen-terminated surface formed prior to GaInNAs deposition may have a significant effect in inducing strong compositional undulation in the QW layer. 5.3.4 Optical Properties of GaInNAs QDs 5.3.4.1 Effect of Nitrogen on Wavelength. In terms of the optical properties of GaInNAs QDs, the principal target is to extend the emission wavelength. As a rough estimation, 1% of N incorporation will cause , 200 meV in energy shift assuming bowing coefficient of 20 eV [81]. The effectiveness of N incorporation on wavelength extension had been experimentally confirmed. Figure 5.5 shows the PL spectrum from a sample with one Ga0.7In0.3As QD layer and one Ga0.7In0.3N0.006As QD layer grown by SSMBE under identical conditions. Separate PL peaks were detected from the two different QD layers. It can be seen that the PL peak was shifted by 45 nm (or , 56 meV) following the introduction of , 0.6% N into the Ga0.7In0.3N0.006As QD layer. This clearly shows the effect of N incorporation on

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Figure 5.5. PL spectra from SSMBE-grown sample with one Ga0.7In0.3As dot layer and one Ga0.7In0.3N0.006As dot layer.

the emission property of GaInNAs QDs. Similar results on red shift in energy from , 1.2 to 1.08 eV were reported for SSMBE-grown Ga0.7In0.3AsN QDs following increase in N content from 0 to , 1% [56]. Ballet et al. [51] have reported RT emission at , 1.28 mm (, 0.97 eV) from InAsN/GaAs QDs with 0.8% N. This represents an 80 meV energy shift compared to emission at 1.18 mm (, 1.05 eV) from InAs/GaAs QDs grown by GSMBE. Furthermore, it was reported that increasing the N content to 2.1% has failed to extend the wavelength further in this experiment. This could be due to non-uniform N concentration in the InAsN QDs and the presence of defects at high N levels. Sopanen et al. [50] have reported PL emission at 1.3 and 1.52 mm from 4 ML-Ga0.3In0.7N0.02As0.96 QDs and 5.5 ML-Ga0.3In0.7N0.04As0.96 grown by GSMBE. Although the PL spectrum was relatively weak and broad, the results paved the way for long wavelength tuning using such QD layers. 5.3.4.2 Effect of Dot Size on Wavelength. Apart from N concentration, the QD size, which depends on the layer thickness, also affects the emission wavelength due to its effect on the quantum confinement. Figure 5.6(a) –(c) shows the 5 K PL spectra of SSMBEgrown Ga0.5In0.5N0.01As0.99 QDs of different layer thicknesses from 4 to 7.5 ML. No PL signal from the wetting layer was detected, and each spectrum shows a strong PL peak originating from the QD layer. Generally, the PL peaks are relatively broad due to fluctuation in QD sizes, and the full width at half maximum (FWHM) ranges from 60 to 90 nm. As the thickness of the dot layer is increased from 4 to 7.5 ML, the PL peak red

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Figure 5.6. 5 K PL spectra of (a) 4 ML-thick, (b) 5 ML-thick, (c) 7.5 ML-thick Ga0.5In0.5N0.01As0.99 QDs.

shifted from 900 to 1100 nm. The shift to longer wavelength is attributed to increase in dot sizes. However, this method has its limitations as the thickness continues to increase, since significant structural degradation will occur as the strain accumulates following increase in thickness. It can be seen that the 5 ML-thick Ga0.5In0.5N0.01As0.99 QD sample exhibits the strongest PL intensity, due to its higher dot density compared to the 4 ML-thick sample. At 7.5 ML, the PL intensity dropped rather significantly, suggesting the formation of straininduced defects caused by high surface coverage. Similar observation is also reported for GaInNAs QDs grown by GSMBE [53]. 5.3.4.3 Effect of Nitrogen on PL Intensity. It is common knowledge that the optical quality of dilute nitride materials degrades following increase in N concentration in the material. Such optical quality degradation in the material is usually more serious at high N levels due to the formation of N-related defects. Sopanen et al. [50] have shown that while the wavelength could be adjusted higher towards 1.55 mm by increasing the N content to 4% N in Ga0.3In0.7As QDs, the PL intensity is 1– 2 orders of magnitude lower. Ballet et al. [51] have observed that the optical properties of InAsN/GaAs QDs are much poorer compared to InAs/GaAs QDs or GaInNAs/GaAs QW, as indicated by , 20 times weaker in PL intensity. However, there are other reports of high-quality GaInNAs QDs grown by various techniques. Hakkarainen et al. [69] have reported enhanced 1.3 mm PL from GaInNAs

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QDs with low N composition, compared to GaInAs QDs grown under identical conditions. Room temperature 1.3 mm PL from a 5-period MOCVD-grown InAs(N)/GaAs QD sample has been reported by Jang et al. [72]. The narrow FWHM of 34 meV and the strong PL yield at RT indicate the formation of high crystal quality in the InAsN QDs. 5.3.5 Effect of Growth Temperature on GaInNAs QDs The growth temperature plays an important role in the formation of self-organized QDs. The effect of growth temperature on GSMBE-grown GaInNAs QD size, density, and optical properties was reported by Sopanen et al. [50]. It was found that the dot density decreases and dot size increases following increase in growth temperature from 370 to 5208C. Similar behaviors were observed for the growth of GaInAs [82], InAs [83], and InP [84] dots on GaAs. PL characterization generally shows decrease in growth temperature which leads to increase in integral intensity, longer wavelength, and reduction in the FWHM. The longer wavelength could be attributed to increase in the actual N composition in the QDs. The reduction in FWHM possibly results from narrowing in the QD height distribution, as AFM measurements showed that the maximum height of the islands decreases at lower growth temperature. Growth temperature for Ga0.3In0.7N0.04As0.96 QDs of , 4208C was suggested as optimum. The effects of growth temperature on CBE-grown GaInNAs QDs was investigated by Makino et al. [63,66], who reported the sensitive dependence of dot density and uniformity on the N concentration. 5.3.6 Effect of Thermal Annealing on GaInNAs QDs It is widely reported that in situ or ex situ thermal annealing of GaInNAs QWs helps to improve the PL efficiency by removing non-radiative recombination centers, via a number of processes possibly involving In –Ga interdiffusion, N –As interdiffusion, and/or atomic rearrangement [85 –88]. Therefore, similar studies on the effects of thermal annealing on GaInNAs QDs have attracted some attention. In an investigation by Makino et al. [68], ex situ rapid thermal annealing (RTA) was performed on CBE-grown GaInNAs QDs at 600, 650, and 7008C for different periods ranging from 30 s to 2 h. It was found that at 600 and 6508C, the PL efficiency increases as the annealing time is increased to a certain value, beyond which the PL intensity decreases. However, RTA at 7008C does not improve the PL intensity. Moreover, the optimum RTA condition for maximum PL intensity is different for GaInNAs QDs of different composition. At all RTA temperatures, it was found that the PL peak energy increases following increase in the annealing time, and higher temperature annealing resulted in greater blue shift for the same annealing time. Furthermore, RTA at 600 and 7008C results in decrease in FWHM of the GaInNAs QD PL peak. Nishikawa et al. [52] reported that RTA of GSMBE-grown Ga0.3In0.7N0.04As0.96 QDs at 600– 8008C for 10– 60 s causes an increase in PL intensity, decrease in PL FWHM, and blue shift in the PL peak.

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We have also investigated the RTA effects on GaInNAs QDs grown by SSMBE. Figure 5.7 shows some preliminary 77 K PL results of our SSMBE-grown Ga0.5In0.5N0.01As0.99 QD samples annealed at 600 and 6808C for 30 s. Unlike other reported observations on CBE- or GSMBE-grown GaInNAs QDs, the PL intensity and PL FWHM decrease with increase in RTA temperature. Moreover, no shift in the PL peak was observed. Further optimization in the RTA conditions is necessary to better understand the annealing effects. 5.3.7 Effect of Intermediate Layer in GaInNAs QDs In the well-studied InGaAs/GaAs QD system, modifying the dot structures by combining layers with different composition has proven to be effective for controlling the physical properties of self-assembled QDs [89,90]. Generally, this method usually involves introducing an intermediate layer before and/or after the QD layer. Such layers are also known as strain reducing layer (SRL) or strain compensating layer (SCL). The intermediate layer has different lattice constant or energy gap compared to the dot layer and barrier layer. Its presence will modify the strain field or quantum confinement conditions of the dot layer. A properly designed intermediate layer can improve the dot

Figure 5.7. Comparison of 77 K PL spectra from Ga0.5In0.5N0.01As0.99 QD unannealed sample and annealed samples at 600 and 6808C for 30 s.

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size uniformity and extend the emission wavelength. There have been some studies on GaInNAs QDs, where GaAsN intermediate layers were inserted between the GaAs barrier and GaInNAs QD layer for extending the emission wavelength of the GaInNAs QDs. Nishikawa et al. [53] reported a study which compared GSMBE-grown GaInN0.02As/ GaAs QD samples with: (a) no intermediate layer, (b) GaAsN0.02 intermediate layer after dots, and (c) GaAsN0.02 intermediate layers before and after dots. Due to lower confinement provided by the GaAsN intermediate layer compared to GaAs, the QD emission wavelength shifts to 1.38 mm at 10 K and 1.48 mm at RT with GaAsN intermediate layer. However, this is accompanied by decrease in the PL intensity. We have investigated the effect of GaAsN intermediate layer on the surface morphology of SSMBE-grown GaInNAs QDs. Figure 5.8 shows the AFM images taken on uncapped 5 ML-thick Ga0.5In0.5N0.01As0.99 QD samples with GaAsN intermediate layer of different thicknesses (0, 5, and 10 nm). Figure 5.8(a) shows GaInNAs QDs grown on GaAs have average diameter d , 33 nm, height h , 5 nm, and surface density r , 8:6 £ 1010 cm22. As seen in Figure 5.8(b), GaInNAs dots grown on 5 nm-thick GaAsN have similar dot sizes and density (d , 30 nm, h , 4:8 nm, r , 1:1 £ 1011 cm22) and appeared to have better uniformity. However, increasing the GaAsN thickness to 10 nm or more resulted in significant increase in surface roughness, as shown in Figure 5.8(c). In this case, the GaInNAs dots appeared rather irregular with poor uniformity. The change in QD uniformity associated with the GaAsN intermediate layer before the dot layer is possibly due to the introduction of composition/thickness modulation by the intermediate layer. The GaAsN intermediate layer may form slight undulations and the resulting surface strain will assume certain periodic characteristic, where preferential GaInNAs QD nucleation on some periodic sites may occur. Furthermore, a GaAsN intermediate layer inserted above the QD layer can reduce the strain between the QD layer and GaAs cap layer. This can lower the formation of interface dislocations. However, an overly thick GaAsN intermediate layer should be avoided to minimize dislocation formation due to strong surface undulations caused by high total strain energy. 5.3.8 Laser Diodes with GaInNAs QDs In year 2000, Makino et al. [62] first reported 77 K pulsed lasing from a Ga0.5In0.5N0.01As0.99 QD laser grown by CBE. The active region includes triple Ga0.5In0.5N0.01As0.99 QD layers, and the device emits at 1.02 mm with threshold current density of 1.9 kA/cm2 under pulsed condition (duty ratio: 1%). Since then, further demonstrations of GaInNAs QD lasers grown by SSMBE have also been reported by Sun et al. [61]. Recently, we fabricated oxide striped edge-emitting laser diodes with Ga0.7In0.3N0.01As0.99 QDs as the active layer. Figure 5.9 shows the schematic representation of the QD laser structure and a cross-sectional TEM of QD active region. The GaInNAs QD active layer and GaNAs intermediate layer were inserted between the nominally undoped GaAs waveguide layers and n- and p-type Al0.35Ga0.65As cladding layers. Figure 5.10 shows the RT light

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Figure 5.8. Comparison of AFM morphology of uncapped Ga0.5In0.5N0.01As0.99 QD samples with different GaAsN0.01 intermediate layer thickness of (a) 0 nm, (b) 5 nm, and (c) 10 nm. The scanned area is 0.5 mm £ 0.5 mm.

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Figure 5.9. Schematic representation of SSMBE-grown GaInNAs QD laser structure and a cross-sectional TEM image of the GaInNAs QD active region.

output vs. current ðL – IÞ characteristic of the GaInNAs QD laser with cavity length of 2000 mm and oxide stripe width of 50 mm operated under CW condition. Lasing started at threshold current of 2.1 A and maximum light power of 16 mW was achieved. The lasing spectrum shown in the inset of Figure 5.10 shows the peak wavelength at 1176 nm with spectral linewidth of 0.3 nm.

Figure 5.10. Room temperature I – V and P – I curves of the GaInNAs QD laser with output power up to 16 mW operating in CW mode. The inset shows the lasing spectrum at around 1.2 mm.

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5.4. OTHER KINDS OF DILUTE NITRIDE QDs

Apart from mainstream investigations on self-organized GaInNAs QDs described above, there have been several reports on other variations of dilute nitride QDs such as H-assisted GaInNAs QDs [91], non-lithographically fabricated GaInNAs:Sb QD arrays [92], stressorinduced GaInNAs QDs [93], and other complex-structure dilute nitride QD systems [94 – 97]. A brief summary of these QD structures follows. GaInNAs QDs grown by atomic H-assisted RF-molecular beam epitaxy have been reported by Oshima et al. [91]. AFM and PL measurements have shown some improvement in the QD properties, possibly due to the suppression of N atom migration and phase separation of the GaInNAs alloy by atomic H. An optimum H2 flow rate is needed for uniform Ga0.53In0.47N0.02As0.98 QD formation. Kouklin et al. [92] reported the fabrication of periodic 3D arrays of GaInNAs:Sb QDs. MBE-grown GaInNAs:Sb multiple QW layers were processed using a non-lithographic fabrication process, which involves the use of a nanopore alumina membrane for lateral patterning followed by reactive ion etching. The fabricated GaInNAs:Sb QDs have average diameter of , 55 nm. The fabrication of stressorinduced GaInNAs QDs by placing InP strained islands on a GaInNAs QW has been reported by Koskenvaara et al. [93]. The QD optical property and its dependence on N concentration were investigated by CW and time-resolved PL measurements. There have been some reports on complex structures of dilute nitride QDs, where GaAsN or GaInNAs is not used as dot material, but as barrier layer or strain-compensating layer surrounding the In(Ga)As QDs. This was shown as a possible method to extend the emission wavelength of InAs QDs. Ustinov et al. [94] reported the growth of InAs/ GaInNAs QDs on GaAs by MBE, and observed an increase in island size compared to InAs/InGaAs QDs. RT PL at 1.55 mm has been demonstrated with comparable intensity to GaInNAs/GaAs QWs emitting at 1.3 mm. Suemune et al. [95 – 97] reported the metalorganic molecular beam epitaxial (MOMBE) growth of InAs QDs capped by a tensile strained GaAsN layer. Using a 10 nm-thick GaAsN0.027 cap layer, the emission wavelength of the InAs QDs was red shifted to 1.55 mm. The observed improvement in homogeneity and luminescence efficiency of the InAs QDs was attributed to the strain compensating effect from the GaAsN layer. The luminescence efficiency was reported to improve up to five times following an increase in N concentration in the GaAsN SCL. Light emitting diodes (LEDs) based on such QDs were found to exhibit high electroluminescence (EL) efficiency at RT.

5.5. SUMMARY AND FUTURE CHALLENGES IN DILUTE NITRIDE QDs

In summary, it can be generally stated that studies on dilute nitride QDs are still in the initial stages. Epitaxial growth characteristics, structural and optical properties of

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GaInNAs QDs are presently under active investigations by many groups. Although GaInNAs QD lasers operating CW at room temperature at , 1.2 mm have been demonstrated, there is still much to be done to further extend the wavelength, reduce the threshold current density and improve the operating lifetime. In terms of wavelength and laser performance, present-day data from GaInNAs QDs are not as good as those from InGaAs QDs and GaInNAs QW devices. Therefore, there is a need for greater research efforts to improve the performance of GaInNAs QD devices. Compared to InGaAs/GaAs QDs, GaInNAs/GaAs QDs faces a key challenge of minimizing the formation of N-induced defects, as more N incorporation is needed to extend the emission wavelength to higher values. Interactions within the quaternary compound itself will not make the growth optimization process any easier to achieve good QD size uniformity and density. Compared to GaInNAs/GaAs QWs, GaInNAs/GaAs QDs will face key challenges to seek solutions to suppress strain-related defects and improve QD size uniformity. Breakthroughs in growth optimization and structure optimization are needed to realize the potential of GaInNAs/GaAs QDs for the application in long wavelength lasers.

ACKNOWLEDGEMENTS

S.F. Yoon would like to thank his co-authors Dr Sun Zhongzhe and Yew Kuok Chuin for their significant contributions, without which this chapter would not have been possible. All authors would like to thank Prof. B.X. Bo of Changchun University of Science and Technology, China for constructive discussions, and Dr Tung Chih-Hang, Du An Yan and Doan My The of the Institute of Microelectronics, Singapore for providing the TEM support. Financial assistance from the Nanyang Technological University and the Singapore-MIT Alliance to carry out this project is gratefully acknowledged.

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Dilute Nitride Semiconductors M. Henini (Ed.) q 2005 Elsevier Ltd. All rights reserved.

Chapter 6

Physics of Isoelectronic Dopants in GaAs A. Mascarenhas, S. Francoeur and S. Yoon National Renewable Energy Laboratory, Golden, CO 80401, USA

Although the nature of the tetrahedral bond pivotal to the physical characteristics of most semiconductors limits the choice of elements available to a narrow portion of the periodic table, the family of semiconductor materials now encompasses many elemental and binary compounds and, due to their technological importance, several of them and their combinations in the form of alloys have been synthesized and studied. For example, almost all possible III– V elemental combinations have been explored and the properties of most semiconductors alloys are now relatively well understood. However, GaAsN and other dilute nitride alloys have been an exception. Concomitant progress in epitaxial growth, characterization, and modeling of semiconductors materials and low dimensional structures have created a significant foundation for the exploration, synthesis and understanding of new and heteroclite combinations of elements, compounds, and alloys. In the last decade, it has been found that the properties of GaAs alloyed with a few percent nitrogen strongly contrast with those typically observed from other alloys. These unusual properties have drawn a great deal of attention as they significantly challenged our understanding of alloys formed from highly dissimilar semiconductor compounds. In this chapter, we discuss the origin of the most puzzling properties of GaAsN. Using modulated electroreflectance and resonant Raman scattering as the primary tools of characterization, we discuss the characteristics of the new optical transitions and resonances observed and unexpected from a zinc-blende alloy and determine the electronic band states involved. From the identification of the conduction band states participating in these transitions, the origin of the unusual band gap dependence and many other distinguishing characteristics of GaAsN naturally follow. In addition to the study of GaAs doped with a small and electronegative atom, we present results on a different but complementary type of alloy: GaAs doped with Bi, a large and less electronegative atom. We find that GaAsBi shows unusual characteristics compared to conventional III –V alloys but analogous to those of GaAsN. As will be demonstrated, GaAs based nitrogen and bismuth alloys provide two complementary perspectives on the same phenomenon. 179

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6.1. NITROGEN ISOELECTRONIC IMPURITIES

The physical origin of the properties of dilute nitride alloys is intimately related to the particular behavior of nitrogen impurities in III– V alloys and it is therefore important to introduce the concept of an isoelectronic impurity. III – V and II –VI alloys doped with nitrogen concentrations of approximately 1016 – 1018 cm23 have been under investigation for a few decades and GaP:N often serves as a prototypical example. This section reviews early results on isoelectronic doping and sets the foundations for the next section discussing effects of disorder on alloys. Semiconductor alloys are generally formed by replacing host atoms by others of identical valence. Whereas an isovalent impurity always creates a perturbation to the host band structure, this perturbation is usually small, hybridizes with the host states and remains unnoticeable. However, if the isovalent impurity and the atom it replaces have very distinct properties, the isovalent impurity can create a significant perturbation to the electronic charge distribution. This perturbation, if strong enough, can trap a charge carrier. For example, substituting In for Ga or P for As in GaAs produces a very weak perturbation whereas substituting N for P in GaP produces excitonic bound states. This difference in behavior can be understood by examining the difference between the intrinsic properties of the host atom and that which it substitutes. A large difference in atomic size and core potential produce a significant perturbation to the local electronic potential, thus creating a highly localized center attractive to one type of carrier via a short-range potential. Isovalent impurities creating bound states are generally referred to as isoelectronic impurities and impurities attractive to electrons and holes are often termed pseudo-acceptors and pseudo-donors, respectively. The trapped carrier can subsequently bind a carrier of opposite charge via coulombic interaction. Therefore, an isoelectronic impurity can bind excitons. Whilst it is easy to compute binding energies for hydrogenic impurities, it is challenging to estimate the binding energies for isoelectronic impurities since the spatial dependence of the impurity potential is difficult to model. Nitrogen in GaP is the most well-known example of an isoelectronic impurity in a III – V alloy. Since nitrogen lacks p orbitals in its core states, it is much more attractive to electrons than phosphorus. Additionally, the Ga– P and Ga – N bond lengths difference leads to lattice relaxation and an important local redistribution of the charge density. These two effects combined result in a perturbed charge distribution around nitrogen creating a region of lower potential energy attractive to electrons. As opposed to the potential created by charged impurities, this potential is not coulombic and has a much shorter range [1]. This tight localization creates a delocalized state in momentum space and therefore borrows its characteristics from all regions of the Brillouin zone, explaining its deep level behavior despite its binding energy being lower than that of hydrogenic impurities. The tightly bound electron then captures a hole via coulombic attraction, forming a nitrogen bound exciton whose decay is easily observed using luminescence. Interestingly, two

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181

isoelectronic impurities close to each other also bind excitons. It has been shown by Thomas and Hopfield [2] that several narrow lines appear in the absorption and luminescence spectra of GaP due to excitons bound to pairs of nitrogen atoms. The exciton binding energy is set by the pair orientation and separation. Since nitrogen atoms occupy the anion sublattice, the binding energy can only assume a series of discrete values. At large separations, the binding energy approaches that of an exciton bound to an isolated nitrogen atom and is located 20 meV below the X conduction band minimum. The binding energy increases with decreasing pair separation and reaches 130 meV for closely spaced nitrogen pairs. Although GaP is an indirect semiconductor, N impurities in GaP are very efficient light emitters since the localized potential surrounding nitrogen atoms strongly couples the impurity wavefunction to all Brillouin zone states and allows for the capture of electrons from the X conduction band minima. The behavior of nitrogen in GaAs appears quite different but is nonetheless qualitatively similar. The perturbation of nitrogen to GaAs is stronger than for GaP and a stronger binding energy is expected. However, the conduction band edge of GaAs is 360 meV lower than that of GaP [3] and therefore the state produced by an isolated nitrogen atom is resonant within the conduction band of GaAs. Wolford et al. demonstrated that it is necessary to apply hydrostatic pressure to observe the luminescence of excitons bound to isolated nitrogen atoms [4]. The shift in energy of the resonant state with pressure is about half that of the band gap and, at 22 kbar, the decay of excitons bound to isolated nitrogen atoms can be observed. Extrapolating the pressure dependence of the nitrogen energy level to ambient pressure, we find that the resonant state is located 150 –180 meV above the conduction band minimum of GaAs. Even if the isolated nitrogen impurity does not bind an exciton unless hydrostatic pressure is applied, the significant interaction between the short-range potentials of two nearby impurities can create bound states. Liu et al. have found that nitrogen pair states also bind excitons in GaAs [5]. Most of the nitrogen pair states are resonant within the conduction band, but two nitrogen pair configurations of low interatomic separation can be observed at ambient pressure [6]. These two states are located 11 and 23 meV below the G conduction band edge. Nitrogen in GaP or GaAs is not the only example of isoelectronic impurity. Table 6.1 lists a few alloys for which isoelectronic impurities create excitonic bound states. For each system, the relative difference in covalent radii between the impurity and the atom it replaces as well as the electronegativity difference is calculated. As can be noticed, an important size and electronegativity difference is generally associated with an isoelectronic impurity behavior. Given that nitrogen creates bound states in arsenides and phosphides, an interesting question arises: what happens when GaAs is doped with nitrogen, not at usual impurity concentrations (, 1018 cm23), but at concentrations where an alloy is typically formed (. 1020 cm23)? It is found that the unusual characteristics of dilute nitrogen alloys are determined by the large size difference and electronegativity difference of the substituent

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Table 6.1. A few known isoelectronic impurities Binary GaP GaP ZnTe CdS InP InP GaAs

Isoelectronic impurity N [2] Bi [7] O [8] Te [9] Sb [10] Bi [11] NNa [5]

Covalent radius difference (%)

Electronegativity difference (%)

32 33 50 44 24 33 36

39 8 64 19 6 8 39

a

Only two nitrogen pair states produce bound states all others being resonant with the conduction band.

nitrogen impurity, establishing a strong parallel between the behavior of the isoelectronic impurity and the behavior of its alloys. The next section demonstrates this relationship by examining the effects of disorder on the band gap of dilute isoelectronic impurity alloys.

6.2. THE FAILURE OF THE VIRTUAL CRYSTAL APPROXIMATION

Several simple semiconductor alloy models have been very successful at modeling and predicting a large number of fundamental characteristics of ternary and quaternary alloys based solely on the properties of the binary parents. Taking into account its simplicity, one of the most successful models is the virtual crystal approximation (VCA). In this approximation, the properties of a semiconductor alloy over its whole concentration range can simply be taken as a weighted average of the properties of its constituents. In other words, this model neglects the distinct atomic identities of the mixed anions or cations and replaces them by an average virtual effective potential. This approximation works best with structural parameters like lattice constants and compressibility factors. It is also used for the interpolation of effective masses, Luttinger parameters, and deformation potentials. However, the VCA cannot account for one important effect observed in almost every alloy: a deviation of band edge energies from a linear dependence on composition. Since this deviation is usually small, it is represented by a quadratic coefficient b added to the interpolation, which is referred to as the bowing coefficient. For example, using this correction, the band gap energy of AB12x Cx would be given by EABC ðxÞ ¼ ð1 2 xÞEAB þ xEAC 2 bxð1 2 xÞ: This relationship is valid not only for the band gap, but also for other energy locations (or energy differences) of the band structure, each having its own distinct bowing. The band gap bowing coefficients for a large number of ternary and quaternary alloys have been characterized and tabulated (for example, see Ref. [12]). To illustrate the importance of this correction, Table 6.2 lists the bowing coefficients for several mixed-cation and mixed-anion systems. Two important observations can be made. First, the bowing coefficient is nearly constant for all mixed

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183

Table 6.2. Bowing coefficients for common semiconductor alloys. Groups of alloys are organized in order of increasing ionicity Mixed cation

eV

Mixed anion

Al–Ga

AlGaAs AlGaSb

0.44 0.5

P–As

Ga –In

GaInP GaInAs GaInSb AlInP AlInAs AlInSb BGaAs

0.65 0.48 0.42 0.48 0.70 0.43 Small [13]

As–Sb

Al–In

B –Ga

P–Sb

IV–N

AlAsP GaAsP InAsP AlAsSb GaAsSb InAsSb AlPSb GaPSb InPSb GaAsN GaPN

eV 0.22 0.2 0.1 0.8 1.43 0.67 2.7 2.7 1.9 ,20

cations. Second, for mixed anions, the bowing coefficient is small for the P– As group and increases with an increasing ionicity or disparity between the two anions. The failure of the VCA to account for the bowing coefficient is intimately related to the main assumptions behind the model. It assumes that an alloy can be treated as a binary compound of known symmetry and without disorder. These assumptions greatly simplify the complexity of the problem, but at an important cost. A more accurate description needs to include the discrete distribution of atoms on the mixed sublattice and take into account the variation in local chemical environments. In this case, the characteristics of the alloy which depend on the statistics of substitution and the symmetry of the system, equal to that of the binary parents in the VCA, are invariably reduced and the translation invariance is lost. The bowing coefficient, as well as other effects such as alloy scattering, are a direct result of atomic scale disorder.1 Two effects contribute to disorder. The first is related to the bimodal distribution of bond lengths whilst the second is related to the fluctuations in electron density at the sites of the mixed sublattice. The first effect was first demonstrated by extended X-ray-absorption fine-structure measurements [14]. In this landmark result, it was found that the In – As and Ga – As bond lengths in InGaAs were almost equal to their bond lengths in InAs and GaAs, irrespective of the In composition. This result demonstrated that important local atomic distortion occurs even though the average lattice constant follows Vegard’s rule (linear interpolation). The atomic lattice relaxation needed to preserve the bond lengths is proportional to the lattice mismatch between two binary semiconductors. Table 6.3 lists the lattice mismatch for several mixed-anion systems. Comparing Tables 6.2 and 6.3, it is 1 Throughout this work, disorder does not refer to lattice irregularities or defects, but to the loss of symmetry associated with the natural variations in local atomic environment for the alloy.

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Table 6.3. Lattice mismatch, covalent radius and electronegativity difference for the mixed-anion systems of Table 6.2 Alloy AlAsP GaAsP InAsP AlAsSb GaAsSb InAsSb AlPSb GaPSb InPSb GaPN GaAsN

Lattice mismatch (%)

Covalent radius difference (%)

Electronegativity difference (%)

3.4 3.6 3.2 8.0 7.6 6.8 11.6 11.2 9.8 19.2 22.8

7 7 7 15 15 15 24 24 24 34 36

0.5 0.5 0.5 6 6 6 7 7 7 32.6 32.6

easy to notice that the bowing coefficient increases with the lattice mismatch between the binary parents. The second contribution to disorder mentioned above follows naturally from the chemical disparity between the internal electronic structure of the two atoms sharing the same sublattice. In contrast to compounds of known symmetry, the electron wave function cannot simply be represented using Bloch functions since the local charge distribution follows the alloy distribution statistics. The charge density variation on the mixed sublattice is proportional to the difference in electronegativity between the two mixed anions. Table 6.3 shows the electronegativity difference for the mixed-anion systems of Table 6.2. As can be seen, the bowing coefficient and the difference in electronegativity also appear correlated. These two contributions to disorder have very important effects on the electronic structures of the alloy: they introduce intraband and interband coupling [15]. Intraband coupling means that different locations of the Brillouin zone within a single band (conduction or valence) interact, mix character and repel each other. Interband coupling means that different bands interact and repel each other. In materials where the band gap is of the order of 1 eV, the intraband coupling tends to dominate since the energy separation between interacting bands is smaller (as an example, 200 meV typically separates the G – L extrema in III –V alloys). Therefore, the intraband coupling dominates and pushes down the G conduction band. This effect is mirrored in the valence band, although to a lesser degree, and an effective reduction of the band gap is observed. Intraband coupling dominates for all alloys listed in Table 6.2 and thus the bowing coefficients are all positive. It is interesting to note that the bowing coefficients are very different for the two systems shown in Table 6.2. The smaller values of the bowing coefficient for mixed-cation systems are related to the relatively lower intraband coupling in these alloys. It has been demonstrated that cation displacements from their ideal zinc-blende position, important in

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mixed-anion alloys, lead to strong intraband coupling. However, anion displacements, important in mixed-cation alloys, do not enhance this intraband coupling [16]. Furthermore, in mixed anions (mixed cations) the lower X-conduction band is of X1 ðX3 Þ symmetry and does (does not) repel the conduction band minimum to lower energy [17]. From the covalent radius and electronegativity difference between nitrogen and other anions, larger deviations from linearity can be expected from nitrogen containing alloys. It is indeed the case. For example, the bowing coefficient for GaAsN is about one order of magnitude higher compared to other alloys. The band gap of cubic GaN is 3.3 eV, therefore the VCA predicts that the band gap of GaAs12x Nx should increase from 1.424 eV by 19 meV per atomic percent of nitrogen. However, it came as an unexpected surprise when Weyers et al. and Kondow et al. reported their band gap measurements of GaAsN in the early 1990s [18,19]. They found that the band gap, instead of increasing, decreased at a rate of , 120 meV/% N. Allowing the bowing coefficient to correct for this large deviation results in a coefficient of approximately 10 –20 eV. This result indicates that the properties of GaAsN deviate not only from what would have been expected from the VCA model, but also from the behavior of other semiconductor alloys. Since this first report by Weyers et al., a lot of activity has been dedicated to unveiling the origin of the peculiar band gap variation and several other distinguishing characteristics have been reported. For example, it has been found that (1) a new optical transition, unexpected from a zinc-blende material, is observed [20,21], (2) in addition to some nitrogen pair states [5], nitrogen cluster states can bind excitons and a large number of sub-band gap states can be observed [22], (3) the conduction band energy dependence on pressure is strongly reduced and no G – X crossover is observed [21], and (4) a large electron effective mass [23] and a very short carrier lifetime degrade the transport characteristics. One of the most significant findings is that of Perkins et al. [20]. In 1999, they reported a new optical transition, completely unexpected from a zinc-blende semiconductor. This new transition, labeled Eþ ; involves the valence band maximum and a resonant state located above the conduction band minimum. As the nitrogen concentration increases, Eþ moves to higher energies at a rate of approximately 2/3 that of the band gap reduction. The origin of the participating conduction band state is central to the understanding of the giant bowing in GaAsN as the origin of both phenomena is closely related. In this chapter, the characteristics of all optical transitions observed are discussed, but the most important results are those related to Eþ ; as its characteristics give important clues to its origin. Many theoretical models have been proposed to explain the properties of GaAsN and the next section briefly describes the most relevant ones that have offered an interpretation for Eþ : Then, in Sections 6.4 and 6.5 where the experimental results are presented, the compatibility between our experimental findings and each theoretical interpretation will be discussed.

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6.3. PREVALENT THEORETICAL MODELS ON DILUTE NITRIDES

The most important models that have been proposed to explain the characteristics of GaAsN and the origin of Eþ are discussed next. The first model proposed to explain the origin of Eþ was suggested by Shan et al. [21]. 6.3.1 The Band Anticrossing Model This model is a simple empirical model. It considers the mutual repulsion between two bands. The first is the conduction band minimum and the second is a resonant state caused by nitrogen in the conduction band of GaAs. This resonant state is the level created by an isolated nitrogen atom in GaAs. This level, Nx ; cannot be observed directly, but by applying hydrostatic pressure on a sample doped with a nitrogen concentration around 1018 cm23, this level drops into the gap and binds excitons whose decay can be monitored in photoluminescence experiments [24]. This resonant level can be observed only at hydrostatic pressures above 22 kbar, but the extrapolation of its energy to ambient pressure indicates that this level is located between 1.67 and 1.70 eV above the valence band maximum or 150 –180 meV above the conduction band minimum at 4 K [25]. At relatively high nitrogen concentration (, 0.5%), Shan et al. proposed that the density of states of this resonant level becomes significant enough to transform into a band and to interact with the conduction band [21]. This assignment was supported by the apparent proximity between the Eþ transition and the Nx resonant level extrapolated to low pressure and room temperature. Therefore, two new bands are created in GaAsN. The bonding state at low energy, E2 ; corresponds to the conduction band edge of GaAsN whilst the antibonding state, Eþ ; forms a new conduction band state. These two bands interact and repel each other. Following an elementary two-level model, the energy of the states resulting from this interaction is given by E^ ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 2 ðEN þ ECB ^ ðEN 2 ECB Þ2 þ 4VCB;N Þ 2

ð6:1Þ

where ECB ðkÞ and EN are the energy of the GaAs conduction band and the nitrogen resonant state, respectively. VCB;N is a parameter describing the coupling between the bands. Using this model, the dependence of E2 (which is the fundamental gap E0 ) and Eþ with concentration can be modeled successfully by adjusting the strength of the interaction, VCB;N ¼ Cx1=2 ; and the energy of the resonant state. This model yields a remarkably good description of the physical properties of the fundamental band gap and Eþ : For example, the flattened dispersion explains the increase in electron effective mass [26] and the low-pressure coefficient of Nx explains the reduced pressure dependence of the conduction band minimum. Because this model provided a simple and satisfactory fit to many characteristics of the alloy, it has been very popular. It has been expanded to a 10-band k·p model [27], it has been supported by a more sophisticated analysis [28],

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and tight-binding models have also been proposed [27,29]. However, it will be shown that the assignment of the Eþ conduction band to a nitrogen-induced level is incompatible with many of our experimental findings. Moreover, this model assumes that the nitrogen resonant states form a well-behaved band, in contradiction with simple phenomenological arguments and more elaborate theoretical models [30]. The band anticrossing model appears to have been the most cited model in the dilute nitride literature in recent years. Therefore, throughout this work, we pay particular attention in describing the shortcomings of this model in favor of a model involving the splitting of the L-conduction band extrema, which, in our opinion, better represents the characteristics of GaAsN and other dilute nitride semiconductors. 6.3.2 Singularities in the Conduction Band Density of States Kent et al. have used a pseudopotential supercell technique to model the band structure of GaAsN [31]. This work studied the conduction band states of GaAsN starting from very dilute concentrations up to 1% N. The main interesting aspect of this calculation is that more than one nitrogen atom was included in the supercell, therefore nitrogen atom interactions could be studied. While this paper mostly concentrated on the characteristics of the conduction band edge and the localized states created by nitrogen pairs and clusters, it also provided an interpretation for Eþ : Adding a few nitrogen atoms to a GaAs matrix produces resonant and bound states, above and below the conduction band, respectively. At ultra low concentration, these states are relatively isolated from each other. At higher concentration, their spatial density increases and their mutual interactions induce broadening and splitting. The resulting effects were analyzed with an effective conduction band density of states as reported by Kent and Zunger [30,31]. It is found that nitrogen produces a complex distribution of localized and quasi-localized states both above and below the conduction band edge. According to these results, the quasi-localized states resonant with the conduction band are the most likely origin for Eþ [32]. Unfortunately, it does not appear that a correlation exists between the energy of the density of states maxima, localized or quasi-localized, and the experimental results. Nonetheless, there is one critical aspect bearing relevance to the interpretation of the Eþ transition. This calculation explicitly took into account the complex interactions between nitrogen states and it was found that the Nx states and the multiple pair configurations states, NNi ; interact and merge together to yield a density of state resembling that of a broad continuum with multiple local maxima. This result raises an important issue concerning the appropriateness of the BAC model since this phenomenological model neglected the multiple and diverse configurations nitrogen atoms can take. Since these configurations have been shown to lead to a complex and irregular distribution of states both below and above the band gap [22,31], the observed conduction band state associated with Eþ is unlikely to be related to nitrogen resonant states as will be demonstrated in Section 6.4.3.

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6.3.3 Symmetry-induced Splitting of the L-conduction Band Both models mentioned above implicitly assumed that the optical transition Eþ was directly related to the nitrogen resonant states. The possibility of a disorder activated transition was first mentioned in Ref. [20] and the work of Szwacki and Boguslawski was the first theoretical work to associate Eþ directly with the singlet derived from L [33]. A single isolated substitutional impurity breaks the translational invariance but preserves the point group symmetry Td : As a consequence, all points of high symmetry of the Brillouin zone collapse to the zone center. Therefore, the wave function at the four inequivalent L1c -valleys can be decomposed using the Td irreducible representation into a singlet, a1 ðLÞ; and a triplet, t2 ðLÞ: The wave functions corresponding to the X1c valleys decompose into a singlet, a1 ðXÞ; and a doublet, eðXÞ: The G1c zone center preserves its symmetry and is labeled a1 ðGÞ: Finally, the wave function of a nitrogen resonant state is represented by a singlet, a1 ðNÞ: All states of identical symmetry interact together and all singlets interact and repel each other in a complex fashion. This effect has been discussed extensively [34,35], but the possibility that Eþ might be related to the a1 ðLÞ singlet was introduced by Szwacki and Boguslawski [33]. In this calculation, it was found that the dependence of the energy position of the a1 ðLÞ singlet with nitrogen composition is close to that measured experimentally for Eþ : To further support this assignment, they have shown that optical transitions from the valence band maximum to a1 ðLÞ and a1 ðXÞ become allowed due to the strong perturbation caused by the potential of nitrogen. While a splitting of L into a singlet and triplet is always obtained in theoretical alloy calculations due to the intrinsic lack of long range translational symmetry, experimental evidence of this splitting has never been experimentally demonstrated in conventional semiconductor alloys. Nonetheless, in the light of the experimental results presented in the next sections, this interpretation is strongly favored.

6.4. ELECTROREFLECTANCE STUDY OF GaAsN

The GaAsN samples were grown epitaxially using either molecular beam epitaxy [36] or Metal-Organic Vapor Phase Epitaxy (MOVPE) on (001) GaAs substrates [20,37]. The epilayers were nominally undoped and grown on an n-type substrate. The n-type substrate was favorable for creating a large electric field modulation since the voltage drop is mostly limited to the epitaxial layer. The typical sample thickness was 0.2 mm. From X-ray diffraction, most samples with nitrogen concentration below 1.5% were coherently strained. Electro-modulated reflectance was used for measuring the energy of optical transitions. The samples were studied in contactless or direct contact mode. In contactless mode, a transparent electrode (an indium tin oxide or inconel coated glass plate) is brought in close proximity with the sample [38]. This mode usually gave satisfactory signal levels and was preferred for the measurement of the lowest energy transitions. However, higher

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sensitivity and signal levels can be achieved using a direct contact configuration. In this ˚ Ti and , 80 A ˚ Au contact layers were evaporated onto the sample. configuration, , 10 A The value of the internal electric field achieved in this mode can be much higher. This mode was preferred for extracting very weak features like Eþ þ D0 and Ep : The spectra were modeled using the third-derivative line shape [39] or the more complex form taking into account the Franz –Keldysh effect [40]. Using the line shape corresponding to the appropriate critical point, the energy, the broadening parameter, and the relative intensity of the optical transition can be reliably extracted. Figure 6.1 shows a typical GaAsN electroreflectance (ER) spectrum taken at 80 K. For most samples, seven optical transitions are observed, but only four were expected from a zinc-blende semiconductor. For reference, Figure 6.2 shows a selected portion of the band structure of GaAs and the position of the relevant conduction and valence bands. E0 is a transition involving the zone-center valence (G8v) and conduction (G6c) bands. This is the fundamental band gap of the alloy. E0 þ D0 is a transition involving the zone-center spin –orbit split-off valence (G7v) and conduction bands (G6c). E1 involves a region of the Brillouin zone close to the L point, between the L4v,5v valence and L6c conduction bands. E1 þ D1 involves the same conduction band state, but the spin – orbit split-off valence band L6v. The location in k-space of E1 and E1 þ D1 is close to the zone boundary L: Therefore, for convenience, these two transitions will be referred to as originating from the L point of the Brillouin zone. For GaAs, these four transitions have been well characterized by ellipsometry [41] and electroreflectance [42].

Figure 6.1. Electromodulated reflection spectrum from GaAs0.99N0.01 measured at 80 K.

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Figure 6.2. Tight-binding calculation of the electronic band structure of GaAs. Only the topmost valence bands and lower conduction bands are shown.

The other three transitions were completely unexpected for a zinc-blende alloy. The first one was first observed by Perkins et al. [20] and shortly followed by Shan et al. [21]. The energy location of this transition is between E0 and E1 : The valence band state related to this transition is the zone-center G8v valence band since a companion transition Eþ þ D0 transition located 341 meV above this is also observed. The fundamental problem consists in reliably identifying the conduction band state involved in this transition, since the band structure of GaAs (or any other zinc-blende semiconductor) does not allow for a critical point in this energy region between E0 and E1 þ D1 : Figure 6.3 summarizes the electroreflectance results measured at 80 K on GaAsN samples with concentrations up to 2.1%. The characteristics of these transitions are discussed next, starting with the fundamental band gap transition. 6.4.1 The Dependence of the Fundamental Band gap As mentioned earlier, the first distinguishing characteristic of GaAsN is the dependence of its band gap as a function of nitrogen concentration. First measured in 1992 by Weyers et al. in photoluminescence experiments and further supported in 1994 by Kondow et al., the band gap of GaAs12x Nx ðx , 2%Þ did not converge towards that of GaN (3.3 eV) as expected, but, surprisingly, rapidly decreased with nitrogen content [18,19]. Figure 6.4 shows the experimental band gap of GaAsN measured using electromodulated reflectance at room temperature as a function of nitrogen concentration. The maximum nitrogen concentration is limited by material quality, which degrades rapidly above , 2.5%. As mentioned earlier, the band gap does not follow the linear interpolation

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Figure 6.3. Compilation of electroreflectance results. The energy of all transitions observed between 0.8 and 3.8 eV is shown.

(dashed line) expected from the VCA. The discrepancy is severe and much higher than what has ever been observed for other alloys. GaAsN is the first semiconductor alloy to exhibit such a large deviation from this simple model. Using this experimental data, we can extract the bowing coefficient, b; as a function of concentration, x: This dependence is shown in Figure 6.5. We observe that this coefficient is very high at low concentrations and rapidly decreases to values around 20 eV and then decreases linearly at concentrations exceeding 0.5%. This non-linearity is interesting and indicates that the mechanisms behind the band gap reduction are strongest at low concentration and weaker at lower values of the band gap, strongly supporting a band repulsion between the conduction band minimum and a higher energy state yet to be identified. The non-linearity of the bowing coefficient clearly indicates that its concept is inappropriate for this extreme case. However, it has already been extensively used and is nonetheless useful for the quantification of this deviation from linearity, but the concentration at which the bowing is calculated must also be specified.

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Figure 6.4. Bandgap of GaAsN as a function of nitrogen content.

There have been several reports published on the temperature dependence of the fundamental band gap. Some of them used photoluminescence spectroscopy [43,44] to measure the temperature dependence even though the presence of strongly localized states has been shown to dominate the emission spectra at low temperature and therefore compromise the identification of the free exciton line shape, if present at all [22,45].

Figure 6.5. Bowing coefficient extracted from the bandgap values shown in Figure 6.4.

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We therefore dismiss the luminescence results since they rarely probe the band edge emission at low temperature. Using absorption spectroscopy, which is more reliable than photoluminescence, Uesugi et al. reported that the band gap temperature dependence of GaAsN with 1% N is reduced to less than 60% of that of GaAs [46]. This effect was seen as an advantageous property, since luminescent emission characteristics from an optical device made with GaAsN could show an improved stability against temperature fluctuations. Figure 6.6 shows electroreflectance spectra taken from four samples with nitrogen concentrations up to 2.1% measured at 80 and 300 K. The band gap energy extracted from these spectra is shown as a black dot. Panel (c) of Figure 6.7 shows the temperatureinduced energy variation for the fundamental band gap, E0 ðG8v 2 G6c Þ; between 300 and 80 K. For simplicity, this quantity will be referred as “energy shift” or DE: For reference, the energy shift commonly measured for GaAs is shown by the dotted horizontal line. This value of 84.3 meV for GaAs was obtained using the recommended Varshni’s parameters, a ¼ 0:5405 meV=K and b ¼ 204 K [12]. As can be seen, the energy shift for GaAsN is almost constant for the whole concentration range studied and very close to that of GaAs.

Figure 6.6. Electroreflectance spectra of E0 measured at 80 and 300 K for several nitrogen concentrations. The bullet indicates the critical point energy of the transition obtained from a line shape fit.

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Figure 6.7. Temperature-induced energy shift between 80 and 300 K for (a) Ep ; (b) Eþ ; and (c) E0 : The dotted lines show the expected shift for the relevant GaAs band edges.

In contrast to the absorption results mentioned above, no significant change in temperature sensitivity is observed. This discrepancy results from the contribution of sub-band gap states to the absorption curves, therefore underestimating the band gap at high nitrogen concentration. Absorption is one of the most fundamental measurements one can perform to probe the band structure of a semiconductor material, but the conventional technique used to extrapolate the band gap energy is most reliable for sharp absorption edges. In the case of materials exhibiting strong broadening (originating from alloying effects, sub-band gap states, band tailing and impurity band formation), the determination of the position of the band gap energy from absorption spectra can be subjective and inaccurate [47]. Since all of these effects have been observed in GaAsN [22,46,48], care must be used in the interpretation of the absorption results. The absorption data shown in Ref. [46] clearly demonstrate this point. Comparing the absorption edge as a function of temperature, one quickly notices that the absorption edge is softer at low temperature and steepest at room temperature. This effect is explained by the presence of sub-band gap states participating in the absorption at low temperature only, therefore underestimating the band gap. The advantage of electroreflectance resides in the measurement of the third derivative of the absorption curve,

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producing a sharper line shape from which the energy of the critical point is better defined and resulting in a more consistent description of the band edge energy. In contradiction to these absorption reports, we find that the temperature sensitivity of the GaAsN band gap is not substantially changed from that of GaAs. The independence of the energy shift with respect to the nitrogen content is in disagreement with the BAC model. According to the authors of this model, the temperature dependence of Nx should be very small [49]. This argument is very reasonable since such a localized state in real space is likely to borrow its properties from the conduction band averaged over the whole Brillouin zone. Such a state is likely to have a small temperature coefficient, i.e. a small energy shift with temperature. Therefore, if Nx mixes with the conduction band minimum, the temperature dependence of E0 should decrease with nitrogen concentration, while that of Eþ should be small but increasing with nitrogen concentration. In contrast to these predictions, we find that the temperature dependence of E0 is relatively unaffected with nitrogen concentration and, as will be demonstrated in Section 6.4.3, the temperature dependence of Eþ exceeds that of E0 : Strong alloying effects are observed in GaAsN. Figure 6.8 plots the measured broadening parameter, G; extracted from the line shape fit as a function of nitrogen concentration. The broadening parameter of E0 increases rapidly as a function of nitrogen concentration. This large broadening can be expected from alloys made from binary systems with large lattice mismatch and electronic energy disparity. For modeling this data, we used the model of Schubert et al. [50]. In this simple model, the broadening of an optical transition is proportional to the variance of the Bernoulli distribution representing

Figure 6.8. Broadening parameter obtained from electroreflectance as a function of nitrogen concentration for E0 ; E1 ; and E1 þ D1 : The lines are fit to the data.

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the probability of finding a given number of nitrogen atoms in a given volume. This distribution can be approximated by a Gaussian distribution since, in the typical volumes considered here, the number of anions, NA ; is large. The full width at half maximum of this distribution, scaled by the change in band gap energy, E0 ðxÞ; as a function of composition, leads to the following expression for the broadening parameter  sffiffiffiffiffiffiffiffiffiffiffiffi  dE0 ðxÞ  xð1 2 xÞ   : GðxÞ ¼ Gð0Þ þ 2:36 dx  NA

ð6:2Þ

Since E0 ðxÞ is known, NA is used as a fitting parameter. This model reproduces quite well the dependence of GðxÞ on E0 : The broadening is associated with the disorder on the anion sublattice, and the rapid broadening is intrinsically associated with the rapid band gap variation with nitrogen composition. Two effects are noticed concerning the spin –orbit split-off valence band transition (SO band). First, the spin –orbit energy decreases and the relative intensity of the E0 þ D0 transition increases with respect to the intensity of the E0 transition. These effects appear to be in contradiction with the widespread assumption that nitrogen has negligible effects on the valence band [21,26,30]. Early on in the study of semiconductor alloys, it was recognized that fluctuations in local potential were important enough to affect the nature of the bonding and the local charge distribution. Since then, the bowing parameter bD0 has been established as a direct consequence of the discreteness of local environments [51,52]. It is common to describe the concentration dependence of D0 using the relation D0 ðxÞ ¼ D0 ðxÞ 2 bD0 xð1 2 xÞ where D0 is the value interpolated from the binary constituents. It is now well accepted that the values for the bowing coefficient are almost always positive, i.e. D0 is decreased with respect to the linear interpolation [12]. In the case of GaAs12x Nx ; D0 decreases, since compared to arsenic, the spin –orbit interaction is weak for atomic nitrogen and results in a small valence band splitting of 17 meV for cubic GaN [12]. Since the spin –orbit splitting for GaAs is 341 meV, the slope of D0 should approximately be 3.3 meV/%. Figure 6.9 shows the valence band splitting measured at 80 and 300 K as a function of nitrogen concentration. The data at 300 K includes the data from Ref. [20]. Within a concentration range between 0 and 2.1%, the valence band splitting measured at 80 K steadily decreases with a slope of approximately 20 meV/%. This tendency is consistent with the splitting measured at 300 K, but the uncertainty in the measurement is higher compared to that of the 80 K data. The tensile strain present in GaAsN cannot account for the deviation of D0 from D0 ðxÞ observed in Figure 6.9. Biaxial strain changes the energy separation between valence bands. Using a 6 £ 6 k·p Hamiltonian to calculate the effects of strain, the energy separation between the light-hole and the spin – orbit valence band increases with a slope equal to þ 5.4 meV/% N. Similarly, the energy separation between the heavy-hole and

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Figure 6.9. Spin–orbit splitting energy as a function of nitrogen concentration. The dotted line represents the interpolated splitting ðD0 Þ and the solid line is a linear fit to the splitting measured at 80 K.

spin – orbit valence bands decreases at a rate of 2 10.8 meV/% N. Therefore, even if we assume that the E0 transition solely originates from the split-off heavy-hole band, which is very unlikely, the slope of E0 þ D0 2 E0HH would still be less than half of the observed value. Even using a larger deformation potential of b ¼ 23 eV as reported in Ref. [53], this slope would not exceed 14 meV/%. This slope is still smaller than the experimental value and since it corresponds to the exaggerated case that E0 solely originates from the higher energy heavy-hole, we rule out strain as the main contribution to the observed reduction of the spin – orbit splitting energy. The faster than expected reduction in the spin – orbit splitting is again a disorder-induced effect. Compositional disorder induces strong intraband and interband mixing [16]. It has been demonstrated theoretically that the bowing of D0 is the result of interband coupling: conduction band s states mix into the valence bands [51]. For example, when four identical anions surround a cation, no mixing occurs. When the cation is surrounded by two types of anions, conduction band s character mixes into the valence bands, reducing the relative weight of the p character, hence reducing the magnitude of the spin –orbit splitting [15,52]. Our second interesting finding concerning E0 þ D0 relates to its intensity. Early on in the study of GaAsN, several groups reported that the intensity of the E0 transition was reduced at high nitrogen concentration [20,54,55]. We observe a similar effect and, in addition, we find that the intensity of the split-off valence band transition follows an opposite trend: it increases in intensity as a function of nitrogen concentration. The inset of Figure 6.10 shows the electroreflectance spectra of GaAs0.99945N0.0055 and GaAs0.983N0.017 measured at 300 K.

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Figure 6.10. Intensity ratio (see Eq. (6.3)) between E0 and E0 þ D0 transitions (solid circles). The absolute intensity of E0 þ D0 is shown on the right scale (empty circles). The inset illustrates the increase of the intensity of E0 þ D0 with increasing the nitrogen concentration.

Relative to the intensity of E0 (normalized to one in Figure 6.10), the intensity of E0 þ D0 for the low concentration sample is barely observable on this intensity scale. This result is similar to what is typically observed from pure GaAs. In contrast, E0 þ D0 is easily observable for the 1.7% sample. Figure 6.10 systematically demonstrates this effect as a function of nitrogen concentration. Since the broadening factor indirectly affects the intensity of the transition, the value of the amplitude was corrected for its influence. Therefore, instead of directly comparing amplitudes ðAÞ; we plot A=G 3=2 ; where G is the broadening parameter. This normalized value takes into account the different values of the broadening parameter between E0 and E0 þ D0 and its variation with nitrogen composition. The relative intensity R plotted in Figure 6.10 is defined as !3=2 IðE0 þD0 Þ GðE0 Þ R¼ : ð6:3Þ IðE0 Þ GðE0 þD0 Þ The transition probability for E0 and E0 þ D0 is strongly affected by nitrogen concentration. As seen in Figure 6.10, the intensity ratio increases remarkably with nitrogen concentration. Although this increase results predominantly from a large intensity reduction for E0 ; it is interesting to note that the absolute intensity of E0 þ D0 increases with concentration. The empty circles, associated with the right axis, represent the intensity

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of the spin – orbit valence band transition, E0 þ D0 : The intensity increases by approximately one order of magnitude over the concentration range studied. This phenomenon is intriguing and cannot be accounted for by change in conduction band effective masses (a doubling of the electron effective mass would change the ratio R by less than a factor of two). Since both transitions share the same conduction band state, the nature of our experimental results seems to suggest that, contrary to common belief, the valence bands are perturbed by the addition of nitrogen and that the valence band maxima and the spin – orbit split-off valence band are affected differently. While it is natural to suggest that the momentum matrix element describing the transition probabilities is affected differently, it is not clear what type of the band mixing can produce the effects observed and this variation in intensity remains unexplained. Even without emphasizing the difficulty in understanding the origin of this effect, the reduction of the E0 intensity might be problematic for the application of GaAsN for optoelectronic devices. 6.4.2 The Broadening of E1 and E1 1 D1 The optical transitions originating along L; in proximity to L; shift to higher energy and broaden considerably with increasing nitrogen concentration. E1 and E1 þ D1 shift to higher energy at a ratio of 13.3 and 10.0 meV/%, respectively. The most striking effect relates to the strong broadening of these two transitions. Figure 6.8 shows the broadening parameter as a function of nitrogen concentration. GE1 and GE1 þD1 start at 27 and 38 meV, respectively. At about 0.8% nitrogen concentration, the line shapes of E1 and E1 þ D1 overlap and thus further complicate an accurate determination of the critical point energy. At 1% nitrogen concentration, GE1 and GE1 þD1 already exceed 80 and 105 meV. This broadening is very important and severely limits the accuracy with which the absolute value and shift of E1 ; E1 þ D1 ; and D1 can be determined. While it has been found that the large broadening parameter for E0 was in part due to the strong value of the derivative found in Eq. (6.2), the origin of the broadening appears to be different for E1 and E1 þ D1 since ldE1 ðxÞ=dxl is one order of magnitude smaller than ldE0 ðxÞ=dxl: This effect is explained by the presence of two unresolved transitions in the vicinity of E1 and E1 þ D1 and is discussed in the next section. 6.4.3 The Origin of E1 and E1 1 D0 The transition Eþ was first reported by Perkins et al. [20,56] and then by Shan et al. [21]. Its discovery completely reshaped the hypothesis behind the various models that had been proposed to explain the band gap reduction and other properties of GaAsN [16,57]. However, the role played by Eþ with respect to the giant band gap bowing has been far from straightforward to unravel. In a short period of time, several theoretical models were proposed initiating an intense debate over their validity and accuracy. The key to the understanding of most GaAsN properties is intimately related to the identification of the conduction band state associated with Eþ :

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As mentioned in a previous section, the main hypothesis behind the BAC model is that Eþ is related to Nx ; the resonant level produced by a single nitrogen atom observed at hydrostatic pressures exceeding 22 kbar in dilute nitrogen doping samples [5,25]. In their paper, Shan et al. made this assignment using only a few data points and did not consider other alternative conduction band states [21]. We find that a careful examination of our extensive data indicates that for zero doping Eþ extrapolates higher than the expected position of Nx ; very close to the energy of the conduction band L point, L6c : Figure 6.11 shows an enlarged portion of Figure 6.3 [58]. A linear regression applied to the data yields an extrapolated energy value of 1.796 ^ 0.020 eV. The uncertainty is taken as the difference between the minimum and maximum extrapolated values allowed by a 95% confidence band. While the experimental data is best represented by a linear dependence, it is not possible to rule out a possible quadratic dependence for Eþ : Applying a quadratic fit (not shown) results in a slightly smaller extrapolated value of 1.770 eV. The impurity level produced by an isolated nitrogen atom resonant with the conduction band is

Figure 6.11. Energy of Eþ ; Ep ; and E1 as a /function of nitrogen concentration. The solid lines are the best fit from linear regressions.

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located between 1.670 and 1.700 eV [25]. This impurity level is at least 70 meV below the extrapolated value obtained for Eþ using a quadratic fit. Eþ extrapolates very close to the position of the L6c conduction band located at 1.815 eV [12], which is the position of the GaAs L-conduction band with respect to the valence band maximum. Figure 6.2 shows a selected portion of the band structure of GaAs. It is interesting to note that the energy separation between the valence band extrema, L4v;5v ; and the valence band maximum, G8v ; is 1.2 eV [59]. Recasting the energy of Eþ by 1.2 eV to higher energy helps clarify the situation. Doing so is equivalent to replacing the G-point valence band maximum origin of the transition by the L-point valence band extremum. This dependence is shown as E0þ in Figure 6.11. As is evident, E0þ at x ! 0 is located close to E1 (3.02 eV), indicating that both transitions originate from the same conduction band state as has been suggested in the electronic band-structure calculation of Szwacki and Boguslawski [33]. Therefore, the conduction band state associated with Eþ is the singlet state issued from L; i.e. a1 ðLÞ: To further support this assignment, we show that the temperature dependence of Eþ agrees very well with the measured temperature dependence of the L6c band minima with respect to the G8v maxima, a necessary requirement for this assignment. Figure 6.12 shows the electroreflectance spectra for Eþ measured at 80 and 300 K for several nitrogen compositions. The temperature-induced shift of Eþ is shown in panel (b) of Figure 6.7. It is very interesting to find that the temperature shift of Eþ significantly exceeds that of E0 for all samples studied. Table 6.4 shows the Varshni’s coefficient and expected temperature shift for the three conduction band extrema. For GaAs, the temperature sensitivity of the L6c conduction band with respect to the G8v valence-band edge is 15 and 36% higher than that for the G and X conduction band minima relative to this edge, respectively. Assuming that a1 ðLÞ has characteristics similar to that of L6c ; it would be reasonable to expect a temperature shift for Eþ similar to that of the G8v 2 L6v band edge. Effectively, the data of Figure 6.7(b) is very well represented by the temperature-induced shift of 98 meV associated with this band edge. This agreement is additional strong evidence in support of the assignment of Eþ with a1 ðLÞ: Moreover, the BAC model predicted a very small temperature dependence for this transition, in clear contradiction with our findings. The broadening parameter associated with Eþ is reminiscent of a well-defined band. Figure 6.13 shows the broadening parameter of E0 and E0 þ D0 as a function of nitrogen concentration. As can be seen, the broadening parameters for both transitions are very similar, in average the broadening parameter of Eþ is only 6% larger than that of E0 þ D0 : Moreover, the broadening parameter of Eþ parallels that of E0 þ D0 : This finding is hardly compatible with the BAC model. According to this model, the nitrogen resonant state Nx interacts with the conduction band minimum to form Eþ : However, this model neglects one very important aspect of nitrogen in GaAs: it forms a multitude of resonant levels. It has been shown that nitrogen pairs also form resonant states which,

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Figure 6.12. Spectra of Eþ at 80 (W) and 300 K (†) for several nitrogen compositions. The lines are fit to the spectra. The low-energy part of the 80 K spectra was truncated for clarity.

just like Nx ; can be pulled out of the conduction band by applying hydrostatic pressure [5,24]. To be consistent, the BAC model should include not only the states produced by an isolated nitrogen atom, but also those formed by the nitrogen pairs whose density of states are comparable or higher than that of Nx for 1% nitrogen doping. Figure 6.14 shows the probability of pair formation as a function of the nitrogen separation Table 6.4. Temperature dependence of the conduction band minima of GaAs relative to the top of the valence band maximum G8v [60]

G6c L6c X6c

a (meV/K)

b (K)

Eð80 KÞ – Eð300 KÞ (meV)

0.5405 0.63 0.46

204 204 204

85 98 72

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Figure 6.13. Broadening parameter of E0 þ D0 and Eþ as a function of nitrogen concentration. The lines are linear fits.

ðPNN ðrÞ ¼ 4pCr 2 expð2 4p3C r 3 Þ; where r and C are the pair separation and the average nitrogen concentration. For example, at a concentration of l%, the probability of a nitrogen atom of forming an isolated state well separated from any other nitrogen atom ˚ ) is very small while the most probable pair configuration is NN6 : (pair separation . 20 A As has been demonstrated in GaP and in GaAs, the energy position of a given pair configuration is very sensitive to the pair separation [2,5]. For the case of GaAs, the pair

Figure 6.14. Probability for forming a pair for nitrogen atoms as a function of pair separation and nitrogen content.

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of smallest separation, NN1 ; is located more than 150 meV below the isolated nitrogen impurity state. Combining the large concentration of various pair states and their energy dispersion as a function of separation, the conduction band edge of GaAsN should be filled with resonant states interacting with each other as demonstrated by the calculations of Kent and Zunger [31]. Therefore, if Eþ were to evolve from a nitrogen related resonant state, all nitrogen pair states need to be considered as well. Furthermore, it would be very unlikely that the complex interaction between all these resonant states and the conduction band minimum produced a well-defined optical transition with characteristics similar to that of a host band-like E0 þ D0 : Because of the small broadening parameter associated with Eþ ; we associate this state with a well-defined host-type band-edge transition like a1 ðLÞ: As has been shown in Figure 6.8, the broadening parameters of E1 and E1 þ D1 increase much faster than that of E0 : This anomalous broadening is simply associated with the presence of an additional transition located between E1 and E1 þ D1 involving a1 ðLÞ and the valence band extremum originating from L4v;5v ; see E0þ in Figure 6.11. In summary, as a result of reduced symmetry and strong intraband coupling, forbidden transitions become optically allowed in dilute GaAsN alloys. Eþ is the first such transition to be observed in the large family of semiconductor alloys. 6.4.4 Another Unusual Transition Ep Another unexpected transition is seen in GaAsN. This transition was first observed by Perkins et al. [61]. It is labeled Ep and its energy position with nitrogen concentration is shown in Figure 6.11. It is not possible at this point to unambiguously identify the origin of this transition, but two alternative possibilities are provided. Ep appears as a rather broad and weak transition on the lower energy side of E1 and can only be observed in direct-contact electroreflectance. (A direct contact can create a significant electrical field modulation for a modest applied voltage.) Several electroreflectance spectra are shown in Figure 6.15. The solid line shows a fit taking into consideration the M1 nature of the E1 and E1 þ D1 critical point. Ep was also modeled using an M1 critical point. While it might not be the most appropriate line shape, the error that this assumption adds to the critical-point energy should be small [41]. As can be seen from Figure 6.15, Ep moves to lower energy at a rate of 2 59 meV/% N and extrapolates, at x ¼ 0 to 2.91 ^ 0.034 eV. While Eþ is observed because of a relaxation of selection rules due to the lack of translational symmetry, a similar origin for Ep is excluded. For example, assigning it to a transition from G8v to a1 ðXÞ is dismissed since this would extrapolate to a much lower energy (1.98 eV). The value of Ep ðx ! 0Þ coincides with the energy of a transition between the L6v split-off valence and the G6c conduction band. However, such a transition should have been accompanied with a lowenergy transition related to the L4v;5v band and, additionally, its energy dependence on nitrogen concentration should be comparable to that of E0 : Since neither of these conditions are satisfied, this possibility is dismissed.

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Figure 6.15. Spectra of Ep ; E1 ; E1 þ D1 at 80 (W) and 300 K (†, shifted to higher energies by the energy indicated). The lines are fit to the spectra.

Following a similar approach used previously on Eþ ; one can recast Ep by 1.2 eV, but this time to lower energy. The result is shown by the line labeled E0p in Figure 6.11. One finds that E0p extrapolates at x ! 0 to 1.710 ^ 0.034 eV which is close to the energy of Nx that corresponds to the resonant level produced by the isolated nitrogen atom in GaAs. Photoluminescence experiments have shown that the isolated nitrogen impurity state becomes a bound state at hydrostatic pressure exceeding , 22 kbar. At ambient pressure and low temperatures, the expected position of this nitrogen level extrapolates to about 150 –180 meV above the conduction band minimum [25]. This energy range is shown in Figure 6.11 by the vertical bold line close to the energy axis. This coincidence suggests that Ep might be related to the nitrogen-induced resonant band in GaAs12x Nx : Panel (a) of Figure 6.7 shows the energy shift of Ep between 80 and 300 K. While the uncertainty is relatively large, the temperature-induced shift is the largest compared to that of E0 and Eþ

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and is very close to the temperature dependence of E1 for GaAs [41], indicating that Ep emulates the temperature dependence of the L valence- to conduction-band edges. This rather high temperature sensitivity is surprising if we assume that Ep originates from the Nx localized resonant level. It has been shown that the wave function of the nitrogen related resonant state projects to all regions of the Brillouin zone of GaAs, demonstrating that this state is highly delocalized in momentum space. Therefore, the temperature sensitivity of the resonant level should approximate the temperature sensitivity of the conduction band states averaged over a large region of the Brillouin zone. This average should be much smaller than that observed in Figure 6.7. Therefore, this result is unfavorable to the assignment of Ep to a nitrogen-induced resonant level. It is possible that Ep ; just like Eþ ; originates from the highly perturbed L conduction band. Taking into consideration interactions between nitrogen atoms, the point group symmetry becomes a subgroup of Td : Therefore, the formation of nitrogen pairs, necessary implies that the degeneracy of the states issued from L is further broken down. Table 6.5 shows the various zone-center states created by the wave function of the four inequivalent L-valleys according to the zone-center symmetry. As can be seen, if the distance between nitrogen atoms is small enough, a mutual interaction occurs, the symmetry is further reduced, and the degenerate triplet state t2 state is broken into multiple states of various symmetry. It has been demonstrated that the dominant configuration at 1% nitrogen doping is that of pairs (see Figure 6.14). Therefore, the degeneracy of the t2 state must be reduced. Since most lower symmetries include at least one singlet state, Eþ can originate from one of these states. In this scenario, both Eþ and Ep share a similar origin, i.e. they appear because of the loss of translational symmetry and a reduction in point group symmetry, respectively. This interpretation is supported by results from resonant Raman measurements, where three resonant features located at energies higher than the band gap extrapolate to L6c at x ! 0 and are presented in the next section [62]. However, even with a large number of data points, it is difficult to reach a definitive conclusion on the origin of Ep due to its weak intensity and broad line shape. It would be very instructive to compare our results with calculated transition probabilities between the valence band maximum and the split states enumerated in Table 6.5. Table 6.5. Decomposition of the L1c-wave function for various zone-center symmetry Configuration

Symmetry

Decomposition

Td D2d C3d C2v C2

a1 þ t2 a1 þ b2 þ e 2a1 þ e 2a1 þ b1 þ b2 2a þ 2b

NAs NN[00h] NN[hhh] NN[0hh] NN[0hk] a; a1 ; a2 ; b; b1 ; b2 are singlets and e is a doublet.

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6.5. RESONANT RAMAN SCATTERING STUDY OF CONDUCTION BAND STATES

In this section, we present a resonant Raman scattering study of GaAsN. This technique provides a different perspective on the resonant conduction band states and essentially complements and supports the interpretation of Eþ presented in the previous section. As will be demonstrated, resonant Raman scattering is a powerful technique to probe subtle changes in the host electronic states induced by nitrogen impurities. For this study, the samples were 0.4 –1.5 mm thick GaAs12x Nx epilayers grown by metal organic chemical vapor deposition on (100) GaAs substrates. More details can be found in Refs. [20,37]. All Raman spectra were obtained in the zðYYÞz configuration, where z and Y represent the [001] and [110] crystal directions, respectively. In this scattering geometry, the zone-center longitudinal optic ðLOG Þ phonon is Raman active but the zone-center transverse optic ðTOG Þ phonon is not. 6.5.1 LOG Intensity Resonance Resonant Raman scattering spectroscopy enables one to probe electronic states by monitoring the enhancements of lattice vibrations occurring at critical points in the joint density of states. Therefore, resonant Raman scattering is a powerful spectroscopic technique to study the electron – phonon interaction and the electronic band structure of semiconductors. More specifically, the Raman scattering response near a resonance can be approximated by 2    k0lHeR lmlkmlHep lmlkmlHeR l0l   Ið~vÞ ,  ð6:4Þ   ð~v 2 Em 2 iGm Þð~v 2 Em 2 ~vp 2 iGm Þ  where l0l and lml represent the initial and the intermediate (resonant) electronic state of energy Em ; Gm is a broadening factor accounting for the finite lifetime of lml; ~v is the incident photon energy, ~vp is the participating phonon energy, and HeR and Hep are Hamiltonians representing the electron – photon and electron – phonon interactions, respectively. The denominator in this last equation mandates a phonon intensity resonance for photon energies corresponding to the energy of the intermediate state lml: For example, phonon intensity resonances in GaAs are observed at photon energies corresponding to the fundamental band gap E0 ; its spin – orbit split-off companion E0 þ D0 ; and E1 [63]. For the case of GaAsN, an additional intensity resonance is observed at an energy close to that of Eþ : Figure 6.16 shows the resonance profile associated with the GaAs-like LOG phonon intensity. As can be seen, a strong intensity enhancement occurs at an excitation energy EI : This energy is close to that observed from the Eþ transition plus the energy of a LOG phonon, indicating the resonance is outgoing. As expected, a weak intensity resonance of the LOG phonon is also observed at the E0 þ D0 transition energy (, 1.7 eV).

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Figure 6.16. LOG phonon intensity resonance profile for GaAs0.922N0.078 measured at T ¼ 80 K: The line is a guide to the eye. Inset: normalized (with respect to the GaAs LOG phonon) Raman spectra excited with photon energies of 1.789 eV (circles) and 1.907 eV (line).

The energy of the LOG phonon intensity resonance ðEI Þ is shown in Figure 6.17 as a function of nitrogen concentration. Although blue shifted by the energy of approximately one LOG phonon, the energy of EI clearly parallels that of Eþ shown in Figure 6.11 and extrapolates to the GaAs L conduction band extrema. We therefore conclude that the intensity resonance observed is associated with the a1 ðLÞ singlet. Again, the nature of intensity resonances further confirms that Eþ is indeed related to a well-defined band edge rather than a distribution of nitrogen resonant states as implied by the band anticrossing model. In addition, the activation of L and X zone-boundary phonons and their resonance at EI demonstrate that the wave function of a1 ðLÞ has a significant projection onto all conduction band extrema (G; L; and X), as expected from a strong interband mixing [64]. 6.5.2 LOG Width Resonance The LOG phonon in ternary semiconductor alloys normally exhibits a (symmetric) linewidth broadening due to alloy-induced disorder. This phenomenon is well understood and the broadening is independent of the excitation energy. Interestingly, Cheong et al. [65] reported a very unusual resonance of the LOG -phonon linewidth at energies below that of the Eþ transition. This unusual effect is illustrated in the inset of Figure 6.16. The Raman spectra measured close to the linewidth resonance maximum (circles) show an asymmetric linewidth broadening compared to the spectra measured away from the resonance (line). The asymmetry of the linewidth is very pronounced on the low energy side and is explained by the activation of LOG phonons with non-zero wave vectors [65].

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Figure 6.17. Energy positions of LOG phonon intensity maximum EI and linewidth maxima of EW and E0W as a function of nitrogen concentration.

The asymmetric linewidth broadening involves optical phonons spanning a significant portion of the Brillouin zone and is associated with the strongly localized potential created by nitrogen atoms and indicates that the intermediate states involved are formed from a broad mixture of Brillouin states. The resonance of the LOG phonon linewidth and the concomitant enhancement of TO/LO phonon intensity ratio for GaAs0.922N0.078 are displayed in Figure 6.18 as a function of the excitation energy. Two distinct maxima, labeled EW and E0W are observed for both the full width at half maximum of the LOG phonon and the TO/LO intensity ratio. The selective activation of non-zone-center phonons only for certain excitation energies also indicates that the asymmetric linewidth broadening is not the usual disorder activated mode ubiquitous in Raman studies of semiconductor alloys, but is related to the presence of an intermediate electronic state in the band structure. Arguments similar to those presented above explain the TO/LO intensity ratio resonance: the activation of non-zone center phonons is associated with a partial relaxation of the momentum conservation rule, strengthening the forbidden TOG intensity clearly beyond that expected from the usual excitation-energy-independent alloy disorder. Since no intensity resonance is associated with either EW or E0W ; we can conclude that optical transitions between the valence band maximum and the corresponding

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Figure 6.18. 80 K resonance profile for the FWHM (squares) of the LOG phonon and TO/LO intensity ratio (circles) for x ¼ 0:78%: Note that the ratio maxima coincide with the FWHM maxima (dotted lines). Lines are guides to the eye.

conduction band states are forbidden, very weak, or their projection onto G is very small. As mentioned earlier, a highly localized potential in real space is delocalized in momentum space, and vice versa. Therefore, the asymmetric linewidth resonance is a strong evidence that the intermediate electronic state involved in this resonance is activated by a localized perturbation significantly perturbing the host electronic states. Figure 6.17 shows the dependence of EW and E0W as a function of nitrogen concentration. The two maxima EW and E0W are distinctly observed for GaAsN samples with nitrogen compositions exceeding 0.35%, below this concentration they are not clearly resolved due to their proximity. The energy of EW is relatively constant with respect to nitrogen concentration whereas that of E0W shifts to lower energies rapidly. It is important to note that the linewidth of the LOG phonon of pure GaAs remains practically constant over an excitation energy range extending from 1.55 to 2.0 eV, i.e. no linewidth resonance can be observed at E0 and E0 þ D0 : Additionally, no linewidth resonance is observed at Eþ or EI in GaAsN [65]. From the data of Figure 6.17, we find that both EW and E0W extrapolate at x ! 0 to the energy of the GaAs L-conduction band extrema. This suggests that both transitions might be associated with this conduction band extrema, just like EI and Eþ : As described in the previous section, the loss of translational invariance due to the presence of nitrogen splits the fourfold degenerate L-conduction band into a singlet and a triplet. An optical transition between the valence band maximum and the singlet is allowed and results in Eþ : At concentrations exceeding 0.5%, the density of states of nitrogen pairs exceeds that of isolated nitrogen (see Figure 6.14) and the symmetry is further reduced. As shown in

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Table 6.5, the symmetry of any nitrogen pair lifts the degeneracy of the triplet into singlets and doublets. The data of Figure 6.17 provide strong evidence in favor of this interpretation and indicate that EI ; EW ; and E0W share the same origin. Whereas the correlation between EI observed in Raman scattering and Eþ observed in electroreflectance is evident, it is more difficult to draw a similar association between E0W and Ep : For example, Ep involves the L-valence band extrema, but E0W involves the G-valence band maximum. However, this does not imply that these two transitions are not related to the same conduction band state since both techniques probe the electronic band structures through different physical mechanisms and are subject to different selection rules. A more complete description of the Raman results can be found in Ref. [66].

6.6. COMPATIBILITY WITH OTHER EXPERIMENTAL RESULTS

Several other experimental results support our assignment of Eþ to a singlet issued from the L-conduction band. (1) Resonant Raman experiments studies report a similar transition observed through an intensity resonance of the longitudinal optical phonon [65]. (2) The reduced pressure dependence of E0 observed by Shan et al. results from the mixing of L-character into the conduction band minimum of GaAsN. In GaAs, the pressure dependence of the conduction band edge with respect to the valence band maximum is 11.8 meV/kbar, while that of the L-point is only 5.2 meV/kbar. Therefore, a reduced pressure sensitivity of the band gap results from the repulsion and mixing primarily between a1 ðLÞ and a1 ðGÞ at low pressure and also with a1 ðXÞ at higher pressure. No crossover was observed, because two states of similar symmetry never cross. In addition, the pressure dependence of Eþ in the low-pressure limit is very close to that of the L-point of GaAs [21], indicating out again the large L-character of Eþ : (3) In high nitrogen concentration samples, ellipsometry hinted to the presence of a small transition above E1 þ D1 [67]. This transition is likely to be related to a transition between the collapsed L6v band and a1 ðLÞ: In our work the nitrogen concentration was not sufficient enough to pull this transition above E1 þ D1 ; but the severe broadening of E1 and E1 þ D1 indicated the presence of additional weak transitions in their vicinity. (4) Using ballistic electron spectroscopy, a L-like band shifting to high energy with increased nitrogen doping was observed [68]. (5) The intrinsically high electron effective mass can be simply explained with the mixing of L-character into the conduction band minimum. The electron effective masses at L are large and a small mixing with the conduction band minimum will dramatically affect the transport characteristics [69]. (6) The bowing coefficient in InGaAsN is smaller than that of GaAsN since the energy separation between L6c and G6c increases with the addition of indium, therefore reducing the strength of the repulsion between a1 ðLÞ and a1 (G ) [70]. Conversely, the bowing coefficient in GaAsSbN can be predicted to be higher than that of GaAsN since the G – L separation decreases with the addition of Sb.

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6.7. A COMPLEMENTARY ALLOY: GaAsBi

Bismuth is the heaviest element of the III – V semiconductor family. Like nitrogen, the size and core electronic structure of Bi are significantly different from those of P and As. In comparison to As, the core electronic potential of Bi is markedly different. It has 50 more core electrons, most of them distributed in two additional d-shells and one new f-shell (besides Erbium, Bi is the only group V element with an f-shell). As a result, the electronegativity is reduced, but the size is much larger. It is therefore reasonable to expect that Bi could also behave as an isoelectronic impurity in GaAs and show unusual alloy properties. Bi indeed forms pseudo-donor bound states in GaP located above the valence band maximum [7]. While it has been predicted theoretically that the isolated Bi impurity does not form a bound state in GaAs [71,72], it yet remains to be investigated experimentally. Even if isolated Bi does not form a bound state like nitrogen in GaAs, the perturbation produced by the Bi localized potential and the surrounding lattice relaxation could significantly perturb the electronic band structure of GaAs and induce a variety of effects qualitatively resembling those observed for GaAsN. From a scientific point of view, GaAsBi is therefore a very interesting alloy and is likely to offer new insights into the physics of isoelectronic doping in III –V semiconductors. The band gap of GaAsBi is expected to decrease with respect to that of GaAs. First, since the band structure of GaBi is likely inverted like that of InBi, mixing GaBi in GaAs should naturally lower the band gap energy. Second, similar to the case of GaAsN, the disorder produced by Bi atoms in the band structure should induce a significant intraband coupling in the conduction and valence bands. This coupling should accelerate the band gap reduction with respect to that expected from the VCA. In this section, we present the band gap dependence of GaAs12x Bix for Bi concentration up to x ¼ 3:6% and find that the band gap reduction exceeds that of all other conventional GaAs-based alloys. The samples were grown by molecular beam epitaxy on GaAs. The GaAsBi layers are between 0.2 and 0.3 mm thick. Details on the growth conditions can be found in Ref. [73]. The Bi concentration was determined from Rutherford back scattering [73]. X-ray diffraction asymmetrical maps revealed that most of the samples were almost fully strained to match the GaAs in-plane lattice constant. Modulated electroreflectance was used to measure the energy of the optical transitions in the vicinity of the fundamental band gap of GaAsBi. Figure 6.19 shows the electroreflectance spectra measured for GaAs12x Bix with x ¼ 0; 0.4, 1.3, 3.1% measured at 300 K. In addition, the spectra of GaAs0.969Bi0.031 measured at 80 K is shown. As x increases, two important effects can be noticed. First, there is a monotonic red shift of the interband transitions, and, second, the strain in the layer splits the heavy- (HH) and light-hole (LH) bands in the high concentration samples. Also, a broadening of the transitions is observed and becomes notable at high concentrations. The value of the band gap was extracted from these spectra by modeling their line shape with

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Figure 6.19. Electroreflectance spectra of GaAs12x Bix : The dotted lines represent fits to the data and the filled circles show the position of the bandgap energy.

the theoretical models mentioned above. The best fit obtained is shown by the dotted line superposed on each spectrum. The critical point energy is represented on the graph by the position of the filled circles. Weak Franz – Keldysh oscillations appear in the spectra of GaAs0.969Bi0.031, at 80 K, but they were neglected in the fit since the extra parameters involved would not have allowed a more accurate determination of the energy of the transitions. Figure 6.20 shows the transition energies as a function of bismuth composition. The filled and empty circles represent the conduction to heavy-hole and conduction to lighthole transitions, respectively. Not all samples showed a significant valence band splitting, we have nonetheless represented these transitions with the symbol for the heavy-hole to conduction band transition. The absolute uncertainty in the transition energy was set to 50% of the broadening parameter determined from the line-shape fitting. The origin of the scatter in the data is not well understood. The dotted line in Figure 6.2 shows a linear regression of the heavy-hole to conduction band transition energy. The linearized dependence of the transition energy with respect to the band gap of GaAs is 2 83 meV/% Bi. This dependence is larger than the one measured from photoluminescence by Oe and Okamoto [74]. Correcting for the epitaxial strain, the concentration dependent change

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Figure 6.20. Bandgap energy as a function of the Bi composition, x:

of the energy gap of free-standing GaAsBi is slightly more pronounced and equals 2 88 meV/% Bi. To calculate this correction, we have used the deformation potentials and ˚ for GaBi [73]. the compressibility constants of GaAs and a lattice parameter of 6.33 A As already mentioned, large variations in the atomic orbital energy and atomic size in mixed-anion alloys have been shown to significantly perturb the band structure of the host material [16] and large deviations from linearity (bowing) were found in nitrogen-doped III– V. For the case of GaAsBi, it is not possible to accurately determine the bowing coefficient since the band gap of GaBi is not known. A calculated value of 2 1.45 eV for zinc-blende GaBi is the best estimate that can be found [75]. Using this value, we find that our experimental values are well represented using a bowing coefficient of 2 5.6 eV. The major source of uncertainty on the bowing coefficient is from the uncertainty on the GaBi band gap. Assuming an uncertainty of ^ 1 eV results in an uncertainty of ^ 1 eV on the bowing coefficient. While this bowing coefficient is small compared to that of GaAsN (b , 15 – 20 eV for GaAs0.99N0.01), it is significantly larger than the ones found for other well-studied III– V alloys (see Table 6.2). It is also interesting to compare the band gap shift of several GaAs-based alloys. As shown in Table 6.6, the band gap shift produced by P, In and Al in GaAs is very modest and only reaches 21 meV/% for Sb. In contrast, the band gap shift induced by Bi is at least exceeding four times that of Sb. While this value is about half that of nitrogen, it is significantly higher than that of conventional semiconductors. In addition, the band gap shift normalized to a unit of strain of GaAsBi is almost equal to that of GaAsN, indicating the similarity between the nature of the band gap reduction for these two alloys. In comparison to other semiconductor alloys, the bowing coefficient and the band gap reduction found for GaAsBi strongly suggest that effects similar to those observed

Physics of Isoelectronic Dopants in GaAs

215

Table 6.6. Bandgap shift of several GaAs-based alloys Element P In Al Sb Bi N

Bandgap shift (meV/%)

Bandgap shift/unit of strain (meV/1025)

15 16 16 21 88 160

0.42 0.22 – 0.27 0.74 0.82

for GaAsN are affecting the band gap dependence well beyond that expected from the VCA. These effects are not surprising since the important size difference between As and Bi leads to a significant charge redistribution in the vicinity of the Bi atoms. While the chemical disorder for GaAsBi might not be as important compared to the case of GaAsN, the charge redistribution caused by the atomic relaxation is important enough to induce intraband coupling and mixing. 6.8. SUMMARY

We present here a summary of the important points presented in this chapter. †

†

†

†

†

The band gap variation of GaAsN as a function of nitrogen composition is unusually severe and leads to a large and composition dependent bowing coefficient. This effect and several other unexpected characteristics are incompatible with standard models describing semiconductor alloys. Several models were proposed to explain the characteristics of GaAsN and the origin of the large band gap reduction, but most interpretations are in contradiction with each other. The temperature-induced shift of the fundamental band gap, E0 ; is not affected by the nitrogen incorporation in contradiction with the prediction of the band anticrossing model. However, the strong dependence of the bowing coefficient on nitrogen concentration demonstrates that the band repulsion is the origin of the band gap reduction. The spin –orbit splitting decreases faster than what is expected from a linear interpolation. Just like the bowing coefficient of the band gap, this is an effect related to disorder. It demonstrates that nitrogen does influence the characteristics of the valence bands as well as the conduction band. The intensity of the fundamental band gap transition decreases rapidly with nitrogen concentration while that of the spin – orbit transition increases. This demonstrates that mixing from unidentified states affects the three valence bands in distinct ways. The details of this effect remain unexplained.

216 †

† †

†

†

†

†

†

†

Dilute Nitride Semiconductors The new optical transition Eþ ; forbidden in zinc-blende alloys, extrapolates at x ! 0 to the position of the L conduction band, indicating that Eþ originates from a singlet state issued from L: The temperature shift of Eþ demonstrates that Eþ has a dominant L-character, further confirming the assignment of Eþ to a1 ðLÞ: The broadening parameter associated with Eþ is comparable to that E0 and E0 þ D0 : This indicates that Eþ originates from a well-defined band edge and not from a nitrogen resonant state as proposed in the band anticrossing model. In contrast to the broadening of E0 ; the broadening of E1 and E1 þ D1 cannot be explained by a large derivative of the energy with respect to the nitrogen concentration (Schubert’s model). The severe broadening is explained by the presence of two unresolved transitions involving the a1 ðLÞ singlet and the L-valence band extrema, L4v;5v and L6v ; appearing between E1 and E1 þ D1 and slightly above E1 þ D1 ; respectively. Intraband coupling between all conduction band singlet states, but predominantly between a1 ðG Þ and a1 ðLÞ; explains the band gap reduction observed for GaAsN. This effect, observed in all semiconductor alloys and quantified by the bowing coefficient, reaches unprecedented levels in GaAsN and results in a non-monotonic dependence of the band gap as a function of nitrogen concentration. The Raman intensity resonance at EI of the LOG phonon originates from the a1 ðLÞ singlet. Just like Eþ ; EI extrapolates to the L-conduction band of GaAs and, therefore, both transitions share the same origin. The nature of phonon intensity resonances further confirms that the conduction band state associated with EI and Eþ is indeed a well-defined band edge rather than a distribution of nitrogen states as implied by the band anticrossing model. An unusual asymmetric linewidth broadening of the LOG phonon is observed at some excitation energies and leads to two remarkable linewidth resonances, EW and E0W : This type of resonance is explained by the activation of LOG phonons with non-zero wave vectors spanning a significant portion of the Brillouin zone and is associated with the strong perturbation created by nitrogen atoms. These two states correspond to two conduction band states formed from a broad mixture of Brillouin states. Whereas the energy of EI , EW and E0W evolve differently as a function of nitrogen concentration, all three states extrapolate to the GaAs L-conduction band at x ! 0: This behavior is very similar to that observed from Eþ and Ep ; and can be interpreted by two subsequent reductions of the space group symmetry: (1) a loss of translational symmetry and (2) a reduction of the point group symmetry from Td to one of its subgroups. Although the lattice mismatch between GaAs and GaBi is expected to be quite large and the solubility very limited, Bi concentrations up to 8 £ 1020 cm23 (3.6%) are

Physics of Isoelectronic Dopants in GaAs

†

217

incorporated in GaAs using molecular beam epitaxy. X-ray diffraction demonstrated that epitaxial layers of relatively good quality are obtained and Rutherford backscattering indicated that Bi atoms are predominantly incorporated substitutionally. The band gap of GaAsBi decreases at a rate of 88 meV/% Bi. Compared to other GaAs-based alloys (expect GaAsN), this band gap variation is unusually large. A large bowing coefficient can be inferred as well, indicating that non-linear effects beyond the VCA come into play. This effect is related to the important intraband coupling induced by the large disruption produced by Bi atoms.

6.9. CONCLUSION

For the first time an alloy induced splitting of the L6c conduction band is experimentally observed in a semiconductor. This transition, optically forbidden in pure III– V alloys, results from the strong perturbation caused by the impurity potential of nitrogen to the host band structure of GaAs. The perturbation creates disorder strong enough to reduce the symmetry of the system, lift the degeneracy of the L-points, and generate a non-vanishing transition probability between the a1 ðLÞ singlet and the valence band maximum. Therefore, intraband coupling between all conduction band singlet states, but predominantly between a1 ðGÞ and a1 ðLÞ; underlies the band gap reduction observed for GaAsN. This effect, observed in all semiconductor alloys and quantified by the bowing coefficient, is profound enough in GaAsN to create a non-monotonic dependence of the band gap as a function of nitrogen concentration. Simple two band (or multi-band k·p) models that only treat the zone center are oblivious to all the above-mentioned effects. Additionally, it should be noted that merely treating the interaction of the isolated nitrogen impurity resonant state misses the key factors strongly influencing the conduction band transport mechanisms. Although the conduction band edge of GaAsN is a well-defined band edge and qualitatively resembles that of an alloy, the presence of nitrogen pair and cluster states positioned both below and above the vicinity of the conduction band significantly affects the transport characteristics of dilute nitride alloys. The large collections of sub-band gap nitrogen impurity states merge together to resemble an impurity band that significantly reduces both the carrier lifetime and the mobility. GaAsBi is a novel alloy that has been recently added to the repertoire of semiconductor materials. Its properties are similar to some of the very distinctive properties that were first observed in GaAsN. We find that the band gap energy dependence on Bi concentration is unusually large, indicating an important deviation from the VCA that has been so successful in the treatment of other more conventional alloys. This effect originates from the strong perturbation of Bi onto the GaAs regular electronic potential, redefining the electronic interactions within the band structure. Although these alloys are very interesting

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scientifically, they also have a potential for enormous technological impact. Nitrogen doped GaAs is a peculiar semiconductor alloy exhibiting a lattice contraction associated with a band gap reduction. The large band gap reduction of GaAs resulting from a small concentration of Bi is also a potential candidate for near-infrared emitters, especially when mixed with nitrogen to form a GaAsNBi alloy.

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Dilute Nitride Semiconductors M. Henini (Ed.) q 2005 Elsevier Ltd. All rights reserved.

Chapter 7

Measurement of Carrier Localization Degree, Electron Effective Mass, and Exciton Size in InxGa12xAs12yNy Alloys A. Polimeni, F. Masia, G. Baldassarri Ho¨ger von Ho¨gersthal and M. Capizzi INFM-Dipartimento di Fisica, Universita’ di Roma “La Sapienza”, Piazzale A. Moro 2, 00185 Roma, Italy

ABSTRACT

We employ photoluminescence under a magnetic field to investigate the electronic properties of InxGa12xAs12yNy/GaAs heterostructures. We studied samples with nitrogen concentration from the doping ðy , 0:01%Þ to the alloy ðy ¼ 5%Þ limit. In the alloy limit, we found that the origin of the radiative recombination at low temperatures (T lower than 100 K) is not excitonic, contrary to previous assignments, and is due to free holes recombining with electrons localized in N-rich regions. The evolution of the electron effective mass, me ; and exciton radius, rexc ; was studied in GaAs12yNy epilayers and quantum wells with N concentration varying from y , 0:01% to y ¼ 2:0%: In particular, by exploiting the capability of post-growth hydrogen irradiation to tune finely the electronic properties of GaAs12yNy, we are able to assess that a major change in me and in rexc takes place within a very narrow interval of N concentrations, which is centred at y ¼ 0:1%: Alloying of GaAs12yNy with In ðx , 0:3Þ results in a shift of such interval to y ¼ 1:0%: 7.1. INTRODUCTION

Recently, nitrogen incorporation in InxGa12xAs-based materials has attracted much interest owing to the strong modifications exerted by N on the band structure of the host lattice. These include a giant band gap reduction [1 –4] and a decrease in the rate at which the band gap depends on hydrostatic pressure [5 – 8] and temperature [5,9 – 18]. Moreover, a strong dependence of the electron effective mass, me ; on the nitrogen concentration has been found by a variety of experimental techniques [19 – 32]. The introduction of N in the host lattice is also a source of a high degree of disorder, which manifests itself on the optical properties of the material. This leads to a sizeable 223

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inhomogeneous broadening of the radiative transitions [11], to a large Stokes shift between absorption and emission [33], and to the presence of localized states, which at low temperatures dominate often the emission spectra [11,12,17,34– 37]. It has been shown that localization phenomena in InxGa12xAs12yNy reflects on the electron transport too [38,39]. Furthermore, InxGa12xAs12yNy alloys show surprising effects when irradiated with atomic hydrogen. Indeed, our group reported a fully tunable and reversible variation of the electronic (i.e. band gap value, response to temperature changes, effective mass, and exciton radius) and structural (lattice constant and lattice vibrational) properties of InxGa12xAs12yNy by means of ex situ H irradiation [40 –49]. In particular, H passivates N atoms in the lattice leading to an effective N concentration, which has allowed us to study the evolution of the material’s properties with N concentration in a very careful manner. The microscopic origin of the surprising effects of H in InxGa12xAs12yNy has been investigated theoretically by many groups [50 – 57] and it has been established that the formation of a specific N-dihydrogen complex (referred to as N –Hp2) is responsible for N passivation. This picture has been questioned very recently on the grounds of infrared absorption measurements [58]. Here, we report on a comprehensive study of the effects of a magnetic field (B ¼ 0 – 12 T) on the photoluminescence (PL) properties of InxGa12xAs12yNy/GaAs heterostructures. The samples investigated and the experimental methods employed are described in Section 7.2. In Section 7.3, we show that the shift of the PL peak energy induced by B decreases sizably and changes its dependence on B from linear to quadratic on going from low to high T: These findings indicate that the PL emission at low temperatures is not excitonic and it is determined, instead, by the recombination of loosely bound electron – hole pairs in which one carrier (electron) is localized by N-induced potential fluctuations and the other carrier (hole) is delocalized. Section 7.4 describes electron effective mass measurements. First, we review the data reported in the literature and the different methods used for obtaining those data. Then, we describe the evolution of the electron effective mass in GaAs12yNy epilayers when N concentration varies from the dilute limit ðy , 0:01%Þ to the alloy limit ðy ¼ 0:5%Þ as measured by magneto-PL. By exploiting the capability of H to tune the band gap of GaAs12yNy, we asses that a major increase in me occurs for y , 0:1%: This change in me parallels the shrinking of the exciton wave function size rexc with increasing N concentration. A similar study performed in GaAs12yNy quantum wells (QWs) with y , ð1:0 – 2:0Þ% shows that me remains nearly constant over this y’s range. Finally, we consider the magneto-PL properties of InxGa12xAs12yNy/GaAs QWs, having x , 30% and y ¼ ð0:7 – 5:2Þ%: For these samples, the electron effective mass increases gradually with y up to a N concentration equal to 1%, namely, one order of magnitude higher than that found in In-free samples. In the last section, we draw the conclusions of our work.

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7.2. EXPERIMENTAL

The samples considered in this review were grown by different techniques on (001)oriented GaAs substrates. One set of samples consists of four 0.5 mm-thick GaAs12yNy epilayers (y ¼ 0.043, 0.1, 0.21, 0.5%) grown by metalorganic vapor phase epitaxy [7]. From the same source we studied GaAs12yNy/GaAs multiple QWs (number of wells equal to three) having thickness L ¼ 20 nm and y ¼ 1:1; 1.4, and 1.8%. Another set of samples was grown by solid source molecular beam epitaxy and consists of 300 nm-thick GaAs12yNy epilayers having y ¼ 0% and y , 0:01%; and InxGa12xAs12yNy/GaAs single quantum wells having x ¼ ð25 – 42Þ% and x ¼ 0%; y ¼ ð0:7 – 5:2Þ%; and QW thickness L ¼ ð6:0 – 8:2Þ nm. In all cases, sample composition and layer thickness were determined by X-ray diffraction measurements. A GaAs1 – yNy epilayer with y ¼ 0:1% was hydrogenated at 3008C by a low-energy ion gun (beam energy , 100 eV) in order to vary finely the effective N concentration into the sample [40 – 49]. PL measurements were carried out in a liquid He optical cryostat for T ranging from 10 to 200 K. The magnetic field was applied parallel to the growth axis of the samples. PL was excited by the 515 nm line of an Arþ laser or the 532 nm line of a vanadate-YAG laser, dispersed by a double 3/4 m monochromator, and detected by a N-cooled Ge detector or by a N-cooled InGaAs linear array.

7.3. SINGLE CARRIER LOCALIZATION IN InxGa12xAs12yNy

We now address the localization degree of carriers involved in recombination processes at low temperatures in InxGa12xAs12yNy by studying the effect of temperature on magneto-PL. Recombination from localized states generally dominates emission processes at low temperatures in semiconductor alloys [59 – 62]. Local fluctuations in the composition lead to an exponential tail of localized states within the crystal forbidden gap [59,63]. The preferential occupancy of these low-energy states by carriers at low T is responsible for asymmetric photoluminescence spectra [11,17,34,35,60,62,64,65], a blue shift of the PL peak energy as the excitation power increases [11,12,34 – 36,65], a decreasing emission decay time of PL with increasing emission energy [15,17,34,35,37,62], and for an anomalous dependence of the PL maximum energy on temperature [11,15,35,36,62]. All these effects are particularly important in InxGa12xAs12yNy. Figure 7.1(a) shows the PL spectra at T ¼ 50 K as a function of the laser power, P; of a QW with x ¼ 0:25; y ¼ 0:011; and L ¼ 6:0 nm. At low P; the PL line shape shows a double-peaked structure. The band at lower energy is characterized by a long low-energy tail due to localized states (LS). The higher energy band in Figure 7.1(a) is due to free exciton (or free states, FS) recombination in the InxGa12xAs12yNy quantum well, instead. Similar features were found in other InxGa12xAs12yNy QWs and epilayers [7,10,35,66] and in a large variety of semiconductor

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Figure 7.1. (a) Photoluminescence spectra recorded on a InxGa12xAs12yNy quantum well for different laser power intensities (P0 ¼ 1:2 W/cm2). FS and LS indicate free and localized states, respectively. PL multiplication factors are given. (b) Photoluminescence spectra recorded on a InxGa12xAs12yNy quantum well for different temperatures (P0 ¼ 3:3 W/cm2). FS and LS indicate free and localized states, respectively. PL multiplication factors are given. The open circles represent the result of a simulation through Eq. (7.2). Eexc indicates the energy position of the free exciton state. The spectra are normalized to their peak intensity.

alloys [60,61,67]. The origin of the LS band was attributed to excitons localized on In – N clusters in InxGa12xAs12yNy/GaAs heterostructures [10] and InGa12yNy/GaN QWs [67]. For increasing P; the FS band increases its intensity with respect to the LS band due to carrier filling of the localized states. Eventually, at the highest power emission the PL spectrum is dominated by the FS band. The presence of localized states can be inferred also from the temperature dependence of the PL spectra shown in Figure 7.1(b). In fact, with increasing T localized carriers are thermally excited out of N-induced potential minima and for T ¼ 70 K mainly free exciton recombination can be detected. Interestingly, the PL lineshape of localized states presents several features common to other semiconductor alloy systems [59 – 61,64,65]. The lineshape of the LS band can be accounted for by alloy fluctuations [60] which give rise to an exponential density of localized states [59,68,69] o n gðEÞ ¼ g0 exp 2 ½ðEexc 2 EÞ=E0 3=2 ;

ð7:1Þ

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where Eexc is the free exciton energy, E0 is a characteristic energy and g0 is a constant. The PL spectrum is then given by [60,61] LðEÞ / gðEÞtðEÞexp½f ðEÞ:

ð7:2Þ

tðEÞ is the carrier radiative lifetime and t21 ðEÞ / 1 þ exp{d½EM 2 ðEexc 2 EÞ}; where d is the inverse of an effective temperature and EM is the energy at which the radiative recombination probability equals the transfer probability toward deeper states [59]. For E , EM ; localized carriers recombine radiatively, whereas, for E . EM ; carriers relax to lower energy states E0 , E: Finally, f ðE; E0 ; Eexc ; d; EM Þ is a function whose expression can be found in Ref. [60]. The open circles superimposed on the PL spectrum at T ¼ 10 K are a simulation using LðEÞ with d ¼ 0:38 meV21, Eexc ¼ 1:153 eV, E0 ¼ 21 meV, and EM ¼ 1:145 eV. The satisfactory agreement between Eq. (7.2) and the experimental PL lineshape confirms that alloy disorder is the main source of carrier localization at low T: As far as the nature of localized carriers is concerned, it is assumed usually that potential fluctuations arising from composition disorder localize excitons. Very recently this assumption has been questioned for GaAs12yNy, where the fast rise time (, 25 ps) of the PL signal was used to establish that radiative recombination at low temperatures occurs between localized electrons and delocalized holes [70]. The degree of localization and/or confinement of carriers in semiconductor heterostructures can be investigated suitably through the dependence of carrier energy levels on magnetic field as measured for instance by magneto-PL [71]. Figure 7.2 shows the PL spectra for different B values of the same InxGa12xAs12yNy QW shown in Figure 7.1(a) and (b) (very similar results have been obtained in all N-containing samples). Parts (a) and (b) of Figure 7.2 show the magneto-PL spectra at T ¼ 30 and 180 K, respectively. As shown before, at T ¼ 30 K the PL lineshape shows a long low-energy tail characteristic of localized state recombination, which is absent at T ¼ 180 K where emission is dominated by free excitons [11,12]; see also Figure 7.1. The shift, DEd ; of the PL peak energy induced by the magnetic field is shown in Figure 7.3 as a function of B for the two measurement temperatures. Since the highest value of the magnetic energy in these samples is comparable with the exciton binding energy, the high T data have been fitted by using a variational method, which will be detailed in Section 7.4. The model does not fit the low T dependence of DEd on B; which is linear at least for B . 4 T. It should be noticed that for any value of B; DEd is higher at low T than at high T (a factor two for B ¼ 12 T). This indicates that at low temperatures the recombining electron – hole pair is more loosely bound than an exciton, either localized or free. Indeed, the interaction of these electron – hole pairs at low T with a magnetic field results in a perturbation stronger than Coulomb attraction and, therefore, in a greater diamagnetic shift with respect to the exciton case. Before continuing, we point out that (i) DEd is independent of T at high temperatures where free excitons only contribute to PL [72], (ii) DEd measured at low T decreases when very high power densities are employed (namely, when free excitons start

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Figure 7.2. (a) Magneto-photoluminescence spectra recorded on a InxGa12xAs12yNy quantum well at T ¼ 30 K and laser power density P ¼ 15 mW/cm2. (b) The same as in (a) but T ¼ 180 K and P ¼ 20 W/cm2. The spectra are normalized to their peak intensity.

contributing to the PL signal), (iii) these effects are absent in the N-free InxGa12xAs QWs studied for comparison purposes. On the basis of these observations, the PL emission at low temperatures can be attributed to recombination of a localized with a delocalized carrier. As for the charge of the localized carriers, one can invoke the model proposed first by Hopfield, Thomas, and Lynch, who suggested that N in GaP is an isoelectronic electron trap [73]. Since N in GaAs shares several common features with GaP:N, we argue that N in InxGa12xAs behaves as an isoelectronic electron trap, too. Consequently, we argue that the potential minima due to N compositional disorder capture electrons with which free holes can recombine, as shown very schematically in the inset of Figure 7.3. Under this hypothesis the electron is strongly localized and the shift of the PL peak with B can be ascribed entirely to the free hole, namely, DEd ¼ ðe~=2mph ÞB where mph is the hole in-plane effective mass. The continuous line in Figure 7.3 is a fit of this formula to the T ¼ 30 K data with mph ¼ 0:074m0 (m0 is the electron mass in vacuum); as B approaches zero, DEd deviates from a linear behavior likely because of a residual electrostatic interaction between electrons and holes. A somewhat similar approach has been used for deriving the electron effective mass from the B-induced shift of free-electron to neutral-acceptor recombinations [74 – 82] and will be used in Section 7.4.

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Figure 7.3. Diamagnetic shift, DEd ; of the PL peak measured in a 6.0 nm-thick In0.25Ga0.75As0.989N0.011 QW at T ¼ 30 K (Full dots) and T ¼ 180 K (open circles) versus magnetic field, B: The dashed curve is a fit to the T ¼ 180 K data by the variational method described in Section 7.4.2. The continuous line is a fit to the T ¼ 30 K data (B . 4 T) by DEd ¼ ðe~=2mph ÞB; where mph is the in-plane hole effective mass. The inset depicts the recombination at low temperatures occurring in InxGa12xAs12yNy in a reciprocal space scheme at k , 0 for B ¼ 0 T (continuous parabolas) and B ¼ 12 T (dashed parabolas). L indicates the localized levels related to nitrogen. Reprinted with permission from Ref. [82], copyright (2004) by the American Institute of Physics.

Figure 7.4. Dependence of the in-plane hole effective mass in InxGa12xAs12yNy quantum wells as a function of the In concentration, x: The dashed lines are the values of the in-plane light (upper line) and heavy (lower line) hole, as estimated by using the Luttinger parameters [83]. Reprinted with permission from Ref. [82], copyright (2004) by the American Institute of Physics.

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Figure 7.4 shows the mph values derived in InxGa12xAs12yNy QWs as a function of the In concentration. Since N incorporation affects mainly the conduction band states, we compare the mph values derived here with those of the heavy and light hole of the N-free InxGa12xAs host. In fact, due to the different types of strain, compressive in InxGa12xAs12yNy and tensile in GaAs12yNy, in-plane heavy and light holes should be considered in the former and latter case. The dashed lines in Figure 7.4 are the InxGa12xAs in-plane hole masses as estimated through the Luttinger parameters [83]. The good agreement of the experimental data with the hole curves supports our hypothesis about the hole nature of the delocalized carrier. As a final comment, our results show that a measure of the properties of extended states through magneto-PL needs to be done at temperatures high enough to get rid of localized carrier contributions. 7.4. MEASUREMENT OF THE ELECTRON EFFECTIVE MASS AND EXCITON WAVE FUNCTION SIZE

N incorporation in InxGa12xAs modifies strongly the electronic properties of the host lattice as it is widely reported in the present book. There is a general consensus that the origin of these modifications is related to the quite strong carrier localization around the N atoms, which is produced by the high electronegativity and small size of the N atoms with respect to those of the replaced As atoms. Different models have been proposed to explain the effects N has on the host material. In a first theoretical model, the strong perturbation of the translational symmetry of the host lattice potential due to N incorporation gives rise to perturbed host states [84]. In turn, this leads to a downward shift of the conduction band (CB) minimum (CBM) for increasing N concentration and to a progressive disappearance of the energy levels of N clusters in the band gap [84]. In a band anticrossing model, instead, a phenomenological repulsive interaction between the CBM and a single N level resonant with the CB continuum of states accounts for most N-related effects [6]. This model has been supported by recent tight-binding calculations [85]. Finally, the effects of the interaction among N atoms and/or clusters and the ensuing impurity-band formation is invoked in a third model [19]. In all the models a decrease in the host band gap is predicted when the N concentration increases, in quite a good agreement with all the experimental data reported from different groups. The effect of N incorporation on the electron effective mass me is more subtle and it may represent a more stringent test for the validity of the different theoretical approaches aimed at explaining the puzzling effects of N in InxGa12xAs12yNy. Unfortunately, the experimental data on me reported in the literature do not show a common and clear trend with increasing N concentration. Figure 7.5 shows the values of the electron effective mass as a function of y for different GaAs12yNy QWs and epilayers as measured by different groups. A large difference both in the me values and trends with y can be observed. The data of Refs. [19,21] were derived

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Figure 7.5. GaAs12yNy electron effective mass as a function of N concentration as derived from the literature (see figure legend).

from a fit of the transition energies of GaAs12yNy QWs within the envelope function approximation, which needs some unknown parameters as the band gap offsets between GaAs12yNy and GaAs. The data of Ref. [19] show a continuous decrease in me with y; which supports the impurity-band formation model proposed therein. In the same N concentration interval, the me values reported in Ref. [21] are very different from those of Ref. [19] and do not change sizably with y: The data of Ref. [22] were determined by combining four different transport measurements and display a decrease in me when y increases. This behavior was justified within a k·p approach [22]. A more direct measurement of me was used by Hai and coworkers through optically detected cyclotron resonance measurements [20]. In this case me increases with y: The data of electron effective mass reported in the literature for InxGa12xAs12yNy alloys display a less scattered distribution with respect to the GaAs12yNy case. This is shown in Figure 7.6. Most of the me data were derived from a fit of the InxGa12xAs12yNy QW transition energies using the electron effective mass as one of the fitting parameters [25 –27, 29,30]. A combination of infrared reflectivity and Hall measurements were employed in Ref. [28], whereas electron energy loss measurements were reported in Ref. [31]. For InxGa12xAs12yNy a rather common behavior can be deduced from the experimental data reported. me increases with increasing y and it tends to saturation for y . 1:0%: We now present the data on the electron effective mass and exciton size determined by us through magneto-PL measurements.

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Figure 7.6. InxGa12xAs12yNy electron effective mass as a function of N concentration as derived from the literature (see figure legend, where different In concentration values are reported).

7.4.1

GaAs12yNy

We describe briefly the PL properties of the investigated samples. Figure 7.7 shows the PL spectra of a set of GaAs12yNy epilayers having different N concentration. At the very early stage of N incorporation in GaAs (N concentration lower than 0.01%, bottommost curve in Figure 7.7), the PL spectrum is characterized by a number of sharp lines (linewidth , 0.5 meV) between 1.40 and 1.48 eV. These lines are attributed to carrier recombination from electronic levels due to N pairs and/or clusters [86 – 91] and are superimposed on a broad band also related to N incorporation. The luminescence intensity of these transitions varies from line to line and increases with y (not shown here). An exact assignment of each line to a given N complex is made rather difficult by the strong dependence of the material optical properties on the growth conditions, as extensively reported in the literature [87,89 –91]. Free-electron to neutralcarbon acceptor, (e, C), and free-exciton, E2 ; recombinations are observed at 1.493 and 1.515 eV, respectively. As the nitrogen concentration is increased further ðy ¼ 0:043 and 0:1%Þ; the energy of the excitonic recombination from the material’s band gap E2 as well as the (e, C) recombination band start red shifting very rapidly, thus coexisting with and taking in the levels associated with the N complexes. The energy of these levels does not change with N concentration [7,89,90]. These features highlight the strongly localized character of the N isoelectronic traps, contrary to that of shallow impurities whose wave functions overlap at smaller concentrations (1016 – 1018 cm23). Eventually, at higher N

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Figure 7.7. Peak-normalized low-temperature (10 K) photoluminescence spectra of GaAs12yNy epilayers with different ys. E2 and (e, C) indicate the free-exciton and free-electron to neutral-carbon acceptor recombinations, respectively. (e, C)-LO indicates the longitudinal optical phonon replica of the (e, C) transition.

concentrations (alloy limit, y . 0:1%) the GaAs12yNy band gap keeps red shifting [92] along with the C-related states [89]. Figure 7.8 shows the PL spectra of another set of GaAs12yNy samples (from the same source of the samples shown in Figure 7.7) consisting of GaAs12yNy/GaAs 20 nm-thick quantum wells. The data have been recorded at a temperature and laser power so as to highlight the contribution of the free-electron to neutral-carbon acceptor (and its LO phonon replica) recombination in the GaAs12yNy well. The contribution of the freeexciton is also indicated in the spectra. We point out that at lower P and T the contribution from localized states becomes predominant and we have not considered these experimental conditions when performing magneto-PL measurements. The presence of the (e, C) transitions in our samples plays an important role in the determination of the electron effective mass as it will be shown in the following. Figures 7.9(a) and (b) show the PL spectra recorded under different B values for GaAs12yNy epilayers having y ¼ 0:043 and 0.1%, respectively. In both the samples, the E2 and (e, C) peak energies blue shift upon application of B at a rate decreasing with increasing N concentration. On the contrary, the emission lines located below the (e, C) band and due to carrier recombination on N complexes remain fixed as B increases, according to the strongly localized character N pairs and clusters have. The different

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Figure 7.8. Peak-normalized low-temperature (30 K) photoluminescence spectra of 20 nm-thick GaAs12yNy quantum wells with different ys. E2 and (e, C) indicate the free-exciton and free-electron to neutral-carbon acceptor recombinations, respectively. (e, C)-LO indicates the longitudinal optical phonon replica of the (e, C) transition.

Figure 7.9. (a) Peak-normalized photoluminescence spectra of a GaAs12yNy epilayer with y ¼ 0:043% taken at different magnetic fields (T ¼ 30 K). E2 and (e, C) indicate the free-exciton and free-electron to neutral-carbon acceptor recombinations, respectively. (b) Same as in (a) but y ¼ 0:1%: Reprinted with permission from Ref. [81], copyright (2003) by the American Institute of Physics.

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Figure 7.10. (a) B dependence of the peak energy of the different recombination bands observed in Figure 7.9(a). (b) B dependence of the peak energy of the different recombination bands observed in Figure 7.9(b). Note that only the (e, C) and E2 transitions display a sizable shift with B:

behavior of localized and extended states can be best observed in Figures 7.10(a) and (b), which show the dependence of the peak energy of each PL emission on magnetic field for the same samples of Figure 7.9. In particular, the E2 band shifts with B at a lower rate than the (e, C) band, owing to the larger Coulomb attraction between the electron and hole in the former case. A qualitatively similar finding is observed in GaAs12yNy/GaAs quantum wells. Figure 7.11 shows the PL spectra recorded at different B values for a 20 nm-thick GaAs12yNy/GaAs QW sample. As shown in Figure 7.8, the free-electron to neutral-carbon recombination is the most intense feature in the PL spectra. We exploit the (e, C) energy shift to derive the electron effective mass in GaAs12yNy for different N concentrations as explained in the following. Figure 7.12 sketches the E2 and (e, C) recombinations in a reciprocal space scheme at k , 0: Following the arguments first invoked by Rossi, Wolfe, and Dimmock [74] and followed by many other authors [75 – 82], the C-related level stays fixed in energy because of the dispersion-less characteristics (i.e. infinite effective mass) of the C impurity level in k-space. On the contrary, the conduction band bottom and the valence band top shift upon application of B: Therefore, in this approximation the shift of the (e, C) transition is ascribed entirely to the shift of the first electron Landau level associated with the conduction band bottom. Figures 7.13 and 7.14 show the B-induced diamagnetic shift, DEd ¼ EðBÞ 2 Eð0Þ; of the (e, C) recombination band for different N concentrations; the data are offset vertically for

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Figure 7.11. Peak-normalized photoluminescence spectra (T ¼ 30 K) recorded at different magnetic fields for a GaAs12yNy quantum well with y ¼ 1:1%: E2 and (e, C) indicate the free-exciton and free-electron to neutralcarbon acceptor recombinations, respectively.

ease of comparison. The dashed lines are a fit to the data by means of the formula for the magnetic field dependence of the bottommost Landau level of the conduction band, i.e. DEd ¼ sB ¼ ð~e=2me ÞB: The slope s of the shift of the (e, C) transition in the B-linear region of DEd provides directly the value of the electron effective mass. Note that at zero magnetic field DEd extrapolates to a negative value, of order of kB T=2; as found in other magneto-PL measurements of the B-induced shift of free-electron to neutral-acceptor

Figure 7.12. Sketch of the free-exciton ðE2 Þ and free-electron to neutral-carbon acceptor [(e, C)] recombinations in a reciprocal space scheme at k , 0 for B ¼ 0 T (continuous parabolas) and B ¼ 12 T (dashed parabolas). C indicates the dispertion-less carbon level in the reciprocal space.

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Figure 7.13. B-induced shift value, DEd ; of the (e, C) peak energy as a function of the magnetic field for different GaAs12yNy epilayers. The continuous lines are fits to the data by DEd ¼ ð~e=2me ÞB: The electron effective mass me is derived directly from the line slope s; whose values are reported in the figure. The data for y ¼ 0% are offset by 4.0 meV, for y , 0:001% by 1.5 meV, for y ¼ 0:043% by 0.1 meV for ease of comparison.

recombinations [75 – 80]. This behavior is usually attributed to the change in the density of states of the system from three- to one-dimension due to the applied magnetic field. In addition, a residual Coulomb attraction between the CB electron and the hole localized on the C acceptor may be responsible for a non-linear behavior at low B values. Figure 7.15 shows the dependence of the electron effective mass on N concentration. Dots and squares refer to GaAs12yNy epilayers and quantum wells, respectively. Two main features can be observed. First, the me values show a steep increase already for y , 0:1% within a very narrow concentration interval. Second, the electron effective mass does not change much from y , 0:1 up to , 2%. We comment briefly on the first finding. Figure 7.7 shows that when increasing y the CB minimum red shifts rapidly while the N-related cluster states (CS) remain pinned in energy. Furthermore, for y , 0:1% the CB minimum crosses the CS and concomitantly the electron effective mass increases suddenly. Such an increase can be attributed to a strong interaction between N-complex states and the states of the CB minimum. The role of CS was invoked as essential for accounting for the electronic properties of dilute nitrides, in particular the band gap reduction [45], and it has been taken into account very recently for explaining the data shown in Figure 7.15 [93]. We have to mention that a band anticrossing model [6,85] provides a means to calculate the electron effective mass. However, this model

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Figure 7.14. B-induced shift value, DEd ; of the (e, C) peak energy as a function of the magnetic field for different GaAs12yNy epilayers and a quantum well (y ¼ 1:1%; full dots). The continuous lines are fits to the data by DEd ¼ ð~e=2me ÞB: The electron effective mass me is derived directly from the line slope s; whose values are reported in the figure. The data for y ¼ 0% are offset by 4.0 meV, for y ¼ 0:21% by 4.0 meV, for y ¼ 0:50% by 1.5 meV for ease of comparison.

Figure 7.15. Electron effective mass versus N concentration for GaAs12yNy epilayers (full dots) and quantum wells (squares). The gray area highlights the concentration interval where the electron effective mass varies most. The dashed line is a guide to the eye. Reprinted with permission from Ref. [81], copyright (2003) by the American Institute of Physics.

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underestimates increase in the electron effective mass, at least for reasonable values of the interaction potential. In order to follow closely the variation of me with the N effective concentration, we performed a study similar to that described above in a sample irradiated at different H doses. As already reported by us, H tunes in a controllable and reversible way the electronic properties of InxGa12xAs12yNy and GaP12yNy [40 –49]. This is illustrated in Figure 7.16 for a GaAs12yNy epilayer ðy ¼ 0:1%Þ: H irradiation leads first to a passivation of the N cluster states (see the second curve from bottom) and then to an apparent reopening of the GaAs12yNy band gap toward that of the GaAs reference (topmost continuous curve). As a matter of fact, both the (e, C) and the E2 recombination bands converge to those of the GaAs reference with increasing H dose, as shown by continuous

Figure 7.16. Peak-normalized photoluminescence spectra of a GaAs0.999N0.001 alloy treated with different hydrogen doses dH : Measurements have been performed at about T ¼ 30 K to reduce the contribution from possible N-related localized states and donor-acceptor pair recombination. The bottommost and topmost spectra refer to an untreated GaAs12yNy and a reference GaAs sample, respectively. Continuous and dashed lines indicate PL spectra taken under zero and 12 T magnetic field, respectively. (e, C) indicates the free-electron to neutralcarbon recombination and E2 indicates the free-exciton recombination. Different laser power densities have been employed for the different samples in order to highlight the presence of both (e, C) and E2 bands. Reprinted with permission from Ref. [49], copyright (2004) by the American Physical Society.

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lines in Figure 7.16. With applying a magnetic field (dashed curves in Figure 7.16), the E2 and (e, C) bands blue shift with increasing B: Notice that the energy separation between these two transitions increases on going from the H-free to the H-treated samples, due to a corresponding decrease in the tensile strain with decreasing the effective N concentration [48]. In fact, for decreasing N concentration the top of the valence band acquires a more pronounced heavy-hole character and, in turn, the binding energy of the acceptor impurity increases. In Figure 7.17, the energy shift, DEd ; of the (e, C) recombination lines are shown as a function of B for GaAs12yNy (both untreated and hydrogenated) and for the GaAs reference. The same analysis performed for the untreated samples (see Figures 7.13 and 7.14) has been applied to the hydrogenated samples. We point out that the slope s of the lines fitting the (e, C) transitions increases with increasing H dose until the slope of the GaAs reference is obtained. Figure 7.18 shows the electron effective mass as a function of the energy of the bandgap exciton. Note that a sound value of me ð¼ 0:065m0 ; where m0 is the electron mass in the vacuum) is obtained for the GaAs reference with this method. Full dots refer to the GaAs12yNy alloy with y ¼ 0:1% for both the untreated sample (gray symbol) and the

Figure 7.17. B-induced shift value, DEd ; of the (e, C) peak energy as a function of the magnetic field for different GaAs12yNy epilayers. The continuous lines are fits of DEd ¼ ð~e=2me ÞB to the data. The electron effective mass me is derived directly from the line slope s; whose values are reported in the figure.

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241

Figure 7.18. Dependence of the electron effective mass on the free-exciton peak energy at 10 K. Filled dots refer to the untreated (gray) and hydrogenated (black) GaAs0.999N0.001 samples, gray triangles refer to GaAs12yNy alloys with different y values (both untreated and irradiated with H). The gray area highlights the concentration interval where the electron effective mass varies most (see also Figure 7.15). The dashed line is a guide to the eye. Reprinted with permission from Ref. [49], copyright (2004) by the American Physical Society.

hydrogenated samples (black symbols). Gray filled triangles are the me values measured in unhydrogenated samples with different N concentration (y ¼ 0; y , 0:01%; y ¼ 0:043; and 0.21% both untreated and H-irradiated). me varies biuniquely with the sample band gap energy, namely, it depends on the effective N concentration in the crystal regardless of how this concentration has been achieved (either by N incorporation in GaAs or by H irradiation of GaAs12yNy). Most importantly, these findings allow monitoring the evolution of the electronic properties of GaAs12yNy in a virtually continuous manner. In particular, the sudden change in me shown in Figure 7.15 is confirmed, thus providing further evidence that N-induced localization effects start at very low values of y: Interestingly, the energy at which the electron effective mass increases abruptly (, 1.485 eV) falls in a spectral region where many N-related complexes emit [7, 86 –91]. In particular, a cluster emitting at 1.478 eV can be observed in the bottommost spectrum of Figure 7.7 ðy , 0:01%Þ: In turn, the interaction between this cluster (or others falling in a nearby energy interval) might be responsible for the large variation in me : Theoretical calculations predict that the electron wave function at the conduction band edge E2 has a given percentage of non-G character because of a translational symmetry breaking of the lattice stemming from N incorporation [89,94]. This results in a sizeable wave function localization despite the fact that the E2 state has an extended character far away from nitrogen [84,94]. Such localization affects the electron effective mass as well as the exciton wave function size. Magneto-PL can be used to estimate the average spatial extent of bound-carrier systems [95]. Several theories and calculation techniques have been developed to study the properties of magnetoexcitons in semiconductors [96 – 101].

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The simultaneous effect of the Coulomb interaction and an external magnetic field on an electron –hole bound system is a difficult problem, which often can be solved only under specific magnetic field limits. For excitons in bulk GaAs12yNy we restrict ourselves to magnetic fields low enough to treat B as a perturbation [95]. Figure 7.19 shows the dependence of the exciton diamagnetic shift on B for different N 2 concentrations. The continuous lines are fits of DEd ¼ aB2 ¼ e2 kreh l=ð8mÞB2 to the exciton diamagnetic shift in the low-field regime (small perturbation limit [95]). reh and m are, respectively, the electron – hole distance and the reduced effective mass of excitons. At very low N concentration, a rapidly decreases by a factor of , 2 with respect to the value it has in GaAs and tends to saturate for y . 0:1% (not shown here). This behavior matches well with that found q forffiffiffiffiffi mffie : By using the me values determined 2 previously, we get an estimate of rexc ¼ kreh l for each sample from the diamagnetic shift formula DEd ¼ aB2 : The rexc values are shown as a function of y in the inset of Figure 7.19. The fast decrease in rexc provides further evidence that N-induced localization effects start at very low values of y: We performed a similar study in hydrogenated GaAs12yNy epilayers. Figure 7.20 shows the shift DEd of the exciton energy as a function of B2 for GaAs12yNy with y ¼ 0:1% (both untreated and hydrogenated, filled symbols) and for the GaAs reference (open symbols). 2 The continuous lines are a fit of DEd ¼ ½e2 kreh l=ð8mÞB2 to the E2 data in the quadratic low-field region similar to what shown in Figure 7.19. The inset of Figure 7.20 shows in

Figure 7.19. Energy shift with magnetic field of the free-exciton recombination E2 for different GaAs12yNy 2 2 2 epilayers. The continuous lines are fits of DEd ¼ ½e2 kreh l=ð8mÞB toffi the data, where kreh l is a fit parameter. The qffiffiffiffiffi 2 l on N concentration. inset shows the dependence of rexc ¼ kreh

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243

Figure 7.20. Energy shift with B2 of the free-exciton recombination E2 for a GaAs0.999N0.001 epilayer. Black symbols refer to the untreated sample, gray symbols refer to hydrogenated samples, and open symbols refer to a 2 2 GaAs reference. The continuous lines in the inset are fits of DEd ¼ ½e2 kreh l=ð8mÞB2 to the data. kreh l is the only fit parameter.

detail the B range where a B2 approximation holds. Figure 7.21 shows the dependence of the exciton size on the exciton band gap energy. Symbols have the same meaning as in Figure 7.18. Similar to the me case, the combined use of untreated and H-irradiated samples allows us to follow the evolution of the electronic properties of carriers in GaAs12yNy in detail, thus providing firm guidelines to models aimed at describing the electronic properties of dilute nitrides.

Figure 7.21. Exciton size dependence on the free-exciton peak energy at 10 K. Filled dots refer to the untreated (gray) and hydrogenated (black) GaAs0.999N0.001 sample, gray triangles refer to GaAs12yNy alloys with different y values. Reprinted with permission from Ref. [49], copyright (2004) by the American Physical Society.

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Dilute Nitride Semiconductors

7.4.2 InxGa12xAs12yNy InxGa12xAs12yNy alloys present several interesting features. Indeed, a preferential formation of In-N over Ga-N bonds in annealed InxGa12xAs12yNy was reported in Refs. [102,103] by using band gap and vibrational mode measurements, respectively. Strain reduction was proposed as the driving mechanisms leading to an In-rich environment of the N atoms [102,103]. Monte Carlo simulations confirmed the experimental findings [104], although recent X-ray absorption measurements showed a much reduced effect of short-range ordering [105]. Another important feature of InxGa12xAs12yNy is the variation of the relative energy distance between the levels introduced by N atoms and the CBM of the host matrix due to In alloying. A slower rate in the band gap reduction upon N incorporation is usually observed in InxGa12xAs12yNy with respect to GaAs12yNy [1 – 4]. Also, the rate at which the band gap depends on temperature as compared with the N-free lattice shows a smaller variation in In-containing than in In-free nitrides [11,12]. We now consider the effect of N on the electron effective mass of InxGa12xAs alloys with high x (, 30%). Figures 7.22(a) and (b) show the magneto-PL spectra at T ¼ 100 K of 6.0 nm-thick In0.32Ga0.68As12yNy QWs having y ¼ 0 and 2.7%, respectively. The data were recorded at a temperature high enough as to have no emission from localized carriers.

Figure 7.22. (a) Peak-normalized photoluminescence spectra recorded at T ¼ 100 K and different magnetic fields for a 6 nm-thick In0.32Ga0.68As12yNy QWs having y ¼ 0%. (b) Same as in (a) but y ¼ 2:7%:

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245

The N-containing sample shows a smaller diamagnetic shift, which is consistent with a heavier reduced mass and smaller wave function extent of the exciton. Since carriers in present samples have an enhanced two-dimensional character because of the strong confining potential provided by the high In concentration ðx , 0:3Þ in the QWs, we analyze the diamagnetic shift of the exciton by considering a variational method in two dimensions. We use the exciton effective mass ðmÞ as an adjustable parameter [100,101]. The Hamiltonian of the system is given by Hr ¼ 2

›2 1 › g2 r2 2 2 : 2 þ 2 r ›r 4 r ›r

ð7:3Þ

r is the exciton radial coordinate in the QW plane, g¼

eB~ ; 2mRy

where Ry is the exciton binding energy Ry ¼

e2 : 8p1a0

1 is the absolute dielectric constant of the host lattice and a0 ¼

4p1~2 me2

is the exciton Bohr radius. The 22=r term in the right-hand side of Eq. (7.3) represents the Coulomb potential [99,100]. The value of m is found by rendering minimum the expectation value of Hr calculated over the trial wave function of the exciton given by [101] ! gr2 ð7:4Þ fðr; l; sÞ ¼ exp 2 2 2lr ; 4s where l and s are two variational parameters. Figure 7.23 shows the result of the fitting procedure applied to the experimental diamagnetic shift values for the two QWs shown in Figure 7.22. The exciton effective mass values are m ¼ 0:039m0 and 0:049m0 for y ¼ 0 and 2.7%, respectively. In order to derive the electron effective mass from our data we set the in-plane effective mass of holes equal to 0:11m0 , in agreement with the data reported in Ref. [106] and shown in Figure 7.4 of Section 7.3. Figure 7.24 shows the dependence of me (full symbols) on N concentration. Data derived from the literature are also shown (open symbols) for comparison purposes. A good agreement is found between our results and those obtained by different experimental techniques. This is in contrast with the scattered values of me reported by various authors in GaAs12yNy (see Figure 7.5).

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Dilute Nitride Semiconductors

Figure 7.23. Diamagnetic shift, DEd ; measured at T ¼ 100 K in an In0.32Ga0.68As0.973N0.027 QW (circles) and in an In0.32Ga0.68As reference QW (squares) versus magnetic field, B: The continuous lines are fits of the variational method reported in Section 7.4.2 to the data. The exciton reduced mass resulting from the fit is reported.

Figure 7.24. N concentration dependence of the electron effective mass me for the InxGa12xAs12yNy samples studied in this work (full symbols) and taken from the literature (open symbols).

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In InxGa12xAs12yNy the dependence of me (and rexc ; not shown here) on y shows two main differences with respect to the GaAs12yNy case. Both me and rexc show a sizable change when y , 1% (one order of magnitude greater than the value found in GaAs12yNy). In addition, the variation in me and rexc occurs over a larger N concentration interval, possibly due to the different indium concentrations considered. These observations point toward a softening of N-related effects in InxGa12xAs, due to a lower degree of interaction between N states and the levels of continuum associated with the conduction band.

7.5. CONCLUSIONS

We studied the electronic properties of InxGa12xAs12yNy/GaAs heterostructures by magneto-PL. The samples investigated cover a N compositional range spanning from the doping to the full alloy limit continuously. Several important aspects emerged from our investigations. (i) We showed that magneto-PL as a function of temperature provides a new clue on the origin of radiative recombination at low temperatures in InxGa12xAs12yNy. Indeed, the shift of the PL peak energy induced by B decreases sizably and changes its dependence on B from linear to quadratic when going from low to high temperatures. This counterintuitive result shows that the radiative recombination at low temperatures (T lower than 100 K) is not excitonic, contrary to previous assignments, and is due to free holes recombining with electrons localized in N-rich regions. (ii) The electron effective mass (and exciton wave function extent) is a much more insightful parameter than the band gap energy in assessing the origin of the puzzling evolution of the electronic properties of dilute nitrides when the N concentration varies. Indeed, with increasing y the electron effective mass shows a sudden change for y , 0:1% (corresponding to a GaAs12yNy band gap value of , 1.48 eV) within a very narrow interval of N concentrations. A crossing between the red shifting CBM extended states and one or more electronic levels in the gap due to N clusters is the likely physical origin of the sudden change in me (and rexc ). Qualitatively similar dependences of me and rexc are found in InxGa12xAs12yNy alloys with x , 30%: In this case a large variation in the electron effective mass and exciton radius occurs for y , 1%: (iii) Finally, our work indicates that an effective mass scheme is applicable also to InxGa12xAs12yNy notwithstanding the large fluctuations in the host crystalline potential, which are induced by N.

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ACKNOWLEDGEMENTS

The authors thank A. Frova for his support throughout this work. We acknowledge the most fruitful collaboration with P.J. Klar and W. Stolz at Philipps-University, Marburg, Germany. We thank M. Stavola and F. Jiang at Leigh University, USA, for far-infrared measurements and fruitful discussions. We are grateful to A. Amore Bonapasta and F. Filippone (CNR-ISM, Roma, Italy) and V. Fiorentini and S. Sanna (Universita’ di Cagliari, Italy) for sharing their theoretical calculations. We thank G. Ciatto (ESRF, Grenoble) and F. Boscherini (Universita’ di Bologna, Italy) for X-ray diffraction measurements. We thank A. Vinattieri (Universita’ of Firenze) and M. Geddo (Universita’ of Parma, Italy) for valuable collaboration. We are grateful to A. Forchel (Wuerzburg, Universtity, Germany) for providing some of the samples studied. We thank A. Zunger and Y. Zhang at NREL, CO, USA for exchanging ideas. We are grateful to A. Miriametro and L. Ruggieri for very valuable technical assistance. This work has been funded by Progetto Giovani Ricercatori, COFIN 2001 (MIUR), and FIRB (MIUR).

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Rossi, J.A., Wolfe, C.M. & Dimmock, J.O. (1970) Phys. Rev. Lett., 25, 1614. Ru¨hle, W. & Go¨bel, E. (1976) Phys. Stat. Sol. (b), 78, 311. Bimberg, D. (1978) Phys. Rev. B, 18, 1794. Dean, P.J., Venghaus, H. & Simmonds, P.E. (1978) Phys. Rev. B, 18, 6813. Zemon, S., Norris, P., Koteles, E.S. & Lambert, G. (1986) J. Appl. Phys., 59, 2828. Zheng, X.L., Heiman, D., Lax, B., Chambers, F.A. & Stair, K.A. (1988) Appl. Phys. Lett., 52, 98. Skromme, B.J., Bhat, R., Koza, M.A., Schwarz, S.A., Ravi, T.S. & Hwang, D.M. (1990) Phys. Rev. Lett., 65, 2050. Masia, F., Polimeni, A., BaldassarriHo¨ger von Ho¨gersthal, G., Bissiri, M., Capizzi, M., Klar, P.J. & Stolz, W. (2003) Appl. Phys. Lett., 82, 4474. Polimeni, A., Masia, F., Vinattieri, A., Baldassarri Ho¨ger von Ho¨gersthal, G. & Capizzi, M. (2004) Appl. Phys. Lett., 84, 2295. Vurgaftman, I., Meyer, J.R. & Ram-Mohan, L.R. (2001) J. Appl. Phys., 89, 5815. Kent, P.R.C. & Zunger, A. (2001) Phys. Rev. B, 64, 115208. (a) Shtinkov, N., Desjardins, P. & Masut, R.A. (2003) Phys. Rev. B, 67, 081202(R); (b) Lindsay, A., Tomic, S. & O’Reilly, E.P. (2003) Solid State Electron., 47, 443 and references therein. Gru¨ning, H., Chen, L., Hartmann, T., Klar, P.J., Heimbrodt, W., Ho¨hnsdorf, F., Koch, J. & Stolz, W. (1999) Phys. Stat. Sol. (b), 215, 39. Makimoto, T. & Kobayashi, N. (1995) Appl. Phys. Lett., 67, 688. Shima, T., Makita, Y., Kimura, S., Sanpei, H., Fukuzawa, Y., Sandhu, A. & Nakamura, Y. (1999) Appl. Phys. Lett., 74, 2675. Makimoto, T., Saito, H., Nishida, T. & Kobayashi, N. (1997) Appl. Phys. Lett., 70, 2984. Zhang, Y., Mascarenhas, A., Geisz, J.F., Xin, H.P. & Tu, C.W. (2001) Phys. Rev. B, 63, 085205. Francoeur, S., Nikishin, S.A., Jin, C., Qiu, Y. & Temkin, H. (1999) Appl. Phys. Lett., 75, 1538. Tisch, U., Finkman, E. & Salzman, J. (2002) Appl. Phys. Lett., 81, 463. Lindsay, A. & O’Reilly, E.P., private communication. Mattila, T., Wei, Su.-H. & Zunger, A. (1999) Phys. Rev. B, 60, R11245. Walck, S.N. & Reinecke, T.L. (1998) Phys. Rev. B, 57, 9088. Yang, S.-R. & Sham, L.J. (1987) Phys. Rev. Lett., 58, 2598. Bauer, G.E.W. & Ando, T. (1988) Phys. Rev. B, 37, 3130(R). Zheng, X.L., Heiman, D. & Lax, B. (1989) Phys. Rev. B, 40, 10523. Hou, H.Q., Staguhn, W., Takeyama, S., Miura, N., Segawa, Y., Aoyagi, Y. & Namba, S. (1991) Phys. Rev. B, 43, 4152. Lee, K.-S., Aoyagi, Y. & Sugano, T. (1992) Phys. Rev. B, 46, 10269. Lee, K.S. & Lee, E.-H. (1994) J. Appl. Phys., 76, 5778. Klar, P.J., Gru¨ning, H., Koch, J., Scha¨fer, S., Volz, K., Stolz, W., Heimbrodt, W., Kamal Saadi, A.M., Lindsay, A. & O’Reilly, E.P. (2001) Phys. Rev. B, 64, 121203(R). Kurtz, S., Webb, J., Gedvikas, L., Friedman, D., Geisz, J., Olson, J., King, R., Joslin, D. & Karam, N. (2001) Appl. Phys. Lett., 78, 748. Kim, K. & Zunger, A. (2001) Phys. Rev. Lett., 86, 2609. Ciatto, G., D’Acapito, F., Grenouillet, L., Mariette, H., De Salvador, D., Bisognin, G., Carboni, R., Floreano, L., Gotter, R., Mobilio, S. & Boscherini, F. (2003) Phys. Rev. B, 68, 161201(R). Wimbauer, Th., Oettinger, K., Efros, Al.L., Meyer, B.K. & Brugger, H. (1994) Phys. Rev. B, 50, 8889.

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Dilute Nitride Semiconductors M. Henini (Ed.) q 2005 Elsevier Ltd. All rights reserved.

Chapter 8

Probing the “Unusual” Band Structure of Dilute Ga(AsN) Quantum Wells by Magneto-Tunnelling Spectroscopy and Other Techniques A. Patane` and L. Eaves School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK

8.1. INTRODUCTION

In recent years, research on dilute nitride GaAs12yNy alloys has become one of the most active research areas in condensed matter physics due to the unusual electronic properties of this material system [1 – 3]. In the ultra-dilute regime ðy , 0:01%Þ; N introduces a single-impurity level at an energy of , 0.2 eV above the conduction band minimum (CBM) of GaAs [4,5]. At higher values of y; the electronegativity of the N atoms combined with the stretching and compressing of neighbouring bonds results in a strong perturbation of the host GaAs crystal, which has significant effects on the band structure of GaAs12yNy. According to a band anti-crossing (BAC) model [6,7], the interaction of the extended G-conduction band states of GaAs with the localised N energy level causes a splitting of the conduction band into two new subbands E2 and Eþ ; and a decrease of the band gap Eg of about 0.1 eV per atomic percentage of N. As a result, the variation of Eg with y in the GaAs12yNy alloy system is characterised by a very large “bowing” effect compared with that found in InxGa12xAs and other semiconductor alloys. The strong red shift of Eg at low y in GaAs12yNy offers exciting possibilities for optical devices in the 1.3 and 1.55 mm wavelength range of interest for optical fibre communications [3]. The BAC model has been used by many groups to describe a variety of optical and transport phenomena in GaAs12yNy. Also it provided a useful tool for designing and understanding the properties of long-wavelength optical devices [3]. However, despite many years of intense research, the electronic properties of this new material system are still not well understood. Pseudopotential calculations [8] and tight binding models [9] confirm the existence of two strongly admixed subbands, E2 and Eþ ; as well as of additional states in the conduction band. The character of E2 is predominantly that of the G-conduction band but it has a significant admixing of states from the L-conduction band minima. The upper Eþ is predominately L-like and acquires an increasing G-character as 253

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y is increased. The coexistence of different local environments in the alloy also complicates the electronic properties of GaAs12yNy. The low solubility of N in GaAs favours the interstitial incorporation of N and the formation of N –N pairs and higher order clusters with associated strongly localised electronic levels at an energy below and above the GaAs CBM [8]. The N-induced cluster states and the quasi-localised perturbed host states generate an “amalgamated” disordered conduction band. It has been argued that for this strongly disordered band structure the k-vector can still be well defined [8]. Only recently it has been proved by theoretical [10] and experimental studies [11] that the “concept of a k-vector remains valid in GaAs12yNy, despite the strong disorder in the alloy” [10] and that GaAs12yNy can have well-defined energy – wavevector dispersions. The magneto-tunnelling spectroscopy (MTS) technique [11] has made it possible to probe directly the conduction band structure of GaAs12yNy at low y (, 0.1%) and to demonstrate that the admixing of the extended GaAs conduction band states with the localised N-impurity states causes a splitting of the conduction band into two highly non-parabolic subbands E2 and Eþ ; thus complementing optical spectroscopy measurements of Shan et al. [6] with applied hydrostatic pressure and validating the BAC model [6,7]. The energy dispersions measured by MTS were also found to be in good agreement with those determined in a recent paper by Lindsay and O’Reilly using a modified form of the BAC model that includes detailed calculations of the electronic structure of the N-impurity and N-cluster states [10]. These recent results have helped to clarify the nature of the electronic states in dilute nitrides and indicate that the unusual conduction band dispersion of GaAs12yNy could be exploited to design novel band-structure-engineered devices. In this chapter, we discuss the use of resonant tunnelling diodes (RTDs) and of MTS to study the electronic properties of dilute nitride GaAs12yNy quantum well (QW) layers. We show that for a small N content (, 0.1%) the E2 and Eþ subbands retain a well-defined band-like character. The E2 and Eþ hybridised subbands have highly non-parabolic energy dispersions and the heavy effective mass states of Eþ are found to have a significant G-conduction band character even at wavevector k ¼ 0: The energy dispersed and spatially extended nature of the GaAs12yNy conduction band states is also clearly indicated by recent studies of the electrical conductivity and magneto-conductivity of a two-dimensional electron gas in modulation-doped n-type GaAs12yNy/(AlGa)As quantum well heterostructures [12]. At low N content (, 0.1%) the electrical conduction occurs through the extended conduction band states of GaAs12yNy, albeit with relatively low mobility due to scattering by N atoms [13]. The modulation doping in these quantumconfined structures provides a significant enhancement of the conductivity with respect to that measured in conventional Si-doped GaAs12yNy bulk layers. The modulation doping separates spatially the Si donors from the N atoms in the GaAs12yNy channel, thus inhibiting the formation of Si – N complexes that are known to degrade the electrical conduction of this material system [14]. In contrast, in the devices with larger y-values

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ðy , 1%Þ; we demonstrate a change in the electronic properties of GaAs12yNy due to formation of a relatively high density (, 1018 cm23) of N-related energy levels below the conduction band edge of GaAs [15]. This chapter is organised as follows. In Section 8.2, we provide a brief overview of our recent research on RTDs based on GaAs12yNy QW layers. This is followed by a description of the electrical characteristics of these devices. In Section 8.3, we describe the MTS technique and how this provides detailed information about the conduction band structure of GaAs12yNy. In combination with photocurrent, capacitance – voltage and photoluminescence spectroscopy studies (Section 8.4), this allows us to probe in detail how the electronic properties are affected by the incorporation of N. We then describe the electrical conductivity of two-dimensional GaAs12yNy channels, and discuss briefly how the unusual electronic properties could be of relevance to novel non-linear electronic devices (Section 8.5). The chapter concludes with a summary (Section 8.6).

8.2. RESONANT TUNNELLING DIODES BASED ON DILUTE NITRIDES

Since the pioneering studies in the early 1970s [16], RTDs have been extensively investigated to study fundamental physical properties in condensed matter systems such as the dynamics of carrier tunnelling, capture and recombination through a QW. For a recent review see Ref. [17]. In particular, the study of electron (and hole) tunnelling in the presence of a magnetic field applied parallel to the QW plane has provided a powerful means of probing in detail the form of the complicated energy –wavevector dispersion curves of carriers at barrier interface [18] and in QWs [19,20]. Of particular interest were the MTS studies of holes in the QWs of III – V AlAs/GaAs heterostructures, which revealed the admixing and anticrossing effects in the dispersion curves of light and heavy hole subbands due to second-order spin –orbit interaction [19]. Since these early magnetotunnelling studies, the MTS technique has been extended to study other novel material systems [11] and/or novel types of RTD heterostructure in which the electrons are subjected to additional quantum confinement [21 – 23]. In this type of structure, MTS has been used to probe the spatial form of the wave function probability densities of the confined states of one-dimensional (quantum wires) [21] and zero-dimensional (quantum dots) [22,23] systems. In this section, we consider in detail how the MTS technique has found a new application in the study of the electronic properties of dilute nitride GaAs12yNy QW layers. Figure 8.1 shows schematically the conduction band profile of a typical GaAs/(AlGa)As RTD under an applied bias V: In this structure, which is used as control sample, an 8 nm thick GaAs quantum well layer is embedded between two 6 nm thick Al0.4Ga0.6As tunnel barriers. Undoped GaAs spacer layers, each of width 50 nm separate the Al0.4Ga0.6As barriers from n-doped GaAs layers in which the doping concentration is increased from

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Figure 8.1. Sketch of the conduction band diagram for a typical GaAs/(AlGa)As RTD under applied bias. This structure is used as control sample.

2 £ 1017 cm23, close to the barrier, to 2 £ 1018 cm23. The thickness of these two n-doped GaAs layers is 50 and 500 nm in the outlet layers of the “sandwich” structure. When a voltage is applied between the top and bottom n-type doped layers, resonant tunnelling through a quantised subband (E0 or E1 ) of the GaAs QW gives rise to a peak in the current – voltage characteristics IðVÞ; whenever the subband is resonant with an occupied state of the emitter accumulation layer, which forms in the spacer layer when a bias is applied. Since the applied voltage provides a means of tuning into the energy of a particular state in the QW, resonant tunnelling permits to probe spectroscopically the QW states. We now focus on how resonant tunnelling can be used to probe the bound states of GaAs12yNy QW layers. As shown in Figure 8.2, when we compare the IðVÞ curves of the control sample ðy ¼ 0Þ and of a sample with nitrogen content y ¼ 0:08%; we find that the resonance E0 due to electrons tunnelling through the lowest energy subband of the QW layer splits into two dominant resonant features, E02 and E0þ ; due to the presence of nitrogen. These two components can be seen more clearly in the IðVÞ measured under illumination (see dashed line in Figure 8.2). The IðVÞ curves clearly indicate the change in the character of the energy levels of the GaAs QW layer due to the N incorporation. According to the BAC model [6,7], the interaction of the extended conduction band states of GaAs with the localised nitrogen level induces a splitting of the conduction band into two subbands E2 and Eþ (Figure 8.2). These are responsible for the E02 and E0þ resonances observed in the sample with y ¼ 0:08%: Tunnelling spectroscopy allows us to determine the energy separation D between the E2 and Eþ subbands at k ¼ 0: As shown in Figure 8.1, the energy scale is determined by the voltage drop Ve between the emitter and the centre of the QW. This represents only a fraction of the total applied bias and can be expressed as Ve ¼ V=f ; where f is the so-called

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Figure 8.2. IðVÞ curves at T ¼ 4:2 K for RTDs incorporating GaAs12yNy QW layers with y ¼ 0 (control samples) and 0.08%. The dashed line is the IðVÞ under illumination for the sample with y ¼ 0:08%: The insets sketch the conduction band profile of the two RTDs at zero bias and the form of the dispersion curves for electron motion parallel to the plane of the QW.

leverage factor. We estimate f by using a simple electrostatic model of our device. The separation d between the free electrons in the emitter and collector sides of the device can be determined from CðVÞ measurements ðd , 100 nmÞ [24] and, assuming that the electric field in this region is uniform, f corresponds to the ratio d=s; where s is the electron tunnelling distance from the emitter to the centre of the QW (see Figure 8.1). The value of s is equal to d 2 dc ; where dc is the distance of the centre of well from the edge of the doped collector layer. Since dc ¼ b þ w=2 þ u þ lc ¼ 60 – 70 nm (where lc , 10 nm is the collector screening length, u ¼ 50 nm is the thickness of the undoped GaAs layer, b ¼ 6 nm is the collector Al0.4Ga0.6As barrier width and w ¼ 8 nm is the QW width), we estimate that s ¼ 30 – 40 nm and f ¼ 2:5 – 3:3: The value of s is consistent with the structure of our device: s cannot be smaller than , 20 nm, since the sum of the barrier width plus the half-width of the well is 10 nm and we also need to take into account the finite spread (, 10 nm) of the electron wave function in the emitter region adjacent to the Al0.4Ga0.6As barrier; on the other hand s cannot be larger than 60 nm, which is the distance of the centre of well from the doped emitter layer. Applying this analysis to the data, we find that D is in the range 0.10– 0.13 eV. The precise determination of D is also limited by the broadening of the current features in IðVÞ; which is caused by scattering mechanisms. When an electron tunnels from the emitter into the QW, it can be scattered by the local

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distribution of impurities and/or defects. This has the effect of broadening the range of QW states with different k-vectors in which electrons can tunnel thus limiting the “resolution” of resonant tunnelling in probing the precise energy position of different QW subbands. The measured value of D is smaller than that predicted by a simple BAC model for y ¼ 0:08% and a hybridisation matrix element CMN ¼ 2:7 eV ðD ¼ 0:2 eVÞ: Other groups have measured larger values of D (. 0.2 eV) layers containing a larger N content (. 0.2%) [25]. Our results suggest that the admixing of the N-impurity level with the GaAs conduction band states is weaker in this very dilute regime ðy ¼ 0:08%Þ: To validate this result we have also measured RTDs with y ¼ 0:2% and found that D ¼ 0:3 – 0:4 eV is in good agreement with previous findings. In contrast, further increase of N smears out the resonances in IðVÞ; strongly quenches the current and shifts to higher biases the threshold voltage at which the current increases rapidly (see Figure 8.3). It is likely that increasing the N content leads to formation of N-cluster states and N-related defects, which affect strongly the potential of the QW and the corresponding IðVÞ characteristics. In the absence of disorder, both the energy and the in-plane component of the momentum of a tunnelling electron are conserved; these are the conditions required to observe a sharp peak and associated negative differential conductance in the IðVÞ curve [17]. The destruction of translational symmetry due to the disordered QW potential tends to break the momentum conservation condition and smears out the resonances, as is observed even for a very small amount of N ðy ¼ 0:08%Þ: The resonances observed in the IðVÞ of this sample can be enhanced by optical excitation. This resonant enhancement of current is discussed in Section 8.4 and is attributed to the effect of screening of the disorder in the QW by

Figure 8.3. IðVÞ curves at T ¼ 4:2 K for RTDs incorporating a GaAs12yNy layer with different values of y:

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the photogenerated holes and to the effect on the current of hole recombination with majority electrons tunnelling in resonant states of the QW.

8.3. MAGNETO-TUNNELLING SPECTROSCOPY TO PROBE THE CONDUCTION BAND STRUCTURE OF DILUTE NITRIDES

The resonant tunnelling experiment described in the previous section provides us with an energy spectrometer to probe the QW bound states around k ¼ 0; but it does not allow us to investigate the k-dependence of the QW subband states predicted by the BAC model. In this section, we describe how the application of a magnetic field perpendicular to the current direction can provide further detailed information about the form of the energy dispersion curves and the nature, impurity- or band-like, of the E2 and Eþ subbands. We show that the experiments also provide a validation of the BAC model. In these experiments, a magnetic field, B; is applied parallel to the QW plane ðX; YÞ: Let a; b and Z indicate, respectively, the direction of B; the direction normal to B in the growth plane and the direction normal to the tunnel barrier, respectively. Semiclassically, the Lorentz force on electrons as they traverse the emitter barrier will impart an additional in-plane wavevector given by Dkb ¼

ð eB ð eB v eBa s a Z a ; dt ¼ dz ¼ ~ ~ ~

ð8:1Þ

where vZ is electron velocity along Z and the integral is over the tunnelling transition (see Figure 8.4) [19]. The same result can be derived rigorously by treating the magnetic field quantum mechanically as a perturbation [26]. According to the quantum mechanical model, the in-plane dispersions of the emitter layer and QW states are displaced along the kb -axis by an amount Dkb given by Eq. (8.1). This has a strong effect on the voltage position of the current resonances in IðVÞ: At zero magnetic field, the peak of the current corresponds to tunnelling of electrons between states in the emitter and QW with the same values of energy and the in-plane wavevector kb ; i.e. Dkb ¼ 0 [17]. In the presence of the magnetic field, electron tunnelling occurs with conservation of the canonical momentum, i.e. Dkb ¼ eBa s=~; and the QW k-states available for tunnelling are shifted by an amount Dkb [19]. This induces a shift to higher voltage of the resonant peaks in IðVÞ (see Figure 8.5). Varying Ba allows us to tune an electron to tunnel into a given kb -state of the well; the voltage tunes the energy so that by measuring the voltage position of the peaks in IðVÞ as a function of B; we can map out the energy –wavevector dispersion curve 1ðkb Þ of the GaAs12yNy QW layer. Note that the magnitude of the shift in kb is proportional to both Ba and s: Since the value of s is relatively large (. 30 nm), an extended range of kb can be probed by using relatively modest magnetic fields (, 12 T) that do not perturb significantly the QW states.

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Figure 8.4. Sketch showing a semiclassical description of the magneto-tunnelling experiment. An electron leaving the emitter layer with mean value kX ¼ 0 gains a momentum DkX ¼ eBY s=~ from the Lorentz force as it tunnels over an effective length s into the QW in the presence of a magnetic field B along Y:

Figure 8.6 shows the B-dependence of the IðVÞ plots under illumination for y ¼ 0:08%: An identical B-dependence of the resonant peaks in the IðVÞ curves was also measured in dark conditions. The data show a shift to higher bias of E02 and E0þ and a general increase of current with increasing B: However, the relative weight of the peaks in IðVÞ related to E02 and E0þ changes significantly with B: The B-dependence of the amplitude of the E02 and E0þ peaks in IðVÞ has the characteristic form of a quantum mechanical admixing effect, i.e. with increasing B; the E02 feature tends to become weaker and disappear whereas the E0þ peak increases significantly in amplitude. Also, the IðVÞ curves show

Figure 8.5. Sketch of the in-plane energy–wavevector dispersion 1ðkÞ curves for the emitter and QW layers at Ba ¼ 0 and Ba – 0: When Ba – 0; the in-plane dispersions of the emitter layer and QW states are displaced along the kb -axis by an amount Dkb : The QW k-states available for tunnelling are shifted by an amount Dkb : This induces the resonant peaks in IðVÞ to shift by DV to higher voltage.

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Figure 8.6. IðVÞ curves under illumination at T ¼ 4:2 K and various B for a RTD with y ¼ 0:08%: B is increased from 0 to 11 T in steps of 0.5 T and is applied parallel to the QW plane. For clarity, the curves are displaced along the vertical axis. The double step decrease of IðVÞ marked by asterisks on one of the high-field curves arises from the instability in the current due to the strong negative differential conductance. The inset shows the differential conductance, dI=dV; plot for B ¼ 0 T:

a further weak feature ðEp Þ; which shifts to higher bias with increasing B and disappears for B . 6 T: This feature is more clearly revealed in the differential conductance plot shown in the inset of Figure 8.6. By carrying out a series of measurements for different orientations of B in the (100) growth plane, we find that both the intensity and bias position of the resonances are isotropic. Figure 8.7(a) shows the B-dependence of the voltage position of the current features E02 ; E0þ and Ep : The VðBÞ plots for E02 and E0þ resemble the dispersion curves 1ðkÞ of the E2 and Eþ subbands calculated by using a two-band anticrossing model of bulk GaAs12yNy (see Figure 8.7(b)) [6,7]. This strongly supports the assignment of E02 and E0þ ; respectively, to electron tunnelling into the N-induced E2 and Eþ subbands of the GaAs12yNy QW layer. However, as shown in Figure 8.7(c), the QW confinement has the effect of modifying the detailed form of the 1ðkÞ curves associated with E2 and Eþ [27]: the hybridisation between the first QW subband states qw0 and the N-impurity level occurs at k-values smaller than those for bulk GaAs. The QW confinement effect also gives rise to additional subbands, E12 and E1þ ; arising from the hybridisation of the higher energy QW subband states qw1 with the N-impurity level. This effect may explain the presence of the Ep resonance and the form of its associated VðBÞ curve. We attribute the weak Ep resonance to electron tunnelling into the E12 states. As shown in Figure 8.7(c), the

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Figure 8.7. (a) The measured voltage positions of current peaks E02 ; E0þ and Ep in IðVÞ as a function of B for the RTD with y ¼ 0:08%: (b) Calculated energy–wavevector dispersion curves for bulk GaAs12yNy (continuous lines) and for bulk GaAs (dotted lines). (c) Energy–wavevector dispersion curves for a GaAs12yNy QW (continuous lines) and for a GaAs QW (dotted lines). The energies are plotted relative to the minimum of the GaAs conduction band and the N content is equal to 0.08%. (d) D1ðkÞ curves derived from data in (a) assuming s ¼ 40 nm and f ¼ 2:5:

energy minimum of the qw1 subband is very close to the N level, which gives rise to a weak E12 energy dispersion, as is observed for Ep : This indicates that the lowered dimensionality of the QW acts to modify significantly the band structure of the GaAs12yNy layer with respect to the bulk case. By measuring the IðVÞ curves for different orientations of B in the QW plane, we find that the voltage position of E02 ; E0þ and Ep do not depend on the orientation of B in the plane. Hence, we deduce that the anisotropy in 1ðkX ; kY Þ for all subbands is negligible in the range of k in which the bands are hybridised. A precise correlation between the measured VðBÞ and 1ðkÞ curves is limited by the fact that the electrostatic leverage factor, f ; the parameter that controls the scale of energy values and the value of the tunnelling distance s are not known precisely. However, by using the simple electrostatic model presented in Section 8.2, we can estimate approximate values. Figure 8.7(d) shows the dispersion curves D1ðkÞ ¼ 1ðkÞ 2 1ð0Þ ¼ ðVðBÞ 2 Vð0ÞÞ=f

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inferred from the VðBÞ plots in Figure 8.7(a) assuming a tunnel distance s ¼ 40 nm and a leverage factor f ¼ 2:5: Note that the shape of the D1ðkÞ curves resembles very closely to those determined by the BAC model. The measured energy dispersions were also found to be in good agreement with those determined recently by Lindsay and O’Reilly using a modified form of the BAC model that includes detailed calculations of the electronic structure of the N-impurity and N-cluster states [10]. The B-dependence of the amplitude of the E02 and E0þ features in IðVÞ reveals interesting details about the nature of the E2 and Eþ subbands. The magnitude of the tunnel current is proportional to the modulus squared of the tunnelling matrix element between the in-plane components of the emitter and QW states. At B ¼ 0; the conservation of the in-plane wave vector implies that the QW states into which an electron can tunnel must have at least a partial G-like character, since the states of the GaAs emitter layer are almost pure G states. Since E0þ is observed at B ¼ 0; we infer that the very weakly dispersed Eþ states have a significant G-conduction character even at k ¼ 0: The strong enhancement of the E0þ resonance at large B and the corresponding increase of the momentum –energy dispersion at large k ðk , BÞ indicate that with increasing k; the Eþ subband states become more delocalised in real space. In contrast, the disappearance of the E02 resonance at large B indicates that the E2 subband states become strongly localised at large k-values. The Ep feature in IðVÞ has a similar dependence as E02 ; which confirms our assignment of this resonance to tunnelling into states of the E12 subband. We also found similar behaviour and welldefined energy dispersions for the subband states of the GaAs12yNy QW layer for N content as large as y ¼ 0:2%: In contrast, the behaviour of the RTDs with larger N content is significantly different and is discussed in Section 8.4. It is of interest to briefly consider why the MTS technique is so well suited to the study of the electronic properties of dilute GaAs12yNy. For the case of electrons bound to selfassembled InAs quantum dots, or to shallow donors in GaAs quantum wells, the spatial extent of the wave function is typically , 10 nm [22,23]. Hence the values of in-plane wavevector of the tunnelling electron generated by the Lorentz force using standard laboratory magnetic fields of up to , 10 T are sufficiently large to map out the form of the eigen-functions in Fourier (momentum) space. In contrast, the electron orbitals associated with the nitrogen sites in GaAs12yNy are much more highly localised, on a length scale smaller than 1 nm [8], so it is impossible to produce an extended Fourier map of the orbitals [28]. The peculiar feature of GaAs12yNy that allows us to carry out these experiments is the hybridisation between the G-conduction band states and the localised levels. This gives the nitrogen-related states a partly G-character over a wide range of energy, and allows electrons from the emitter accumulation layer, which have a pure G-character, to tunnel into these states; the partial G-character allows us to “tag” the hybridised states using MTS. Furthermore, the felicitous location of the isolated nitrogen level at about 0.2 eV ðT ¼ 4 KÞ above the CBM of GaAs is particularly well suited to the

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MTS technique. In GaAs/(AlGa)As heterostructures, the effective tunnelling distance is typically no more than about 40 nm, so the increase of in-plane kinetic energy of the tunnelling electron gained from the combined effect of the Lorentz force and the applied electric field is , 0.2 eV for an applied field of 10 T. Hence the band dispersion predicted by the BAC model can be tested experimentally over the appropriate range of energy and wavevector. We conclude this section by noting that our MTS measurements demonstrate clearly how the confinement provided by the QW modifies the E2 and Eþ subbands from their form in bulk GaAs. Shan et al. [6] have used hydrostatic pressure to manipulate the E2 and Eþ subbands; quantum confinement is an alternative means of controlling the band structure which, as we discuss in Section 8.5, may offer exciting possibilities for realising new band-structure-engineered devices. 8.4. ELECTRONIC PROPERTIES: FROM THE VERY DILUTE REGIME (,0.1%) TO THE DILUTE REGIME

In this section, by using a combination of tunnelling, capacitance –voltage CðVÞ; photoluminescence (PL) and photocurrent (PC) spectroscopy techniques, we demonstrate that the electronic properties of the GaAs12yNy QW layer change significantly when the N content is increased above about 0.1– 0.2% [15]. As shown in Figure 8.3, increasing y has the effect of smearing out the resonant peaks in IðVÞ; quenching the current and shifting to higher biases the threshold voltage at which the current increases rapidly. The monotonic shift to higher biases of the IðVÞ curve with increasing y is consistent with the formation of deep energy levels lying below the GaAs CBM. These are likely to be due to N-cluster states and/or N-related defects [8]. At zero bias, equilibrium is established by electrons diffusing from the doped GaAs layers into these low-energy levels. Negative charge in the well gives rise to two depletion layers in the regions beyond the Al0.4Ga0.6As barriers and a corresponding band-bending that inhibits the current flow at low voltages. We investigated this charging effect using CðVÞ measurements. Figure 8.8(a) shows the CðVÞ curves at T ¼ 4:2 K for the RTDs with y ¼ 0; 0.08 and 0.93%. The capacitance is defined as C ¼ dQ=dV; where dQ ¼ 2dQem 2 dQQW ¼ dQdep is the incremental change of the negative charge in emitter layer ðdQem Þ and in the QW ðdQQW Þ for an incremental change in the applied voltage dV: The corresponding increase in the positive charge in the collector depletion layer is dQdep [29,30]. In the control sample ðy ¼ 0%Þ; the capacitance rises at a relatively low bias since an accumulation layer quickly forms close to the emitter barrier when the bias is gradually increased. In contrast, the CðVÞ curves of samples with y . 0% show an almost constant capacitance (, 26 pF) over an extended voltage range between zero bias and the threshold voltage Vth : This value of capacitance is consistent with the separation d between the edges of the two doped GaAs layers ðd , 120 nmÞ at zero bias. For V . Vth the capacitance increases rapidly.

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Figure 8.8. (a) The measured CðVÞ characteristics at T ¼ 4:2 K for the RTDs with y ¼ 0; 0.08 and 0.93% for mesa of radius r ¼ 100 mm: Vth indicates the threshold voltage for the increase of capacitance. (b) Sketches of the potential profile for RTDs containing N at V ¼ 0 V; V , Vth and V ¼ Vth : (c) Dependence on N content of the volume density of electrons trapped in the GaAs12yNy QW layer, QQW =e; determined by applying a simple electrostatic model to the CðVÞ data.

Note that the value of Vth is also close to the bias value at which the current increases sharply. This behaviour can be explained by the fact that at zero bias electrons accumulate in the QW, and depletion layers form in the nominally undoped GaAs region beyond the Al0.4Ga0.6As barriers (see Figure 8.8(b)). This gives rise to a relatively wide region of dielectric containing no free carriers. At zero bias, the positive charge associated with each depletion layer is equal to half the negative charge in the QW layer ðQQW Þ: Therefore,

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a significant applied voltage ð, Vth Þ is required to start filling with electrons the GaAs layer adjacent to the emitter barrier and hence to increase the capacitance. As sketched in the band diagram of Figure 8.8(b), Vth is the applied voltage required to reach flat band conditions on the emitter side of the device. Assuming that the negative charge in the QW layer ðQQW Þ does not change between V ¼ 0 and V ¼ Vth ; then the value of QQW is Ð Ð determined using the relation V0 th CdV ¼ C0 Vth ¼ V0 th dQdep , QQW =2; where C0 is the constant value of capacitance measured for V , Vth : Using the experimental values of C0 and Vth ; we estimate that the volume density of electrons trapped in the well is QQW =e ¼ 2C0 Vth =epwr 2 ¼ 2:6 £ 1017 ; 1.0 £ 1018, 1.1 £ 1018 and 1.2 £ 1018 cm23, for samples with y ¼ 0:08; 0.43, 0.93 and 1.55%, respectively, where r ¼ 100 mm is the radius of the mesa and w ¼ 8 nm is the well width. These electron densities are much smaller than the density of isolated N atoms, which varies from 1.8 £ 1018 cm23 for y ¼ 0:08% to 3.4 £ 1020 cm23 for y ¼ 1:55%: The CðVÞ data indicate the formation in the well of an increasing number of deep energy levels, which can trap electrons. From the values of Vth for y . 0:08% we estimate that these levels are located below the E2 subband at an energy equal to eV0 ¼ eVth =2 , 0:45 eV below the GaAs CBM. This value is in good agreement with the energy position of the N –As interstitial defect calculated in Ref. [31]. Also it is likely that N-related clusters are also present and contribute to the trapping of electrons. The volume density of trapped electrons in the QW can give rise to appreciable scattering of tunnelling electrons and is likely to be responsible for the strong suppression of current at large y: The current can be partially recovered by optical excitation due to the effect on the current of photo-created holes that recombine with majority electrons tunnelling in the QW [15]. Figure 8.9(a) illustrates the dynamics of carriers when the device is excited with light of energy larger than that of the GaAs band gap ðlexc ¼ 633 nmÞ [32]. Electrons are electrically injected from the negatively biased GaAs emitter layer into the well. At the same time, light creates photocarriers in the GaAs layers. The electric field in the electron depletion layer (on the right-hand side of the barrier in Figure 8.9(a)) separates the oppositely charged carriers created in this region: the photoelectrons are swept into the positively biased electron collector, whereas the holes are attracted by the negatively biased electron emitter and form an accumulation layer adjacent to the right-hand tunnel barrier. When electrons and photo-generated holes tunnel into the well, some of the electrons can recombine with the holes. In turn this affects the tunnel current. The emptying of N-related states by the holes leads to an increase in the number of electrons that tunnel into the QW and to a corresponding enhancement of the current resonances in IðVÞ as clearly observed for y ¼ 0:08% (see Figures 8.2 and 8.9(b)). For this sample, the photocreated holes are likely to partially screen the disordered potential of the QW and tend to restore the momentum conservation condition required to observe clear current resonances in IðVÞ: In contrast for y . 0:08%; the optical excitation produces a general increase of current but does not reveal resonances in IðVÞ: For each sample with y . 0:08%; only a broad peak in the photo-induced current can be observed (see Figure 8.9(b)); the bias

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Figure 8.9. (a) Sketch of the potential profile and carrier dynamics for a RTD in forward bias (negative biased substrate) with above-band gap illumination. (b) Photocurrent (PC) intensity versus the applied bias for RTDs containing N. Each diode was excited with above-band gap laser light (633 nm) and power densities ,0.1 W/cm2. The shape of the PCðVÞ curves is not affected by the level of illumination.

position of this peak increases with increasing y: We attribute this broad photo-induced peak in the current to the effect of holes on electrons tunnelling through states of the disordered conduction band of the GaAs12yNy layer. When an electron tunnels through the two barriers non-resonantly, its dwell time in the QW is given approximately by the time for a single transit of electrons across the well. Since this time is very short (, 1 ps), it is unlikely that off-resonance electrons can recombine with the holes. Therefore, the current of majority electrons tunnelling though the QW is weakly affected by light and the photoinduced current is small. In contrast, when an electron tunnels resonantly into a bound state of the QW, its dwell time is much longer, which leads to a larger probability for recombination with the holes and hence to a larger photocurrent signal. Figure 8.10(a) shows the dependence on the light excitation energy, hnexc ; of the PC intensity at an applied bias corresponding to the current peak in the PCðVÞ curve of each

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Figure 8.10. (a) PC spectra measured at 4 and 295 K for RTDs with y ¼ 0:08; 0.43, 0.93 and 1.55%. Each diode was biased at voltages corresponding to the peak in the current of the PCðVÞ curves shown in Figure 8.9(b). For each value of y; the vertical and horizontal arrows indicate the energy position of the N-related absorption line at T ¼ 4:2 K and the corresponding thermal shift when T is increased to 295 K. (b) Energy dependence of the peak in intensity of the N-related PC band at 4.2 and 295 K. Continuous lines are the energies calculated from the BAC model for the interband transition between the quantised electron and hole levels of the QW at 4.2 and 295 K. The circles and triangles are data points. (c) Energy dependence of the energy peak of the N-related PC and PL bands at 4.2 K. The dotted line is a guide to the eye. The continuous line is the calculated energy for the interband transition between the quantised electron and hole levels of the QW at 4.2 K. The vertical arrowed line represents the Stokes shift between the PC and PL bands.

sample. The low temperature ðT ¼ 4:2 KÞ PC spectra of all structures clearly reveal a current enhancement for hnexc . 1:5 eV; which arises from carriers photo-created in the GaAs layers on each side of the barriers and QW. The PC spectra also reveal a weaker band that shifts to low energy when the amount of N is increased (see vertical arrow in Figure 8.10(a)). We assign this to the effect on the tunnel current of holes photo-created in the GaAs12yNy QW layer. This photo-induced current enhancement depends on the optical absorption of the QW and provides us with a means of investigating the conduction band states of GaAs12yNy.

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We use the BAC model to estimate the energy position of the E2 QW subband states. As shown in Figure 8.10(b), the dependence on y of the energy of the transition between the quantised electron states of E2 predicted by the BAC model and lowest subband heavyhole states of the QW describes quite accurately our low temperature PC data. The BAC model also accounts for the energy shift of the N-related PC feature when T is increased from 4.2 to 295 K. However, the BAC model cannot explain the energy position of the PL emission, which shows a significant red shift in energy with respect to the PC absorption. This shift is referred to as the Stokes shift, SS (see Figure 8.10(c)). The increasing value of SS with increasing y and the corresponding energy broadening of the PC spectrum indicate the existence of a broad energy distribution of N-related localised states in the vicinity of the E2 subband edge. The strong dependence of the CBM on N content creates large variations in the electron energy due to statistical compositional alloy fluctuations. Also N-clusters form strongly localised levels. In a PL experiment, carriers relax into the lowest energy levels before recombining. Therefore, the PL is often dominated by transitions involving N-related localised states and is red shifted with respect to the absorption spectrum. According to the simple model for the Stokes shift in Ref. [33], if the disorder extends over a scale much larger than the carrier diffusion length, carriers relax into local minima before recombining. In particular, in the presence of a distribution of energy levels of linewidth, W; the PL reflects the distribution of local minima and SS ¼ 0:55W [33]. Our PC data suggests energy broadening as large as W , 0:1 eV for y , 1:55%; which corresponds to a value of SS , 0:06 eV consistent with the large SS obtained from comparing the PL and PC data. These studies clearly indicate that the optical absorption of GaAs12yNy at high y ðy . 0:1 – 0:2%Þ is dominated by interband transitions involving the E2 subband states, which are energy broadened due to disorder effects. The disorder in the QW and carrier trapping on deep N-related states break the momentum conservation condition required to observe sharp resonances in IðVÞ and explains the strong quenching of current and smearing of the resonances in IðVÞ at high y:

8.5. CONDUCTION IN DILUTE NITRIDES AND FUTURE PROSPECTS

The optical and transport studies in the RTDs show that for a small N content (, 0.1 –0.2%) the GaAs12yNy states retain a well-defined band-like character with associated highly non-parabolic energy subbands. This leads us to suggest that GaAs12yNy is of potential interest for novel band-structure-engineered devices. Of particular interest is the inflection point of the lowest-energy subband E2 ðkÞ corresponding to a maximum electron velocity, at relatively modest wave vectors k; considerably smaller than the size of the Brillouin zone (see bottom inset of Figure 8.11). At energies above this point, the subband has a region with negative effective mass. This property could be exploited in devices in which electrons are accelerated by an electric field to their peak velocity, thus

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Figure 8.11. Longitudinal ðrxx Þ and transverse ðrxy Þ resistivity as a function of B at T ¼ 2 K for a two-dimensional GaAs12yNy channel with y ¼ 0; 0.1 and 0.4%. The insets show the shape of the Hall bar ðW ¼ 50 mm and L ¼ 310 mmÞ and the energy–wavevector 1ðkÞ dispersion curves of the E2 and Eþ subbands in the QW. The k-vector is expressed in units of p=a; where a is the lattice constant of GaAs.

leading to non-linear conduction, analogous to that occurring in Gunn diodes [34]. The upshift of subband energies arising from the quantum well confinement provides a means of manipulating the energy dispersion curves of the subbands so as to optimise the performance of this type of device.

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Our MTS experiments have also confirmed that GaAs12yNy possesses a fully developed energy gap between the hybridised E2 and Eþ conduction subbands. By controlling the doping of the GaAs12yNy layer, the Fermi energy could be aligned with this gap, thus creating a new type of insulator. This effect could be exploited in devices as the insulating state could be switched to conducting by means of a gate or by the application of a strong electric field. To investigate the potential of dilute nitrides for these novel electronic devices, we have investigated fundamental electronic transport properties, such as the electron mobility and the nature of the electron conduction, i.e. whether it is mediated by free carriers (band-like conduction) and/or by carrier hopping between localised states [12]. For this study we have used a series of modulation-doped n-type GaAs12yNy/(AlGa)As single quantum well heterostructures with y ¼ 0; 0.1 and 0.4% grown by molecular-beam epitaxy on a semiinsulating (SI), (100)-oriented GaAs substrate. The growth sequence was the following: a 2 mm thick GaAs buffer layer, a 50 nm thick Al0.38Ga0.62As undoped spacer layer, a 1 nm thick GaAs spacer layer, a 13 nm thick GaAs12yNy channel, a 1 nm thick GaAs spacer layer, a 10 nm thick Al0.38Ga0.62As undoped spacer layer, a 30 nm thick Al0.38Ga0.62As layer doped with Si at 1 £ 1018 cm23 and a 17 nm GaAs cap layer. Transport measurements in Hall bars were performed in the temperature range T ¼ 2 – 300 K and with magnetic fields, B; up to 14 T, applied perpendicular to the plane of the QW. At low temperature ðT ¼ 2 KÞ; a white light bulb was used to illuminate the sample to increase the carrier concentration through the persistent photoconductivity effect. This allowed us to adjust the electron density ne of the two-dimensional electron gas (2DEG) in the GaAs12yNy QW at T ¼ 2 K from minimum values in the range 2 – 4 £ 10 11 cm 22 , in dark conditions, up to maximum values of persistent ne approximately equal to 7 £ 1011 cm22. Figure 8.11 shows the longitudinal ðrxx Þ and transverse ðrxy Þ resistivity as a function of B at T ¼ 2 K for all samples after illumination. Shubnikov –de Haas (SdH) oscillations and quantum Hall-like plateaus can be seen in all samples, although they are very weak in the sample with the higher N content, even at the largest value of persistent ne : We found that the modulation provides a significant enhancement (i.e. more than a factor of 2) of the conductivity with respect to that measured in samples in which Si donors are incorporated in the GaAs12yNy QW layer. The use of modulation doping [35] in dilute nitride QWs is of value as it separates spatially the Si donors from the N atoms in the QW. This inhibits the formation of Si – N complexes that are known to degrade the carrier concentration and mobility of GaAs12yNy [14]. From the slope of the rxy versus B curves in Figure 8.11, we determine a carrier density ne equal to 7.0 £ 1011, 4.6 £ 1011 and 4.7 £ 1011 cm22 in samples with y ¼ 0; 0.1 and 0.4%, respectively. Similar values were also obtained from the period in B21 of the SdH oscillations and from the voltage position of the quantum Hall plateaus. The value of persistent ne decreases slightly with increasing temperature up to

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Figure 8.12. T-dependence of m for a two-dimensional GaAs12yNy channel with y ¼ 0; 0.1 and 0.4% in the dark (dashed lines) and after illumination (continuous lines þ points). The continuous lines are guide to the eye. The inset shows the values of m measured at T ¼ 300 K (triangles) and those calculated according to a 21 semiclassical scattering model with (continuous line, m21 ¼ m21 N þ mph ) and without (dashed line m ¼ mN ) the contribution of phonon scattering.

about 150 K. For higher T; ne approaches its equilibrium dark value equal to 4 £ 1011, 2 £ 1011 and 3 £ 1011 cm22 in samples with y ¼ 0; 0.1 and 0.4%, respectively. These data indicate that at sufficiently high carrier concentrations the conduction occurs through the extended states of the conduction band of GaAs12yNy albeit with low values of the electron mobility, m: From the measured values of rxx and ne at different temperatures, we find that m is strongly reduced with increasing the amount of N (see Figure 8.12), as was also found in previous work [36 – 39]. For the GaAs12yNy QW with y ¼ 0:1%; we estimate that m ¼ 0:2 m2 =V s (0.1 m2/V s) at 4 K (300 K), which corresponds to an electron mean free path at low temperature of about 22 nm. Also, the T-dependence of m differs significantly in the three samples: in the control sample, m decreases monotonically with increasing temperature as expected for a metal-like behaviour and an increasing phonon scattering rate with increasing T; in contrast, in the N-containing samples, m shows a very weak temperature dependence for T . 100 K and as the temperature is decreased, m tends to decrease markedly for y ¼ 0:4% below 80 K, and slightly for y ¼ 0:1% below 10 K.

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The weak T-dependence of m observed in the N-containing samples for T . 100 K indicates that the contribution of elastic collisions by alloy disorder, defects and/or impurities is significantly larger than that due to inelastic collisions with phonons. In a recent paper [13], it was shown that electron scattering by N atoms has a strong effect on the electron mobility, which can be expressed as pffiffiffiffiffiffiffiffiffiffi  p 2   3mp kB T m dEc 2 3 m21 ¼ p a y; ð8:2Þ N e dy 2~2 p where y is the N content, kB is Boltzmann’s constant, e is the electron charge, a is the GaAs lattice constant, mp is the electron effective mass and dEc =dy is the derivative of the conduction band edge energy with respect to y: We have used Eq. (8.2) to estimate the contribution of electron scattering by N atoms to the electron mobility at room temperature by using for mp and dEc =dy the values calculated according to the BAC model. The predicted dependence of mN on y describes qualitatively our data (see inset of Figure 8.12) and data reported in the literature for similar undoped GaAs12yNy layers [36]. A better agreement is obtained if we take into account the contribution to m of phonon 21 scattering ðmph Þ; using the relation m21 ¼ m21 N þ mph ; where mph is the value of the electron mobility measured at T ¼ 300 K in the control sample for which m , mph at high T (see continuous line in the inset of Figure 8.12). Additional scattering mechanisms not considered in this model, such as electron scattering by long-range potential fluctuations of the GaAs12yNy channel due to alloy disorder and/or N-related defects, could account for the discrepancy between the data and the theoretical curve. Also as discussed below the N-induced localised states affect strongly the nature of the electrical conduction. Figure 8.13(a) shows the B-dependence of rxx at 2 K for different values of ne ; for sample with y ¼ 0:4%: With decreasing ne ; the channel conductivity decreases and the SdH oscillations weaken. Also, rxx and m show a stronger dependence on temperature (see Figures 8.12 and 8.13(b)). These data suggest a crossover from a band-like conduction regime to a regime of electron hopping between N-related localised states with decreasing electron concentration. As shown in Figure 8.13(b) in the dark, the T-dependence of r is consistent with the relation r ¼ r0 exp{ðT0 =TÞ1=3 }; which is a Mott-type law for variablerange hopping conduction in two-dimensional systems [40]. The parameter T0 is related to the density of states at the Fermi level, gF ; and the characteristic electron hopping length, lh ; through the relation T0 ¼ CðkB gF l2h Þ21 ; where C ¼ 13:8 is a constant [40]. For our data, T0 ¼ 110 K and lh ¼ 50 nm: This analysis and the value of the hopping length, which is much larger than the typical distance, d; between N isolated impurities ðd , 2 nm at y ¼ 0:4%Þ; indicate the existence of large-scale fluctuations in the potential of the GaAs12yNy channel, which are probably due to N-compositional fluctuations. These experiments and the analysis indicate that when there is a sufficient carrier concentration in the GaAs12yNy channel, the conduction occurs through the extended conduction band states of GaAs12yNy, albeit with relatively low mobility due to scattering

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Figure 8.13. (a) rxx as a function of B at T ¼ 2 K for different carrier concentrations ne : The measurements were performed at a constant current I ¼ 10 mA: (b) T-dependence of r measured in the ohmic regime of the I – Vx curves in the dark (circles) and after illumination (stars). The continuous line is a fit to the r data by the relation r ¼ r0 exp{ðT0 =TÞ1=3 }; where r0 and T0 are constants. The dotted line is a guide to the eye. All data are for a two-dimensional GaAs12yNy channel with y ¼ 0:4%:

by N atoms. In contrast, at low carrier concentrations and/or high N content, the electrical conduction is controlled by carrier hopping.

8.6. SUMMARY AND CONCLUSIONS

In this chapter we have reviewed our recent investigations into the nature of the electronic states in GaAs12yNy quantum wells. Our magneto-tunnelling experiments have allowed us to map out the form of the unusual energy –wavevector dispersion curves of GaAs12yNy, which results from the hybridisation of the extended conduction band states with a highly localised energy level associated with isolated N atoms [11]. These measurements validate the BAC model [6,7,10] and complement optical spectroscopy measurements of Shan et al. [6] with applied hydrostatic pressure. We have also described the results of conventional magneto-conductivity measurements of two-dimensional electrons confined in a Si-modulation doped GaAs12yNy quantum well. We have shown that modulation doping of Si is of value as it inhibits the formation of Si – N defects [14]. We investigated electrical conductivity and SdH effects over a range of electron carrier concentrations and measured electron mobility up to 0.2 m2/V s, consistent with conduction through extended band states [12]. An interesting outcome of these works is that there is a well-defined k-vector for the hybridised band states of GaAs12yNy ðy , 0:1%Þ over an extended range of energy. Of potential interest is the presence of an inflection point in the 1ðkÞ dispersion and an

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energy gap between the E2 and Eþ subbands of the GaAs12yNy QW. The further manipulation of the dispersion curves by changing the degree of quantum well confinement may offer the possibility of exploiting the unique band structure of GaAs12yNy alloys for a new type of non-linear hot electron device.

ACKNOWLEDGEMENTS

This work is supported by the Engineering and Physical Sciences Research Council (United Kingdom). This manuscript reviews the work of many people. We are particularly grateful to J. Endicott, D. Fowler, J. Ibanez, O. Makarowski, P.N. Brunkov and M. Bissiri, who carried out much of the experimental programme and to M. Hopkinson, R. Airey and G. Hill (Department of Electronic and Electrical Engineering, University of Sheffield, UK) who grew and processed our samples. We also acknowledge L. Geelhaar and H. Riechert (Infineon Technologies, Corporate Research Photonics, Munich, Germany) for the growth of the modulation-doped heterostructures. We have had helpful discussion with all of the above colleagues and also with E. O’Reilly, A. Zunger, M. Henini, C.T. Foxon and A. Forchel.

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[14] Yu, K.M., Walukiewicz, W., Wu, J., Mars, D.E., Chamberlin, D.R., Scarpulla, M.A., Dubon, O.D. & Geisz, J.F. (2002) Nat. Mater., 1, 185. [15] Patane`, A., Endicott, J., Iba´n˜ez, J., & Eaves, L. (2004) J. Phys.: Condens. Mater., 16, S3171. [16] Chang, L.L., Esaki, L. & Tsu, R. (1974) Appl. Phys. Lett., 24, 593. [17] Mizuta, H. & Tanoue, T. (1995) The Physics and Applications of Resonant Tunnelling Diodes, Cambridge University Press, Cambridge. [18] Snell, B.R., Chan, K.S., Sheard, F.W., Eaves, L., Toombs, G.A., Maude, D.K., Portal, J.C., Bass, S.J., Claxton, P., Hill, G. & Pate, M.A. (1987) Phys. Rev. Lett., 59, 2806. [19] Hayden, R.K., Maude, D.K., Eaves, L., Valadares, E.C., Henini, M., Sheard, F.W., Hughes, O.H., Portal, J.C. & Cury, L. (1991) Phys. Rev. Lett., 66, 1749. [20] Gennser, U., Kesan, V.P., Syphers, D.A., Smith, T.P., Iyer, S.S. & Yang, E.S. (1991) Phys. Rev. Lett., 67, 3828. [21] Beton, P.H., Wang, J., Mori, N., Eaves, L., Main, P.C., Foster, T.J. & Henini, M. (1995) Phys. Rev. Lett., 75, 1996. [22] Vdovin, E.E., Levin, A., Patane`, A., Eaves, L., Main, P.C., Khanin, Yu.N., Dubrovskii, Yu.V., Henini, M. & Hill, G. (2000) Science, 290, 122. [23] Patane`, A., Hill, R.J.A., Eaves, L., Main, P.C., Henini, M., Zambrano, M.L., Levin, A., Mori, N., Hamaguchi, C., Dubrovskii, Yu.V., Vdovin, E.E., Tarucha, S., Austing, D.G. & Hill, G. (2002) Phys. Rev. B, 65, 165308. [24] We model the diode as a parallel plate capacitor with capacitance C ¼ 10 1r A=d; where 10 is the permittivity constant in vacuum, 1r is the relative permittivity of GaAs, A is the area of the mesa and d is the distance between the fronts of the free carrier regions on the emitter and collector sides of the device. From the CðVÞ curve of sample with y ¼ 0:08%; we estimate that d varies from 140 to 100 nm for V increasing from 0 V to biases close to the voltage position of the current resonances in IðVÞ. [25] Klar, P.J., Gruning, H., Heimbrodt, W., Koch, J., Hohnsdorf, F., Stolz, W., Vicente, P.M.A. & Camassel, J. (2000) Appl. Phys. Lett., 76, 3439. [26] Davies, R.A., Newson, D.J., Powell, T.G., Kelly, M.J. & Myron, H.W. (1987) Semicond. Sci. Technol., 2, 61. [27] For bulk GaAs12yNy, we calculate the energy dispersion curves of the E2 and Eþ subbands by using the relation E^ ðkÞ ¼

[28] [29] [30] [31]

 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 2 ðEM ðkÞ þ EN Þ ^ ðEM ðkÞ 2 EN Þ2 þ 4yCMN ; 2

where EM ðkÞ is the energy– wavevector dispersion curve of GaAs, EN is the energy position of the N-related level (EN ¼ 1:725 eV at 4.2 K) and CMN is the hybridisation matrix element ðCMN ¼ 2:7 eVÞ: For the case of the GaAs12yNy/Al0.4Ga0.6As QW, we use the same relation but with EM ðkÞ equal to the energy– wavevector dispersion curve for each subband of the GaAs/ Al0.4Ga0.6As QW. Neumann, A., Patane`, A., Eaves, L., Belyaev, A.E., Gollub, D., Forchel, A. & Kamp, M. (2003) IEE Proc. Optoelectron., 150, 49. Leadbeater, M.L., Alves, E.S., Eaves, L., Henini, M., Hughes, O.H., Sheard, F.W. & Toombs, G.A. (1988) Semicond. Sci. Technol., 3, 1060. Schubert, E.F., Capasso, F., Hutchinson, A.L., Sen, S. & Gossard, A.C. (1990) Appl. Phys. Lett., 57, 2820. Zhang, S.B. & Wei, S.-H. (2001) Phys. Rev. Lett., 86, 1789.

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[32] Skolnick, M.S., Simmonds, P.E., Hayes, D.G., Higgs, A.W., Smith, G.W., Pitt, A.D., Whitehouse, C.R., Hutchinson, H.J., White, C.R.H., Eaves, L., Henini, M. & Hughes, O.H. (1990) Phys. Rev. B, 42, 3069. [33] Yang, F., Wilkinson, M., Austin, E.J. & O’Donnell, K.P. (1993) Phys. Rev. Lett., 70, 323. [34] Gunn, J.B. (1963) Solid State Commun., 1, 88. [35] Dingle, R., Sto¨rmer, H.L., Gossard, A.C. & Wiegmann, W. (1978) Appl. Phys. Lett., 33, 665. [36] Mouillet, R., de Vaulchier, L.-A., Deleporte, E., Guldner, Y., Travers, L. & Harmand, J.C. (2003) Solid State Commun., 126, 333. [37] Li, W., Pessa, M., Toivonen, J. & Lipsanen, H. (2001) Phys. Rev. B, 64, 113308. [38] Kurtz, S.R., Allerman, A.A., Seager, C.H., Sieg, R.M. & Jones, E.D. (2000) Appl. Phys. Lett., 77, 400. [39] Young, D.L., Geisz, J.F. & Coutts, T.J. (2003) Appl. Phys. Lett., 82, 1236. [40] Shklovskii, B.I. & Efros, A.L. (1979) Electronic Properties of Doped Semiconductors, Nauka, Moscow, Springer, Berlin, 1984.

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Dilute Nitride Semiconductors M. Henini (Ed.) q 2005 Elsevier Ltd. All rights reserved.

Chapter 9

Photo- and Electro-reflectance of III –V-N Compounds and Low Dimensional Structures J. Misiewicz, R. Kudrawiec and G. Sek Institute of Physics, Wroclaw University of Technology, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland

Modulation spectroscopy (MS) utilizes a general principle of experimental physics, in which a periodically applied perturbation leads to derivate-like features in the optical response of the sample. Therefore, the objective of MS is to change some parameter of the sample (internal modulation) or of the measuring system (external modulation) so as to produce a change in the optical reflectance or transmittance spectrum of the sample. In either case the changes are usually small so the differential spectra are closely related to the derivate of the absolute spectrum with respect to the modified parameters [1,2]. The derivate nature of MS emphasizes features localized in the photon energy region of interband transitions of semiconductor structures and suppresses uninteresting background effects. Also weak features that may not have been detected in the absolute spectra are often enhanced and a large number of sharp spectral features can be observed even at room temperature (RT). Mentioned advantages of MS spectroscopy are illustrated qualitatively in Figure 9.1, which compares three types of spectra obtained at room temperature for a typical GaInNAs/GaAs single quantum well (SQW). While the reflectance spectrum (R) is characterized by broad features, the photoreflectance (PR) spectrum is dominated by a series of very sharp lines with zero signal as a baseline. In PR spectrum we observe transitions related to absorption in the GaInNAs/GaAs QW and GaAs barrier. In the case of QW, both the ground state (11H) and excited state transitions (EST) are observed. For example, photoluminescence (PL) probes only the ground state transition. Combination of PL (emission-type experiment) and PR (absorption-type experiment) is a powerful tool to investigate the nature of recombination processes. So far, a large number of experimental techniques involving internal or external modulation or their combinations have been developed to yield different kinds of information about a sample. In the case of III – V-N compounds and their low dimensional structures mainly electromodulation techniques (i.e. PR and ER) were successfully applied to determine the optical properties of these structures. Only few reports have been devoted to other modulation techniques like piezomodulation [3,4]. We will focus only on the electromodulation spectroscopy. In order to present both possibilities of this technique 279

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Figure 9.1. Comparison of room temperature reflectance (a), photoreflectance (b), and photoluminescence spectra (c) of a GaInNAs/GaAs single quantum well structure.

and the most actual “state of the art” about MS in nitrogen diluted III– V compounds and their structures we have introduced sections devoted to principles of electromodulation spectroscopy, analysis of experimental data, experimental setup, and review of experimental results which were published up to date. A broad discussion about principles of MS can be found in Refs. [1,2,5,6].

9.1. PRINCIPLES OF ELECTROMODULATION IN ELECTRO- AND PHOTO-REFLECTANCE SPECTROSCOPY

The condition to obtain electromodulation spectra (PR or ER) is the existence of a built-in electric field in the structure being under investigation (this condition is usually fulfilled in the majority of structures, because every good quality structure possesses a surface electric field) or an application of the external field. In electroreflectance, an applied electric field is modulated so as to produce a periodic variation in the dielectric function. The electric field can be applied to the sample in a variety of ways by electric contacts or without them. In the last mode, “so-called” contactless electroreflectance (CER), sample is put in a light transparent capacitor. The other mode of ER, which is also contactless technique, is the PR. In photoreflectance, the modulation of the electric field in the sample is caused by photoexcited electron – hole pairs created by the pump source (usually laser) which is chopped with a given frequency.

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The photon energy of the pump source should generally be band gap of the semiconductor being under study. There is also a possibility to use a below band gap modulation through the excitation of impurity or surface states [7]. The mechanism of the photo-induced modulation of the built-in electric field FDC is explained in Figure 9.2 for the case of an n-type semiconductor. Because of the pinning of the Fermi energy EF at the surface, there exists a space-charge layer. The occupied surface states contain electrons from the bulk (Figure 9.2(a)). Photoexcited electron – hole pairs are separated by the built-in electric field, with the minority carrier (holes in this case) being swept toward the surface. At the surface, the holes neutralize the trapped charge, reducing the built-in field from FDC to FDC 2 FAC ; where FAC is a change in the built-in electric field (Figure 9.2(b)). As it is seen, a built-in electric field in the sample is necessary for photogenerated electromodulation of the dielectric function. In PR spectroscopy, relative changes in the reflectivity coefficient are measured. The changes can be defined as DR R 2 Ron ¼ off : R Roff

ð9:1Þ

In the above expression Roff and Ron are the reflectivity coefficients, when the pump beam (laser) is off and on, respectively. These normalized changes can be related to the perturbation of the dielectric function ð1 ¼ 11 þ i12 Þ expressed as [1,2] DR ¼ að11 ; 12 ÞD11 þ bð11 ; 12 ÞD12 ; R

ð9:2Þ

Figure 9.2. Schematic representation of the photoreflectance effect (a), and the photo-induced changes in electronic bands at the surface built-in electric field (b), for an n-type semiconductor.

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where a and b are the Seraphin coefficients, related to the dielectric function, and D11 and D12 are related by Kramers – Kronig relations. We will discuss the line shapes of the PR response in terms of electromodulation mechanisms. Electromodulation can be classified into three categories depending on the relative strengths of characteristic energies [8]. In the low-field regime l~Vl # G; where ~V is the electro-optic energy given by ð~VÞ3 ¼

q2 ~ 2 F 2 : 2m

ð9:3Þ

In the above equation, F is the electric field and m is the reduced interband mass in the direction of the field. In the intermediate-field case, when l~Vl $ G and qFa0 p Eg (a0 is the lattice constant), the Franz –Keldysh oscillations (FKO) appear in the spectrum. In the high-field regime the electro-optic energy is much greater than the broadening, but qFa0 < Eg so that Stark shifts are produced. Recently, Pollak [2] and Glembocki and Shanabrook [5] provided a most detailed theoretical background of the electro- and photoreflectance technique. 9.1.1 Line Shape Analysis Electro- and photo-reflectance spectra of simple, lightly doped systems, measured under low field conditions, can often be modeled using Aspnes’ third derivate functional form (TDFF) [8], so-called Lorentzian line shape DR ¼ Re½C eiu ðE 2 Eg þ iGÞ2m  R

ð9:4Þ

where Eg is the critical point (CP) energy, G is broadening parameter ðG , ~=tÞ; C and u are the amplitude and phase factor, respectively. The term m refers to the type of CPs, i.e. the nature of optical transitions, namely: m ¼ 2; 2.5 and 3 for an excitonic transition, a three-dimensional one-electron transition and a two-dimensional one-electron transition, respectively. This formula is appropriate at low temperatures for the high quality structures. At room temperatures the Lorentzian dielectric function is inappropriate and Eq. (9.4) must be replaced by a more general formula (Eq. (9.5)) " # DR C eiu ½GðzÞ þ iFðzÞ ¼ Re ; ð9:5Þ R E2 where GðzÞ and FðzÞ are the electro-optic functions and broadening is included via the normalized energy z ¼ ðE0 2 E þ iGÞ=~u: Eq. (9.5) becomes complex for the Gaussianlike form of dielectric function. Such form of Eq. (9.5) is called as first derivate Gaussian line shape (FDGL), and this form is the most appropriate at higher temperatures (e.g. room temperature) and/or for a highly inhomogeneous sample.

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It is worth noticing that there is a range of temperature where the line shape is an intermediate form between Lorentzian and Gaussian [2,5]. An alternative method for estimating Eg ; G and C (but not u) has been developed based on a Kramers – Kronig transformation of the PR (or ER) spectrum [9 – 11]. In this case, the complex PR function is defined as Dr~ðEÞ ¼ DrR ðEÞ þ iDrI ðEÞ ¼ DrðEÞeiQðEÞ ;

ð9:6Þ

where the measured value of ER or PR signal is equal to DR ¼ DrR ¼ Dr cos Q: R

ð9:7Þ

After mathematical considerations similar to that carried out for other optical constants functions [10], the Kramers –Kronig relation for the complex PR function (Eq. (9.6)) can be written as 2E0 ðEb DR 1 DrI ðE0 Þ ¼ P dE; ð9:8Þ 2 2 p Ea R E0 2 E Ð where P means the principal value of the integral and ðEa ; Eb Þ is the energy range in which DR=R is measured. The values of Ea and Eb should be chosen in a way that DR DR ðEa Þ ¼ ðE Þ ¼ 0 R R b having all the oscillations interesting for us inside this range. Knowing the values of DrI the modulus Dr can be determined by means of the simple formula: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi   DR 2 Dr ¼ þðDrI Þ2 ; ð9:9Þ R which can be treated as the modulus of PR resonance. In the framework of standard fitting procedure, the modulus of PR resonance is defined by Eq. (9.10) lDrðEÞl ¼

lCl ; ½ðE 2 E0 Þ2 þ G2 n=2

ð9:10Þ

In order to plot the modulus C; E0 ; u; and G parameters have to be determined by using the fitting procedure. The advantage of Kramers –Kronig analysis (KKA) is to avoid the fitting procedure. It is very useful when for example the line shape of PR data changes between Lorentzian- and Gaussian-like. The integrated modulus of PR resonance is interpreted as the oscillator strength of the optical transition while E0 and G are the transition energy and the transition broadening, respectively. The broadening is related to the sample quality and temperature.

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Figure 9.3. Photoreflectance spectrum (open points) of GaInNAs/GaAs SQW in the vicinity of ground state transition, and its analysis by using standard fitting procedure (a) and the Kramers– Kronig approach (b). Note the same dependencies of modulus of DR=R determined by using standard fitting procedure and Kramers–Kronig approach ðDrÞ-solid lines.

A comparison of the analysis of PR data by using standard fitting procedure and KKA is shown in Figure 9.3. The panel (a) shows experimental data (open points) which are fitted by Eq. (9.4) with m ¼ 3 (dashed line), together with the modulus of the resonance Eq. (9.10) (solid line). Panel (b) shows the same experimental data (open points) with the modulus of PR resonance obtained by using KKA Eq. (9.9) (solid line). The dashed line in Figure 9.3(b) shows the DrI obtained from Eq. (9.8). 9.1.2

Experimental Details

A schematic diagram of the photoreflectance apparatus is shown in Figure 9.4. The probe light is a monochromatic beam obtained from a quartz halogen lamp dispersed through a monochromator. This beam of intensity I0 is focused on the sample. The laser (pumping) beam illuminates the same spot of the sample. The laser beam is chopped with frequency of a few hundred Hz. The photon energy of the pump source should be generally above the band gap of the semiconductor being investigated. A He – Ne laser (the energy range below 1.96 eV) or Arþ ion laser (the energy range below 4.5 eV) is used as typical pump sources. The intensity of the laser light can be adjusted by a variable, neutral density filter. The light reflected from the sample is detected by a photodiode or a photomultiplier. In order to prevent the detection of laser light, an appropriate longpass glass filter is used in front of the photodetector. The signal separator, connected to the detector, separates the signal into

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Figure 9.4. A scheme of apparatus for photoreflectance measurements.

two components: DC component proportional to I0 R and AC component proportional to I0 DR: The AC component is measured with a lock-in amplifier. A computer divides the AC signal by the DC component giving the photoreflectance spectrum, DR=RðEÞ; where E is the photon energy of the incident beam. In the case of photoreflectance, it is important for the apparatus to have good filtering of the stray laser light, because it has the same frequency (chopped) as the signal of interest and can easily be detected. The scattered pump light can be reduced by means of an appropriate longpass filter in front of the detector. Furthermore, the laser illumination can produce a band gap photoluminescence, which under certain conditions is more intense than the DR signal. This problem can be eliminated e.g. by using long-focal-length optics.

9.2. BAND STRUCTURE OF (Ga,In)(As,Sb,N) BULK-LIKE LAYERS

The first step in the understanding of physical properties of low dimensional semiconductor structures and advanced devices, e.g. laser structures, is to determine the band structure of bulk layers. An intensive progress in this field was possible due to the applications of the optical MS. A summary of this issue is presented in this section.

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A reduction of the band gap exceeding 0.1 eV per atomic percent of N content was observed in GaNxAs12x for x , 0:015 already in 1992 by Weyers et al. [12]. However, Ga(In)NAs compounds were investigated by using MS for the first time only in the end of the 1990s [13 –20]. Significant progress in describing the effect of N on the electronic structure of III – V-N alloys has been made due to investigations of the pressure dependent PR spectra of GaInNAs alloys [14]. Shan et al. [14] investigated thick (0.5 – 5 mm) GaInNAs layers grown by MOVPE. In this chapter the authors have observed an extra feature ðEþ Þ on a higher energy side of the PR features related to the fundamental band gap transition (E2 transition) and the transition from the top of the spin – orbit split-off valence band to the bottom of the conduction band ðE2 þ D0 Þ (see Figure 9.5). While the E2 and E2 þ D0 transitions shift to lower energy with the

Figure 9.5. PR spectra of Ga12xInxNyAs12y samples: (top) Ga0.92In0.08As ðy ¼ 0Þ; the E0 and E0 þ D0 transitions are observed; (middle) Ga0.95In0.05N0.012As0.988, the E2 and E2 þ D0 transitions shift to lower energy, and a new feature Eþ appears; (bottom) Ga0.92In0.08N0.023As0.977 (this sample has the same In content as the top sample), the addition of more N pushes the E2 and E2 þ D0 to lower energy and Eþ to higher energy. The arrows indicate the transition energy positions [14].

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increasing In and N concentrations, the Eþ transition moves in the opposite direction. This demonstrates that the splitting between E2 and Eþ increases with N content. In order to explain the experimental data and their pressure dependencies Shan et al. have proposed a simple band anticrossing (BAC) model, which is presented briefly in the next part of this section. Very similar experimental results were simultaneously obtained by Perkins et al. [15] for Ga(In)NAs layers. These researchers measured ER spectra for a series of GaNxAs12x thick layers (1 – 7 mm) with x , 0:03 as well as two quaternary Ga0.95In0.05N0.013As0.987 and Ga0.92In0.08N0.022As0.978 layers. The author has observed the fundamental band gap transitions ðE0 Þ; the transition from the spin –orbit split-off valence band ðE0 þ D0 Þ and an additional transition (denoted Eþ ) for x . 0:008 (see ER spectra in Figure 9.6). It is seen in Figure 9.7, that E0 decreases monotonically with increasing nitrogen content and the E0 þ D0 transition shifts with the band gap energy at constant offset of , 0.3 eV. Unlike E0 and E0 þ D0 ; Eþ feature increases with increasing nitrogen content. The lack of interaction between E0 þ D0 and Eþ indicates that Eþ transition corresponds to an electronic transition between the valence band maximum and a level above conduction band minimum. Optical transitions above Eþ transition were investigated by using MS by Perkins et al. [20]. Figure 9.8 shows ER spectra for GaAs and GaN0.01As0.99 layers obtained by these authors. Besides E0 ; E0 þ D0 ; and Eþ transitions, a PR feature related to Eþ þ D transition is observed in this figure. The two remaining resonances, E1 and E1 þ D1 which includes the VB splitting D1 ; correspond to L-line related transitions occurring along the k-space (111) direction near to and including the zone-edge L-point. The E1 and E1 þ D1 transitions in GaNAs

Figure 9.6. Electroreflectance spectra for a 2 mm thick GaAs0.978N0.022 film on a GaAs substrate. The band gap transitions ðE0 Þ at 1.19 eV as well as the transition from the spin–orbit spin-off valence band ðE0 þ D0 Þ at 1.52 eV are easily seen. An additional weak feature ðEþ Þ at 1.83 eV is more clearly seen in the second spectra shown at 10 £ and offset for clarity. The fitted line shape for the E0 þ D0 and Eþ transitions are shown with dashed lines and offset for clarity [15].

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Dilute Nitride Semiconductors

Figure 9.7. Electroreflectance spectra for GaAs12xNx [(a)–(h)] and GaInAsN [(i) and (j)]. Note the different scale used for each panel as well as the expanded scale within each panels used to display the above band gap transitions with more clarity. For the GaAs12xNx samples, the nitrogen content ranges from x ¼ 0 (a) to x ¼ 0:028 (h). For the GaInAsN samples, the compositions are Ga0.95In0.05As0.987N0.013 (i) and Ga0.92In0.08As0.978N0.022 (j) [15].

are not sensitive to N mole fraction and strongly broadened compared to GaAs. The weak feature labeled by p seems to be nitrogen-induced transitions because it evidently appears after incorporation of nitrogen [20]. Perkins et al. assumed that the Ep transition originates from the VB L-point where there is a large density of states (DOS) due to the flat VB dispersion. All the experimental results demonstrate that incorporation of N into GaAs or GaInAs affects mostly the conduction band and has a negligible effect on the electronic structure

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Figure 9.8. Electroreflectance spectra for a GaAs film at T ¼ 300 K (panel a) as well as for a GaAs0.99N0.01 film at T ¼ 300 K (panel b) and T ¼ 90 K (panel c). In panel c, the dashed or dotted lines show the fitted line shape with the solid circles (†) showing the fit determined critical point [20].

of the valence band. As it was mentioned earlier, the significant progress in the description of the conduction band was possible due to the measurements of the pressure dependencies of E2 and Eþ transitions in PR spectroscopy. Shan et al. [14] have determined the energy positions of the E2 and Eþ transitions in the Ga0.95In0.05N0.012As0.988 layer as a function of applied hydrostatic pressure. A classical anticrossing behavior of the two branches was observed (see Figure 9.9). In this model the incorporation of nitrogen atoms into a host matrix compound (GaAs or GaInAs) leads to a strong interaction between the conduction band and a narrow resonant band formed by the nitrogen states. The interaction between the extended conduction states of the matrix semiconductor and the localized nitrogen states is treated as

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Figure 9.9. Change of the E2 and Eþ transition energies in Ga0.95In0.05N0.012As0.988 as a function of the applied pressure. The open triangles are PR data and the filled triangles are photomodulated transmission data. The solid lines are model calculation results for the band anticrossing. The dashed, dotted, and dot-dashed lines are the pressure dependence of the G and X conduction band edges of the Ga0.95In0.05As matrix and the N level relative to the top of the valence band, respectively. The inset shows a PR spectrum taken at 4.5 GPa. The narrow PR spectra feature at energy below Eþ originates from the GaAs substrate [15].

a perturbation which leads to the following eigenvalue problem E 2 EM VMN V E2E MN

ð9:11Þ

N

where EM is the conduction state of the matrix semiconductor, EN is the localized state related to nitrogen atoms, and VMN is the matrix element describing the interaction between EM and EN : Solving the eigenvalue problem gives the following subbands energies  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 2 E þ EM ^ ½EN 2 EM 2 þ 4VMN E^ ¼ : ð9:12Þ 2 N So far, the Eþ transition was also reported in other papers [21 – 24]. However, the character of this transition is still unclear. Especially, that the relative intensity between

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291

E2 and Eþ changes from sample to sample. It can indicate that the character of Eþ transition changes between direct and indirect. Already, Shan et al. [14] have observed that the increase in hydrostatic pressure causes a change in the ratio of the PR signals associated with the E2 and Eþ transitions. Within BAC model such behavior may suggest that with the increase of the hydrostatic pressure the character of the E2 branch changes from extended EM -like to localized EN -like and the character of the Eþ branch from localized-like to extended-like (see Figure 9.9). The exact nature of the N-induced perturbation of the electronic band structure and the origin of Eþ transition is still controversial. Calculations in the framework of an empirical pseudopotential method have shown that the band structure of Ga(In)NAs compounds is more complicated [25 –27]. The band structure includes two types of electronic states. First, nitrogen pairs or other atomic cluster states which are created randomly in the bulk during growth. The localized energy states due to nitrogen-related clusters are formed around the conduction band either in the gap or in the continuum of the band. Second, the perturbed host states represent mixing of the G – X – L and other conduction states by the N-induced perturbation. Hence, we rather should have a coupling and anticrossing of G; X; L edges instead of the two-level BAC approach where only the interaction of the conduction band with the localized nitrogen level is taken into account. Therefore, using the BAC model actually means that we replace the complex interaction with higher energy states by coupling to only one “effective” nitrogen level to get a simple empirical description of the Ga(In)NAs band structure. In general, the “effective” nitrogen level may not correspond to a real state. However in order to find the band gap energy of GaInNAs compound the BAC model is rather sufficient. The advantage of the BAC model is its simplicity and quite good agreement with experimental data, hence many authors use the BAC model as the appropriate theoretical approach. In the case of GaInNAs compounds, theoretical calculations and experimental investigations have shown that the band gap energy in this compound is not well defined. During the epitaxial growth of GaInNAs compound the chemical dynamical processes occurring at the surface favor Ga – N bonds instead of In – N [28]. The surface state is quasi-frozen during the non-equilibrium growth process, hence, after growth an N atom is surrounded by four Ga atoms. However, such atom configurations lead to a crystal structure with “small atom –small atom” and “large atom –large atom” arrangements which is less preferable in terms of strain than “small atom – large atom” environment. Consequently, the annealing process leads to formation of different nitrogen-nearest neighbor environments, i.e. N-centered N – Ga42mInm ð0 # m # 4Þ short-range-order clusters. The change of N bonds after annealing is one of the most interesting features of GaInNAs compound. Kim and Zunger have studied theoretically the distribution of bonds using Monte Carlo simulation and found that the number of In – N and Ga – As bonds increases relative to random alloys [27]. So far, the Fourier transform infrared (FTIR) absorption confirms that Ga – N bonds are most frequent after growth [29,30].

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The formation of In –N bonds after annealing has been observed in Raman spectroscopy [31,32] and infrared transmission [32 –34]. There is a general consensus that post-grown annealing increases the number of In – N bonds instead of Ga – N. The change in N bonds has important consequences for the band gap energy. With the change in N environment from Ga-rich to In-rich due to annealing a blue shift of band gap energy is expected. This phenomenon was observed many times in PL spectroscopy. However, any fine structure of the band gap energy was not observed in PL spectra due to its sensitivity to defect states as well as to the ground state transition only. Klar et al. [35] have investigated QW structures grown by MOVPE and have shown that the appearance/increase of In – N bonds leads to a change in the band gap energy ðEg Þ; and that for the same composition ðx and yÞ different band gaps can occur by rearranging of the N environments from Ga-rich to In-rich. The particular gaps can be usually probed by MS. The multiple character of band gap energy for GaInNAs layers was already investigated in Ref. [36]. The authors have analyzed photoreflectance spectra from Ga0.942In0.058N0.028As0.972 layers lattice matched to GaAs. The layers were annealed under different conditions. XRD and Raman data confirm that the as-grown and annealed GaInNAs layers have the same content and different nitrogen nearest-neighbor environments, i.e. N – Ga42mInm 0 # m # 4 short-range-order clusters [36]. The environment changes from Ga-rich, for the as-grown layer, to In-rich for annealed layers. PR spectra obtained for these layers together with their modulus obtained by using KKA are shown in Figure 9.10. It is seen that the PR spectra change significantly upon annealing. A set of at least three discrete transitions at well-defined, sampleindependent energies is resolved with the maximum in oscillator strength hoping to higher energies upon annealing. For the as-grown sample, the main PR feature can be interpreted as being due to band-to-band transitions related to the N –Ga4 configuration (“4Ga” for short). A second feature, located at about 25 meV higher energy (Figure 9.3(b)), can be assigned to the presence of a second nitrogen configuration, such as “3Ga1In”, co-existing in that particular sample. Upon annealing at 8008C, the signal arising from the 4Ga configuration decreases, while that from the 3Ga1In configuration is significantly increased, and a new feature assigned to the 2Ga2In configuration appears at the high-energy side. Upon annealing at 9008C, the 3Ga1In signal disappears and the 2Ga2In is enhanced. Hence, the annealing-induced blue shift of GaInNAs band gap energy, which is usually observed in this system, has been evidently identified as the change in the intensity of PR resonances related to different N –Ga42mInm configurations. The coexistence of two well-resolved band gaps confirms a cluster-like character of GaInNAs material. Klar et al. [35] have found that for the annealed high In-content strained GaInNAs quantum wells the most preferred configuration is 1Ga3In. Corresponding features as well as features due to the extreme 4In configuration are not detected in PR spectra GaInNAs layers lattice matched to GaAs. A reason for this could be the relatively small amount

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Figure 9.10. PR spectra of Ga0.942In0.058N0.028As0.972 layers (a); Kramers–Kronig modulus of PR signals (b). Three different nitrogen nearest-neighbor environments are suggested to be found, two of which co-exist in the same sample giving rise to two different band gaps with an energy splitting of 25 meV [36].

of indium incorporated in these samples ðx ¼ 0:058Þ; preventing the formation of indiumrich 1Ga3In and 4In atom configurations.

9.3. (Ga,In)(As,Sb,N)-BASED QUANTUM WELL STRUCTURES

Most optoelectronic devices adopt QW structures. Hence, the knowledge of the band gap energy, the number of confined electron and hole states, the electron effective mass and the band gap alignment is necessary. In this section, we present a photoreflectance approach to investigate these issues. Within this approach the theoretically predicted QW transition energies are compared with those obtained by using MS. Unknown parameters of GaInNAs/GaAs QW structure, like e.g. the band gap alignment or the electron

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effective mass, are deduced from this comparison. Such an approach has been applied many times to InGaAs/GaAs [37], InGaAs/InAlAs [38], or InGaAs/InGaAsP [39] QW structures. In the case of Ga(In)NAs-based QW structures PR spectroscopy has been applied in Refs. [40 –59]. The band gap alignment and/or electron effective mass have been determined from the PR data by Heroux et al. [45], Choulis et al. [48], and Misiewicz et al. [49]. 9.3.1 Theoretical Approach Modulation spectroscopy, besides the energy of ground state transition, yields energies of barrier and higher order QW transitions. For square-like QWs, allowed transitions between hole subbands (index n) and electron subbands (index m) obey the selection rule n 2 m ¼ even: In these circumstances wave function mixing can occur and this rule may be violated, causing “parity-forbidden” transitions, n 2 m ¼ odd; to be observed [2, 5]. Therefore, forbidden as well as allowed transitions can be observed in modulation spectroscopy. A comparison of such experimental data with theoretical models enables to verify information about the QW thickness, strain, QW and barrier compositions, effective mass of carriers, and band gap alignments. In addition, some unknown material parameters can be determined on the basis of comparing theoretical calculations with experimental data. For example, the band gap alignment has to be determined in this way because this parameter cannot be measured directly. The heterojunction band gap alignment can be determined by the so called band offset ratio defined for conduction band edge as QC ¼

DEC ; DEC þ DEVHH

ð9:13Þ

where DEC is the discontinuity in the conduction band (CB) between the two materials and DEVHH is the discontinuity in the heavy-hole valence band (VB). One of the simplest theoretical approaches to calculate the energy level structure in GaInNAs-based QW systems has been presented in Ref. [49]. The authors have performed the calculations of QW energy levels within the framework of the usual envelope function approximation [60] without the excitonic effect. In order to find the band gap energy of GaInNAs compound, the authors adopt the BAC model with typical parameters: EN ¼ pffiffi 1:65 eV; EM ¼ Eg ðGaInAsÞ; and CNM ¼ 2:7 eV, for equation VMN ¼ CMN x where x is the nitrogen concentration. These parameters are not varied with the increase in nitrogen and indium contents. According to the BAC model, the influence of nitrogen-localized states on the valence band structure is neglected. Hence, the assumption that the effective mass of light- and heavy-hole does not change after adding of nitrogen atoms is justified. Due to the high lattice mismatch between Ga(In)NAs well and GaAs barrier the strain effects are included in the calculations. The biaxial strain is calculated based on the Pikus – Bir Hamiltonian [61] as in Ref. [45]. The energy shifts due to hydrostatic dEH and shear

Photo- and Electro-reflectance of III – V-N Compounds dES strain components equal

  C12 dEH ¼ 2a 1 2 1; C11   C dES ¼ 2b 1 2 2 12 1; C11

295

ð9:14Þ ð9:15Þ

where 1 is the strain tensor in the plane of the interfaces, C11 and C12 are elastic stiffness constants, and a and b are the hydrostatic and shear deformation potentials, respectively. All the parameters are obtained by linear interpolation between the parameters of a relevant binary semiconductor [62]. In Ref. [49] the authors considered mpe and Qc as fitting parameters. The procedure for matching experiment with theory is given as follows. The QW transition energies are calculated as a function of mpe using the hole effective masses taken from the literature and the nominal QW parameters, i.e. compositions, thickness. These energies are then compared with those found from the PR spectra using a plot similar to that shown in Figure 9.11. Here, the experimental transition energies are shown as full points while those calculated from the model are shown as lines. To obtain a match, the QC is varied until the intersection of each experimental and theoretical line in Figure 9.11 occurred close to a single value of mpe ; indicated in Figure 9.11 by a vertical dotted line. Using this method, the optimum match between theory and experiment could be judged by eye, the greatest

Figure 9.11. The illustration of the method used to achieve a match of theoretical QW transition energies (lines) with those found from fitting the PR spectra (points). The vertical dashed line shows the deduced electron effective mass. The sample selected to this illustration is a 9 nm thick Ga0.72In0.28As/GaAs SQW which PR spectrum is shown in Section 9.3.2. Obtained mass and conduction band offset well agree with values reported in the literature for such SQWs.

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weight being given to the most dominant, ground state and excited allowed QW transitions in the PR spectrum. Very similar procedure for matching experiment with theory is reported in Refs. [37 – 39]. Figure 9.11 shows the matching procedure for Ga0.72In0.28As/GaAs SQW structures. A good agreement between experimental data and theoretical calculations is obtained for the nominal QW thickness and content, and effective masses and the conduction band offset taken from the literature [62]. In the case of Ga12xInxNyAs12y/GaAs SQW the nominal QW thickness and content are assumed, and the most optimal value for the mpe and QC is investigated. In addition it is assumed that the light- and heavy-hole effective mass is the same as for reference Ga12xInxAs/GaAs SQW. More advanced approach to calculate energy levels in GaInNAs/GaAs QWs is presented in Ref. [48]. In order to calculate QW transitions the authors used a 10-band k·p model with parameters derived from tight-binding supercell calculations. 9.3.2 Energy Level Structure of GaInNAs/GaAs QWs In order to present the evolution of energy level structure after the introduction of nitrogen atoms into GaInAs well, Misiewicz et al. [49] have selected four subsets of GaInNAs/ GaAs SQWs with different indium and nitrogen contents. The first subset consists of three samples with In content of 28%, QW with 9 nm and nitrogen concentration of AR, 0% (reference sample); A1, 0.35% and A2, 0.5%. In the second subset there are three samples with In content of 36%, QW width of 7.2 nm and nitrogen concentration of BR, 0% (reference sample); B1, 0.7% and B2, 1%. The third subset consists of four samples with In content of 41%, QW width 9 nm and nitrogen concentration of CR, 0% (reference sample); C1, 2%; C2, 3.7% and C3, 5.2%. The fourth subset was grown by MOVPE in opposition to the three above grown by MBE. This subset consists of three samples with In content of 34%, QW width of 6.5 nm and nitrogen concentration of DR, 0% (reference sample); D1, 0.5% and D2, 0.8%. All the samples have a , 100 nm thick GaAs capping layer. The last subset was selected in order to compare the quality of MOVPE and MBE GaInNAs/GaAs QWs. More details about the samples can be found in Ref. [49]. Figures 9.12 and 9.13 show room temperature PR spectra of three subsets of SQWs grown by MBE and one subset of SQWs grown by MOVPE, respectively. Using GaInAs/ GaAs QW as a starting point to study the effect of nitrogen incorporation has several advantages, like e.g. easier identification of PR resonances of N-containing QWs. All the PR spectra are dominated by GaAs band gap bulk-like signal above the energy of 1.4 eV. Below this energy the QW-related transitions are observed. The arrows in Figure 9.12 indicate transition energies obtained from the fitting procedure to the PR data using the FDGL model, the most appropriate form of PR resonances in the case of confined transitions, like those in QWs, at room temperature [5]. The identification of all QW transitions was possible on the basis of calculations described in the previous section. The notation nmHðLÞ denotes the transition between nth heavy-hole (light-hole) valence

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Figure 9.12. Room temperature PR spectra of Ga0.72In0.28NxAsx21/GaAs (subset “A”) (a), Ga0.64In0.36NxAsx21/ GaAs (subset “B”) (b), Ga0.59In0.41NxAsx21/GaAs (subset “C”) SQWs (c) grown by MBE [49].

subband and mth conduction subband. The resonance at the lowest energy is connected with the 11H transition which is a fundamental one in such QWs. Besides the 11H transition, PR spectra show a 11L transition (i.e. the lowest energy transition for lightholes) and transitions between excited QW states: 22H, 12H, 21H, and 32H. The transitions 12H and 21H are forbidden ones but due to the presence of a surface electric field in the structure [63] or other imperfections of QW it is possible to observe such transitions in PR measurements. The magnitude of surface electric field in a semiinsulating structure decreases exponentially with the increase of distance to the surface. If a QW is close to the surface its potential can be changed and the symmetry of QW can be lost [63]. Usually, the surface electric field is very weak and 100 nm cap is sufficient to separate QW from the surface electric field. However, in some cases the field can be stronger and can affect QW. In this case forbidden transitions are allowed and can be visible. The Stark shift of QW transitions caused by the surface electric field can be neglected because we are in the low field limit ðF , 1 kV=cmÞ: In this regime of electric field only the selection rules change significantly while energies of QW transitions shift very weakly. In our structures, the existence of a surface electric field is confirmed by the presence of GaAs-related FKO [64]. The magnitude of the field changes from sample to sample. On the basis of FKO period, it has been estimated that the surface electric field is 14, 21, and

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Figure 9.13. Room temperature PR spectra of Ga0.66In0.34NxAsx21/GaAs (subset “D”) SQWs grown by MOVPE. Vertical arrows and dash indicate energies obtained from calculations and the fit by FDGL, respectively [50].

25 kV/cm for sample A1, A2, and A3, respectively; , 6 kV/cm for all subset “B”; 16 kV/ cm for sample C3; 13, 19, and 26 kV/cm for samples D1, D2, and D3, respectively. The surface electric field was not estimated for samples C1, C2, and C4, because FKOs were not observed for these samples. The fact that the nominally forbidden transitions are better visible for the structures with the surface electric field higher than 13 kV/cm indicates that the surface field changes the square-like profile. It is one of the reasons why the oscillator strength of nominally forbidden transitions is stronger in some cases. Also, other factors like, e.g. random alloy fluctuations, a hole wave function mixing can influence the selection rules. Such factors seem to be especially important for the subset “C”. In this case, the GaIn(N)As layer is strongly strained due to the high concentration of In atoms. The strain introduces additional imperfections which influence the selection rules of ideal square-like QW. Therefore, the nominally forbidden transitions are enhanced for this set of QWs. Their amplitudes change from sample to sample due to variation of imperfections in these structures. Regarding the behavior of QW transitions after adding of nitrogen, it is seen that with the increase in nitrogen content, all the QW transitions shift towards lower energies.

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The analysis of the shift with the increase in nitrogen content seems to be the most interesting for the subset “D”, due to a strong PR signal and significant intensity of forbidden transitions. The arrows in Figure 9.13 indicate the transition energies obtained on the basis of calculations. The energies are in good agreement with energies obtained from the fit of the PR data by FDGL (compare arrows and vertical dash). The energy difference between heavy-hole levels remains almost constant after addition of nitrogen atoms. It results from a weak nitrogen-induced change in QW valence band and negligible changes in heavy-hole effective mass. The red shift of QW transitions comes mainly from the shift of electron levels and two factors influence its value. The first is an increase in QW depth and the second is an increase in electron effective mass. The impact of these two factors increases with the increase in nitrogen content. For the nitrogen free SQW the indium content is so high that the band alignment for light-hole is of type II leading to indirect light-hole related transitions in real space. The energy difference between fundamental light- and heavy-hole transitions does not change significantly after adding of nitrogen. This confirms the fact that the light-hole transitions remain indirect despite that nitrogen atoms reduce the strain in the QW layer and hence also the axial (shear) component of the strain responsible for the valence band splitting. These features evidently show that the incorporation of nitrogen atoms into GaInAs/GaAs QW influences mainly the conduction band while the valence band remains almost unchanged. 9.3.2.1 Electron Effective Mass Determination. In the framework of the BAC model the electron effective mass equals 2 3 1 1 6 EM 2 EN 7 ð9:16Þ 41 2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 5; p ¼ me 2mM 2 2 ðE 2 E Þ þ 4xC M

N

NM

where mM is the electron effective mass in the host matrix (i.e. GaInAs compound). According to Eq. (9.16) an increase in the electron effective mass with the increase in nitrogen content takes place. This phenomenon has been confirmed experimentally [44,49, 54,65 –68]. In the case of mpe taken from BAC model, i.e. Eq. (9.16), Misiewicz et al. [49] have shown that the agreement with experimental data is not satisfactory for GaInNAs with high In concentration. Figure 9.14 shows mpe obtained in Ref. [50] for GaInNAs/GaAs QWs with different indium and nitrogen contents (open points) together with mpe values obtained by other authors [45,48,65,67,68] (remaining points). First, it has been found that mpe in GaInNAs is bigger than in GaInAs with the same indium concentration. Second, the mpe increases with the increase in nitrogen concentration. Obtained mpe agrees with the BAC model only in the range of low indium and nitrogen concentrations. The variation of BAC parameters does not change the mpe value sufficiently (see BAC curves in Figure 9.14). Therefore, the electron effective mass cannot be taken after the BAC model if we want to calculate

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Figure 9.14. The electron effective mass as a function of N concentration obtained for GaInNAs/GaAs QWs. Open points represent experimental data obtained in this work: A subset “A” (28% In); W subset “D” (34% In); (e subset “B” (36% In); f subset “C” (41% In); S Ga0.62In0.38N0.053As0.947/GaAs SQW (sample analyzed in Section 9.3.2 and marked as QW1). Remaining points represent literature data: † [48]; B [65]; [67]; P 5% In, Q 9% In, w 14% In, V 14.5% In, R 20% In in Ga12yInyNxAs12x/GaAs MQW [45]; £ 25% In, 32% In, O 34% In, £ 38% In in Ga12yInyNxAs12x/GaAs QW [68]; [49].

energy levels of GaInNAs/GaAs QW in the framework of the BAC approximation of GaInNAs band gap energy. The authors have found that in the range of investigated indium and nitrogen contents the influence of indium concentration on mpe can be neglected and mpe can be approximated by formula: mpe ¼ ð0:072 þ 0:011xÞm0 ;

ð9:17Þ

where x is the nitrogen concentration in percent. The obtained formula gives the electron effective mass close to values obtained by BAC model for GaNAs compounds (see Figure 9.14). In the case of GaInNAs compounds, an increase in In content leads to significant decrease of mpe within the BAC approach as seen in Figure 9.14. Such strong change in mpe due to the incorporation of In atoms at the same N content is not observed. The mpe increase is a feature which is attributed to the presence of N atoms. An influence of In atoms on mpe is not excluded, however, BAC predictions are rather valid. The influence of In content on mpe value can be neglected at the first approximation as in Eq. (9.17) [49].

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9.3.2.2 Conduction Band Offset Determination. Besides mpe parameter the QC is the second free parameter in our calculations. This parameter is crucial for the temperature characteristic of laser structures. It is important to have the type I structure with a deep confinement potential for electrons and suitably deep potential for holes. Misiewicz et al. [49] determine the conduction band offset on the basis of matching of PR data with theoretical calculations. Figure 9.15 shows the QC parameter for the GaInNAs/GaAs QWs with different indium and nitrogen concentrations obtained in Ref. [49] (open points) and taken from other authors [48,65,67] (remaining points). In the case of QW investigated in Ref. [49] the indium content is relatively high ð28% , In , 41%Þ and in this range of indium content the QC for GaInAs/GaAs system is almost the same (i.e. QC ¼ 0:8) [69]. The incorporation of a small quantity of nitrogen atoms ðN , 5%Þ in InGaAs does not change QC drastically in comparison with InGaAs material with the same indium concentration. Hence, at the first approximation it can be assumed that QC for GaInNAs/GaAs system is the same as for GaInAs/GaAs one. At the end of this section the authors would like to pay attention to the fact that such additional factors like (i) different nitrogen nearest-neighbor environments and (ii) N-related defects are not included in the above considerations. It could lead to some dissonances between the experiment and calculations, because it has been found that these

Figure 9.15. The conduction band offset in GaInNAs/GaAs structure versus N concentration and In concentration (inset). Open points represent experimental data obtained in this work: A subset “A” (28% In); W subset “D” (34% In); e subset “B” (36% In); f subset “C” (41% In); S Ga0.62In0.38N0.053As0.947/GaAs SQW (sample analyzed in Section 9.3.2 and marked as QW1). Remaining points represent literature data: † [48]; [67]; B 10% In, O 20% In, P 30% In in Ga12yInyN0.007As0.993/GaAs QW [65]; [49].

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two factors have a significant influence on the band gap structure of Ga(In)NAs compounds. These aspects are discussed in the following subsections. Moreover, a small difference of nitrogen concentration between the real value and determined from experiments in GaInNAs layer leads to essential discrepancy in calculation of the GaInNAs band gap energy. Therefore, the simplest approach to calculate energy levels of the QW is fully justified. Within this approach two essential results have been confirmed. First, the mpe increases after adding of nitrogen atoms. Second, the QC in GaInNAs/GaAs system is almost the same as in GaInAs/GaAs one. These two conclusions confirm the fact that nitrogen atoms modify mainly the conduction band. 9.3.3 Energy Level Structure of Step-Like GaInNAs/Ga(In)NAs/GaAs QWs The step-like GaInNAs/Ga(In)NAs/GaAs QW structures make it possible to achieve 1.3 and 1.55 mm emission at a lower nitrogen and/or indium content [70 – 73]. So far, optical properties of such step-like QWs have been mainly investigated in PL spectroscopy [70 – 73] which probes only the ground state transition. Therefore, the energy level structure of the step-like QW system is unknown from the experimental point of view. Also, it is difficult to make theoretical predictions for such a system due to the lack of

Figure 9.16. Energy level structures for three different QW systems obtained for some indium and nitrogen contents: (a) GaInNAs/GaAs, (b) GaInNAs/GaNAs/GaAs, and (c) GaInNAs/GaInNAs/GaAs [49].

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material parameters for the nitrogen diluted compounds, especially the band offset. Therefore, experimental investigations of the number of confined states in such 1.3 and 1.55 mm laser structures seem to be very interesting from both fundamental and application point of view. Figure 9.16 shows a comparison of the energy level structure for three different QW structures. This figure demonstrates the main idea of step-like QW system and is useful to explain features observed in PR spectra. Figure 9.17 shows PR spectra for step-like Ga0.66In0.34NxAs12x/GaN0.011As0.989/GaAs QW structures with nitrogen content x ¼ 0:007 (curve (ii)) and x ¼ 0:008 (curve (iv)). In addition, PR spectra of Ga0.66In0.34NxAs12x/GaAs SQWs, i.e. reference sample with the same nitrogen content (x ¼ 0:007 curve (i) and x ¼ 0:008 curve (iii)) are shown in Figure 9.17. All these structures were grown by MBE. In the case of reference SQWs, the 11H and 22H transitions are clearly visible. Also, the 11L transition, with light-hole state having bulk-like 3D properties, is noticeable. After the introduction of GaN0.011As0.989 step-like barrier the 11H transition shifts to red by 26 and 31 meV for the QW structure with nitrogen content of x ¼ 0:007 and x ¼ 0:008; respectively. The 22H transition shifts to red three times more than the 11H one mainly due to a significant shift of the second

Figure 9.17. Room temperature PR spectra of step-like QW structures tailored at 1.3 mm. (a) Ga0.64In0.34N0.007As0.993 (8 nm)/GaAs SQW (reference sample) (i), Ga0.66In0.34N0.007As0.993 (8 nm)/GaN0.011As0.989 (8 nm)/GaAs QW structure (ii); (b) Ga0.64In0.34N0.008As0.992 (8 nm)/GaAs SQW (reference sample) (iii), Ga0.66In0.34N0.008As0.992 (8 nm)/GaN0.011As0.989 (8 nm)/GaAs QW structure (iv) [49].

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electron level. In addition, some resonances have appeared in PR spectrum above the 22H transition. These transitions are related to a higher than the second electron level. However, only the 33H transition has been identified because on the basis of calculations only three confined states for heavy-holes have been obtained. The energy level structure of the valence QW does not change significantly due to almost flat valence band alignment for GaN0.011As0.989/GaAs system as it is seen in Figure 9.17(b). The essential changes in the hole-level structure appear after incorporating GaInNAs step-like barrier (see Figure 9.16). In this case new confined states appear for holes above the step-like GaInNAs barrier. Transitions related to these states are observed in PR spectrum of such a step-like QW structure. Figure 9.18(a)– (c) shows PR spectrum for GaInNAs/GaAs (QW1), GaInNAs/GaNAs/ GaAs (QW2), and GaInNAs/GaInNAs/GaAs (QW3) structures, respectively. In the case of QW1 structure the PR spectrum exhibits features typical for high nitrogen content GaInNAs/GaAs QWs, i.e. a weak PR signal and very broad PR resonances. It indicates that the quality of these structures is much worse than the previously discussed 1.3 mm QW structures. Similar features are observed for QW2 structure, but in this case the PR signal is already about one magnitude stronger due to the lower nitrogen content. The other

Figure 9.18. Room temperature PR spectra of QW structures tailored at 1.55 mm: (a) Ga0.62In0.38N0.053As0.947 (8.2 nm)/GaAs SQW; (b) Ga0.61In0.39N0.025As0.975 (8.5 nm)/GaN0.04As0.96 (3.7 nm)/GaAs QW structure; (c) Ga0.63In0.37N0.02As0.98 (8.2 nm)/Ga0.965In0.035N0.03As0.097 (8 nm)/GaAs QW structure [49].

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interesting feature is the lack of PR resonance in the 1.1 –1.35 eV range despite the fact that new electron levels have appeared after incorporating GaNAs step-like barrier. Transitions related to the new electron levels are not observed in them because as was mentioned earlier no new confined states for holes have appeared after the introduction of GaNAs step-like barrier. Due to the selection rules the transitions between the hole subbands with index n ¼ 1; 2 and the new electron subbands with index m ¼ 3; 4; 5; … will be weak. In the case of QW3 structure, the GaInNAs step-like barrier causes the QW profile changes, as it is seen in Figure 9.16, and new confined heavy-hole states with index n ¼ 3; 4; 5; … appear. Hence, in PR spectrum nmH transitions with index higher than 3 can be observed. Such ESTs are visible in the PR spectrum of QW3 structure (see Figure 9.18(c)). However, due to a small energy difference between the states confined above the step-like barrier the ESTs are not resolved and the PR signal looks similar to FKO. 9.3.4 Energy Level Structure of Sb Containing Ga(In)NAs/GaAs QWs The other approach in order to shift the laser emission of GaInNAs/GaAs system to 1.55 mm is to introduce Sb atoms to GaInNAs compound [74 –76]. It makes it possible to obtain low band gap energy at relatively low nitrogen content. In this case the role of nitrogen atoms in GaInNAsSb compounds is the assurance of the deep confinement potential for electrons because for GaInAsSb/GaAs system the conduction band alignment is between types I and II depending on the content. An example of PR and PL spectra for a Sb containing GaInNAs/GaAs system is presented in this section. Figure 9.19(a) shows PL and PR spectra of MBE grown sample with a GaInAs/GaAs SQW (reference QW) and a GaInNAsSb/GaNAsSb/GaAs QW structure. In the case of PL spectrum, it is seen that the integrated PL intensity is bigger for a Sb containing QW structure. If we neglect the non-radiative processes which are related to defects we should expect an increase in PL intensity for Sb containing QW structure due to an increase in the QW depth in comparison to the depth of reference QW. The increase in the broadening of PL emission for the Sb containing QW structure is mainly attributed to significant alloy fluctuations in GaInNAsSb compounds, because in general, it is expected that the five component compound possesses bigger inhomogeneities than a three component one. PR spectrum of this sample is in good accordance with the PL one. The ground state transitions are found at the same energy both in PR and PL spectra. The broadening of PR resonance is bigger for Sb containing structure. Above the 11H transition some ESTs are observed. However, a further analysis of the EST is rather difficult due to a weak knowledge of the material parameters for Sb containing Ga(In)NAs compounds and the conduction band offset for Ga(In)NAsSb/GaAs system. In addition, PR resonances related to the excited QW transitions are not defined precisely because alloy inhomogeneities cause a significant broadening of PR resonances. Figure 9.19(b) shows PL and PR spectra of MBE grown sample with a Sb containing Ga(In)NAsSb/GaAs QW structure which is very similar to the previous one, but this

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Figure 9.19. Room temperature PL and PR spectra of Sb containing Ga(In)NAsSb/GaAs QW structures. (a) Sample with a GaInAs/GaAs SQW (reference QW) and a Ga0.64In0.36N0.012As0.973Sb0.015 (7 nm)/ GaN0.02As0.88Sb0.1 (5 nm)/GaAs QW structure. (b) Sample with a Ga0.6In0.4N0.015As0.97Sb0.015 (8 nm)/ GaN0.024As0.856Sb0.12 (5 nm)/GaAs QW structure [49].

sample is without a reference GaInAs/GaAs SQW. Hence, the analysis of excited QW transitions does not interfere with PR resonances related to other QW as in the previous sample. In this case in PL spectrum besides the 11H emission an emission between higher energy levels is observed. The PR spectrum is similar to the PR spectrum of previous Sb containing QW structure. The 11H transition observed in PR agrees with that observed in PL. In addition, the PR signal related to excited QW transitions is well correlated with the PL emission observed in this spectral region. The emission band observed between 0.9 and 1.1 eV is not a tail of the emission peak related to the ground state, because the shape of this band is not a tail-like, i.e. exponential shape. This band is attributed to a recombination between excited states. Such a recombination is visible because an occupation of excited states by carriers takes place at room temperature. This band disappears with the decrease of temperature. Therefore, PR resonances between 0.85 and 1.2 eV are attributed to the excited QW transitions. The PR resonances associated with the excited transitions are not resolved due to the high value of the broadening parameter. These resonances are not resolved either at low temperatures because phonon-related broadening is smaller than the broadening due to alloy inhomogeneities.

Photo- and Electro-reflectance of III – V-N Compounds 9.3.5

307

Broadening of PR Resonances

The broadening of PR (or ER) resonance is due to the electron – phonon interaction, alloy inhomogeneities and QW width fluctuations. Hence, an analysis of this parameter seems to be very useful while investigating the deterioration of optical quality due to the incorporation of nitrogen atoms in GaInAs compound. Figure 9.20 shows the broadening parameter of the 11H transition for QWs analyzed in Section 9.3.2. It is seen that the broadening of PR resonance increases with the increase in nitrogen content for all subsets of QWs. The increase in the broadening parameter is mainly attributed to an increase in GaInNAs alloy inhomogeneities due to the introduction of nitrogen atoms [49]. The increase in inhomogeneities is due to the tendency of nitrogen atoms to clusterization (i.e. creation of nitrogen pairs or other clusters) [26] and formation of N-related defect states (nitrogen interstitials, Ga vacancy complexes) [77]. Moreover, the band structure of GaInNAs compounds strongly depends on nitrogen nearest-neighbor environment [35]. The mentioned phenomena lead to band gap fluctuations and to a tail of the DOS as in Figure 9.21. This scheme of band structure assumes unusual band gap fluctuations. Usually, alloy content fluctuations lead to band gap fluctuations where both conduction and valence bands possess local minima. Nitrogen content fluctuations in III –V-N compounds, like GaNAs, GaInNAs, and GaNAsSb, lead to a specific variation in the energy band gap. In this case, the variation in the band gap is mainly due to the changes of a conduction band, while the changes of a valence band can be neglected [51,78]. Such

Figure 9.20. The broadening G of PR resonance related to 11H transition for the subset “A”, “B”, “C”, and “D” [49].

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Figure 9.21. Band gap diagram of GaInNAs compound. Only the fluctuations in the conduction band have been assumed [49].

behavior is simple to explain within the BAC model which assumes that the resonant nitrogen level interacts only with the conduction band of host matrix (i.e. compound without nitrogen atoms). The magnitude of the interaction strongly depends on the nitrogen content and a small fluctuation in nitrogen content leads to an essential fluctuation in conduction band minima. Also, the change of GaInNAs band gap due to the change in the nitrogen nearest-neighbor environment leads to fluctuations in conduction band minima only. Moreover, a non-homogeneous distribution of the N-related defects, which are located close to a conduction band, also affects only the conduction band. On the basis of such a model it is easy to explain unusually broad PR resonance and high value of Stokes shift for QWs with smooth interfaces. Hence, within an assumed model, the increase in broadening parameter indicates an increase in the magnitude of conduction band fluctuations and/or an increase of DOS tails. It is equivalent to the redistribution of nitrogen atoms between different nitrogen nearest-neighbor environments and/or the increase in the number of N-related defects. In the case of MOVPE-grown QWs, the G parameter increases by the factor of 1.2, 2.4, and 3.0 for QWs with 0 (reference QW), 0.5, and 0.7% of nitrogen content, respectively. The bigger broadening obtained in the case of MOVPE structures may be related to lower quality of the structures grown by MOVPE compared to MBE ones. But in this case, the G increase has to have an additional origin, because these structures possess rather good optical properties and the factor of G increase is significantly bigger for N containing QWs than for N free QWs (1.2 versus 2.2 and 3.0). It indicates that an additional phenomenon is responsible for such a large value of the broadening. The additional phenomenon is associated with the presence of different nitrogen nearest-neighbor environments. These different environments of nitrogen atoms appear due to annealing (this phenomenon is discussed in detail in Section 9.4). Within the assumed band gap diagram (see in Figure 9.21) the co-existence of different nitrogen nearest-neighbor environments leads

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to bigger fluctuations in conduction band [51]. In the case of MBE-grown QWs different environments of N atoms are probably not present, because these structures were not annealed. The other environments of N atoms are expected mainly for annealed QWs.

9.4. THE INFLUENCE OF POST-GROWN ANNEALING ON GaInNAs STRUCTURES

The N-containing structures are usually annealed in order to reduce N-related defects. It significantly increases the PL efficiency but it simultaneously shifts band gap energy to blue [79 –81]. The origin of the blue shift is still controversial. In the case of GaInNAs compounds it is established that the increase in band gap energy after annealing is due to the change in nitrogen nearest-neighbor environment from Ga-rich to In-rich [35,36,58]. However, it is not excluded that other phenomena affect the band gap energy. Especially, that a blue shift of the band gap energy has been observed for post-grown annealed GaNAs compounds [78,82], i.e. compound without In atoms. Another phenomenon which could be responsible for the blue shift of band gap energy is a reduction of DOS tail by postgrown annealing [78]. It is rather established that post-grown annealing leads to a reduction of N-related defects. Hence, it should influence DOS tail and thereby the band gap energy. These issues are considered in this section. 9.4.1 Bulk Layers Figure 9.22(a) –(c) shows PL and PR spectra for as-grown and annealed GaN0.02As0.98, Ga0.95In0.05N0.2As0.98, and GaN0.02As0.9Sb0.08 layers, respectively. It is noted that the three layers possess different strains. The GaNAs ternary layer is tensely strained ð1 ¼ 27:9 £ 1023 Þ and its PL and PR spectra, shown in Figure 9.22(b), clearly exhibit two structures which are related to the heavy- and light-hole splitting. The GaInNAs layer is almost lattice matched to GaAs substrate ð1 ¼ 20:7 £ 1023 Þ; and thereby unstrained. In consequence, the top of the valence band, i.e. the light- and heavy-hole band, is not splitted, and a single structure is observed in the PR spectra. In the case of GaNAsSb compound, the layer is compressively strained ð1 ¼ 4:5 £ 1023 Þ: Such strain leads to an essential splitting of the valence bands. The line shape of PR spectrum confirms the splitting. In the case of PR measurements, which are not sensitive to defect related states, absorption between extended states is observed. At room temperature these resonances are associated with the band-to-band absorption. The negligible Stokes shift between emission and absorption (i.e. PL and PR transitions) indicates that the band-to-band recombination of free carriers is dominant in PL at room temperature. A piece of every sample has been annealed at the same conditions, i.e. at 7508C for 10 min. The structural properties of the samples were carefully analyzed, comparing

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Figure 9.22. Room temperature PL and PR spectra of as-grown and annealed GaN0.02As0.98 (a), Ga0.95In0.05N0.2As0.98 (b), and GaN0.02As0.9Sb0.08 layers (c). PR spectra are fitted by FDGL curves [49].

their characteristics before and after annealing. High resolution X-ray diffraction (HRXRD) did not reveal any changes in the average composition of these two samples. In addition, transmission electron microscopy (TEM) did not show any significant alloy fluctuations, suggesting that composition uniformity was not affected by annealing. It indicates that the compound content is the same before and after annealing. Moreover, it has to be noted that the transition energies are not sensitive to possible interdiffusion at the interfaces, since the layer is thick enough to cause negligible quantum confinement (bulk-like case). PL and PR spectra for annealed layers are presented in the bottom part of Figure 9.22. A blue shift of the band gap energy is observed for the three compounds. The blue shift equals 20, 27, and 54 meV for GaNAs, GaInNAs, and GaNAsSb layers, respectively. These shifts cannot be attributed to an atom outdiffusion, because it has been excluded by structural investigations. Hence, this phenomenon has been attributed to the effect of the change in nitrogen nearest-neighbor environment and the effect of the reduction of DOS tail [78]. Both the effects appear as a result of the annealing and their magnitude depends on the conditions of the annealing. The effect of the nitrogen nearest-neighbor environment is important only for GaInNAs compound while for GaNAs compound this effect is absent. Hence, the blue shift for this compound is smaller than for GaInNAs one. In the case of GaNAsSb layer the effect of nitrogen environment can also be important. However, no theoretical predictions have been done so far. The effect of the reduction of DOS tail due to

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annealing can be different for every sample because the DOS tail usually changes from sample to sample. Such a tail is the origin of the effect of band gap shrinkage. The postgrowth annealing reduces shrinkage effect due to the reduction of the DOS tail. It leads to a blue shift of the band gap energy. Within the band gap diagram shown in Figure 9.21 it is proposed that N-related defects create energy levels close to the conduction band and they are the origin of the DOS tail. A DOS tail of the valence band is neglected in these considerations because the theoretical predictions show that N-related defects form energy levels only near the conduction band [25]. The presence of a DOS tail for the three layers was strongly manifested in low-temperature PL spectra [78]. In general, an interplay between the two effects is expected for GaInNAs system. The interplay depends on both sample quality and annealing conditions. 9.4.2 Quantum Well Structures A blue shift of the QW emission due to annealing has been reported many times for GaInNAs/GaAs QWs. Klar et al. [35] have investigated in photoreflectance the MOVPE grown MQW annealed under different conditions. The authors have observed a fineenergy structure of QW transitions and they have attributed it to annealing induced change in the nitrogen nearest-neighbor environment. Kudrawiec et al. [58] have investigated MBE grown SQWs, which were also annealed under different conditions. In this case, the authors have shown that the blue shift of the 11H feature is attributed to both change in nitrogen nearest-neighbor environment and atom interdiffusion across QW interfaces. In this section we present the PR approach to investigate this phenomenon. Results reported in Ref. [58] have been selected to presentation in this section. Investigated samples are 7 nm thick Ga0.64In0.36N0.01As0.99/GaAs SQW structures grown by MBE on (001) GaAs substrates. These SQW structures were annealed under different temperature and duration conditions. Samples annealed at 6508C for 120 s, at 7008C for 90 s, and at 7508C for 60 s are presented in this section. In the case of high quality GaInNAs layer (i.e. the layer with the low nitrogen content) the influence of DOS tail can be neglected. The negligible presence of DOS tail in these SQWs is confirmed by small enhancement of PL intensity after annealing. Such behavior of PL intensity indicates that before annealing the number of defects is low. Therefore in this case, the DOS tail is neglected and only the effect of atom interdiffusion across QW interfaces and the effect of nitrogen nearest-neighbor environment are considered. Figure 9.23 shows PR spectra for the SQWs investigated in the vicinity of the heavyhole ground state transition (11H) recorded at 10 K together with curves approximating these spectra [58], and the modulus of particular PR resonances. For the non-annealed SQW a rather broad signal is observed. It could be suggested that such a broad contour is connected with multiple QW-related excitonic transitions. However, it fits with a single PR resonance reasonably well and no more transitions can be distinguished in this case. The broadening parameter obtained equals 19 meV and is approximately four times

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Figure 9.23. Low temperature PR spectra of as-grown and annealed Ga0.64In0.36N0.01As0.99/GaAs SQWs together with fitted curves [58].

greater than that obtained for the reference nitrogen free sample (see Figure 9.23). In the case of the annealed structures, a splitting of the fundamental transition is clearly visible, hence PR spectra have been fitted using two resonances. The transition at the lower energy (labeled M) has a broadening parameter comparable with the non-annealed SQW, while the second one (labeled S) has almost the same parameter as in the case of the reference structure (see Figure 9.12). Such a pair of transitions cannot be explained by a superposition of heavy- and light-hole related features. The fundamental light-hole transition was observed at a much higher energy (see Section 9.3.2). Such a splitting of the 11H transition has previously been observed for MOVPE grown GaInNAs/GaAs QW, and has been attributed to the various nitrogen nearest-neighbor environments in the GaInNAs alloy [35]. In accordance with the calculations of Klar et al. [35], the fundamental transition can be split into five. In the case of Ga0.64In0.36As0.99N0.01/GaAs QW the energy difference between the lowest energy (4Ga) and highest energy (4In) transition is about 50 meV and the difference between neighboring transitions is approximately equal (10 meV in this case). The range of 50 meV is illustrated in Figure 9.23 by a dashed line between the arrows. It may be assumed that the broadening parameter for each of these five possible transitions is comparable and is likely to be slightly larger than

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for the reference SQW (due to some extra disorder caused by the fourth component of the alloy). Wherever the energy difference between consecutive transitions is similar to the broadening parameter, the individual PR resonances are usually not distinguishable (as for non-annealed sample). However, if one transition is enhanced and has a significantly higher intensity (PR amplitude) than the others, then this resonance should be visible against the background of the other resonances. Such a case is observed in our annealed QWs. On the basis of its location this second resonance has been attributed to the 1Ga3In nitrogen configuration. This agrees very well with the calculations of Kim and Zunger using Monte Carlo simulations of a GaInNAs supercell [26]. They showed that the configuration of one gallium and three indium atoms around a nitrogen atom is the most favorable. During a process of fast growth of the quaternary layer the 4Ga configuration, with strongly strained Ga – N bonds, is most frequently obtained. The annealing procedure allows a (so-called short range order) redistribution of atoms in the crystal lattice and the system tends to one with minimal energy, namely most favorable atom configuration (1Ga3In in this case). The final distribution should depend on the parameters of the annealing process. Klar et al. [35] observed that as the annealing temperature increases the higher energy transitions (related to more indium atoms) start to dominate in the PR spectrum. The second resonance for all the annealed structures is associated with the 1Ga3In nitrogen configuration, but then its energy should be independent of the annealing conditions. Kudrawiec et al. [58] have observed that the “S” feature intensity (PR amplitude) increases with the rise in the annealing temperature (a higher annealing temperature favors the most probable configuration), whereas both the “M” and “S” PR transitions shift to higher energies when the annealing temperature increases. The latter shift can be attributed to the changes in the shape of the QW due to atom diffusion across the QW interface. The total annealing-induced blue shift of the ground state transition is caused by two effects: changes in the nearest-neighbor configuration of nitrogen atoms and changes in the QW profile. However, as shown in Figure 9.23, the value of the energy shift is not the same for “M” and “S” features (the “M” line shifts more rapidly as the annealing temperature increases). If we compare the values of this energy difference for each line between the samples annealed at 650 and 7508C, we obtain 13 and 31 meV for the “S” and “M” transitions, respectively. The first shift is caused entirely by changes in the QW profile (assuming that this is related to the 1Ga3In configuration), whereas the latter must be related to some additional effect. We have to remember that this “M” feature is multiresonance. Therefore, if the individual resonances are redistributed after annealing in such a way that the higher energy ones became more intensive, then this results in an apparent shift of the whole “M” feature. This explanation of the annealing-induced blue shift of the QW transition was also supported by the PL experiment [54]. In general, it is expected that the creation of In – N bonds instead of Ga –N ones can depend on many factors like the kind of growth process (MBE or MOCVD), growth parameters (e.g. growth temperature) and the conditions of post-growth treatment.

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Figure 9.24. Room temperature PR spectra of as-grown (a), annealed at 6508C (b), and 7508C (c) GaInNAs/GaAs MQWs. The MQWs were grown at 4708C [83].

The influence of growth temperature on the process of the changing of the nitrogen nearest-neighbor environment is investigated in Ref. [83]. The authors have investigated two sets of MQWs grown at different temperatures and annealed at the same conditions. Figure 9.24 shows PR spectra obtained for MQW grown at 4708C and annealed at different conditions. PR features related to the interband absorption in QW are indicated by arrows in Figure 9.24. On the basis of the calculations like in Ref. [49], the three QW-related resonances have been attributed to the transition between first heavy-hole and first electron subbands (11H), first light-hole and first electron subbands (11L), and first heavy-hole and second electron subbands (12H). The PR signals are different for different samples but vary systematically from one sample to another. For the as-grown sample, all three QW transitions possess complex character and they cannot be fitted by one Lorentzian or Gaussian PR resonance. Such PR line shape is composed of few resonances which are associated with the presence of different nitrogen nearest-neighbor environments in this sample (N – Ga42mInmð0 # m # 4Þ short-range-order clusters). The energy of PR resonance has been determined by KKA and is considered to be an “effective” energy of the QW transition. In the GaInNAs/GaAs QW system the hole level in valence QW is accurately defined, while the electron level in conduction QW strongly depends on

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Figure 9.25. The normalized Kramers– Kronig modulus of PR spectrum in the vicinity of 11H transition. Solid and dashed lines correspond to MQWs grown at 410 and 4708C, respectively. Curves (a), (b), and (c) correspond to as-grown, annealed at 650 and 7508C MQWs, respectively [83].

nitrogen nearest-neighbor environment. Such result has been obtained within tight binding calculations [35] and it is also intelligible in the framework of BAC model [14], based on the assumption that the nitrogen resonant level interacts only with the conduction band. For as-grown MQWs the dominant part of 11H resonance is associated with a N – Ga4 environment (4Ga for short). The remaining resonances, existing within the 11H transition, can be attributed to a trace of the second nitrogen environment, 1In3Ga, coexisting in the sample. Very similar behavior is observed for both 11L and 11H transitions. A comparison of the normalized modulus of PR spectrum for two sets of MQWs grown at different temperatures (410 and 4708C) and annealed under the same conditions is shown in Figure 9.25. The vertical dotted lines indicate expected band gap energies for different nitrogen nearest-neighbor environments taken after Ref. [35]. For as-grown samples the two spectra are almost the same (see curves (a) in Figure 9.25), while for annealed samples they are significantly different (see curves (b) and (c) in Figure 9.25). It is clearly seen that the “effective” blue shift is smaller for samples grown at 4708C than for samples grown at 4108C. It means that the magnitude of energy shift strongly depends on the initial structural configuration and number of point defects. In the case of as-grown

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MQWs the 4Ga is the dominant nitrogen environment and 3GaIn is the second environment which is present in the GaInNAs layer. The same distribution between magnitudes of 4Ga- and 3GaIn-related peaks indicates that for the two sets of MQWs the initial nitrogen environments are similar. The lower concentration of As vacancies in the GaInNAs layer grown at higher temperature is one of the possibilities which can explain the smaller blue shift. However, the real reason is rather more complicated and is difficult to settle. Besides As vacancies other point defects, like, e.g. Ga vacancies (promoted by limited diffusion of cations onto the growing surface at low temperatures), could influence the process of N bonds reconfiguration. In conclusion, the correlation between growth temperature and the magnitude of blue shift indicates that In –N bond formation is a point-defect-assisted phenomenon.

9.5. PHOTOREFLECTANCE INVESTIGATION OF THE EXCITON BINDING ENERGY

It is expected that even low concentrations of N atoms should influence the free exciton binding energy, mainly due to the increase in the electron effective mass. So far, a few reports have been devoted to this issue [59,68]. The main problem encountered during exciton binding investigations is the quality of nitrogen diluted III –V compounds. These compounds generally contain non-radiative defect states. Consequently, free exciton recombination might be absent or very weak, despite the fact that features related to free exciton absorption are observed in reflectance spectra [78]. Hence, in most cases, temperature dependent PL is not suited to the determination of free exciton binding energy, especially in bulk-like layers. In the case of N containing quantum wells, magnetophotoluminescence has been successfully applied to determine the exciton binding energy [68,84]. However, due to the large value of binding energy in such QW structures [85] and the large broadening of the PL line (, 10 – 20 meV), a high magnetic field is required (32 T in Ref. [84]). Photoreflectance is an alternative approach to investigate the free exciton binding energy of dilute III– V nitrides. In this approach a detailed analysis of the PR line shape has led to an accurate determination of the nature and the energy location of DOS CPs. It has allowed us to separate the exciton and band-toband components observed in PR spectra. Such an analysis of PR data has been often applied to different semiconductor compounds [86 – 88]. In the case of III – V-N compounds the exciton binding energy was investigated in a GaNAs layer by Kudrawiec et al. [89] and in a GaInNAs/GaAs QW by Geddo et al. [59] Figure 9.26 shows the PR spectrum of the GaN0.02As0.98 layer measured at 60 K, together with different calculated spectra. In a first attempt, spectra were calculated using two band-to-band transitions (short dashed line; m ¼ 2:5) or two excitonic transitions (dashed line; m ¼ 2). As seen in Figure 9.26, these calculations do not satisfactorily

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Figure 9.26. PR spectrum of a GaN0.02As0.98 layer recorded at 60 K (open points) together with different fitting curves. The short dashed and dashed lines represent the fitting of PR data using two band-to-band ðm ¼ 2:5Þ and two excitonic ðm ¼ 2Þ resonances, respectively. The solid line represents the fit using four resonances, two excitonic and two band-to-band. The contribution of the individual PR resonances (i.e. their moduli) to the total approximating curve is presented at the bottom part of this figure [89].

reproduce the experimental data. To improve the agreement with experiment, both exciton and band-to-band contributions were considered. Therefore, the next calculated spectrum included the contributions of four PR resonances, two related to excitonic absorption and two related to band-to-band absorption. In this case, the fit reproduces experimental data very well (see the solid line in Figure 9.26). Moreover, the decomposition of the fitting curve between individual PR resonances gives acceptable PR lines. The moduli of the individual PR resonances are shown at the bottom of Figure 9.26. The broadening parameters for each PR resonance are comparable and equals 9.7, 9.8, 8.1, and 9.5 meV for

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LH exciton, LH band-to-band, HH exciton, and HH band-to-band transitions, respectively. Such a large excitonic broadening is expected for the GaNAs compound, due to the huge bowing in this material. Some theoretical predictions for the level of excitonic broadening were made by Senger and Bajaj [90], and our experimental results are in close agreement with these predictions. The splitting of the excitonic and band-to-band contributions is a direct measurement of the exciton binding energy, and can be extracted from our fitting procedure with four PR resonances. This was done in the 40 – 100 K temperature range. This temperature range is appropriate, because the excitonic resonance and band-to-band contributions are comparable. On the other hand, as the temperature increases, the contribution of excitonic resonance decreases. As a consequence, above 120 K, the fit with four resonances is no longer valid, but a satisfactory fit is obtained with two band-to-band transitions. For this reason, the exciton binding energy was determined only below 100 K. The results are presented in Figure 9.27 for LH and HH related excitons. It has been found that the LH and HH exciton binding energies are 4.5 ^ 0.5 and 6.5 ^ 0.5 meV, respectively. The HH exciton binding energy is much larger than the binding energy in GaAs. This phenomenon is mainly attributed to the N induced increase in the electron effective mass, which was estimated as being , 60% higher in comparison to the me in a GaAs host matrix. Geddo et al. [59] have analyzed the line shape of PR feature related to the fundamental transition for GaInNAs/GaAs SQW in detail. The authors obtained a PR feature that should be fitted by two resonances at 90 K (see Figure 9.28); one related to an excitonic absorption and second to a band-to-band absorption. In this way, Geddo et al. determined the 1HH exciton binding energy in GaInNAs/GaAs SQW as being 8.5 meV. It indicates that the incorporation of 1.1% of N atoms into GaInAs/GaAs SQW leads to , 30%

Figure 9.27. The binding energy of LH and HH free exciton determined at different temperatures [89].

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Figure 9.28. Photoreflectance spectrum at 90 K of the N containing sample. Decomposition into exciton (continuous line) and band-to-band (dashed line) contribution to the 1HH feature is reported. Thick line indicates the best fit to the experiment (open circles) [59].

increase in the binding energy [59]. In this case, the increase in the exciton binding energy is also associated with the N induced increase in the electron effective mass. 9.6. MANIFESTATION OF THE CARRIER LOCALIZATION EFFECT IN PHOTOREFLECTANCE SPECTROSCOPY

The carrier localization effect has been observed many times in PL spectroscopy. This effect has also been confirmed by PR spectroscopy [90,91]. In the case of PR the carrier localization effect which is present at low temperatures leads to a decrease of PR signal due to a weakness of the band bending photomodulation. Figure 9.29(a) and (b) shows the temperature dependence of PR spectrum for GaNAs and GaInNAs samples which are analyzed in Section 9.4.1. Figure 9.30 shows temperature dependence of transition intensity obtained by using KKA of PR spectra. A decrease of transition intensity with the decrease of temperature is observed for the GaNAs and GaInNAs layers. Such an unusual behavior of the PR signal is not observed for highquality semiconductor compounds, like, e.g. GaAs or InP. In the case of GaNAs and GaInNAs compounds PR signal at low temperatures decreases, because carriers induced by pump beam are immediately localized on some potential fluctuations and cannot move. Such phenomenon weakens the modulation of built-in electric field. With an increase in temperature the thermal energy increases and the localization energy can be exceeded, which is reflected in the possibility for carriers to move. Such behavior induces an increase in the modulation efficiency, because moving carriers allow a change in the built-in electric field.

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Figure 9.29. Temperature dependency of PR spectrum for Ga0.95In0.05N0.02As0.98 (a) and GaN0.02As0.98 (b) layers. The insets show PL spectra [91].

A decrease in photomodulation efficiency at low temperatures due to the carrier localization effect has also been observed for GaInNAs/GaAs QW structures [92]. It has been found that with the increase in nitrogen content the effect of carrier localization is enhanced and PR signal at low temperature decreases drastically. An example of this effect is shown in Figure 9.31. This figure shows the ratio of transition intensity at 300 and 10 K

Figure 9.30. Integrated modulus of PR obtained from Kramers–Kronig analysis versus temperature. In the case of GaN0.02As0.98 layers the presented intensities are the sum of LH and HH transition intensities [91].

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Figure 9.31. Ratio of room (300 K) and low temperature (10 K) PR amplitudes versus the nitrogen content for the series of Ga0.59In0.41NxAs12x/GaAs SQWs [92].

for the subset “C” of SQWs. It is clearly visible that with the increase in nitrogen content the ratio rises due to the decrease of PR intensity at 10 K. The carrier localization effect is usually observed for nitrogen diluted GaAs and GaInAs layers and QWs. Hence, the low-temperature PR measurements could be limited, especially for structures with high nitrogen content, because with the increase in nitrogen mole fraction the carrier localization effect is stronger and makes difficult the band bending photomodulation.

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[40] Sek, G., Ryczko, K., Misiewicz, J., Fischer, M., Reinhardt, M. & Forchel, A. (2000) Thin Solid Films, 380, 240. [41] Grenouillet, L., Bru-Chevallier, C., Guillot, G., Gilet, P., Duvaut, P., Vannuffel, C., Million, A. & Chenevas-Paule, A. (2000) Appl. Phys. Lett., 76, 2241. [42] Shirakata, S., Kondow, M. & Kitatani, T. (2001) Appl. Phys. Lett., 79, 54. [43] Choulis, S.A., Weinstein, B.A., Hosea, T.J.C., Kamal-Saadi, M., O’Reilly, E.P., Adams, A.R. & Stolz, W. (2001) Phys. Status Solidi (b), 223, 151. [44] Polimeni, A., Capizzi, M., Geddo, M., Fisher, M., Reinhard, M. & Forchel, A. (2001) Phys. Rev. B, 63, 195320. [45] Heroux, J.B., Yand, X. & Wang, W.I. (2002) J. Appl. Phys., 92, 4361. [46] Heroux, J.B., Yand, X. & Wang, W.I. (2002) J. Vac. Sci. Technol. B, 20 (3), 1154. [47] Sitarek, P., Ryczko, K., Sek, G., Misiewicz, J., Fisher, M., Reinhardt, M. & Forchel, A. (2003) Solid-State Electron., 47, 489. [48] Choulis, S.A., Hosea, T.J.C., Tomic, S., Kamal-Saadi, M., Adams, A.R., O’Reilly, E.P., Weinstein, B.A. & Klar, P.J. (2002) Phys. Rev. B, 66, 165321. [49] Misiewicz, J., Kudrawiec, R., Ryczko, K., Se˛k, G., Forchel, A., Harmand, J.C. & Hammar, M. (2004) J. Phys. Condens. Matter, 16, 3071. [50] Geddo, M., Pezzuto, R., Capizzi, M., Polimeni, A., Gollub, D., Fisher, M. & Forchel, A. (2002) Eur. Phys. J. B, 30, 39. [51] Kudrawiec, R., Sek, G., Ryczko, K., Misiewicz, J., Sundgren, P., Asplund, C. & Hammar, M. (2003) Solid State Commun., 127, 613. [52] Misiewicz, J., Sitarek, P., Ryczko, K., Kudrawiec, R., Fische, M., Reinhardt, M. & Forchel, A. (2003) Microelectron. J., 34, 737. [53] Misiewicz, J., Sek, G., Kudrawiec, R., Ryczko, K., Gollub, D., Reithmaier, J.P. & Forchel, A. (2003) Microelectron. J., 34, 351. [54] Hetterich, M., Grau, A., Egorov, A.Yu. & Reichert, H. (2003) J. Appl. Phys., 94, 1810. [55] Choulis, S.A., Tomic, S., O’Reilly, E.P. & Hosea, T.J.C. (2003) Solid State Commun., 125, 155. [56] Shirakata, S., Kondow, M. & Kitatani, T. (2003) J. Phys. Chem. Solids, 64, 1533. [57] Derluyn, J., Moerman, I., Leys, M.R., Patriarche, G., Sek, G., Kudrawiec, R., RudnoRudzinski, W., Ryczko, K. & Misiewicz, J. (2003) J. Appl. Phys., 94, 2752. [58] Kudrawiec, R., Sek, G., Misiewicz, J., Gollub, D. & Forchel, A. (2003) Appl. Phys. Lett., 83, 2772. [59] Geddo, M., Guizzetti, G., Capizzi, M., Polimeni, A., Gollub, D. & Forchel, A. (2003) Appl. Phys. Lett., 83, 470. [60] Bastard, G. (1992) Wave Mechanics Applied to Semiconductor Heterostructures, Les Editions de Physique, Paris. [61] Pikus, G.E. & Bir, G.L. (1959) Sov. Phys. Solid State, 1, 136; 1, 1502. [62] Vurgaftman, I. & Meyer, J.R. (2003) J. Appl. Phys., 94, 3675 and there in. [63] Kudrawiec, R., Sek, G., Sitarek, P., Ryczko, K., Misiewicz, J., Wang, T. & Forchel, A. (2004) Thin Solid Films, 450, 71. [64] Shen, H. & Dutta, M. (1995) J. Appl. Phys., 78, 2151. [65] Hetterich, M., Dawison, M.D., Egorov, A.Yu., Bernklau, D. & Riechert, H. (2000) Appl. Phys. Lett., 76, 1030. [66] Skierbiszewski, C., Perlin, P., Wisniewski, P., Knap, W., Suski, T., Walukiewicz, W., Shan, W., Yu, K.M., Ager, J.W., Haller, E.E., Geisz, J.F. & Olson, J.M. (2000) Appl. Phys. Lett., 76, 2409. [67] Pan, Z., Li, L.H., Lin, Y.W., Sun, B.Q., Jiang, D.S. & Ge, W.K. (2001) Appl. Phys. Lett., 78, 2217. [68] Baldassarri Ho¨ger von Ho¨gersthal, G., Polimeni, P., Masia, M., Bissiri, M., Capizi, M., Gollub, D., Fischer, M. & Forchel, M. (2003) Phys. Rev. B, 67, 233304.

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[69] Joyce, M.J., Johnson, M.J., Gal, M. & Usher, B.F. (1988) Phys. Rev. B, 38, 10978. [70] Bian, L.F., Jiang, D.S., Lu, S.L., Huang, J.S., Chang, K., Li, L.H. & Harmand, J.C. (2003) J. Cryst. Growth, 250, 339. [71] Fischer, M., Gollub, D., Reinhardt, M., Kamp, M. & Forchel, A. (2003) J. Cryst. Growth, 251, 353. [72] Li, L.H., Patriarche, G., Lemaitre, A., Lemaitre, L., Largeau, L., Travers, L. & Harmand, J.C. (2003) J. Cryst. Growth, 251, 403. [73] Pavelescu, E.-M., Peng, C.S., Jouhti, T., Konttinen, J., Li, W., Pessa, M., Dumitrescu, M. & Spanulescu, S. (2002) Appl. Phys. Lett., 80, 3054. [74] Ungaro, G., Le Roux, G., Teisser, R. & Harmand, J.C. (1999) Electron. Lett., 35, 1246. [75] Li, L.H., Sallet, V., Patriarche, G., Largeau, L., Bouchoule, S., Travers, L. & Harmand, J.C. (2003) Appl. Phys. Lett., 83, 1298. [76] Bank, S., Ha, W., Gambin, V., Wistey, M., Yuen, H., Goddard, L., Kim, S. & Harris, J.S., Jr. (2003) J. Cryst. Growth, 251, 367. [77] Li, W., Pessa, M., Ahlgren, T. & Decker, J. (2001) Appl. Phys. Lett., 79, 1094. [78] Kudrawiec, R., Sek, G., Misiewicz, J., Li, L.H. & Harmand, J.C. (2004) Eur. Phys. J. B, in press. [79] Pan, Z., Miyamoto, T., Sato, S., Koyama, F. & Iga, K. (1999) Jpn. J. Appl. Phys., 38, 1012 Part 1. [80] Shirakata, S., Kondow, M. & Kitatani, T. (2002) Appl. Phys. Lett., 80, 2087. [81] Albrecht, M., Grillo, V., Remmele, T., Strunk, P., Egorov, A.Yu., Dumitras, Gh., Riechert, H., Kaschner, A., Heitz, R. & Hoffmann, A. (2002) Appl. Phys. Lett., 81, 2719. [82] Grenouillet, L., Bru-Chevallier, C., Guillot, G., Gilet, P., Ballet, P., Duvaut, P., Rolland, G. & Million, A. (2002) J. Appl. Phys., 91, 5902. [83] Kudrawiec, R., Pavelescu, E.-M., Andrzejewski, J., Misiewicz, J., Gheorghiu, A., Jouhti, T. & Pessa, M., J. Appl. Phys. 96, 2909. [84] Senger, R.T., Bajaj, K.K., Jones, E.D., Modine, N.A., Waldrip, K.E., Jalali, F., Klem, J.F., Peake, G.M., Wei, X. & Tozer, S.W. (2003) Appl. Phys. Lett., 83, 5425. [85] Ryczko, K., Sek, G. & Misiewicz, J. (2002) Solid State Commun., 112, 323. [86] Hildebrandt, S., Murtagh, M., Kuzmienko, R., Kircher, W. & Schreiber, J. (1995) Phys. Status Solidi (a), 152, 147. [87] Mishima, T., Misura, M., Ozaki, S. & Adachi, S. (2002) J. Appl. Phys., 91, 4904. [88] Ozaki, S., Mishima, T. & Adachi, S. (2003) Jpn. J. Appl. Phys., 42, 5465. [89] Kudrawiec, R., Misiewicz, J., Li, L.H. & Harmand, J.C., 27th International Conference on Semiconductor Physics, Flagstaff, USA. [90] Senger, R.T. & Bajaj, K.K. (2003) J. Appl. Phys., 94, 7505. [91] Kudrawiec, R., Misiewicz, J., Li, L.H. & Harmand, J.C. (2003) Appl. Phys. Lett., 83, 1379. [92] Kudrawiec, R., Misiewicz, J., Fischer, M. & Forchel, A. (2004) Phys. Status Solidi (a), 201, 364.

Dilute Nitride Semiconductors M. Henini (Ed.) q 2005 Elsevier Ltd. All rights reserved.

Chapter 10

Band Anticrossing and Related Electronic Structure in III-N-V Alloys W. Walukiewicz, W. Shan, J. Wu, K.M. Yu and J.W. Ager III Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

10.1. INTRODUCTION

The novel material properties of III-N-V alloys were first discovered in the early 1990s. In the quest to close the gap between the nitrides and arsenides thus to achieve the goal of fabricating light emitting devices covering the entire visible spectral region, Weyers and coworkers succeeded in growing GaNxAs12x alloys using plasma-assisted metalorganic chemical vapor deposition (MOCVD) [1]. Surprisingly, they found that these alloys exhibit a considerable red shift in photoluminescence (PL) and absorption edge rather than the expected blue shift. Furthermore, the application of simple interpolation between the properties of the end point materials using first- or second-order polynomials within the virtual crystal approximation (VCA), in which the random alloy potential is approximated by a periodic lattice of average atomic potential [2 – 4] and has the trend of increasing band gap energy with decreasing lattice constant, led to unrealistically large and compositiondependent bowing parameters [5 –9]. The discovery of the large band gap bowing in GaNAs has led to a very active fundamental and applied research on a number of group III-N-V alloys. However, only very recently has the significance of this research for the basic understanding of the electronic structure of these alloys been fully appreciated. Developing an understanding of the unusual properties of these alloys has become a challenge for the existing theoretical electronic band structure calculation methods. From the beginning, it was obvious that the VCA could not be used to understand the large perturbations of the crystal lattice associated with the replacement of a column-V atom with a small, highly electronegative N atom. The effects of N incorporation at a very low, impurity-like, concentration on the properties of III– V compound semiconductors have been studied for almost four decades [10]. Even at these low concentrations nitrogen has a pronounced effect on the material properties. For example, efficient electroluminescence is observed in GaP, an indirect gap semiconductor, when it is doped with nitrogen. The emission was attributed to the formation of highly localized, acceptor-like states [11]. The origin of these states has been 325

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Dilute Nitride Semiconductors

elucidated from the calculations based on the tight binding approximation [12]. These showed that the incorporation of any isovalent impurity into a semiconductor material produces localized, acceptor-like state. The energy location of the state is determined by the nature and the strength of the local potential introduced by the isovalent impurity. Theoretical calculations clearly show that the energy levels of elements with high electronegativity are located at energies lower than those of more metallic impurities. Thus replacement of As with P produces an energy level high in the conduction band of GaAs whereas substitution of As with highly electronegative N results in a level located close to the conduction band minimum. The difference in the location of the energy levels of the isovalent impurities is the key to understanding the different types of semiconductor alloys. In the case of “wellmatched alloys” with a small electronegativity difference between constituent elements, the energy levels of the isovalent impurities are not observable as they are located deep in the conduction band [12]. Increasing the impurity content towards alloy-like concentrations leads to a relatively weak interaction between the impurity and the extended band states. This results in an incremental modification of the semiconductor band structure, which occurs mostly in the energy range away from the conduction band minimum. On the other hand, in the cases where the electronegativity difference between constituent elements is fairly large, incorporation of highly electronegative impurities gives rise to localized energy levels close to the conduction band edge. At impurity-like concentrations such levels preserve their separate identity and can be observed as discrete levels. However, at higher, alloy-like concentrations, the strong hybridization between the localized and extended states drastically modifies the electronic structure close to the conduction band minimum resulting in large changes of the optical and electrical properties of such highly mismatchedalloys (HMAs). Initial band structure calculations predicted large, N-induced band gap reductions in such alloys, although they were not accurate enough to be directly compared with experiments [13,14]. It is now generally accepted that the unexpectedly strong effect of N on the band gap is related to the fact that replacement of atoms such as As with the much smaller and more electronegative N atom leads to a large, local perturbation of the crystal lattice potential. Extensive experimental and theoretical studies over the past decade have led to several proposals aimed at understanding of the origin of the large band gap reduction [15]. In this chapter, we show that the effect of nitrogen on the electronic band structure of dilute nitrides can be consistently described in terms of an anticrossing interaction between localized nitrogen states and the extended conduction band states of the semiconductor matrix. The interaction leads to a significant modification of the band structure of the dilute III-N-V alloys. All the experimentally observed dramatic changes of the electrical and optical properties that have been observed experimentally can be fully explained by this interaction.

Band Anticrossing and Related Electronic Structure in III-N-V Alloys

327

10.2. BAND ANTICROSSING MODEL

It is well known that an isolated N atom introduces a localized state with energy level EN in conventional III – V materials. In most cases, this level is located very close to the conduction band edge. For example, it lies at about 0.25 eV above the conduction band edge in GaAs and less than 0.1 eV below the conduction band edge in GaP. The existence of such states has been predicted by theoretical calculations within the tight binding approximation framework [11], and confirmed by experimental measurements under hydrostatic pressure [16,17]. As expected for a localized state, a much weaker pressure dependence of the N energy level was observed in GaAs compared to the conduction band edge. The level was also found to move into the band gap when GaAs is alloyed with AlAs [18]. The highly localized nature of the N states suggests that there is only a weak hybridization between the orbits of N atoms and the extended states of the semiconductor matrix. The electronic band structure of the host crystal is not significantly affected at these low nitrogen concentrations. However, alloying a few atomic percentage of nitrogen with III – V compounds drastically modifies the electronic band structure. The electronic structure of GaNxAs12x can be described by considering the interaction between the localized states and extended states within the many-impurity Anderson model [19]. The total Hamiltonian of the system is the sum of three terms [20,21]: H¼

X

Ekc cþ k ck þ

X j

k

1 X ik·j Ejd djþ dj þ pffiffiffi ðe Vkj cþ k dj þ h:c:Þ: N j;k

ð10:2:1Þ

The first term is the Hamiltonian of the electrons in the band states with energy dispersion Ekc : The second term corresponds to the electron localized on the jth impurity site with energy Ejd : The third term describes the change in the single electron energy due to the dynamical mixing between the band states and the localized states. Following Anderson’s scheme, the hybridization strength is characterized by the parameter Vkj defined by [19] Vkj ¼

X

eik·ðl2jÞ

ð

ap ðr 2 lÞHHF ðrÞwd ðr 2 jÞdr;

ð10:2:2Þ

l

where aðr 2 jÞ and wd ðr 2 jÞ are the Wannier function belonging to the band and the localized wave function of the impurity on the jth site, respectively. HHF ðrÞ is the single electron energy described in the Hartree –Fock approximation [19]. The Fourier transform of the retarded Green’s function, Gkk0 ðEÞ ¼ Rck lcþ k0 S; satisfies the following equation of motion [22] þ þ ERck lcþ k0 S ¼ k½ck ; ck0 þ l þ R½ck ; Hlck0 S:

ð10:2:3Þ

In Eq. (10.2.3), k· · ·l represents the thermodynamical ensemble average. As follows from the commutation relations between the operators, an integral equation for Gkk0 has

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the form Gkk0 ¼ dkk0 Gð0Þ kk þ

1 ð0Þ X ~ iðk2k00 Þj G Gk00 k0 Ve N kk k00 j

ð10:2:4Þ

c þ 21 0 where Gð0Þ is the unperturbed Green’s function, and the kk0 ¼ dkk ðE 2 Ek þ i0 Þ renormalized interaction parameter is given by V~ ¼ Vkj ·Vk0 j =ðE 2 Ejd Þ < V 2 =ðE 2 Ejd Þ; ð10:2:5Þ

where V is the average value of Vkj ; assuming weak dependencies on k and j: For the single impurity case, Green’s function in Eq. (10.2.4) can be solved analytically and the exact solution has been obtained [19]. The hybridization term produces a profound effect on the electronic structure of the system. Considering finite but dilute concentrations of impurities, 0 , x p 1; the single-site coherent potential approximation (CPA) is adequate for the many-impurity system [23,24]. In the CPA treatment, a configurational averaging is performed neglecting correlations between positions of the impurities. Consequently the space translational invariance of the average Green’s function is partially restored, and k resumes its well-defined properties as a good quantum number. In momentum space, the diagonal Green’s function in CPA can be written as [20,23,24]: " #21 V 2x c Gkk ðEÞ ¼ E 2 Ek 2 : ð10:2:6Þ E 2 Ed 2 ipbV 2 r0 ðEd Þ The new dispersion relations are determined by the poles of Gkk ðEÞ: The solutions are given by an equivalent two-state-like eigenvalue problem pffiffi   c   Ek 2 EðkÞ V x   ð10:2:7Þ  ¼ 0;  p ffi ffi d  V x E þ iGd 2 EðkÞ  where Gd ¼ pbV 2 r0 ðEd Þ is the broadening of Ed in the single-impurity Anderson Model. V is the value of Vkj averaged over k and j; and r0 is the unperturbed density of states (DOS) of Ekc : In this approximation, the effective contribution of r0 is represented by its value evaluated at Ed and multiplied by a prefactor b that is to be determined by experiments. If Gd ¼ 0; Eq. (10.2.7) is reduced to the BAC model with two restructured dispersions for the upper and lower conduction subbands [25],  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 E^ ðkÞ ¼ ð10:2:8Þ ðEkc þ Ed Þ ^ ðEkc 2 Ed Þ2 þ 4V 2 x : 2 pffiffi If the broadening Gd is non-zero but small, so that 2V x q pbV 2 r0 ðEd Þ and lEkc 2 Ed l q pbV 2 r0 ðEd Þ; an approximate analytical solution for Eq. (10.2.7) can be obtained E~ ^ ðkÞ < E^ ðkÞ þ iGd

½E^ ðkÞ 2 Ekc  ; E^ ðkÞ þ iG^ ðkÞ: ½E^ ðkÞ 2 Ekc  þ ½E^ ðkÞ 2 Ed 

ð10:2:9Þ

Band Anticrossing and Related Electronic Structure in III-N-V Alloys

329

The real part, E^ ðkÞ; is defined in Eq. (10.2.8) by the BAC model. The imaginary part of the dispersion relations defines the hybridization-induced uncertainty of the energy. Note that the imaginary part in Eq. (10.2.9) is proportional to the admixture of the localized states ðldlÞ to the restructured wave functions ðlE^ ðkÞlÞ in the two-state-like-perturbation picture described by Eq. (10.2.7) [26]

G^ ðkÞ ¼ lkdlE^ ðkÞll2 ·Gd :

ð10:2:10Þ

Figure 10.1 shows the dispersion relations given by Eq. (10.2.8) for GaN0.005As0.995 near the Brillouin zone center. The broadening of the dispersion relations is given by the imaginary part of Eq. (10.2.9). The hybridization parameter V ¼ 2:7 eV used in the calculations was obtained from the fitting of Eq. (10.2.8) to the experimentally determined pressure dependence of the band gap of GaNxAs12x [25,27]. Figure 10.2 shows that this single fitting parameter provides a very good agreement with the experimental data reported by a number of research groups [28 – 31]. The hybridization induced modifications of the electronic structure have large effects on the properties of HMAs. For example, the broadening parameter that defines a finite lifetime for the lowest conduction band lE2 ðkÞl through the uncertainty principle imposes a limit to the mobility of free electrons that conduct current in the lowest conduction band:

m¼

et ðkF Þ e~ < p : p m2 ðkF Þ m2 ðkF Þ·G2 ðkF Þ

ð10:2:11Þ

Figure 10.1. Conduction band restructuring for GaN0.005As0.995. The broadening of the dispersion curves of the newly formed subbands illustrates the energy uncertainties as defined in Eq. (10.2.8). All the energies are referenced to the top of the valence band of GaAs.

330

Dilute Nitride Semiconductors

Figure 10.2. Comparison between the experimentally observed and calculated band gap reduction of GaNxAs12x as a function of N concentration. The calculations are based on the BAC model with V ¼ 2:7 eV, EC ¼ EM ¼ 1:42 eV, and Ed ¼ EN ¼ 1:65 eV.

The mobility is affected by the level broadening as well as by the BAC-induced enhancement of the DOS electron effective mass that can be calculated from the dispersion E2 ðkÞ in Eq. (10.2.8) [32,33] " #    k V 2x p 2  p  ; ð10:2:12Þ ¼ m0 1 þ d m2 ðkF Þ ¼ ~  dE2 ðkÞ=dk k¼kF ðE 2 E2 ðkF ÞÞ2 where mp0 is the electron effective mass of the unperturbed dispersion Ekc : The Fermi wave vector kF and Fermi energy EF ¼ E2 ðkF Þ are determined by the free electron concentration ðnÞ calculated from the restructured DOS [34] ð rðEÞdE nðEF Þ ¼ : ð10:2:13Þ 1 þ exp½ðE 2 EF Þ=kB T The restructured DOS is given by the imaginary part of Green’s function as shown in the following expression: X 1 1 ð rðEÞ ¼ Im Gkk ðEÞ ¼ r0 ðEkc ÞIm½Gkk ðEÞdEkc : ð10:2:14Þ p p k The integration converges rapidly with Ekc in a small range that is proportional to x: The calculated perturbed DOS for GaNxAs12x with several small values of x is shown in Figure 10.3. Note that the anticrossing interaction leads to a dramatic redistribution

Band Anticrossing and Related Electronic Structure in III-N-V Alloys

331

Figure 10.3. Density of states of GaNxAs12x for a range of values of x as compared with the unperturbed DOS. The two black dots on each curve indicate the energy positions of the E2 and Eþ subband edges. The vertical dashed line indicates the original position of the nitrogen localized level.

of the electronic states in the conduction band. The most striking feature of the DOS curves is the clearly seen gap between Eþ and E2 that evolves with increasing N content. In Green’s function calculation, the k dependence of Vkj is assumed to be weak on the momentum scale we are interested in. In Eq. (10.2.5), the parameter Vkj is averaged over the impurity sites and in k space. In the simplest case, all the impurity atoms are of the same type, so that the j dependence of Vkj is removed. The k dependence of Vkj can be estimated from Eq. (10.2.2). Assuming that the Hartree –Fock energy varies slowly in space and can be replaced by a constant 1HF ; one obtains X ik·l ð p Vk ¼ 1HF e ð10:2:15Þ a ðr 2 lÞwd ðrÞdr: l

Due to the localized character of both aðrÞ and wd ðrÞ; the overlap integral in Eq. (10.2.15) is essentially zero when they are located on two sites far apart from each other. In an attempt to model the k-dependence of Vk ; the integral in Eq. (10.2.15) is replaced by an exponentially decaying function , expð2l=ld Þ; and one obtains Vk ¼ 1HF

X l

eik·l2l=ld ¼

V0 : ð1 þ l2d k2 Þ2

ð10:2:16Þ

There is experimental evidence indicating that the values of Vk at the L point in GaNxAs12x [35] and at the X point in GaNxP12x [36] are about 3– 4 times smaller than

332

Dilute Nitride Semiconductors

the Vk at the G point. This ratio corresponds to a localized wave function decay length ðld Þ of the order of the lattice constant. This result indicates that the off-zone-center conduction band minima are affected by the anticrossing interaction only when their energies are close to the localized level. This is consistent with recent measurements of the optical properties of InyGa12yNxAs12x alloys, which have shown that alloying with N has only very small effects on the high energy transitions at large k vectors [33]. The dispersion relations given by Eq. (10.2.8) were obtained considering only the interaction between N states and the extended states close to the G minimum. A more general result has been obtained by Lindsay et al. [37,38] using the k·p approximation. It has been argued that the conventional k·p model must be modified to include two extra spin-degenerate nitrogen states so that 10 bands are needed to describe the electronic band structure of GaNAs/GaAs and related heterostructures. In addition, detailed studies on the nearest-neighbor environment of the substitutional N atoms in GaInNAs have shown that the fundamental band gap energy in quaternary dilute nitride alloys is fairly sensitive to the local environmental conditions especially in the case of quantum well structures [39,40]. The approach is applicable to a larger range of electron energies and has been successfully used to model optical gain in GaInNAs based lasers [41]. 10.3. EXPERIMENTAL EVIDENCE OF BAND SPLITTING AND ANTICROSSING CHARACTERISTICS

10.3.1 Synthesis of III-N-V Using Ion Implantation and Pulsed Laser Annealing A large variety of III-N-V alloys including GaNAs, GaInNAs, AlGaNAs, GaNP, and InNP have been extensively studied. So far the majority of those samples were grown by either metalorganic vapor phase epitaxy (MOVPE) with dimethylhydrazine as nitrogen source or gas-source molecular beam epitaxy (MBE) using a RF plasma nitrogen radical beam source. During the course of studying the fundamental properties of III-N-V alloys, we have also developed a new method for synthesizing III-N-V alloys. Nitrogen implantation followed by rapid thermal annealing (RTA) was initially found to be a practical and convenient method for the formation of diluted III-N-V alloys [42 –44]. The fundamental band gap energy for the ion-beam-synthesized thin films of GaNxAs12x, InNxP12x and AlyGa12yNxAs12x after Nþ implantation into GaAs, InP and AlyGa12yAs was found to decrease with increasing N implantation dose in a manner similar to that observed in epitaxially grown thin films. In GaNxAs12x the highest value of x achieved using Nþimplantation and conventional RTA technique was 0.006; this corresponds to an N activation efficiency of , 15%. In the course of optimizing the annealing conditions in these studies, it was found that, in GaNAs formed in this way, the substitutional NAs is thermally unstable at temperatures higher than 8508C and will precipitate to form N-related voids [45]. Most recently, pulsed laser melting (PLM) of N-implanted III– Vs has been found to dramatically improve the incorporation of N on the group-V element site [46,47]. In PLM,

Band Anticrossing and Related Electronic Structure in III-N-V Alloys

333

the near surface absorption of a single intense laser pulse instantaneously melts the implant-damaged or amorphized layer. This is followed immediately by rapid epitaxial regrowth from the liquid. Epitaxy is seeded at the solid – liquid interface by the crystalline bulk in a manner very similar to liquid phase epitaxy (LPE) but with the whole process occurring on a much shorter time scale, typically between 1028 – 1026 s [48,49]. Figure 10.4 shows a series of photoreflectance (PR) spectra from GaAs implanted with increasing amounts of N processed by PLM with an energy fluence of 0.34 J/cm2 and subsequently by RTA at 9508C for 10 s. Such PLM – RTA post-implantation treatments represent the “optimum” process conditions found to date and the samples so formed have clear, sharp optical transitions. The amount of N incorporated in the As sublattice (“active” N) for the GaNxAs12x layers formed by this method can be estimated using the BAC model and is , 40– 60% of the implanted value. This is over five times higher than

Figure 10.4. PR spectra measured from a series of samples implanted with increasing amounts of N (ximp) and processed by PLM at an energy fluence of 0.34 J/cm2 and subsequent RTA at 9508C for 10 s.

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that observed in samples processed by RTA only [42]. Such a drastic improvement can be attributed to the extremely short melt duration (, 2 £ 1027 s) and a re-growth process that greatly promotes N substitution in the As site and inhibits the formation of nitrogen related voids [45]. In addition to the enhanced N incorporation, the dilute nitride layers synthesized by Nþ-implantation followed by PLM – RTA were also found to be thermally stable up to annealing temperatures . 9508C. This improved sample synthesis technique provides a convenient and reliable method, in addition to conventional epitaxial growth techniques, for preparing large variety of dilute nitride samples. 10.3.2 Optical Transitions Associated with the Split Conduction Band Edges The splitting of the conduction band into two non-parabolic subbands predicted by the BAC model has been unambiguously observed in GaNxAs12x and Ga12yInyNxAs12x using photomodulation spectroscopy [25,27,50]. Figure 10.5 shows photorefluctance

Figure 10.5. PR spectra of MOCVD-grown GaNxAs12x samples with different N concentrations.

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spectra recorded from GaNxAs12x samples. The PR spectrum of GaAs ðx ¼ 0Þ exhibits two sharp derivative-like spectral features corresponding to the transition from the top of valence band to the bottom of the conduction band (E0 transition), and the transition between the spin – orbit split-off band and the conduction band minimum (E0 þ D0 transition). For N containing samples, in addition to the PR spectral features related to the transition across the fundamental band gap (E2 transition) and the transition from the top of the spin –orbit split-off valence band to the bottom of the conduction band (E2 þ D0 transition), an extra feature ðEþ Þ appears at higher energies in the PR spectra. With increasing N concentration, the E2 and E2 þ D0 transitions shift to lower energy, the Eþ transition moves in the opposite direction. Shown in Figure 10.6 are the E2 and Eþ transition energies in Ga12yInyNxAs12x as a function of N concentration reported by several different groups [50 – 52]. The non-linear dependence of the transition energies on N concentration can be well described by the BAC model using a coupling constant V ¼ 2:7 eV: The band anticrossing effects have also been observed in other group III– V materials alloyed with nitrogen including GaNxP12x [53], InNxP12x [7,43,44], GaNxSbyAs12x 2 y [54], and InNxSb12x [55]. For instance, the change of the band gap energy of gas-source MBE-grown InNxP12x as a function of N content is shown in Figure 10.7. The band gap energies of the samples were determined by absorption and PR measurements. The incorporation of nitrogen reduces the band gap in the same manner as in the case of Ga12xInxNyAs12y shown in Figure 10.2. The best fit to the experimental data using the BAC model yields the energy position of EN < EV þ 2:0 eV for the localized N-level and the coupling constant of V ¼ 3:5 eV for the InNxP12x alloy system.

Figure 10.6. Dependence of E2 and Eþ transitions on N composition. The solid and dotted lines represent the BAC model predictions for Ga12yInyNxAs12x ðy ¼ 3xÞ and GaNxAs12x, respectively [52].

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Figure 10.7. Bandgap energy of InP12xNx as a function of nitrogen concentration. The solid line is a fit based on the BAC model.

10.3.3 Effects of Pressure and Temperature Several measurements on the effects of applied pressure on the optical transitions observed in GaNxAs12x and Ga12yInyNxAs12x have been reported [25,27,56– 58]. Figure 10.8 shows the pressure dependence of the band gap energy of Ga12yInyNxAs12x measured by PL in comparison with the pressure dependencies for the GaAs G; L; and X points [57]. It is clear that the addition of a small (2%) amount of nitrogen into GaInAs to form Ga12yInyNxAs12x radically alters the pressure dependence of the band gap energy. The pressure dependence of the optical transitions associated with the E2 and Eþ subband edges in an In-free GaN0.015As0.985 sample and a Ga0.95In0.05N0.012As0.988 sample measured by PR are shown in Figure 10.9. The anticrossing behavior of two strongly interacting energy levels with distinctly different pressure dependencies is unmistakably observed [25,27]. The E2 transition has a strong dependence at low pressures and gradually saturates at high pressures, whereas the Eþ transition has weak pressure dependence at low pressures and displays a much stronger dependence at high pressures. The solid lines through the experimental data in the figure are results of calculations using Eq. (10.2.8). The best fits to the data yield the energy of the nitrogen state, EN ¼ EV þ 1:65 eV for both samples at atmospheric pressure, independent of In concentration [27]. These results prove that the effects of alloying with In on the band gap can be separated from the shifts produced by the interaction with N states, allowing for an independent determination of EM from a given In concentration in Ga12yInyNxAs12x alloys. The observed change in the dependence of the E2 and Eþ transitions on pressure indicates that the application of pressure gradually changes the character of the E2 -subband edge from

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Figure 10.8. Experimental (dots) and theoretical (solid line) dependence of the band gap energy shift versus pressure at 4 K for 2% nitrogen in Ga12yInyNxAs12x. The dotted lines are the calculated pressure dependencies for the GaAs G; L; and X points. The vertical axes are offset by the respective Ga12yInyNxAs12x and GaAs band gap energies. The inset shows the 4 K ambient pressure photoluminescence spectrum [57].

extended EM -like to localized EN -like, and the character of the Eþ -subband edge from the localized-like to extended-like. Such a transformation can be generalized by the schematic examples of the calculated band structure based on the BAC model shown in Figure 10.10. The interaction between the localized isoelectronic states and the extended conduction band states has a pronounced effect on the dispersion relation of the two conduction subbands E2 and Eþ : The effect of the interaction is most pronounced for the states located close to EN : If the localized state is located within the conduction band of the matrix that corresponds to the low-pressure situation, as depicted in Figure 10.10(a), the conduction band states at the E2 edge retain mostly the extended EM -like character and those at the Eþ edge have a more localized and EN -like character. The lower conduction subband narrows drastically as the energy position of EN level moves down relative to the bottom of the conduction band as applied pressure increases. Narrowing of the band indicates a gradually increased contribution of the localized nature to the lowest subband, leading to a highly non-parabolic dispersion relationship that induces an enhancement of the effective mass and the DOS in the lower subband [51]. If the localized states is located below the conduction band edge at high pressures, as illustrated in Figure 10.10(b), the conduction subband edges E2 and Eþ

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Figure 10.9. Effects of pressure on the optical transitions associated with the E2 and Eþ transitions in GaN0.015As0.985 and Ga0.95In0.05N0.012As0.988.

switch their character: the E2 subband states assume the highly localized nature and Eþ subband states possess the character of extended state. The large enhancement of the effective mass in the lower E2 ðkÞ subband as a function of electron energy and externally applied pressure has been observed by the pressure dependence of the transitions between quantum confinement states in GaNxAs12x/GaAs multiple quantum wells [40,59]. The effect of pressure on the lowest confinement transition energy ðEN¼1 Þ in GaNxAs12x/GaAs MQW samples induces a relatively strong non-linear pressure dependence and a decrease rather than an increase in the total confinement energy DE with pressure. The decrease in DE in the GaN0.016As0.984/GaAs MQW sample can be explained by the pressure-induced enhancement in the electron effective mass described by the BAC model [59]. In addition, the pressure dependence of the transitions involving higher quantum confined states was observed to decrease with increasing quantum number n despite the pressure coefficient of the barrier material being greater than that of the well material. This strong decrease in the pressure coefficient with increasing quantum number n directly reflects the strong non-parabolic dispersion

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Figure 10.10. Illustration of the effects of band anticrossing on the G conduction band structure: (a) the highly electronegative isoelectronic impurity induced localized state resonant with the conduction band; (b) the localized state located below the conduction band. The solid lines are the restructured E2 and Eþ subbands resulting from the band anticrossing interaction between the localized states (dash-dotted line) and the extended states of the conduction band (broken line).

of the conduction band in GaNxAs12x, indicating that the higher the energy above the conduction band edge, the bigger is the electronic effective mass [40]. The thermal properties of GaNxAs12x and Ga12yInyNxAs12x alloys and in related quantum well structures have also been extensively studied [52,58,60 – 62]. Considerable reduction in the temperature dependence of the band gap energy in GaNxAs12x and Ga12yInyNxAs12x alloys was observed in those studies. Figure 10.11 shows the temperature-dependent energy shift of the absorption edge measured on GaNxAs12x alloy samples with different N concentrations. The temperature dependence of the band gap energy is reduced as the N concentration increases. Such a reduction in the temperature dependence was explained using the BAC model. Since the shift of the lower subband E2 depends on the energy difference between the EN and EM ; one should expect a less pronounced temperature dependence of the band gap energy with the EM of a host semiconductor matrix located below EN : The solid lines in the figure are the calculated results based on the BAC model by just considering the temperature dependence of the extended states of the GaAs conduction band [61]. It is noted that in the optical absorption measurements reported by Skierbiszewski the temperature dependence of Eþ appeared to be stronger than that of E2 [52]. The result seemed to be somewhat contradictory since the change in the Eþ transition energy with

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Figure 10.11. Temperature dependence of the absorption edge of the GaAs and GaNAs alloys measured for the different N compositions. The open circles are measured results the solid lines are calculated for the respective N compositions [61].

temperature should be weaker than the E2 transition based on the BAC model assuming that the N-related state does not vary much with temperature. However, the much more significant broadening of the Eþ subband edge (see Figure 10.1) as compared to the E2 subband edge as discussed in Section 10.2 may play a significant role in the thermal effect on the E2 and Eþ transitions. In addition, the effect of the Eþ -subband edge resonant with the E2 -subband continuum that tends to lead an underestimated transition energy by absorption measurement should also be taken into account. 10.3.4 Effects of the Higher Conduction Band Minima Alternative interpretations of some of the observed effects discussed above such as the appearance of Eþ transition and the pressure dependence of the E2 and Eþ transitions have been proposed [35,50,56,57,63– 71]. Some studies have argued that the observed changes in the conduction band structure are a result of interactions between states originating from the extended states of the G; L and/or X conduction band minima. It has been argued that incorporation of N breaks the crystal symmetry and splits the degenerate L and X minima into the a1 and t2 states. The a1 states strongly interact with the states at

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the G minimum leading to a downward shift of the conduction band edge. The close proximity of the L minimum energy at EV þ 1:705 eV to the energy of the localized N-state EN < EV þ 1:65 eV was invoked in the argument that the interaction with either of these states could be responsible for the Eþ and E2 transitions [35,50]. It was also proposed that the impurity-like band of interacting nitrogen pairs and cluster states is responsible for the downward shift of the conduction band edge in GaNAs [70,71]. Several groups have studied the N-induced effects on the L conduction band edges by measuring the E1 ðL4V ;5V – L6C Þ transition near the L points of the Brillouin zone in GaNxAs12x using different experimental methods [35,50,70 – 73]. The change in the energy of the E1 transition, as well as the shift of E2 and Eþ transitions, determined by PR measurements, as a function of the N concentration in GaNAs is shown in Figure 10.12 [72,73]. It is clear from the figure that the E1 transition shifts to higher energy at a much slower rate than the Eþ transition. On the other hand, the relative energy shift of the Eþ transition as a function of N concentration is, within the experimental uncertainties, the same as downward shift of the E2 transition that represents the fundamental band gap reduction in the GaNAs samples. This salient feature is a typical characteristic of two-level anticrossing interaction in which the upward shift of the upper state and the downward shift of the lower state are exactly the same in magnitude. The much slower upward shift of the E1 compared to the Eþ transition energy rules out the possibility that the Eþ can be associated with N-induced GV – LC transition. The slow, monotonic increase in the E1 transition energy

Figure 10.12. Measured energies of the E1 transition, as well as the E2 and Eþ transitions in GaNxAs12x. The shift of E1 transition is less than 20% of that of Eþ transition. The arrows mark the energy position of EM and EN with respect to the top of the valence band in GaAs matrix. The dotted and dashed lines are for guiding eyes.

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with N concentration and the lack of a splitting of the L-band edge are also in disagreement with the theoretical calculations [63 – 66] attributing the Eþ spectral feature to transitions from GV to configuration weighted average of nitrogen-like a1 ðNÞ and L-like a1 ðLC Þ states. To further elucidate the role of the higher energy minima, the effects of N on the band structure of Ga12yAlyAs alloys were investigated. In these alloys, the G band-edge minimum shifts from about 0.5 eV below in GaAs to slightly over 0.5 eV above the X conduction band minima in AlAs. The large relative energy shift is expected to strongly affect the strength of the interaction between those two minima. Ga12yAlyNxAs12x alloys used in the study were synthesized by implanting nitrogen ions into MOCVD-grown AlyGa12yAs epitaxial films on GaAs substrates followed by post implantation thermal annealing. Energy positions of the experimentally observed Eþ and E2 transitions for a GaN0.0085As0.9915 and four Ga12yAlyNxAs12x samples are shown in Figure 10.13.

Figure 10.13. The E2 and Eþ transition energies measured for Al12yGayNxAs12x samples. Open circles represent E0 transitions in samples with x ¼ 0: The dependence of the G; X and L conduction band edges on the AlAs mole fraction in AlGaAs alloys are shown by the solid lines. The dashed line represents the estimated change of the EN position with Al content. The inset shows a comparison of PR spectra measured on the Al0.35Ga0.65As samples with (solid line) and without N (dashed line).

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The dependencies of the energies of the G; L and X conduction band minima on the Al content in AlyGa12yAs are shown in the figure. The band gap E0 measured in the as-grown wafers was used to determine the Al concentration of the Ga12yAlyAs epitaxial films. The inset in Figure 10.13 shows a comparison of the PR spectra between an as-grown Al0.35Ga0.65As sample and an Nþ-implanted Al0.35Ga0.65NxAs12x sample. As illustrated in Figure 10.13, the positions of the Eþ and E2 transitions can again be well explained assuming an anticrossing interaction between states at the G minimum and the localized nitrogen state EN whose energy depends on the Al content as EN ¼ 1:65 þ 0:61y eV. It is interesting to see that the Eþ transition lies above the G conduction band minimum even at the indirect band gap region of the AlyGa12yAs matrix. The results illustrate clearly that an interaction between the X and G minima or the L and G minima only due to N-induced symmetry breaking but without taking the N levels into account, as proposed in Refs. [57,63 –66], cannot account for the positions of the experimentally observed Eþ and E2 transitions. Also, there is no clear correlation between the location of the X conduction band edge and the E2 and Eþ transition energies. For example, the X-edge lies close to the Eþ transition in the sample with y ¼ 0:35; but as much as 0.17 eV above the Eþ transition energy in GaNAs. This would not be possible if an interaction between G and X were responsible for the Eþ band edge shift.

10.4. NOVEL ELECTRONIC AND TRANSPORT PROPERTIES OF III-N-V ALLOYS

10.4.1 Enhancement in Maximum Electron Concentration As has been discussed above, the BAC model not only explains the band gap reduction in dilute III-N-V nitrides but it also predicts that the N-induced modifications of the conduction band will have profound effects on the transport properties of those material systems [51]. In particular, the downward shift of the conduction band edge and the enhancement of the DOS effective mass will lead to much enhanced maximum free electron concentration nmax : The maximum achievable electron and/or hole concentration is an important criterion in the design of semiconductor devices. A universal rule that predicts the maximum free carrier concentration achievable by doping has been developed and shown to be valid for a wide variety of semiconductor materials [74 – 76]. The rule is based on the amphoteric native defect model that relates the type and concentrations of compensating native defects responsible for dopant compensation to the location of the Fermi level with respect to a common energy reference. According to this model GaAs is predicted to exhibit limitations on the maximum free electron concentration. Experimentally, the maximum electron concentration nmax in GaAs achievable under equilibrium conditions is limited to about 1018 –1019 cm23 [77].

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Figure 10.14. Comparison of the measured maximum electron concentration with the calculated values as a function of N fraction in Ga123xIn3xNxAs12x. Two different cases of the calculated nmax are shown: one includes effects of downward shift of the conduction band only (dashed curve) and the other includes both the band shift and the enhancement of the density of states (solid curve). The calculated nmax for samples with no N (i.e. when only the effects from the band gap lowering produced by In incorporation are considered) are also shown in the figure (dotted curve). The shaded area indicates the range of Se concentration in these samples.

Figure 10.14 shows the electron concentration in Se-doped MOCVD-grown Ga123xIn3xNxAs12x films with x ¼ 0 – 0:033 measured by Hall effect and electrochemical capacitance –voltage (ECV) technique [32]. Since the Se atomic concentrations in these films are at least an order of magnitude higher than the free electron concentration (in the range of 2– 7 £ 1020 cm23), the measured free electron concentration shown in Figure 10.14 can be considered to be the maximum achievable free electron concentration, nmax : Figure 10.14 shows that the nmax increases strongly with the N content x with a maximum observed value of 7 £ 1019 cm23 for x ¼ 0:033: This value is , 20 times of that found in a GaAs film (3.5 £ 1018 cm23) grown under the same conditions. The muchenhanced nmax in Ga123xIn3xNxAs12x films can be explained by considering the N-induced conduction band modifications. According to the amphoteric native defect model the maximum free electron concentration is determined by the Fermi energy which is constant with respect to the Fermi stabilization energy EFS [74]. Therefore the downward shift

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of the conduction band edge toward EFS and the enhancement of the DOS effective mass in GaInNAs lead to much larger concentration of uncompensated, electrically active donors for the same location of the Fermi energy relative to EFS : The calculated nmax as a function of x for Ga123xIn3xNxAs12x due to the downward shift of the conduction band caused by the level anticrossing only, as well as that including the increase in the effective mass, calculated using Eqs. (10.2.13) and (10.2.14), are shown in Figure 10.14. Comparison of the experimental data with the calculation shows that in order to account for the large enhancement of the doping limits in III-N-V alloys both the effects of band gap reduction and the increase in the effective mass have to be taken into account. While Se-doped Ga123xIn3xNxAs12x alloys grown by MOCVD have shown enhanced nmax in accordance with the BAC model, similar behavior is also observed in Sþ-implanted GaNxAs12x thin film [78]. Figure 10.15 displays the carrier concentration profiles measured by ECV technique for the S-implanted GaNxAs12x ðx , 0:008Þ and

Figure 10.15. Ionized net donor concentration profiles for the GaNxAs12x films and the SI-GaAs standard measured by the electrochemical capacitance–voltage (ECV) technique. The short-dashed curve is the calculated distribution of implanted S atoms. The dashed horizontal lines indicate the theoretical free electron concentrations in Ga12xNxAs by considering only the effects of the downward shift of the conduction band (band edge only) and both the effects of band gap reduction and density of states effective mass enhancement (band edge þ effective mass).

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SI-GaAs samples after RTA. A striking difference in the free electron concentration n measured in the SI-GaAs and the GaNxAs12x samples is observed. In the Sþ-implanted SIGaAs sample, n , 2:5 £ 1017 cm23 was measured in the bulk of the implanted layer, with a higher n , 5 £ 1017 cm23 towards the end of the implantation profile. The theoretical nmax in GaNxAs12x due to the N-induced conduction band modification within the framework of the BAC model and the amphoteric native defect model is , 1 £ 1019 cm23 for the GaN0.008As0.992 sample. This value is in a reasonably good agreement with the measured concentration of 6 £ 1018 cm23 shown in Figure 10.15. Attempts were also made to form n-type GaNxAs12x thin films with high electron concentration by co-implantation of N and a dopant element in GaAs [79]. Figure 10.16 shows a comparison of the ECV determined free electron concentration profiles for the GaAs samples implanted with S alone and co-implanted with S and N (S þ N) after RTA at 9458C for 10 s. The calculated, as-implanted S and N atomic distributions are also shown in the figure. The most prominent difference in the electron concentration profiles between the S only and (S þ N) samples is the much enhanced electron concentration in ˚ ) near the surface. The region with lower the (S þ N) sample in a narrow region (, 500 A electron concentration at , 0.1– 0.2 mm below the surface coincides with a region with

Figure 10.16. The ECV measured net donor concentration profiles for the GaAs samples implanted with S alone and S þ N after RTA at 9458C for 10 s. The calculated atomic profiles for both the implanted S and N are also shown.

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excess As due to the implantation process that makes the substitution of S atoms into the As sites more difficult [79]. In addition, larger concentrations of the compensating VGa acceptors are also expected in the As-rich region. A reduced availability of group V sites and an increased VGa concentration in the region lead to the minimum in the electron concentration. The effect is exacerbated in the (S þ N) sample where both S and N compete for the same group V element sites. Considering both the band gap reduction and the large enhancement of the electron effective mass, the high nmax in the near-surface region of the (S þ N) sample (, 1.5 £ 1019 cm23) implies that the N content in this thin near-surface diluted nitride layer is x ¼ 0:0032: This value is in good agreement with the calculated N concentration in the surface region ðx < 0:003 – 0:01Þ: With this N content the conduction band edge is shifted downward by 77 meV and the conduction band effective mass at the Fermi energy is , 3 times higher than that of GaAs [80]. 10.4.2 Decrease in Electron Mobility It has been widely recognized that the incorporation of small amounts of nitrogen into GaAs leads to a drastic reduction of the electron mobility. The typical mobility of GaNxAs12x films ranges from , 10 to a few hundred cm2/V s, [81,82] which is over an order of magnitude smaller than the electron mobility in GaAs at comparable doping levels. Figure 10.17 shows the change in room-temperature mobility of Ga0.93In0.07N0.017As0.983:Si

Figure 10.17. Room-temperature electron mobility of Ga0.93In0.07N0.017As0.983:Si plotted as a function of electron concentration. The calculated mobilities limited by the conduction band broadening ðm1 Þ and by the random field scattering ðm2 Þ are shown. The calculated Fermi energy is referenced to the bottom of the lowest conduction band ðE2 Þ:

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when the electron concentration is reduced by RTA due to SiGa –NAs formation. The mobility shows a non-monotonic dependence on the electron concentration with a maximum at n , 5 £ 1018 cm23. The room-temperature mobility ðm1 Þ calculated from Eq. (10.2.11) is shown as short-dashed curve in Figure 10.17. Also shown is the Fermi energy as a function of n calculated from Eq. (10.2.13). At high electron concentrations when the Fermi energy approaches the original energy level of N localized states in In0.07Ga0.93As0.983N0.017 (located at , 0.30 eV above the conduction band edge of EM ; or 0.54 eV above the conduction band edge of E2 ), the mobility is largely suppressed by the strong hybridization between lEN l and lEM ðkÞl: At n ¼ 2 £ 1019 cm23 ; the energy broadening and the scattering lifetime at the Fermi surface are estimated to be 0.25 eV ˚ , which is only a third and 3 fs, respectively. The mean free path of free electrons is about 5 A of the average distance between the randomly distributed N atoms. Therefore, at this electron concentration the homogeneous broadening resulting from the anticrossing interaction is the dominant scattering mechanism that limits the electron mobility. As is seen in Figure 10.17, at high concentrations the electron mobility calculated from the BAC model is in a quantitative agreement with the experiment. It should be noted that this very good agreement has been obtained without any adjustable parameters. At lower electron concentrations the mobility starts to decrease, deviating severely from m1 : This effect can be attributed to the scattering of the conduction electrons by the random fields caused by the structural and compositional disorder in the alloy. It is well known that in partially disordered semiconductors as the Fermi level decreases from the degenerate doping into the non-degenerate doping regime, the conduction electrons experience increasingly strong scattering from the potential fluctuations. As a result the mobility decreases monotonically with decreasing electron concentration [83,84]. In the case of Ga12yInyNxAs12x alloys the main contribution to the potential fluctuations originates from the random N distribution. An estimate for the electron mobility limited by the random field scattering ðm2 Þ is shown in Figure 10.17. The solid curve in Figure 10.17 takes into account the contributions of both the level broadening and random alloy scattering effects 21 that limit the mobility ðm ¼ 1=ðm21 1 þ m2 ÞÞ: This calculated mobility reproduces the nonmonotonic behavior of the mobility measured over two decades of change in electron concentration. 10.4.3 Mutual Passivation in III-N-V Alloys In contrast to the observed enhancement of the doping activation of the group VI elements (S, Se), Si and N co-implantation in GaAs only resulted in a highly resistive layer [85]. This asymmetry in the behavior of group VI and IV donors can be explained by an entirely new effect in which an electrically active substitutional group IV donor and an isovalent N atom passivate each other’s electronic effects [86]. This mutual passivation occurs in GaNxAs12x doped with group IV donors (Si and Ge) through the formation of nearest neighbor IVGa – NAs pairs.

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Figure 10.18. Electron concentrations of Si-doped GaAs and Ga0.93In0.07N0.017As0.983 as a function of annealing temperature for 10 s. The dependence of the electron concentration on RTA temperature for a MOCVD-grown Se-doped Ga0.92In0.08N0.024As0.976 film is also included.

Figure 10.18 shows the free electron concentration in MBE-grown Si-doped Ga0.93In0.07N0.017As0.983 and GaAs, as well as a MOCVD-grown Se-doped Ga0.92In0.08N0.024As0.976 thin films after RTA for 10 s in the temperature range of 650 – 9508C. The Si and Se doping levels in these samples are in the range of 2– 9 £ 1019 cm23 and , 2 £ 1020 cm23, respectively. For both GaAs:Si and GaInNAs:Se samples, only slight decreases in electron concentrations, from 1.6 £ 1019 to 8 £ 1018 cm23 for GaAs:Si and 3 £ 1019 to 2 £ 1019 cm23 for GaInNAs:Se, are observed as the results of high temperature RTA. Such a decrease in the electron concentration in GaAs is in agreement with the equilibrium maximum electron concentration (in the range of 1018 –1019 cm23) [87]. The much higher electron concentration in the Se-doped GaInNAs sample is also consistent with the enhanced donor activation efficiency resulting from the N-induced modification of the conduction band structure [34]. On the other hand, the free electron concentration in the GaInNAs:Si sample drops from 1.1 £ 1019 cm23 in the as-grown film to 3 £ 1017 cm23 after RTA at 9508C for 10 s. In fact, RTA at 9508C for 120 s further reduces the electron concentration to , 1015 cm23. The reduced electrical activity of Si donors in GaNxAs12x alloys can be attributed to the formation of nearest neighbor SiGa – NAs pairs. The highly electronegative N atom strongly binds the fourth valence electron of Si, preventing it from acting as a hydrogenic donor. Such an explanation suggests that, because of the localized nature of the N-states in GaNxAs12x, the passivation is limited to group IV donors that occupy Ga sites. This is supported by the small change in electrical behavior observed in the GaInNAs:Se thin film

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in which both the N and Se reside in the As sublattice, and therefore, cannot form nearest neighbor passivating pairs. It should be pointed out that the mutual passivation effect discussed here differs from the previously observed, much less stable and reversible passivation of the activity of N atoms with hydrogen [88]. In the latter case hydrogen does not have any effect on the material properties by itself. The well-defined onset temperature of about 7008C for the observed reduction of electron concentration in GaInNAs:Si shown in Figure 10.18 roughly corresponds to the annealing condition that allows the Si atoms to diffuse over a length equal to the average ˚ ) [86]. The diffusiondistance between randomly distributed Si and N atoms (, 7 A controlled passivation process is analyzed in the context of Si diffusion mediated by both neutral Ga vacancies (V0Ga) and triply negatively charged Ga vacancies (V32 Ga ) [89]. Figure 10.19 shows the isothermal annealing effects of the normalized free carrier concentration of the GaInNAs:Si sample for annealing temperatures in the range of 650– 8208C. Calculations based on Si diffusion via V0Ga and V32 Ga vacancies are shown as dashed lines in the figure. The calculations agree very well with the experimental data. According to the diffusion model, at high annealing temperatures or long annealing time, the Fermilevel independent, V0Ga-mediated diffusion becomes increasingly important. This is reflected in the fact that the ln½n=n0  , t curves approach a linear dependence at high temperatures or long anneal times.

Figure 10.19. Normalized free electron concentration as a function of annealing time at different annealing temperatures. The dashed curves represent the results from analytical calculations based on Si diffusion via Ga vacancies.

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Since isovalent N is responsible for a massive modification of the electronic structure of GaNxAs12x alloys, the question arises to what extent the passivation process affects the N-induced modification of the electronic structure of the alloys. PR measurements on the GaInNAs:Si sample show that the band gap energy increases with increasing RTA temperature. Annealing of the sample at 9508C increases the gap by about 35 meV. If this increase is attributed to deactivation of the N atoms, the concentration of the deactivated N is approximately equal to 0.004 £ 2.2 £ 1022 cm23 < 8 £ 1019 cm23, which is close to the initial total Si concentration in the as-grown sample. This is consistent with the formation of SiGa –NAs pairs being responsible for the mutual passivation of both species. This scenario of the passivation process is further corroborated by PL measurements on the GaInNAs:Si sample. A strong PL emission peaked at ,0.8 eV is observed when the sample is mutually passivated, indicating the presence of deep states associated with the SiGa –NAs pairs [86]. The general nature of the mutual passivation effect is supported by the investigations of GaNxAs12x layers doped with Ge, another group IV donor. Ge-doped GaNxAs12x layers were synthesized by sequential implantation of Ge and N ions into GaAs followed by a combination of PLM and RTA [47]. The passivation of the N activity by the Ge atoms is

Figure 10.20. PR spectra measured from a series of ion beam synthesized Ge-doped GaNxAs12x samples RTA at 9508C for durations of 5–120 s. The inset shows the band gap energies determined from the PR measurements.

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Figure 10.21. Free electron concentrations of the 2% Ge and 2% N þ 2% Ge samples after PLM þ RTA at increasing temperatures for 10 s obtained by Hall effect measurements. Electron concentration for the 2% N þ 2% Ge sample after PLM þ RTA at 9508C for 60 s is also shown.

illustrated in a series of PR spectra presented in Figure 10.20. The band gap energies obtained from the PR spectra are shown in the inset as a function of the duration of 9508C RTA. A fundamental band gap transition at 1.24 eV is observed for GaAs samples implanted with 2% N alone after PLM –RTA at 9508C for 10– 120 s, corresponding to a GaNxAs12x layer with x , 0:01: In contrast, the band gap of the samples co-implanted with N and Ge (2% N þ 2% Ge) after PLM increases from 1.24 to 1.42 eV (band gap of GaAs) as the RTA duration increases to 60 s, revealing that all NAs sites are passivated by Ge. The gradual increase in the band gap of the 2% N þ 2% Ge sample as a function of RTA temperature and/or time duration can be attributed to the passivation of NAs by GeGa through the formation of nearest neighbor GeGa – NAs pairs. Figure 10.21 shows a comparison of the electron concentration of the 2% N þ 2% Ge and 2% Ge samples followed by PLM – RTA for 10 s in the temperature range of 650– 9508C. The electron concentration of both samples approaches 1019 cm23 after PLM. For the 2% Ge sample, thermal annealing after PLM drives the system toward equilibrium with an electron concentration of , 1 £ 1018 cm23 which is consistent with the amphoteric character of Ge in GaAs [90]. The electron concentration of the 2% N þ 2% Ge samples, on the other hand, drops over two orders of magnitude to less than 1017 cm23 as the samples are subjected to RTA at temperatures higher than 6508C. The changes in the band gap and the electrical behavior in the Ge-doped GaNxAs12x sample show that the activities of Ge donors and isovalent N mutually passivate each other

Band Anticrossing and Related Electronic Structure in III-N-V Alloys

353

via the formation of NAs – GeGa pairs, just as was the case in Si-doped GaNxAs12x. Mutual passivation of Si and N has also been recently observed in Si-doped Ga0.48In0.52NxP12x [91]. All these results clearly demonstrate the general nature of this phenomenon.

10.5. CONCLUSIONS

The effect of N on the electronic band structure in dilute III-N-V nitrides has been explained in terms of a band anticrossing interaction between highly localized N states and the extended conduction band states of the semiconductor matrix. The interaction leads to a splitting of the conduction band into two non-parabolic subbands. The downward shift of the lower subband edge relative to the valence band is responsible for the reduction of the fundamental band gap. The profound effects on the optical and electrical properties of the dilute nitrides such as the significant increase in the electron effective mass and the drastic decrease in the electron mobility can all be quantitatively account for using this model. The BAC model not only explains the unusual optical and electronic properties of HMAs but also to predict new effects that have been later experimentally confirmed. Although this chapter is limited to the review of properties of group III-N-V alloys, it should be emphasized that these alloys are only a subgroup of a much broader class of materials whose electronic structure is determined by the anticrossing interaction. Most notably, it has been shown that II-O-VI alloys in which column VI anions are partially replaced with O atoms have the properties quite analogous to those of III-N-V alloys [92 – 96]. Furthermore, the anticrossing interaction is not limited to the conduction band only. It has been found that the partial replacement of an electronegative Se or S anions in ZnSe or ZnS with more metallic Te atoms, for instance, leads to the formation of highly localized, donor-like states close to the valence band edge. For alloy-like concentrations of Te, the anticrossing interaction between the Te levels and the extended states of the valence band induces a drastic modification of the electronic structure [97]. In fact that the interaction is fully responsible for a large band gap reduction in Se- and S-rich ZnSexTe12x and ZnSxTe12x alloys. The discovery of the general nature of the BAC interactions offers an interesting opportunity to design a large variety of HMAs with desired properties. One of the many attractive features of the HMAs is that small variations of the composition produce large changes in the values of the material parameters. Improvement of the concentration of electrical active donors demonstrated in GaInNAs alloys suggests that the large BAC-induced shifts of the conduction or valence band could be used to overcome severe limitations on the n- or p-type doping in some II –VI compounds. It would be very interesting to explore if incorporation of small amounts of O could improve n-type doping of ZnOxTe12x or incorporation of Te into ZnS could lead to p-type ZnTexS12x. Studies of many of the possible highly mismatched semiconductor alloys are only on their very early

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stages. A great deal of effort and devotion is required in order to fully realize the fundamental significance of these materials as well as their potentials for practical applications.

ACKNOWLEDGEMENTS

The authors are very grateful to Dr J.F. Geisz and Prof. C.W. Tu for providing the samples used in this study. Special thanks to E.E. Haller, P.Y. Yu, J. Beeman, M.A. Scarpulla, and O. Dubon for invaluable discussions and technical assistance. This work is supported by the Director, Office of Science, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, of the US Department of Energy under Contract No. DE-AC0376SF00098.

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Dilute Nitride Semiconductors M. Henini (Ed.) q 2005 Elsevier Ltd. All rights reserved.

Chapter 11

A Tight-binding Based Analysis of the Band Anti-Crossing Model and Its Application in Ga(In)NAs Alloys E.P. O’Reillya, A. Lindsaya, S. Fahya,b, S. Tomic´c and P.J. Klard a

NMRC, University College, Lee Maltings, Prospect Row, Cork, Ireland Department of Physics, University College Cork, Cork, Ireland c Computational Science and Engineering Department, CCLRC Daresbury Laboratory, Warrington, Cheshire WA4 4AD, UK d Department of Physics and Material Sciences Center, Philipps-University, Renthof 5, D-35032 Marburg, Germany b

ABSTRACT

The Band Anti-Crossing (BAC) model describes the strong band gap bowing at low N composition x in Ga(In)NxAs12x in terms of an interaction between the conduction band edge (CBE) and a higher lying band of localised nitrogen resonant states. We use an sp3sp tight-binding (TB) Hamiltonian here to investigate the BAC model and its application. We demonstrate that the alloy CBE (the so-called E2 level) can be described very accurately by the BAC model, in which we treat the nitrogen levels explicitly using a linear combination of isolated nitrogen resonant states (LCINS). We also use the LCINS results to identify a higher lying resonance (the Eþ level) in the full tight-binding calculations, showing that at low N composition Eþ forms a sharp resonance in the conduction band G-related density of states, which broadens rapidly at higher N composition when the Eþ level rises in energy to become degenerate with the larger L-related density of states. We then present an analytical technique through which it is possible to calculate both the electron confined state energies and conduction band dispersion in Ga(In)NAs square quantum well (QW) structures. This analytical model provides a consistent fit of the ground and excited state transition energies measured across a wide range of samples. Turning to the conduction band dispersion, we show that the two-level BAC model must be modified to give a quantitative understanding of measured electron effective mass values. We demonstrate that the unexpectedly large mass values observed in some GaNAs samples are due to hybridisation between the CBE and nitrogen states close to the band edge. Finally we show that there is a fundamental connection between the strong composition dependence of the CBE energy and the n-type carrier scattering 361

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cross-section in Ga(In)NxAs12x alloys, imposing general limits on the carrier mobility, comparable to the highest measured mobility in such alloys. 11.1. INTRODUCTION

The semiconductor alloy gallium (indium) arsenide nitride has attracted considerable attention in recent years. When a small fraction of arsenic atoms in GaAs is replaced by nitrogen the energy gap initially decreases rapidly, at about 0.1 eV per % of N for x & 0:03 [1], with the measured CBE mass also showing unexpectedly large values [2 –6]. This behaviour is markedly different to conventional semiconductors, and is of interest both from a fundamental perspective and also because of its significant potential device applications. The strong bowing opens the possibility of using GaInNAs to get optical emission on a GaAs substrate at the technologically important wavelengths of 1.3 and 1.55 mm, considerably expanding the capabilities of GaAs for optoelectronics [7 – 10], as discussed elsewhere in this book. Our understanding of conventional III – V alloys has been built up through a range of approaches. Much progress is based on the use and application of relatively simple models, such as effective mass theory and the envelope function method [11 –13] to describe electronic states in quantum wells and heterostructures. These simple and wellestablished models are underpinned and informed by more detailed and fundamental theoretical calculations, as well as by comparison with a wide range of experimental data. The issue we review here is the development of appropriate models to describe the electronic structure of dilute nitride alloys. Two complementary approaches have been taken to explain their extreme behaviour, one based on detailed band structure calculations [14 – 18], the other on an experimentally observed band-anti-crossing (BAC) effect [19]. The two approaches have been highly successful in describing the band edge energies, and their variation upon annealing [20,21]. The BAC model has also been successfully applied to interpret photoreflectance measurements both of bulk and quantum well (QW) GaNAs samples, identifying a higher energy feature (Eþ) observed in bulk samples [19,22,23], and also providing a consistent interpretation of QW excited state transition energies across a wide range of samples, and as a function of hydrostatic pressure [24,25]. Despite the wide success of the BAC model, there has until recently been one significant set of experimental data which has remained unexplained, namely the observed composition dependence of the CBE effective mass in Ga(In)NAs alloys. Both the BAC model and detailed calculations predict an enhancement of the CBE mass compared with GaAs. The BAC model provides a good estimate of the measured mass at very low N compositions [6] ðx , 0:05%Þ and also in indium-containing samples [5], but significantly underestimates the mass in GaNxAs12x for x . 0:1% [3 –6]. The electron relative effective mass, mpe ; has now been determined using a range of different techniques, with a consistent

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363

trend emerging of unexpectedly large relative mass values in GaNxAs12x, such as mpe ¼ 0:13; 0.12 and even 0.19 for x ¼ 0:1% [6], 1.2% [4] and 2.0% [4]. These measured mass values provide a stringent test of any model describing the electronic structure of GaNxAs12x and related alloys. We review in this chapter how these mass values and several other previously unresolved aspects of the band structure of Ga(In)NxAs12x can be quantitatively understood by combining the insights and approach of the empirical BAC model with the detailed information available from band structure calculations. The approach we present gives results in excellent quantitative agreement with experiment, providing a clear understanding of the observed variations in mpe ; and even predicting in several instances a non-monotonic variation of mass with pressure. Our results also show clearly why the higher energy feature labelled Eþ only emerges for x * 0:2% in photoreflectance measurements of bulk GaNxAs12x [22,24]. They are also relevant to the recent direct observation of the conduction band dispersion in GaN0.0008As0.9992 QWs using magnetotunnelling spectroscopy [26], and provide further insight into the low mobility values generally observed in Ga(In)NxAs12x alloys [2,27,28]. It is well established that when a single N atom replaces an As atom in GaAs, it forms a resonant defect level above the CBE of GaAs [29,30]. This defect level arises because of the large difference in electronegativity and atomic size between N and As [31 – 33]. A major breakthrough was achieved for dilute nitride alloys with the demonstration by Walukiewicz and co-workers (using hydrostatic pressure techniques [19]) that the reduction in energy gap in Ga(In)NxAs12x is due to a BAC interaction between the CBE and higher lying localised nitrogen resonant states. Experimental studies of ultra-dilute nitride alloys show a range of resonant defect levels above the CBE due to the formation of N complexes. These include, e.g. that a gallium atom with two N neighbours gives a resonant defect level close to the low temperature CBE of GaAs [23,24,30]. Similar states are found in empirical pseudopotential [16,17] and tight-binding [34] studies of N complexes. Such calculations support many aspects of the BAC model, but also provide additional insight into the role of disorder and nitrogen clustering in GaNAs alloys. We will show below that many features in the band structure of dilute nitride alloys can be understood by modifying the two-level BAC model to explicitly include the effects of nitrogen clusters and interactions between neighbouring nitrogen atoms placed at random within the alloy. The approach we take here is to first consider ordered GaNAs, reviewing the insights we have obtained using a carefully parameterised tight-binding method to describe the electronic structure [21,35]. Using ordered structures, we derive explicitly a two-level BAC model in Section 11.2 to describe the CBE, showing that the concept of localised N resonant states can remain valid even up to x , 0:25: We turn in Section 11.3 to consider application of the BAC model to describe the electronic structure of GaNAs/GaAs QW structures. We present an analytical expression

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through which it is possible to calculate both the electron confined state energies and conduction band dispersion in Ga(In)NAs square QW structures, showing that these confined state energies are in very good agreement with those obtained from more detailed calculations. This analytical two-level model can then be used to provide a consistent fit of the ground and excited state transition energies measured across a wide range of samples. The analytical model provides useful insight into several aspects of the confined state behaviour in Ga(In)NAs/GaAs heterostructures. We use the sp3sp tight-binding Hamiltonian in Sections 11.4 and 11.5 to consider in more detail the effects of disorder, investigating how the inevitable disorder in the N distribution in Ga(In)NAs modifies the BAC model and its predictions. We show in Section 11.4 that even in a disordered alloy the band gap bowing and composition dependence of E2 can still be described very accurately by the BAC model, but with the BAC now explicitly treating the random distribution of N resonant states [34]. We then extend the analysis in Section 11.5, to show that the inclusion of disorder effects can give a quantitative understanding of the measured variation of effective mass with x in Ga(In)NxAs12x, and of the behaviour of the Eþ level at very low N compositions ðx & 0:2%Þ [36]. We switch direction in Section 11.6, to consider in particular the consequences of the strong band gap bowing on electron mobility in dilute nitride semiconductors. We show a fundamental connection between the CBE energy and the n-type carrier scattering cross-section in the ultra-dilute limit, imposing general limits on the carrier mobility in such alloys [28,37]. Within an independent scattering approximation, the carrier mobility is estimated to be , 1000 cm2/V s for a N atomic concentration of 1%, comparable to the highest measured mobility in high-quality GaInNAs samples at these N concentrations, but higher than that found in many samples. We speculate that consideration of a continuous band of N cluster states, as introduced in Sections 11.4 and 11.5, should further reduce the calculated mobility, to values in closer agreement with experiment. Overall, we conclude that a clear understanding is emerging concerning the electronic structure of dilute nitride alloys. Significant progress has been made, both through the use of the BAC model and more detailed theoretical studies, giving a quantitative description of the electronic structure, and enabling predictive design and analysis of GaInNAs-based heterostructures and optoelectronic devices.

11.2. NITROGEN RESONANT STATES IN ORDERED GaNxAs12x STRUCTURES

The BAC model explains the extreme band gap bowing observed in InyGa12yNxAs12x in terms of an interaction between two levels, one at energy Ec associated with the extended CBE state cc0 of the InGaAs matrix, and the other at energy EN associated with the localised N impurity states cN ; with the two states linked by a matrix element

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365

VNc describing the interaction between them [19]. The CBE energy of Ga(In)NxAs12x, E2, is then given by the lower eigenvalue of the determinant


EN VNc


ð11:1Þ
:


V E Nc c A resonant feature associated with the upper eigenvalue, Eþ, has also been observed in photoreflectance measurements [19,22,23], appearing in GaNxAs12x for x * 0:2% and remaining a relatively sharp feature until x , 3%; beyond which composition it broadens and weakens, when the resonant state becomes degenerate with the L-related conduction band levels [34]. Although this two-level model provides a good description of the variation of E2 and Eþ with composition and annealing, it undoubtedly omits much of the detail of the band structure. Detailed calculations of large disordered clusters of GaNxAs12x confirm the behaviour of E2, while the Eþ state is also observed over a limited range of x [16,17]. In addition, a series of N-related states are observed, with energies varying from close to the E2 level up towards Eþ [16]. These states are of secondary importance in understanding the band gap variation. We will show when we introduce a modified form of the BAC model in Sections 11.4 and 11.5 that these states are key to understanding the observed variation of conduction band effective mass, and also of Eþ. To investigate the resonant state cN ; and its behaviour, we have developed an accurate 3 p sp s tight-binding Hamiltonian to describe the electronic structure of GaInNxAs12x [21]. This Hamiltonian fully accounts for the observed experimental data, and also gives results in good agreement with pseudopotential calculations [14,16,38,39]. To investigate the resonant state, and its behaviour, we calculated the electronic structure of ordered GaNxAs12x supercells [21,35]. By comparing the calculated CBE states cc1 and cc0 in large supercells (Ga864N1As863 and Ga864As864, respectively), we can derive the nitrogen resonant state cN0 associated with an isolated N atom. In the BAC model of Eq. (11.1), cc1 ; the eigenfunction for E2, is a linear combination of the GaAs unperturbed CBE wave function, cc0 ; and the nitrogen resonant state cN0 ;

cc1 ¼ acc0 þ bcN0

ð11:2Þ

cc1 2 acc0 pffiffiffiffiffiffiffiffiffi 1 2 a2

ð11:3Þ

with cN0 then given by

cN0 ¼

where a ¼ kcc1 lcc0 l: We find that cN0 is highly localised, with over 50% of its probability density on the N site and the four neighbouring Ga atoms (Figure 11.1). Because the N resonant state is so highly localised in Figure 11.1, it is reasonable to expect that, as we increase the N density, we can associate a similar resonant level with each nitrogen site. To test if this is so, we compared the calculated resonant wave functions

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Figure 11.1. Calculated probability density of nitrogen resonant state, lcN0 l2 ; projected onto the group V atoms in the (001) plane of a Ga500N1As499 supercell, with the N atom situated in the centre of the plot, at ð0; 0; 0Þ; and the other group V atoms at lattice points aðm=2; n=2; 0Þ; 25 # m; n # 5, m þ n even.

cN for a series of increasingly smaller unit cells with the resonant state, cNð0Þ ; predicted by taking a linear combination of resonant wave functions from large unit cell calculations. We showed that to a very good approximation we can write the resonant wave function cN at the zone centre as N 1 X cN < cNð0Þ ¼ pffiffiffiffi cN0;n N n¼1

ð11:4Þ

where cN is represented by a linear combination of N isolated N states cN0;n located on an ordered array of sites n ¼ 1; …; N; within the supercell. Figure 11.2(a) shows lkcN lcNð0Þ ll2 ; the modulus squared of the overlap between the predicted and calculated resonant states for simple cubic (filled diamond) and face-centred cubic (filled circle) nitrogen arrays. The overlap between the predicted and exact wave functions is almost unity, for x & 0:05; and remains over 94% for the simple cubic structures, even up to x ¼ 0:25 (a Ga4N1As3 unit cell). This shows that the nature of the perturbation is indeed related to localised N states, even as far as x ¼ 0:25 and, as a consequence, suggests we can use a similar representation to accurately describe the N-related states and CBE in disordered GaNxAs12x structures. We note that the overlap between the predicted and calculated resonant wave functions drops to , 70% for the case of a Ga4N1As3 2 £ 2 £ 1 face-centred cubic structure [35]. This occurs because there is an infinite chain of nitrogen second nearest neighbours in this structure. The symmetry is reduced about the N atoms in such a chain compared with isolated N states primarily due to the unsymmetric nature of the lattice distortion parallel and perpendicular to the chain direction. This reduction in symmetry significantly modifies the resonant state wave function.

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Figure 11.2. (a) Overlap between calculated and predicted resonant wave functions in simple cubic (filled diamond) and face-centred cubic (filled circle) supercells. (b) Resonant state energy, EN, as a function of composition based on a full calculation (solid data points) and a simplified model (open data points). (c) Conduction band edge energy, E, of GaNxAs12x, calculated using the full Hamiltonian (solid data points), and two versions of the two-band model of Eq. (11.1) (solid line and open data points).

The filled data points in Figure 11.2(b) show the calculated resonant energy, EN, for each structure, found by evaluating kcN lHlcN l directly, while the filled data points in Figure 11.2(c) show the calculated reduction in the CBE energy as a function of N concentration in the ordered structures considered. The calculated values of EN follow a non-monotonic trend, with the value of EN generally being larger in the simple cubic than in the face-centred cubic supercells considered, due to the directional dependence of the resonant state wave function [40] and of the perturbing potential, DVN, introduced when an As atom is replaced by N. The open data points in Figure 11.2(b) show the value of EN calculated for each structure by directly evaluating kcNð0Þ lHlcNð0Þ l: These estimated values, EN(0), are in

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Dilute Nitride Semiconductors

excellent agreement with the values of EN obtained from the full calculation. Finally, the open data points in Figure 11.2(c) were obtained by using the estimated values, EN(0) in Eq. (11.1), with Ec assumed to vary linearly and VNc explicitly calculated as kcNð0Þ lDVN lcc0 l: The very good agreement between the full calculation and this modified two-band model confirms the validity of the two-band model, although we see that the resonant state energy used, EN, does depend on local environment, as discussed further below.

11.3. ANALYTICAL MODEL FOR QUANTUM WELL CONFINED STATE ENERGIES AND DISPERSION

11.3.1 Confined State Energies Considerable insight can be gained into the conduction band (CB) structure of conventional semiconductor QW structures using a one-band effective mass model to derive simple analytical expressions for confined state energies and in-plane effective mass [11,13]. We outline here the derivation of equivalent simple expressions based on the two-band BAC model for GaNAs heterostructures, showing that the expressions presented are very useful to treat the conduction band dispersion in actual GaNAs structures [25]. We first extend the BAC Hamiltonian to describe the variation of the conduction band dispersion with wavevector k in bulk GaNxAs12x by rewriting Eq. (11.1) as ! VNc EN þ ak2 : ð11:5Þ HðxÞ ¼ VNc Ec þ bk2 The band dispersion is introduced via the two diagonal terms involving a and b, with b ¼ ~2 =2m0 mpc ; where mpc is an appropriately chosen CBE effective mass for the host matrix, and a (usually set to zero) describes the dispersion of the nitrogen resonant band. We have used Eq. (11.5) to determine an analytical expression for the zone centre ðkk ¼ 0Þ confined state energies Ei and in-plane effective masses in a GaNAs QW structure, centred at the origin and of width 2L [25]. We outline the derivation here for even states. To find the allowed solutions we initially assume that the parameter a is small and positive, solve Schro¨dinger’s equation in the well and in the barrier, and then apply appropriate boundary conditions at the well –barrier interface. (We set a ¼ 0 at the end of the derivation, as in previous calculations [2,41,42].) We can solve Eq. (11.5) to find two states at energy E within the well, one of which ðkz2 Þ is a propagating and the other ðkzþ Þ an evanescent state, with wavevectors kz^ along the z (growth) direction. The general even two-component solutions of Schro¨dinger’s equation, CðwÞ ðzÞ; are then given within the well ðlzl , LÞ by ! ! aN2 aNþ ðwÞ cosðkz2 zÞ þ B2 coshðkzþ zÞ C ðzÞ ¼ B1 ð11:6Þ ac2 acþ

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369

where aNðcÞ^ describes the amplitudes of the states projected onto the nitrogen resonant state (unperturbed CBE state), with laN^ l2 þ lac^ l2 ¼ 1: Turning to the barrier (where Ec ¼ Ec0 at ambient pressure), to ensure wave function matching across the interface, we include a resonant state at energy EN above the CBE, and set VNc ¼ 0; as this state does not interact with the CBE. This resonant state plays no part in determining the confined state energy and wave functions, but is formally required to solve the envelope function equation. Because the resonant and CBE states are decoupled in the barrier, the evanescently decaying barrier wave function C ðbÞ ðzÞ; required to match the well solution is given in the right-hand barrier ðz . LÞ by ! ! 0 1 ðbÞ expð2kz2 zÞ þ C2 expð2kzþ zÞ C ðzÞ ¼ C1 ð11:7Þ 1 0 where bk2z2 ¼ Ec 2 E and ak2zþ ¼ EN 2 E; respectively. The allowed solutions of Schro¨dinger’s equation must satisfy appropriate boundary conditions across the interface (at z ¼ L). We require for finite a in Eq. (11.5) that each component of the wave function is continuous,

C ðwÞ ðz ¼ LÞ ¼ C ðbÞ ðz ¼ LÞ and also that a

0

0

b

!

dCðzÞ dz

ð11:8Þ

ð11:9Þ

is continuous across the interface [13,25]. We have four unknown quantities in Eqs. (11.6) and (11.7), and from Eqs. (11.8) and (11.9) four boundary conditions for even solutions of the envelope-function equation, through which we can derive a 4 £ 4 determinant which must be satisfied for allowed even solutions [25]. It can be shown that as a ! 0; the coefficients B2 and C2 also ! 0, and we require only that the conduction band component p21 of the envelope function and b times its derivative are continuous, where b / mcw in the p21 well, and /mcb in the barrier (see Figure 11.3). This leads to an expression for the confined state energy very similar to that for the conventional one-band effective mass model: kz2 k tanðkz2 LÞ ¼ z2 : mpcw mpcb

ð11:10Þ

The relationship between energy E and wavevector kz2 in the well can be determined by solving the 2 £ 2 Hamiltonian of Eq. (11.5), to give when a ¼ 0: 2 bkz2 ¼

2 VNc þ E 2 Ec : EN 2 E

ð11:11Þ

A similar expression to Eq. (11.10) can also be used for odd states, with tanðkz2 LÞ replaced by 2cotðkz2 LÞ:

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Figure 11.3. Schematic plot of the conduction band character lfc ðzÞl (solid line) and nitrogen band character lfN ðzÞl (dashed line) of the first electron state in the conduction band of a GaNAs/GaAs QW, showing that lfc ðzÞl2 is continuous across the well/barrier interface, while lfN ðzÞl2 ¼ 0 in the barrier.

To demonstrate the validity and usefulness of Eq. (11.10), Figure 11.4 shows the calculated room temperature variation of confined electron state energy as a function of well width, 2L; in a GaN0.02As0.98/GaAs QW structure. The zero of energy is taken at the GaAs CBE. The dashed line shows the results calculated using the 10-band k·p

Figure 11.4. Well width dependence of the conduction band zone centre confined state energies of GaN0.02As0.98/GaAs quantum wells calculated using a 10-band k·p Hamiltonian (dashed line), and by solving Eq. (11.10) (solid line).

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371

Hamiltonian [43] we have previously used when fitting experimental transition energies in GaNAs/GaAs QWs [24,44,45], while the solid line shows the results calculated using the analytical model of Eq. (11.10). Full details of the parameters used in Figure 11.4 are given in Ref. [25]. It can be seen that the analytical expression of Eq. (11.10) provides an excellent estimate of the ground state confinement energy and of several of the excited state energies, but starts to overestimate the 10-band excited state energies when they approach the GaAs CBE energy. This discrepancy at higher energy arises because the twolevel model overestimates the conduction band dispersion at larger wavevector k: A similar discrepancy is observed when comparing the one-band effective mass model with the results of eight-band k·p calculations in conventional semiconductor alloys [13]. We have tested and proved the two-band model of Eq. (11.10) and the 10-band k·p method by comparing calculated and experimental values of the interband transition energies in over 20 GaNxAs12x/GaAs QWs with well widths between 2 and 25 nm and 0:01 , x , 0:04, grown by molecular beam epitaxy (MBE) as well as by metal-organic vapour-phase epitaxy (MOVPE). The samples were studied by photomodulated reflectance (PR) spectroscopy at 300 K and under hydrostatic pressures up to 2.0 GPa [44 –46]. Figure 11.5 shows an example of the quality of the fit which can be obtained, comparing the experimentally determined transition energies of a series of GaNxAs12x/GaAs QWs of different width with those calculated using the 10-band k·p model and the analytical model of Eq. (11.10). The MBE-grown samples (open circles) had a composition

Figure 11.5. Comparison of transition energies in GaNxAs12x/GaAs QWs of different width extracted from photomodulated reflectance spectra with those calculated using the 10-band k·p model (dashed lines) and the analytical model of Eq. (11.10) (solid lines). Solid data points: MOVPE samples with x ¼ 1:8%; open data points: MBE samples with x ¼ 1:6%; theoretical fit assumes x ¼ 1:7%:

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x ¼ 0:016ð^0:001Þ; while the MOVPE samples (solid circles) had x ¼ 0:018ð^0:001Þ: The theoretical fit was carried out using material parameters for x ¼ 0:017: The agreement between experiment and the 10-band k·p calculation is very good throughout the series for all allowed transitions eihhi between the ith confined electron and heavy-hole states. The analytical model using the material parameters deduced from the 10-band k·p Hamiltonian gives excellent agreement with the full calculation and with experiment up to the e3hh3 transition. The differences between the models increase for higher QW transitions. This is to be expected: we have already seen in Figure 11.4 how the two-band Hamiltonian of Eq. (11.5) underestimates the conduction band non-parabolicity of GaNAs and hence overestimates slightly the confinement energy of the higher lying conduction states, ei ði . 3Þ: The excellent fit in Figure 11.5 confirms the importance of including the BAC interaction to describe the conduction band dispersion in Ga(In)NAs heterostructures. Previous studies (e.g. Ref. [47]) have shown that it is not possible to fit both the ground and excited state transition energies using a conventional eight-band k·p Hamiltonian, or assuming a parabolic conduction band dispersion. It is essential to include the strong conduction band non-parabolicity due to the BAC interaction. Nevertheless, it is important to acknowledge that the fit presented in Figure 11.5 is not unique. We can in particular vary the assumed value of the valence band offset over quite a wide range, without degrading the quality of the fit in Figure 11.5. This is initially surprising. Photoreflectance and photoluminescence excitation data played a key role in determining the band offset ratio in conventional semiconductor alloys, such as GaAs/ AlGaAs [48]. For such alloys, however, most of the key band structure parameters are known accurately from measurements on the bulk materials, and there is effectively only one parameter, the valence band offset, which can be varied when fitting to the measured interband transition energies. This is not the case for dilute nitride alloys, where there still remains uncertainty in many parameters, including, e.g. the coupling parameter VNc, nitrogen resonant state energy, EN, and even the composition dependence of the host CBE energy, Ec. As a consequence, it is possible to vary the valence band offset over a relatively wide range, and by making minor adjustments to other parameters still obtain a good fit to all of the experimental data [25]. This does not negate the model presented here, but means that further work is still required to identify the best choice for the assumed variation of valence band offset with composition. 11.3.2 Effective Masses Having shown that the two-band model of Eq. (11.5) can give electron ground and excited state confinement energies in good agreement with more complete calculations using a 10band k·p Hamiltonian, we now turn to use the two-band model to describe the electron effective mass in bulk GaNAs and within the plane of GaNAs/GaAs QW structures. The mixing between the N levels and the CBE modifies the band dispersion in GaNxAs12x

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373

relative to the uncoupled band mass. The dispersion close to the alloy band edge can be found by diagonalising the two-band Hamiltonian of Eq. (11.5) with a ¼ 0 and then retaining terms to order k2 as E2 ðkÞ ¼ E2 þ

~2 k2

ð11:12Þ

2m0 lac2 l2 mpc

where E2 ¼

ffi E N þ Ec 1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 ðEN 2 Ec Þ2 þ 4VNc 2 2

ð11:13Þ

and where lac2 l2 was introduced in Eq. (11.6) and is given (at wavevector k ¼ kz ) by 0 1 2 1B EN 2 Ec 2 bkz C ffiA lac2 ðkz Þl2 ¼ @1 þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð11:14Þ 2 ½E 2 E 2 bk2 2 þ 4V 2 N

c

z

Nc

with laN2 l2 ¼ 1 2 lac2 l2 the corresponding composition-dependent squared amplitude of the nitrogen character of the given conduction band state. Before deriving the electron effective mass in a GaNAs/GaAs QW structure, we first recall the calculation of the in-plane (parallel) effective mass, mpi ; for the ith confined subband in a conventional III– V QW structure. This is given in the one-band model by [49,50] 1 PðwÞ PðbÞ ¼ ip þ ip p mi mcw mcb

ð11:15Þ

where mpcw ðmpcb Þ describes the in-plane conduction band dispersion in the well (barrier) ðwÞ material. PðwÞ and PðbÞ are the probabilities of finding the ith confined state in i i ¼ 1 2 Pi the well and in the barrier, respectively, with PðwÞ given by i PðwÞ ¼ i

sinð2kz2 LÞ=2kz2 þ L 2

2

2

2

lac2 l cos ðkz2 LÞ=kz2 þ sinð2kz2 LÞ=2kz2 þ L

ð11:16Þ

for even states and PðwÞ ¼ i

2sinð2kz2 LÞ=2kz2 þ L lac2 l sin ðkz2 LÞ=kz2 2 sinð2kz2 LÞ=2kz2 þ L

ð11:17Þ

for odd states, where kz2 is defined in Eq. (11.11), and ac2 ¼ 1 for a one-band Hamiltonian. The continuity of Ci across the well/barrier boundary requires, using Eqs. (11.8) and (11.9) for the one-band model, that B1 cosðkw LÞ ¼ C1 expð2kb LÞ

ð11:18Þ

for even states, where kw and kb are the one-band analogues of kz2 and kz2 ; respectively. PðwÞ 1 typically starts to decrease for the ground state band as the well width, 2L; drops

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below about 5 nm in a conventional QW [51,52]. This is due both to a reduction in the integration range in Eqs. (11.16) and (11.17), and also because the value of kb gets smaller in the barrier region, both of which effects lead to significant wave function penetration into the barrier. The calculated wave function penetration and in-plane mass can be determined in the two-band model using first-order perturbation theory, with the in-plane band edge effective mass, mpi given by ðwÞ 1 PðbÞ 2 Pi i ¼ l a l þ c2 mpi mpcw mpcb

ð11:19Þ

where mpcw is the unperturbed conduction band mass in the well material (bottom righthand term of Eq. (11.5)). Eq. (11.19) leads to a modified behaviour compared with Eq. (11.15). Firstly there is significantly less wave function penetration into the barrier. This arises because the boundary condition equivalent to Eq. (11.18) is given in the two-band model by

ac2 ðkz2 ÞB1 cosðkz2 LÞ ¼ C1 expð2kz2 LÞ

ð11:20Þ

and as ac2 ðkz2 Þ decreases with increasing confinement energy, due to the BAC effects, so too will the relative magnitude of C1 : In other words, wave function matching only occurs with the conduction band component of the well wave function, as illustrated previously in Figure 11.3. As the confinement energy increases, the reduction in ac2 ðkz2 Þ tends both to reduce the wave function penetration into the barrier, and also to increase the average effective mass within the well. Hence the zone-centre effective mass, mpi ; tends to increase with decreasing well width, and also with increasing confinement energy (increasing i) for a fixed well width [25].

11.4. INFLUENCE OF DISORDER ON NITROGEN RESONANT STATES, E2 AND E1 IN GaNxAs12x

Overall, Figures 11.1 and 11.2 clearly demonstrated that the CBE in GaNxAs12x is being perturbed and pushed downwards due to its interaction with a higher lying resonant state, centred on the nitrogen atoms. This justifies the introduction and application of the twolevel BAC model to describe bulk and low-dimensional Ga(In)NAs samples. The calculations in Section 11.2 assumed ordered GaNxAs12x structures. How will the inevitable disorder present even in a random alloy modify the conclusions of the previous sections? To answer this question, we now extend the tight-binding and two-level model to disordered GaNxAs12x supercells. We first consider a set of 1000 atom supercells containing up to 15 randomly distributed N atoms. In these supercells we fit the number, but not the distribution, of N – N pairs

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to the number given statistically, so that each cell contains n isolated N sites and p N – N pairs. For each configuration, we used the GULP molecular relaxation package [53] to calculate the equilibrium positions of all the atoms, using a parameterised valence force field (VFF) model, while using Ve´gard’s law to vary the unit cell basis vectors as aðxÞ ¼ xaGaN þ ð1 2 xÞaGaAs : The calculated relaxed bond lengths are in good agreement with those obtained from ab initio pseudopotential calculations [39]. In a disordered supercell, we again expect the GaNxAs12x CBE to be formed as a Linear Combination of Isolated Nitrogen resonant States (LCINS) interacting with the unperturbed CBE, lcc0 l (LCINS model). For the supercells considered here, we have n resonant basis states, lcN0;i l; associated with isolated N resonances ði ¼ 1 2 nÞ and 2p resonant basis states associated with the p N – N pairs (lcNNþ;j l and lcNN2;j l; j ¼ 1 2 p; which are even and odd, respectively, about the Ga site at the centre of the N – N pair. We write the sp3sp Hamiltonian H of the Ga500Nnþ2pAs5002n 2 2p supercell as H ¼ H0 þ DVN þ DVNN

ð11:21Þ

where H0 is the Ga500As500 Hamiltonian, DVN the sum of defect potentials associated with the n isolated N atoms and DVNN the sum of defect Hamiltonians associated with the p N –N pairs. In extension of the approach for ordered structures, we now determine the GaNxAs12x CBE E2 and the N-related conduction band levels by constructing and solving a ðn þ 2p þ 1Þ £ ðn þ 2p þ 1Þ Hamiltonian matrix involving the GaAs CBE wave function, lcc0 l; and the n þ 2p N-related states. We use the sp3sp Hamiltonian to evaluate explicitly each matrix element, Hab ¼ kca lHlcb l

ð11:22Þ

where a and b ¼ N01 ; …; N0n ; NNþ1 ; …; NNþp ; …; NN21 ; …; NN2p and c0. We also evaluate the overlap matrix, S; which has non-zero off-diagonal matrix elements Sab ¼ kca lcb l; due to the overlap between N resonant states centred on different sites within the supercell. The eigenvalues 1a of the LCINS model are then obtained by solving the matrix equation Hua ¼ 1a Sua

ð11:23Þ

with the eigenstates fa then given by

fa ¼

n X i¼1

uaN0;i cN0;i þ

p X

ðuaNNþ; j cNNþ; j þ uaNN2; j cNN2; j Þ þ uac0 cc0 :

ð11:24Þ

j¼1

Figure 11.6 shows the results of the CBE energy and its G1c character calculated using the full tight-binding (filled squares) and LCINS (open triangles) methods for five significantly different random structures of a 1000 atom Ga500NmAs5002m supercell containing (i) m ¼ 5; (ii) m ¼ 10 and (iii) m ¼ 15 nitrogen atoms. The figures clearly show that both the CBE energy and its fractional G1c character are given accurately by

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Figure 11.6. Variation in (a) the conduction band edge energy, and (b) its fractional G1c character between several different random Ga500NmAs5002m supercell structures calculated using the full tight-binding (filled squares) and LCINS (open triangles) methods for m ¼ (i) 5, (ii) 10 and (iii) 15.

the LCINS model. There is excellent correlation in the variation between different random structures. For example, in the supercell calculations containing m ¼ 15 N atoms, the maximum variation in CBE energy between different random structures is , 70 meV, while the maximum variation in CBE energy between the LCINS and full tight-binding calculations is only , 7 meV. This excellent correlation confirms the validity of describing the E2 state, and the band gap bowing, as being due to an interaction between localised N resonant states and the host CBE. The Eþ state was observed in photoreflectance measurements [22,23], appearing in GaNxAs12x for x * 0:2% and remaining a relatively sharp feature until x , 3%; beyond which composition it broadens and weakens. The Eþ state was also observed at low N concentrations in pseudopotential calculations, but proved difficult to track to higher compositions [17]. Using the LCINS model, we identify here why Eþ is difficult to observe at higher compositions, by explicitly projecting the LCINS Eþ eigenvector fþ onto the eigenstates of a series of full sp3sp calculations. We will further consider the low composition case ðx & 0:2%Þ in the next section. The top six panels in Figure 11.7 show the evolution of the Eþ state as given by the full sp3sp Hamiltonian and highlighted using

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Figure 11.7. Projection of the LCINS Eþ level onto the conduction band states of disordered 1000-atom GaNxAs12x supercells, with x ¼ 0.4, 0.8, 1.0, 1.4, 2.0 and 3.0%, showing the broadening of the Eþ resonance in the L-related GaAs density of states (shown on a similar scale in [eV-atom]21). The arrow indicates the position of the LCINS Eþ level. The bottom two panels show the broadening of the Eþ level for x ¼ 1% with increasing hydrostatic pressure, when Eþ becomes degenerate with the X-related density of states. Note the change in the y-axis scale on the different panels.

LCINS for a series of 1000 atom supercell structures containing between 0.4 and 3% of randomly distributed N atoms. The first four panels ðx ¼ 0:4 – 1:4%Þ show Eþ as a very strongly highlighted feature, with a long, quickly decaying tail over higher energy states. The Eþ state begins to break-up and spread out significantly in the next two panels (x ¼ 2:0 and 3.0%). This change in the nature of Eþ is consistent with experiment, which shows a relatively strong feature at Eþ for x , 1% and which then becomes weaker and broader with increasing x up to , 3% where it is hardly distinguishable at all [22]. We conclude that the strength of the resonance peak depends on where Eþ lies in the density of states of the host system, forming a sharp resonance in the conduction band G-related density of states at low x; which broadens rapidly at higher N composition when the Eþ energy becomes degenerate with the larger L-related density of states. A similar effect can be observed with the application of hydrostatic pressure, which shifts the G conduction states up and X states down in energy with respect to the L conduction band edge.

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This is illustrated in the bottom two panels of Figure 11.7, which show the broadening of the Eþ level as the X level moves down with increasing pressure, and Eþ becomes degenerate with the X-related density of states. Overall, we conclude from our detailed analysis of the full band structure calculations that the CBE in GaNxAs12x is indeed being perturbed and pushed downwards due to its interaction with a higher lying band of localised nitrogen resonant states. We now turn to consider the effects of this band of localised nitrogen states on the conduction band dispersion and, in particular, on the band edge effective mass.

11.5. CONDUCTION BAND STRUCTURE AND EFFECTIVE MASS IN DISORDERED GaNxAs12x

We can gain further insight into the band structure of a disordered GaNNMAsN2M supercell by first diagonalising the M £ M matrix linking the individual N states, lca l; to get M nitrogen cluster states, fNl ; with energy 1l and then evaluating the interactions between the set of cluster states fNl and the CBE, cc0 : Figure 11.8(a) shows (i) the N state energies 1l and the CBE self-energy kcc0 lHlcc0 l (thin line) of an exemplar Ga500N13As487 disordered supercell (x ¼ 2:6%; 2N – N pairs included), and (ii) the calculated zone-centre

Figure 11.8. (a) Calculated N cluster state energies 1l and CBE energy in a Ga500N13As487 supercell (i) before and (ii) after inclusion of interaction with CBE; (b) supercell band dispersion calculated using tight-binding (dots) and LCINS method (solid lines).

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379

eigenvalues due to interactions between these cluster states and the unperturbed CBE state, cc0 : The dots in Figure 11.8(b) show the band dispersion along the z-direction of this supercell, calculated using the full tight-binding method. Very good agreement is obtained at the zone centre between the full calculations and the LCINS results, further confirming that the LCINS method describes well both the CBE and the series of N-related states which lie above the CBE. The solid lines in Figure 11.8(b) show the LCINS conduction band dispersion away from the zone centre, calculated using a k·p model which includes the standard Kane matrix element linking the valence band maximum with the unperturbed CBE state, cc0 [21,54]. The close agreement between the LCINS k·p and the full tight-binding calculations for the lowest conduction bands confirms the validity of describing these states in terms of interactions between localised (but interacting) N resonant states and the unperturbed host matrix CBE. Because N introduces such a strong perturbation, the results of an individual calculation such as those in Figure 11.6 or 11.8 depend strongly on the statistical distribution of the N atoms, including, e.g. the number of N – N pairs in the cluster, and the presence or otherwise of larger and less common N clusters. How then can we probe the average conduction band properties of randomly disordered GaNxAs12x alloys? Figures 11.2, 11.6 and 11.8 each demonstrate the importance of the nitrogen cluster state energies 1l ; and the strength of their interactions Vl ¼ kfNl lHlcc0 l with the CBE. We therefore investigate key aspects of the conduction band electronic structure by placing M ¼ 8000 – 10; 000N atoms at random in an ultralarge GaNxAs12x supercell, with the composition x determined by the size of the supercell considered. The large values of M are chosen to ensure minimal statistical variation between different random supercells. The histograms in Figure 11.9 show the distribution of the N state energies 1l ; and their interaction with the CBE state cc0 for x ¼ 0:1; 0.2, 0.84 and 1.8%, respectively, where we plot in each case VN ðEÞ ¼

X

lVl l2 TðE 2 1l Þ

ð11:25Þ

where TðxÞ is a top-hat function of width 2 meV and unit area. It can be seen that for very low N composition ðx #, 0:2%Þ; most of the interaction arises from states which lie close to the isolated N resonant level energy (EN ¼ 1:666 eV at 300 K; 1.706 eV at 0 K in our calculations). A small feature due to N –N pairs is observed about 1.446 eV at 300 K (1.486 eV at 0 K), with another weak feature at 1.594 eV at 300 K (1.634 eV at 0 K), due to second-neighbour N atoms on opposite corners of a cubic unit cell face. The energy spectrum of the N cluster states broadens considerably at higher N compositions, and a small number of isolated N states start to be observed below the N – N pair states, due to the random formation of a small proportion of larger N clusters in the supercell.

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Dilute Nitride Semiconductors

Figure 11.9. Calculated distribution of N cluster state energies, 1l at low temperature, weighted by their interactions, lVl l with the conduction band edge state for four bulk GaNxAs12x compositions, with x ¼ 0:1; 0.21, 0.84 and 1.80%, respectively.

Extending the BAC model to these ultralarge supercells, we now calculate the effects of the interaction between these bands of N-related states and the unperturbed CBE wave function, cc0 ; diagonalising the ðM þ 1Þ £ ðM þ 1Þ matrix linking cc0 with the M N-related levels. Figure 11.10 shows the calculated LCINS spectrum projected onto the unperturbed CBE wave function, X GG ðEÞ ¼ laGi l2 T2 ðE 2 Ei Þ ð11:26Þ where aGi is the amplitude of the ith eigenstate, of energy Ei ; on cc0 ; and T2 ðxÞ is a narrow top-hat function of unit height. The results in Figure 11.10 and related calculations are in excellent agreement both with the BAC model and with experiment. Firstly, the interaction between the N resonant states and the CBE pushes the band edge downwards in energy. We find that the CBE (defined as the low energy state with greatest G character)

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381

Figure 11.10. Calculated LCINS spectrum projected onto the unperturbed conduction band edge wave function cc0 for four bulk GaNxAs12x compositions, with x ¼ 0:1; 0.21, 0.84 and 1.80%, respectively.

passes through the N –N pair states between x ¼ 0:1 and 0.2% at low temperature, consistent with experiment [23]. The CBE shifts further down in energy relative to the N – N pair states at 300 K. Secondly, we observe the emergence of the Eþ level, with a single state with significant G character observed at higher energies for x * 0:2%: The Eþ level is not observed in GaNxAs12x samples with x # 0:1%: We see from Figure 11.10 that this is due to the width of the band of N-related resonant states even at such low N compositions: the Eþ state from the BAC model is degenerate and thus hybridises with this relatively wide N-related band, and so is not observed experimentally until higher nitrogen compositions. One key feature of Figure 11.10 is contrary to the two-level BAC model. When the CBE and N band interact with each other in Eq. (11.1), the fractional G character, fGc ;

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Dilute Nitride Semiconductors

of the lower eigenvalue, E2, must always exceed 50% ðfGc . 0:5Þ: We see in Figure 11.10, e.g. for x ¼ 0:2% that fGc ¼ 0:52; while fGc ¼ 0:32 for x ¼ 1:8%: The reduced values of fGc occur when E2 is close in energy with N – N pair or other cluster states. Because of this accidental (near-)degeneracy, E2 hybridises with these N-related states, thus leading to the reduced fGc value. In the k·p model of Figure 11.8, the CBE effective mass is approximately proportional to the energy gap, and inversely proportional to fGc and the valence band fractional G character, fGv : The filled circles (triangles) in Figure 11.11 show the low temperature electron effective mass determined by a range of experimental techniques in bulk (QW) GaNxAs12x samples [3 – 6]. The solid line shows the predicted variation of the band edge effective mass in bulk GaNxAs12x using the two-level BAC model of Eq. (11.5) [41]. This model significantly underestimates the measured mass even for x as low as 0.1%. The open symbols show the low temperature mass calculated for selected compositions, x, using the LCINS model, where we assume that mpe ¼ mpe0

Eg ðxÞ Eg0 fGc fGv

ð11:27Þ

with mpe0 ¼ 0:0667 and Eg0 ¼ 1.512 eV for GaAs. Eg ðxÞ is the LCINS calculated energy gap, and fGv is taken to vary [55] as 1 2 x:

Figure 11.11. Solid data points: measured low temperature electron effective mass mpe in bulk (circles) and QW (triangles) samples. Open symbols (solid line): mpe calculated using LCINS (BAC) method. Inset: calculated variation of mpe with pressure in a bulk GaN0.002As0.998 epilayer at T ¼ 0 K:

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383

The calculated and experimental data are in remarkable agreement with each other, confirming that hybridisation between the conduction band edge and nitrogen cluster states causes the observed enhancement of effective mass values. The density of N cluster states close to E2 varies both with composition x and with hydrostatic pressure p at a fixed composition in Ga12yInyNxAs12x. The inset in Figure 11.11 shows the predicted variation of mpe with hydrostatic pressure, p, at T ¼ 0 K in a GaN0.002As0.998 bulk epilayer. The mass mpe will initially increase with pressure, as the band edge passes through the N –N pair states, and should then drop rapidly with pressure towards the BAC value in the range of 0.5– 1.5 GPa, before again increasing as hybridisation with higher lying N states occurs about 2 GPa. We also include negative pressure (to 2 2 GPa) in the inset. Although this cannot be achieved directly, a similar effect can be achieved by adding indium, because the CBE moves down relative to the nitrogen states with increasing y in Ga12yInyNxAs12x, thus accounting for the BAC-like masses observed in GaInNAs samples [5]. The application of hydrostatic pressure to GaInNAs should cause a significant increase in mpe ; as the CBE passes through the lowest N-related levels. We note also from Figure 11.11 that there can be a very low density of N cluster states close to E2 at moderate N composition (e.g. x , 0:8%), giving a value of mpe close to the BAC value in such samples. We see from Figure 11.11 that a near-degeneracy with N cluster states significantly changes the band dispersion at the conduction band minimum. How will higher energy N states affect the conduction band dispersion? To address this issue, we have used a modified k·p model to calculate the conduction band dispersion for a series of bulk GaNxAs12x structures, adding a valence band state lcv0 l to the LCINS model of Section 11.4, and including a k-dependent Kane matrix element, k·p, linking lcv0 l to the LCINS host matrix conduction band state lcc0 l: Figure 11.12 shows the conduction band dispersion calculated for bulk GaNxAs12x with x ¼ (a) 0.2%, (b) 0.84% and (c) 1.8%, respectively. The dispersion is presented both for (i) T ¼ 0 K and (ii) T ¼ 300 K. The thick data points show LCINS states with . 10% G1c character; the thin data points are for 0.5– 10% G1c character, while the grey shading indicates states with 0.1– 0.5% G1c character. The zero of energy is taken relative to the GaAs valence band maximum. The inclusion of N cluster states modifies the calculated band dispersion compared with that expected using the two-level BAC model of Eq. (11.5). At very low N compositions ((a), x ¼ 0.2%), two anti-crossing features are found in the lowest CB, one near the band minimum due to interactions with N – N pairs, and a second at about 1.6 eV, due to N – N second neighbours. With increasing N composition, the anti-crossing with the N –N pair states becomes more pronounced and the concept of a band dispersion starts to break down at larger k values (e.g. for (c) x ¼ 1.8%, k * 0:1p=a; E . 1:4 eVÞ: The BAC model has been widely applied to investigate the conduction band dispersion in Ga(In)NAs, being used, e.g. both to analyse the gain characteristics of GaInNAs/GaAs

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QW laser devices [43,56,57], and also to interpret excited state transition energies in Ga(In)NAs QW structures [24,25]. Although Figure 11.12 shows that the BAC model can break down at higher energies, we conclude that it is still generally valid for such applications, particularly at room temperature. Firstly, comparing Figures 11.12(i) and (ii), we see that the breakdown of band dispersion in GaNxAs12x occurs further from the band edge at 300 K than at 0 K, because of the difference in relative temperature dependence of the nitrogen state and CBE energy [23,58]. Secondly, previous calculations have shown that replacing gallium by indium in GaInNAs shifts the host CBE downwards, and also pushes the energy of the N cluster states upwards relative to the cluster state energies in GaNAs. We conclude therefore that the range of applicability of the two-level BAC model increases both with temperature and with indium content. Nevertheless, it may now be worthwhile to re-consider the interpretation of some previous photoreflectance measurements, particularly where unexpected features were observed in the spectra [59], to see if some of these features might be due to BAC with lower lying N-related defect levels.

Figure 11.12. Conduction band dispersion calculated for bulk GaNxAs12x using LCINS method, with x ¼ (a) 0.2%, (b) 0.84% and (c) 1.8%, respectively. The dispersion is presented both for (i) T ¼ 0 K and (ii) T ¼ 300 K.

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Figure 11.12. Continued (T ¼ 300 K).

11.6. ALLOY SCATTERING AND MOBILITY IN DILUTE NITRIDE ALLOYS

There was until recently little progress in developing models to describe the transport and mobility properties of dilute nitride alloys. Even for idealised random alloys, these properties are difficult to analyse precisely because N introduces such a strong perturbation to the band structure of Ga(In)As. This must lead to strong alloy scattering. There is a well-established model [60], based on the Born approximation, to describe the relatively weak alloy scattering which occurs in conventional semiconductor alloys. This model is, however, entirely insufficient for extreme alloys such as GaNAs, underestimating the alloy scattering cross-section by over two orders of magnitude [28,37]. We describe below how the strong scattering due to N atoms substantially limits the electron mobility in dilute nitride alloys, consistent with the maximum mobility observed experimentally of order 1000 cm2/V s [61]. We have calculated the scattering cross-section for an isolated N impurity in GaAs using S-matrix theory (distorted Born wave approach). This was previously applied to successfully describe resonant scattering due to conventional impurities in GaAs [62,63]. For a sufficiently localised perturbation, DVN, the total scattering cross-section s for

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Dilute Nitride Semiconductors

an isolated impurity is given by

 1 mp 2 s¼ lkcc1 lDVN lcc0 ll2 V2 p ~2

ð11:28Þ

where m p is the electron effective mass at the band edge and V is the volume of the region in which the wave functions are normalised. The state cc0 is the G-point conduction band Bloch wave function (in the absence of the N atom) and cc1 is the exact band-edge state in the presence of the N atom. The Born approximation is equivalent to setting cc1 ¼ cc0 in the required matrix elements. It is often used in the discussion of conventional alloy and impurity scattering [60] but is entirely inadequate for the case of N defect scattering in GaAs. Consider a perfect crystal for which the electron Hamiltonian is H0 and the CBE state has wave function cc0 and energy Ec0. When we introduce a single N atom into a large volume V of the otherwise perfect lattice, the new Hamiltonian, H1 ¼ H0 þ DVN ; leads to a modified band edge state cc1 with energy Ec1. We re-write the scattering matrix element as kcc1 lDVN lcc0 l ¼ kcc1 lH1 2 H0 lcc0 l ¼ ðEc1 2 Ec0 Þkcc1 lcc0 l:

ð11:29Þ

Because kcc1 lcc0 l ! 1 for sufficiently large V; we derive that at low impurity concentrations

Vkcc1 lDVN lcc0 l ¼

dEc dn

ð11:30Þ

where Ec is the CBE energy and n is the number of impurities per unit volume. Substituting Eq. (11.30) in Eq. (11.28), and noting that n is related to the concentration x by n ¼ 4x=a30 ; where a0 is the GaAs unit cell dimension, the scattering cross-section for an isolated impurity is then given by

p 2   1 m dEc 2 6 s¼ a0 : ð11:31Þ 16p ~2 dx This result is key: it establishes a fundamental connection between the composition dependence of the CBE energy and the n-type carrier scattering cross-section in the ultradilute limit for semiconductor alloys, imposing general limits on the carrier mobility. We show this by using an independent scattering model to extend the isolated N result of Eq. (11.31) to the case of a dilute nitride alloy, GaNxAs12x. In such a model, the mean free path l of carriers depends on the scattering cross-section s for a single defect and the number of defects n per unit volume as l21 ¼ ns: Assuming such a classical model and the values of m p and dEc/dx at x ¼ 0; we estimate for a N content of 1% a mean free path of only 15 nm. This is still more than an order of magnitude larger than the average N separation, suggesting that an independent scattering model should remain appropriate in

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Figure 11.13. Room temperature variation of alloy-scattering-limited electron mobility, m, in GaNxAs12x, calculated using Eq. (11.32).

the dilute random alloy. The mobility m is related to the mean free path l as m ¼ et=mp ; with the scattering time t ¼ l=u; where u is the electron root mean square speed. Setting u 2 ¼ 3kT=mp ; where T is the temperature, we estimate that the mobility m is given by [28]

m

21

pffiffiffiffiffiffiffiffiffi p 2   dEc 2 3 3mp kT m ¼ a0 x: 4pe dx ~2

ð11:32Þ

Figure 11.13 shows the estimated variation of the room temperature electron mobility with x in GaNxAs12x, calculated allowing both m p and dEc =dx to vary with x based on the two-level model of Eq. (11.5). The electron mobility is estimated to be of order 1000 cm2/V s when x ¼ 1%; of similar magnitude to the highest values observed to date in dilute nitride alloys [61] but larger than that found in many samples, where m , 100 – 400 cm2 =V s [2,27,64 –67]. We note that factors omitted in the calculation here, including the influence of N –N nearest-neighbour pairs and clusters [16,34], may contribute to limiting the mobility in actual samples [37]. In addition, film quality and composition fluctuations may also play a role in some samples. The intrinsic alloyscattering-limited mobility should be larger in GaInNAs samples, due to the weaker band gap bowing observed in indium-containing samples [24].

11.7. CONCLUSIONS

In summary, we have reviewed some of the insights gained using the tight-binding method to analyse the BAC model, and its application to describe the electronic structure of GaInNAs and related alloys. Using the tight-binding method, we confirmed that N forms

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a resonant state above the CBE in Ga(In)As, and that the interaction of the N resonant states with the CBE accounts for the strong band gap bowing observed in Ga(In)As. We explicitly demonstrated that the alloy CBE (often referred to as the E2 level) can be described very accurately by the BAC model, in which we treat the nitrogen levels explicitly using a linear combination of isolated nitrogen resonant states (LCINS). We also use the LCINS results to identify a higher lying resonance (the Eþ level) in the full tightbinding calculations, showing that at low N composition Eþ forms a sharp resonance in the conduction band G-related density of states, which broadens rapidly at higher N composition when the Eþ level rises in energy to become degenerate with the larger Lrelated density of states. We then presented an analytical technique based on the BAC model to calculate both the electron confined state energies and conduction band dispersion in Ga(In)NAs square QW structures. This analytical model provides a consistent fit to the ground and excited state transition energies measured across a wide range of samples. The model can be readily applied to describe any GaInNAs-based QW structures. Turning to the conduction band dispersion, we showed that the two-level BAC model must be modified to give a quantitative understanding of measured electron mass values. We demonstrated that the unexpectedly large electron effective mass values observed in some GaNAs samples are due to hybridisation between the CBE and nitrogen states close to the band edge. Finally we showed that there is a fundamental connection between the strong composition-dependence of the CBE energy and the n-type carrier scattering cross-section in Ga(In)NxAs12x alloys, imposing general limits on the carrier mobility, comparable to the highest measured mobility in such alloys. We conclude that the methods and insights presented here provide a very good basis for further investigation and analysis of this material which is fascinating both for its fundamental properties and also because of its potential device applications.

ACKNOWLEDGEMENTS

We would like to thank many colleagues for useful discussions and collaboration on the electronic structure of GaInNAs. These include Alf Adams, Aleksey Andreev, Stelios Choulis, Robin Fehse, Jo¨rg Hader, Jeff Hosea, Stephan Koch, Henning Riechert and Bernie Weinstein. We are grateful for financial support from Science Foundation Ireland, EPSRC (UK), and DFG (Germany).

REFERENCES [1] Weyers, M., Sato, M. & Ando, H. (1992) Jpn. J. Appl. Phys., 31, L853. [2] Skierbiszewski, C. (2002) Semicond. Sci. Technol., 17, 803.

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Dilute Nitride Semiconductors M. Henini (Ed.) q 2005 Elsevier Ltd. All rights reserved.

Chapter 12

Electronic Structure Evolution of Dilute III – V Nitride Alloys P.R.C. Kent University of Tennessee, Knoxville, TN 37996, USA

12.1. INTRODUCTION

Interest in the dilute nitrides has been primarily motivated by the large band gap bowing readily observed in few percent nitrogen GaPN and GaAsN samples. However, many other properties are now known to be different from conventional non-nitride alloys, such as GaAsP and InGaAs. Chief among these differences are the appearance of localized impurity levels within the band gap seen in photoluminescence (PL), high effective masses, anomalous pressure dependence, and Stokes’ shift between emission and absorption. In this chapter, we review the theoretical atomistic approaches that have successfully explained this heterogeneous behavior in GaAsN, GaPN, InGaAsN, and related materials. A careful comparison with experimental results is given in conjunction with the calculated data. 12.2. PHENOMENOLOGY OF DILUTE III –V NITRIDES

Mixed anion nitrides exhibit a duality in their electronic and transport properties, showing both homogeneous (bulk-like) and heterogeneous (fluctuating) behavior. One observes homogeneous, bulk-like characteristics, such as resonances within the continua, rigid shift of the conduction band with temperature and pressure, the appearance of new bulk-like absorption edge such as Eþ and a split E1 : Significantly, the popular “band anticrossing” (BAC) model of Shan et al. [1] only addresses this homogeneous behavior. However, one also notes characteristics of heterogeneous localization centers and alloy fluctuations, such as a distribution of various nitrogen pairs and clusters whose levels are within the forbidden energy gap, Stokes’ shifts between emission and absorption, emission blue shift upon increased excitation power, band tails with long decay times and asymmetric line shapes. These heterogeneous localization characteristics are particularly apparent in PL (versus absorption) and pertinent to the design of photo-emitting devices such as LEDs and lasers. E-mail address: [email protected]

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Theoretical approaches to the electronic structure of alloys can be divided into isomorphous and polymorphous models. In an isomorphous (“single shape”) model, one considers a single (or very few) atomic environment(s) that span the entire alloy structure. Clearly, explicit consideration of lattice relaxation, localization, and charge-transfer effect is excluded in such high-symmetry models. The most popular isomorphous alloy model applied to the dilute III– V nitrides is the BAC [1], in which the alloy is constructed from a single substitutional nitrogen impurity, embedded in the host, e.g. GaAs, with a composition-dependent coupling to the conduction band minimum (CBM). This model treats only the perturbed host states (PHS), but in describing the alloy in terms of a single impurity motif, it ignores fluctuations due to inhomogeneities. Although this model permits remarkable fitting to measured bulk-like absorption quantities such as composition, pressure and temperature-dependent band gaps Eg ðxÞ; Eg ðpÞ; and Eg ðTÞ; the entire phenomenology of alloy fluctuation behavior evident experimentally remains unexplained. Furthermore, the dimension of alloy electronic structure evolution with composition is lost because the composition dependence underlying the model is, by construction, smooth. Polymorphous (“many shapes”) alloy models focus on the central property that distinguishes disordered random alloys from ordered compounds, namely the existence of many distinct local atomic environments [2,3]. Critically, these models are able to address both the bulk-like features addressed by the isomorphous models and, in addition, properly address the characteristics due to heterogeneous localization centers and alloy fluctuations. The empirical pseudopotential approach [4,5] successfully describes the transition between the two types of behavior as a function of concentration and pressure. In GaP12xNx for example, the Ga atom can be surrounded by five distinct near-neighbor structures, PmN42m with 0 # m # 4; nitrogen pairs can have arbitrary separation in the alloy, etc. Even a random distribution of impurities creates clusters by chance. Once different local environments are acknowledged, the phenomena of localization and fluctuation follow naturally. For example, some impurity clusters may induce a large enough perturbation with respect to the bulk to split a level into the gap. Different clusters then create different levels, leading to an inhomogeneous distribution. Like in the isomorphous alloy models, PHS are allowed. However, unlike such models, cluster states (CS) are also included, and these two types of states can interact. The plurality of different CS is responsible for most of the characteristics of dilute nitrides observed in PL. Here, we review a polymorphous model of dilute III – V nitrides [4,5] based upon large-scale atomistic supercell calculations and the empirical pseudopotential method (EPM). This model provides a straightforward explanation of a wide variety of experimentally observed phenomena, whether observed in PL or absorption and photoluminescence excitation (PLE). These calculations are also able to address the issue of short-range ordering in quaternary alloys, such as InGaAsN, with only simple

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extensions. In the following sections, we review the details of the method and give a detailed comparison with experiment.

12.3. EMPIRICAL PSEUDOPOTENTIAL METHODOLOGY

In this section we review the key features of the EPM. This method satisfies the key requirements for modeling the dilute nitrides: many different local environments are explicitly included through the use of large, atomistically relaxed supercells, and accurate band gaps and impurity levels are obtained through the use of carefully fit pseudopotentials. A recent overview of the method, although in the context of InGaAs alloys and InAs/GaAs superlattices, has been given in Ref. [6]. 12.3.1 Atomistic Geometries The first step in any atomistic band-structure calculations consists of describing the microstructure and nanostructure of the system under investigation. We do so by generating supercells, and distribute cations and anions at the corresponding atomic sites of these supercells. This distribution must be consistent with the investigated atomic ordering, if any, as well as with the intended alloy concentration. Furthermore, when studying disordered alloys, the atomic distribution must be random and the supercells must be as large as possible in order to reproduce the different possible chemical environments. It is often necessary to average the physical properties of different supercell realizations of random alloys to be able to accurately predict the properties of the actual physical system, due to practical limitations in the size of supercell that can be easily calculated. The following geometries were used as “input” in recent EPM studies: isolated nitrogen, pairs, clusters, random alloys, and disordered alloys with short range order (SRO), etc. 12.3.1.1 Atomic and Structural Relaxation. Once the atomic configuration has been decided, atomic relaxation must be taken into account to be able to accurately reproduce the electronic properties of nitride alloys. Neglecting or poorly approximating atomic relaxation leads to incorrect predictions of electronic and optical properties [7]. This implies that the atoms, initially placed at the ideal sites of the underlying lattice, should move away from these ideal locations to the positions corresponding to the minimum total energy. However, unlike conventional ab initio techniques, the EPM scheme is not a total energy method and does not provide forces, but rather “only” band energies and wave functions. The relaxed atomic positions must therefore be obtained from an independent technique; typically the valence force field method (VFF) is used [8,9]. In this method

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the forces between atoms are calculated using a simple “balls and springs” Hamiltonian (or Keating potential) which includes both bond-stretching (a) and bond-bending (b) terms. The parameters of the VFF method that are typically used are fit to experimental elastic constants [9] for non-nitrides, and fit to LDA results [10] for nitrides. Despite its simplicity, the VFF approach was demonstrated to yield a good agreement with firstprinciples results for the internal atomic coordinates of anion-mixed nitride alloys [5,11]. 12.3.1.2 Construction and Fitting of Atomic Pseudopotentials. The crystal potential VðrÞ is written as a superposition of screened atomic pseudopotentials va ðrÞ; where a ¼ Ga, In, N, As, etc. These modern pseudopotentials are (i) specified continuously at all reciprocal lattice vectors (and hence can be applied to large unit cells), (ii) fit to the bandoffsets of the different fitted materials, (iii) fit to the measured bulk effective masses and LDA-calculated deformation potentials, (iv) local-environment dependent, and (v) explicitly depend on strain. The pseudopotential for each atom is written as a product va ðq; 1Þ ¼ va ðqÞ½1 þ gTrð1Þ;

ð12:1Þ

and va ðqÞ ¼

X

al;a expð2bl;a ðq 2 cl;a Þ2 Þ

ð12:2Þ

l¼1;4

where al;a ; bl;a ; cl;a ; and g are fitted parameters, and 1 is the local strain tensor at each atomic site. Potentials satisfying conditions (i) –(v) were used in many recent applications. Initially the EPM did not use the strain dependent term [11], i.e. g ¼ 0; although strain was implicitly included in the fit. This term permits an improved fit of the individual deformation potentials of the valence band maximum and conduction band minimum states. This form of potential was used for GaAsN and GaPN alloys in Refs. [4,5,12,13]. In later work by Bellaiche et al. [14,15], the strain part of Eq. (12.1) was refined by incorporating two different strain contributions: the microscopic (local) 1mi strain—which occurs in any alloy made of lattice-mismatched compounds—and the macroscopic (homogeneous) 1ma strain—which for instance appears when applying pressure to a material. In this case, the pseudopotential was written as va ðq; 1mi ; 1ma Þ ¼ va ðqÞ½1 þ gTrð1ma Þ½ðgmi þ xfmi ÞTrð1mi Þ

ð12:3Þ

where x is the nitrogen composition of the nitride alloys, and where the microscopic strainrelated gmi and fmi parameters are fitted to reproduce some selected properties of ternary alloys. This refined strain formulation and new fitted potentials were used in Refs. [14 –18] to study (Ga,In)(As,N) and Ga(As,P,N). These calculations most accurately reproduced the experimentally observed band gaps, particularly for epitaxially strained systems. However, the qualitative physical picture and trends were found to be unchanged.

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12.3.1.3 Solving the Supercell Hamiltonian. Once the relaxed atomic configurations are obtained via VFF and the atomic pseudopotentials are constructed, we can use the EPM technique to calculate the optical and electronic properties of very large supercells, typically up to 30,000 atoms [19]. Practically, the electronic eigenfunctions of the Hamiltonian ( ) 1 2 X 2 7 þ va ðRa;n Þ ci ¼ 1i ci ð12:4Þ 2 a;n expanded in a plane-wave basis

Cj ðrÞ ¼

G max X

AjG eiGr :

ð12:5Þ

G

The eigenfunctions and eigenvalues of this Hamiltonian are determined by using the folded spectrum method [20]. This numerical technique produces single-particle eigensolutions in a given energy window without having to obtain and orthogonalize to lower energy eigensolutions. As a result, the overall method scales linearly in computational time with the number N of atoms in the supercell, while conventional band structure methods—that require both self-consistency of the crystal potential and knowledge of all occupied levels—exhibit a time scaling of N 3 : Although plane waves have been used in all nitride calculations of this sort, alternate approaches such as realspace finite difference or multigrids are also applicable. 12.4. ELECTRONIC STRUCTURE EVOLUTION OF DILUTE NITRIDES

Based on the calculated results, the evolution of the electronic structure can be divided into three regions: (i) dilute impurity physics, (ii) an intermediate nitrogen concentration regime where the duality of localized and delocalized states is most evident, and (iii) a nitrogen concentration regime where the electronic structure around the band gap appears more conventional, but localized states still remain at higher energies. In the following section, we review the behavior of the alloy as a function of increasing nitrogen concentration. A graphical summary is given in Section 12.5. 12.4.1 Dilute Impurity Regime The fundamental physics of dilute nitride impurities in GaAs is characterized by the formation of nitrogen localized near band gap CS. Historically, only the a1 ðNÞ level, resonant 150 –180 meV above the CBM has been identified [21], but small clusters of nitrogen atoms create other levels. The CS result from the differences in atomic size and orbital energies between the nitrogen and arsenic atom it substitutes. Our empirical pseudopotential calculated a1 ðNÞ level is at Ec þ 150 meV and Ec þ 180 meV for 4096 and 13,824 atom cells, respectively, in close agreement with experiment.

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To consider the role of small nitrogen aggregates formed during growth, we have considered a number of prototypical clusters: pairs, triplets, clusters of multiple nitrogens around a single gallium, and directed chains of nitrogen atoms. Many other clusters are possible, particularly in higher nitrogen concentration alloys, even on the basis of random statistics. A full description of different clusters is given in Refs. [5,13]. Here, for clarity, we concentrate on two types of clusters. In Figure 12.1(a) – (d), we show the calculated wave functions and energy levels for a Ga-centered tetrahedron with its four vertices occupied by P42pNp, with 0 # p # 4: Note that p ¼ 1 corresponds to an isolated impurity, and p ¼ 2 to a first nearest neighbor N – N pair. All the wave functions of the induced CS are highly localized around the central gallium atom and neighboring nitrogens. We see that the levels become deeper as p increases, consistent with the fact that on an absolute scale the CBM of GaN is , 0.76 eV below that of GaP. We also considered, Figure 12.1(e) – (h), extended [1,1,0]-oriented chains of increasing length, motivated by the comparatively deep nature of even a [1,1,0]oriented pair (p ¼ 2; above, Figure 12.1(b)). Consisting of 3; 4; 5; … nitrogen atoms we observed that each additional atom in the chain produced successively deeper levels. Similar results are found in GaAs [5], except that the initial isolated impurity level, p ¼ 1; is located above the CBM. Additional nitrogens lower this level into the gap, in exact analogy to GaP. In general, we find that an increased local concentration of nitrogen atoms of any orientation induces deep, dipole allowed levels. It is not necessary that the nitrogens be immediate neighbors. Small nitrogen aggregates therefore can contribute to below band gap PL even at low impurity concentrations. We now compare the theoretical results, above, with the experimental situation. In the ultra-dilute regime (nitrogen concentration x , 0:01%) one observes: (i) Localized, single-impurity levels appear near the band gap [21 – 25]: In conventional isovalent alloys such as GaAs:P or GaAs:In the ensuing perturbation potential VAs 2 VP or VGa 2 VIn is too weak to create a bound state in the gap. In contrast, absorption and PLE of GaP:N and GaAs:N show the “Nx center” due to anionsubstitutional isolated nitrogen. In GaP:N this level appears as in impurity-bound exciton at ECBM 2 33 meV below the CBM [22 –25], whereas in GaAs:N it appears as a sharp resonance at ECBM þ 180 meV [21,26 – 28] above the CBM. The existence and location of these localized states is entirely consistent with the CS calculated above, and further described in Refs. [4,5,13]. (ii) Anomalously small pressure dependence of single impurity states is observed: Shallow, effective-mass like impurity levels (GaAs:Zn or GaAs:Si) are constructed from the wave function of the single nearest host crystal state. Consequently, when pressure is applied, these impurity levels change their energy at the same rate as the energetically nearest host crystal state [29]. In contrast, the impurity levels in dilute GaP:N and GaAs:N have anomalously small pressure coefficients: In GaP:N the energy

Electronic Structure Evolution of Dilute III– V Nitride Alloys 399

Figure 12.1. Calculated wave function isosurfaces and energy levels of (a)–(d) Ga-centered nitrogen clusters, and (e)– (h) (110) directed nitrogen chains in GaP, calculated in 4096 atom cells. For simplicity, only the neighboring gallium atoms are depicted. Isosurfaces are drawn at 20% of maximum. (Supercell size: 4096 atoms).

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of the impurity-bound exciton is almost pressure independent [30,31], whereas the X1c CBM of the GaP host crystal descends at a rate of 2 14 meV/GPa. In GaAs:N, the nitrogen level moves with pressure to higher energies at a much slower rate (, 40 meV/GPa [27,28]) than the G1c CBM of GaAs [32] (þ 110 meV/GPa). These small pressure coefficients are usually indicative of localization, whereby the wave function is constructed from many bands of the host crystal, rather than from the nearest host crystal state [33]. Examination of calculated wave functions [5,13] finds this to be the case. (iii) Sharp PL lines appear due to impurity clusters: Even random substitution of impurities onto the atomic sites of a host crystal creates, by chance, impurity pairs and higher order clusters. In conventional isovalent III– V alloys, such pairs give rise to broad resonances, within the valence and conduction continua [2,3,34 – 36], but no gap levels. In contrast, in GaPN and GaAsN, the N – N pairs form discrete levels inside the band gap extending in GaP down to ECBM 2 160 meV [25,37 –39] and in GaAs down to ECBM 2 10 [27,28,40] or ECBM 2 80 meV [41 – 43]. Similar clusters do not appear to create deep levels in ordinary, non-nitride, alloys. 12.4.2 Intermediate Regime Figure 12.2 depicts the calculated spectral dependence of the average localization P ðiÞ a 1=Ra for localized and quasi-localized levels of GaPN. Panel (a) shows the localized single-impurity a1 ðNÞ state, selected pair, triplet and quadruplet (GaP(N3) and Ga(N4)) CS, appearing inside the band gap. These wave functions are highly localized. Panel (b) shows the more extended perturbed X; L; and G host states, and the edge of the conduction band, denoted by the bold arrow “ECBE”. As the nitrogen concentration increases, Figure 12.2(d), (f), (h), (j) shows that the edge ECBE of the CBM (vertical heavy arrow) moves rapidly to lower energies, due to anticrossing and repulsion with higher energy members of the PHS. At the same time, the energy of the CS is pinned and remains fixed, as these highly localized states do not strongly interact with each other. The energies and wave functions of the CS remain essentially unchanged with composition. As the edge of the PHS moves rapidly to lower energies (“optical bowing”) this broad band of states sweeps past the discrete CS one by one. At a critical composition xc (which depends on the degree of randomness in the samples), the deepest CS is overtaken by the moving PHS. Near xc ; the CBM is an “amalgamated state” formed from both semi-localized states and more delocalized parts. As we will see below, this duality in the amalgamated state can lead to unusual physical effects. For higher nitrogen concentrations exceeding xc (Figure 12.2(g)), the CS are well inside the conduction band, and the states near the edge are more extended. In Figure 12.3 we show the calculated electronic structure evolution for GaAsN, following the same conventions as for Figure 12.2. Comparing the two systems, we see a broadly similar behavior, except that xc is smaller in GaAs. We see the conduction band

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Figure 12.2. Calculated spectral dependence of average nitrogen localization for (left) nitrogen localized “cluster states” and (right) quasi-localized “perturbed host states” of GaPN for selected nitrogen compositions. The vertical arrows show the position of the alloy conduction band edge ECBE.

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Figure 12.3. Calculated spectral dependence of average nitrogen localization for (left) nitrogen localized “cluster states” and (right) quasi-localized “perturbed host states” of GaAsN for selected nitrogen compositions. The vertical arrows show the position of the alloy conduction band edge ECBE.

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edge (CBE, also called “E2”) plunges down in energy as xN increases, sweeping past the most localized CS already by x , 0:6%. At the same time, the t2 ðL1c Þ band appears constant in energy, at Ec þ 0:4 eV; while the upper edge of the PHS (also called “Eþ” [1]) appears for x , 0:6% and moves up in energy as xN increases. This broad band represents mostly delocalized or weakly localized a1 PHS. We now compare the theoretical results, above, with the experimental situation. In the intermediate concentration regime (up to , 1% nitrogen), one observes (i) Red shift between absorption/PLE and emission is observed: In high structural quality random, direct-gap III– V alloys, absorption and emission occur at the same energy. In contrast, already at a concentration of 0.05– 0.1% nitrogen in GaAs, the emission lines are red shifted with respect to absorption [44]. At higher concentrations the shift increases in energy [41,45]. This is consistent with low energy CS lying below the conduction band edge of the dilute alloys. (ii) Composition – pinning of the impurity pair energy levels is seen: The sharp emission lines from the pair levels remain initially at a fixed energy as the nitrogen composition increases both in GaP:N [46] and in GaAs:N (0.05 – 0.1% [44]). This surprising pinning suggests that the impurities do not interact with each other. This behavior is characteristic of deep transition metal impurities in semiconductors [33,47], but not of hydrogenic impurities (Si:P,As) which readily broaden into bands and shift in energy as their concentration increases [48]. The pinning behavior is captured in empirical pseudopotential calculations (e.g. “N – N” states in Figure 12.2). As the concentration increases further, the PL from pair states becomes asymmetric, with a sharp high-energy cut-off and a low energy tail [39,49 –52], where the carriers have anomalously long lifetimes [51,53,54]. At yet higher concentrations, all of the pair/cluster lines disappear into a single, broad emission line [46,52,55]. This behavior contrasts with conventional alloys where the emission line is featureless at all alloy compositions. This evolution of PL is consistent with the downwards descending conduction band edge sweeping past the CS, as nitrogen is added. (iii) Selective delocalization of localized states on application of pressure: Under hydrostatic pressure, multiple PL lines (CS) emerge from the conduction continua in dilute alloys into the band gap [27]. However, a careful accounting of PL lines in 0.25 –0.4% superlattices [56] demonstrates that certain PL lines are absent in the higher concentration alloys, even though they would be expected to be well inside the band gap at high pressure. Explicit EPM calculations [57] of nitrogen clusters within dilute nitride alloys, Figure 12.4, reveal that the disappearance of certain lines under pressure can be attributed to partial localization of CS with increased nitrogen concentration, resulting in higher pressure coefficients. These data show conclusively that the nitrogen localized CS are not completely unchanged with increased nitrogen concentration.

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Figure 12.4. Calculated pressure dependence of cluster states in GaAsN. “D” and “L” denote delocalized and localized states, respectively. (a) Isolated nitrogen in GaAs, (b) N–N–N triplet in GaAs, (c) the well-developed 1.5% GaAsN alloy, (d) the 1.5% alloy containing the N–N–N triplet.

12.4.3 Conventional Alloy Regime Once all of the sharp lines of pairs/clusters disappear, additional unexpected effects remain: (i) The band gap shows huge, and composition dependent optical bowing: In conventional AxB12xC isovalent III –V alloys the band gap Eg ðxÞ changes with respect to the composition-weighted average of the constituents with constant bowing coefficient (usually , 1 eV). In GaP12xNx and GaAs12xNx the bowing is huge and composition dependent, being largest at small x: , 26 eV at x , 1% and , 16 eV at x . 1% [58]. This observation is highly consistent with the large bowing observed in all EPM calculations: even after all of the band gap CS have been swept into the conduction band, additional CS form with the conduction band as nitrogen is added. This further lowers the band edge. (ii) The electron mass is anomalously heavy but decreases with concentration: In conventional alloys the mass changes monotonically with composition [32]. The reduction of the band gap upon N addition (bowing) will reduce the effective mass,

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whereas mixing of L and X character in the predominantly G-like CBM due to the impurity potential will increase the mass. The balance between these effects will depend on the nitrogen concentration. In conventional alloys the second effect is absent. Small amounts (, 1%) of nitrogen increase the 0:066me mass of pure GaAs to , 0:4me [59] or 0:12 – 19me [60], but subsequent addition of nitrogen appears to reduce the electron mass [59]. As the Fermi energy moves further into the conduction band, the effective mass becomes higher [61]. In GaP, 2.5% nitrogen creates a large mass of , 0:9m0 [50], compared with the X band effective masses ðmpk , 0:25me ; mp’ , 4:8me [32]). In EPM calculations, the increased mass is inferred from the mixing of non-G (heavy mass) states into the predominantly G-derived conduction band edge of GaAs. (iii) The reduction in band gap with increased temperature slows down with nitrogen addition: Band gaps are always reduced as temperature is increased [32]. However, in conventional alloys the temperature coefficient is close to the concentration-weighted average over the constituents. This reduction in PL energy with increased temperature slows down dramatically with small addition of nitrogen to GaAs [62,63] and GaP [64]. Furthermore, the intensity of the PL lines of conventional alloys decreases with increasing temperature, but this decrease is accelerated by nitrogen addition, especially at low temperatures [65]. (iv) The energy of the PL lines is blue shifted as the excitation power increases [53], indicating occupation of previously empty states (so excitation must now occupy higher energy states). This is also known to occur in alloys containing localized, quantum dot-like clusters [66]. (v) The emission decay time becomes longer with decreasing emission energy. In other words, the states that are deeper in the gap (lower emission energies) have weaker dipole transition elements (or equivalently, less G character and more off-G character) [67].

12.5. SUMMARY OF ELECTRONIC STRUCTURE EVOLUTION

In Figure 12.5 we graphically display the key features of the electronic structure evolution of the dilute nitrides. The results described for GaAsN and GaPN in the previous section are believed to be a generic property of impurity systems where resonant states occur near the conduction band edge, e.g. for oxygen in II –VI as well as other dilute III –V nitrides. The degree to which CS influence the band edge properties depends on the relative position of the impurity level and bulk CBM. From left to right: when nitrogen is first added, a nitrogen localized resonant state is formed inside the conduction band (Section 12.4.1). As additional nitrogen is added, further localized “CS” form. Near-neighbor nitrogens form relatively deep states, some of

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Figure 12.5. Illustration of the electronic structure evolution of dilute nitride alloys.

which are inside the band gap. Repulsion between the CS and the host states of the material forces the conduction band edge down in energy. The CS remain pinned at fixed energy. In the intermediate regime (Section 12.4.2), near amalgamation, the conduction band has lowered further, such that there is a mixture of localized and delocalized states very close to the conduction band edge. In GaAsN, the valence band edge increases in energy slightly (type I offset with GaAs). Eventually (Section 12.4.3) the band edge has swept past all of the CS, so that near conventional alloy behavior is restored. However, the CS are still present at high energy, and they continue to influence the band gap, pressure dependence, and effective mass of the alloy. The existence of both localized and delocalized states near the band edge explains many of the anomalous properties of these materials. 12.6. PHENOMENOLOGY OF DILUTE NITRIDE QUATERNARIES

The quaternary nitride alloys hold great promise for technological applications. The addition of a fourth component to a ternary nitride alloy enables the lattice constant to be matched to a chosen value, such as the lattice constant of a GaAs or InP substrate. However, the introduction of a fourth component not only complicates growth, but also introduces additional local environments that modify the electronic structure. 12.6.1 InyGa12y As12xNx The (Ga12yIny)(As12xNx) alloys hold great promise for overcoming the poor temperature characteristics of conventional long-wavelength lasers [68 – 71], and are a key candidate

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material for high-efficiency multi-junction solar cells [72]. The relationship between the indium and nitrogen concentrations leading to a perfect lattice match of (Ga12yIny) (As12xNx) with GaAs or InP has been indicated in Ref. [14], assuming Vergard’s rule. For GaAs, an approximate 3:1 In:N ratio is appropriate. Quaternaries distinguish themselves from ternary alloys by the non-uniqueness of the number of bonds of each cation –anion type. The ratio between the number of A –C and B – C bonds in (A12xBx)C ternaries is simply 12 x:x while the number of GaAs, InAs, GaN and InN bonds in (Ga12yIny)(As12xNx) alloys is not only related to the compositions x and y but also depends on the possible short-range atomic ordering of the quaternary. Short-range atomic ordering in (Ga12yIny)(As12xNx) may seriously affect its optical and electronic properties since atomic ordering is known to alter the band gap and electronic wave functions in the anion-mixed Ga(As12xNx) ternary system [73]. This observation raises two questions [18]: what is the effect of the different kinds of atomic bonds with respect to the disorder (Ga12yIny)(As12xNx) alloy, and what are the consequences of SRO on the optical properties? The first question was answered by using Monte Carlo (MC) simulations for which the internal energy incorporates strain effects, as predicted by the VFF approach, and chemical bond energies [18]. These calculations revealed that, in (Ga12yIny)(As12xNx) alloys lattice matched to GaAs, nitrogen atoms prefer to be surrounded by In atoms whereas As prefers to bound with gallium atoms. In other words, the number of (large cation – small anion) In – N and (small cation – large anion) Ga –As bonds increases relative to the random system. The most important results of these simulations is that SRO (Ga12yIny)(As12xNx)/ GaAs is expected to increase the band gap with respect to the random alloy case, and results in the emergence of a band tail of localized states at the CBM due to different clusters of nitrogens surrounded by varying numbers of indium and gallium atoms. This prediction has now been confirmed in several X-ray absorption experiments, e.g. Refs. [74,75]. A blue shift of the apparent band gap on annealing of (Ga12yIny)(As12xNx) samples is now a standard observation, but this can also be due to diffusion of the component elements out of active device layers and in to barrier materials. 12.6.2 GaAs12x 2 yPyNx The GaAs12x 2 yPyNx alloy differentiates itself from the GaInAsN alloys by possessing three different anions. In the phosphorus rich, dilute nitride limit, it exhibits a deep-gap impurity level. As arsenic is added, replacing phosphorus, the host GaAsP material also exhibits an indirect to direct gap crossover. For example, inserting dilute nitrogen into GaAs0.5P0.5 alloy generates an impurity level located 130 meV below the conduction band minimum of GaAs0.5P0.5 [76 –78]. A recent study [16] characterized the transition from the nitrogen dilute impurity region to the band-like region. Disordered Ga(As0.52xP0.52xN2x) systems were modeled by (randomly) substituting arsenic and phosphorus atoms by nitrogens inside large supercells

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containing either 1000 or 1728 atoms. Ref. [16] focused on random alloys with very low nitrogen concentrations (lower than 1.5%), and the formation of neighbors nitrogen pairs or nitrogen clusters was not taken into account. The main prediction of this computational study was that the transition from impurity-to-band-like behavior of the first conduction state occurs for nitrogen concentrations around 0.4%. In other words, adding a very few percent of nitrogen changes the character of the lowest unoccupied state in Ga(As0.52xP0.52xN2x). This transition was described in terms of two different processes. The first process is an anticrossing repulsion between the deep-gap nitrogen impurity level and the delocalized G1c-like conduction state of the nitrogen-lacking Ga(As0.5P0.5) system. The second process is an interaction between nitrogen impurity deep-gap states that results in the formation of a nitrogen subband. As the nitrogen composition x increases, these two processes lead to a delocalization of the lowest conduction state mainly within the nitrogen sublattice, and to a strong decrease of the single particle gap: incorporating only 1% of nitrogen into GaAs0.5P0.5 was predicted to reduce the gap by around 300 meV relative to the GaAs0.5P0.5 alloy. This is somewhat larger than the reduction measured and predicted for GaAsN, approximately 150 –200 meV per 1% nitrogen.

12.7. FUTURE CHALLENGES OF NEW NITRIDE MATERIALS

Several new nitride materials have recently been grown in order to explore new areas of the optical spectrum, and to examine different methods for achieving lattice-matched conditions. These new materials will provide a strong test of the different theoretical models developed so far. 12.7.1

InSb12xNx

Semi-metallic behavior in InSb12xNx [79] has recently been observed in high-resolution electron energy loss spectroscopy in nominally 6% nitrogen samples. The low band gap of bulk InSb permits the apparent occurrence of band gap closure above approximately 2% nitrogen. Although predicted to occur in wider band gap materials such as GaAs and GaP, in practice this band gap closure has not been experimentally achievable due to the low nitrogen solubility. Additionally, if well-controlled growth and high carrier mobilities are achieved, improved infra-red devices may result. The reduction of the band gap is expected within the BAC approximation, and by simple extrapolation of existing observations for GaAsN and GaPN. However, these projections neglect any potential interactions between the valence and conduction bands. A further complication is the likely formation of indium or nitrogen rich regions, owing to the large lattice constant mismatch of 23%.

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12.7.2 GaAs12x2 ySbxNy GaAs12x2 ySbxNy [80 – 82] is a direct competitor to the more established InxGa12xAs12yNy system. Less nitrogen is required to reach a specific band gap in the antimonide than in the indium-containing quaternary. However, magnetoluminescence measurements [81] can only be explained by assuming extremely localized hole carriers, in contrast to the indium quaternary where there is no evidence for hole localization. The existence of additional localization centers may benefit certain emission-based applications, but may act to reduce the lifetime of carriers in absorption-based applications. Although the conduction state properties of the antimonide alloy appear similar to those of GaAsN, additional investigations are required in order to understand the hole (valence band) physics. 12.8. CONCLUSIONS

We have given an overview of the modern EPM and its application to the dilute III – V nitrides. Detailed analysis of supercell models of the nitrides supports the theory of alloy formation involving the interactions between nitrogen-induced localized CS with many PHS. Supercell calculations of small nitrogen clusters show that comparatively few nitrogens can introduce very deep, below band gap states, and thus details of nitride alloy nanostructure are fundamental to determining nitride alloy properties. Pseudopotential modeling has also provided several predictions to be checked by experiment. The EPM distinguished itself from the phenomenological BAC model [1] which ignores CS beyond the isolated nitrogen and uses a single host state, thus failing to explain the phenomena associated with the existence of numerous local environments in the alloy. The existence of CS is most strongly evident in PL, where these states appear pinned in energy as a function of nitrogen concentration, and in pressure dependent measurements, where their distinct non-host-like (or “deep level”) nature is immediately apparent. ACKNOWLEDGEMENTS

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[65] Onabe, K., Aoki, D., Wu, J., Yaguchi, H. & Shiraki, Y. (1999) MOVPE growth and luminescence properties of GaAsN alloys with higher nitrogen concentrations. Phys. Status Solidi (a), 176, 231– 235. [66] Mattila, T., Wei, S.H. & Zunger, A. (1999) Electronic structure of “sequence mutations” in ordered GaInP2 alloys. Phys. Rev. Lett., 83, 2010– 2013. [67] Takahashi, M., Moto, A., Tanaka, S., Tanabe, T., Takagishi, S. & Karatani, K. (2000) Observation of compositional fluctuations in GaNAs alloys grown by metalorganic vaporphase epitaxy. J. Cryst. Growth, 221, 461– 466. [68] Xin, H.P. & Tu, C.W. (1998) GaInNAs/GaAs multiple quantum wells grown by gas-source molecular beam epitaxy. Appl. Phys. Lett., 72, 2442– 2444. [69] Kondow, M., Uomi, K., Niwa, A., Kitatani, T., Watahiki, S. & Yazawa, Y. (1996) GaInNAs: a novel material for long-wavelength-range laser diodes with excellent high-temperature performance. Jpn. J. Appl. Phys., 35, 1273– 1275. [70] Nakahara, K., Kondow, M., Kitatani, T., Yazawa, Y. & Uomi, K. (1996) Continuous-wave operation of long-wavelength GaInNAs/GaAs quantum well laser. Electron. Lett., 32, 1585– 1586. [71] Sato, S., Osawa, Y., Saito, T. & Gujimara, I. (1997) Room-temperature pulsed operation of 1.3 mm GaInNAs/GaAs laser diode. Electron. Lett., 33, 1386– 1387. [72] Kurtz, S.R., Allerman, A.A., Jones, E.D., Gee, J.M., Banas, J.J. & Hammons, B. (1999) InGaAsN solar cells with 1.0 eV band gap, lattice matched to GaAs. Appl. Phys. Lett., 74, 729– 732. [73] Bellaiche, L. & Zunger, A. (1998) Effects of atomic short range order on the electronic and optical properties of GaAsN, GaInN, and GaInAs alloys. Phys. Rev. B, 57, 4425– 4431. [74] Tournie, E., Pinault, M.A. & Guzman, A. (2002) Mechanisms affecting the photoluminescence spectra of GaInNAs after post-growth annealing. Appl. Phys. Lett., 80, 4148– 4150. [75] Ciatto, G., Boscherini, F., D’Acapito, F., Mobilio, S., Baldassarri, G., Polimeni, A., Capizzi, M., Gollub, D. & Forchel, A. (2003) Atomic ordering in (InGa)(AsN) quantum wells: an In K-edge X-ray absorption investigation. Nucl. Instrum. Methods Phys. Res. B, 200, 34 – 39. [76] Nelson, R.J. (1982) Excitons, North-Holland, Amsterdam. [77] Hjalmarson, H.P., Vogl, P., Wolford, D.J. & Dow, J.D. (1980) Theory of substitutional deep traps in covalent semiconductors. Phys. Rev. Lett., 44, 810–813. [78] Jaros, M. & Brand, S. (1979) Electronic states associated with the substitutional nitrogen impurity in GaPxAs12x. J. Phys. C, 12, 525–539. [79] Veal, T.D., Mahboob, I. & McConville, C.F. (2004) Negative band gaps in dilute InNSb alloys. Phys. Rev. Lett., 92, 136801. [80] Lourenco, S.A., Dias, I.F.L., Pocs, L.C., Duarte, J.L., de Oliveira, J.B.B. & Harmand, J.C. (2003) Effect of temperature on the optical properties of GaAsSbN/GaAs single quantum wells grown by molecular-beam epitaxy. J. Appl. Phys., 93, 4475– 4479. [81] Senger, R.T., Bajaj, K.K., Jones, E.D., Modine, N.A., Waldrip, K.E., Jalali, F., Klem, J.F., Peake, G.M., Wei, X. & Tozer, S.W. (2003) Magnetoluminescence properties of GaAsSbN/ GaAs quantum well structures. Appl. Phys. Lett., 83, 5425– 5427. [82] Peake, G.M., Waldrip, K.E., Hargett, T.W., Modine, N.A. & Serkland, D.K. (2004) OMVPE of GaAsSbN for long wavelength emission on GaAs. J. Cryst. Growth, 261, 398–403.

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Dilute Nitride Semiconductors M. Henini (Ed.) q 2005 Elsevier Ltd. All rights reserved.

Chapter 13

Theory of Nitrogen –Hydrogen Complexes in N-containing III –V Alloys A. Amore Bonapasta and F. Filippone CNR—Istituto di Struttura della Materia (ISM), Via Salaria Km 29,3, CP 10, 00016, Monterotondo Stazione, Rome, Italy

13.1. INTRODUCTION

The properties of nitrogen and its complexes with hydrogen in III– V-N dilute alloys where the group-V element is partially replaced by N, like GaAsyN12y, GaPyN12y and InxGa12xAsyN12y, have been investigated extensively in recent years [1 – 12]. These efforts have been motivated by two surprising phenomena observed in these peculiar semiconductors. First, III – V alloys generally follow the virtual crystal approximation (VCA), that is, the properties of an ABxC12x alloy can be related to a crystal potential VðxÞ expressed by a linear interpolation of those of the binary constituents, e.g. VðxÞ ¼ xVAB þ ð1 2 xÞVAC : On the contrary, in an N-containing III– V alloy, the presence of some percent of N induces an impressive, non-linear reduction of the band gap energy of the host III –V semiconductor [1] as well as a large increase in the electron effective mass [11]. Only a reduction of the lattice constant of the host semiconductor, also induced by N, seems compatible with VCA [10]. A second surprising phenomenon concerns the effects of the inclusion of atomic hydrogen on the properties of the N-containing alloys. Hydrogenation leads indeed to a full neutralization of both the electronic and structural effects of nitrogen. More specifically, hydrogenation recovers both the band gap energy of the host material [4,6,8,13] and the shape of the bottom of the GaAs conduction band, which is directly related to the electron effective mass [11]. Further, the inclusion of atomic hydrogen neutralizes the reduction of the host lattice constant induced by N [10]. These passivating effects of H are rather surprising because N is an isoelectronic impurity. This implies that simple models generally used to explain the H passivation of shallow impurities cannot be invoked in the present case. These models are based on the stabilizing effects induced by the formation of an acceptor– donor complex and on a qualitative analysis of the chemical valence of the impurity [14,15]. In detail, it is E-mail address: [email protected] (A. Amore Bonapasta).

415

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Dilute Nitride Semiconductors

Figure 13.1. Atomic configurations of two mono-hydrogen complexes in GaAsyN12y: (a) N – Hþ BC ð – GaÞ; (b) ðGa – ÞN – Hþ AB : BC and AB indicate a bond centered and an antibonding site of H, respectively.

assumed that a H atom in a III –V semiconductor behaves as a donor or an acceptor depending on the site where it is located. For instance, a H atom located at a bond centered (BC) site of a GaAs bond (see Figure 13.1(a)) [16], where there is a piling up of electronic charge, tends to lose its electron, thus inducing a donor level in the GaAs gap. It may also give rise to a Hþ ion that is stable at the BC site, where it is screened well by the electronic charge of its Ga and As neighbors. On the other hand, a H atom at an antibonding (AB) site of a GaAs bond (see Figure 13.1(b)) [16] or at a Td site [17], which are located in a region poor in electronic charge, tends to reach the stable electronic configuration of He by trapping one electron, thus inducing an acceptor level in the energy gap. In particular, it can give rise to an isolated H2 ion stable at the Td site and having slight interactions with its neighboring atoms. In the presence of a shallow acceptor, e.g. a substitutional Si in the anionic site of GaAs (SiAs), a HBC atom can compensate the acceptor, diffuse as a Hþ ion and bind to the ionized acceptor by forming an “on-line” SiAs – HBC(–Ga) complex (similar to the complex of Figure 13.1(a)), which is stabilized by the presence of the SiAs acceptor and the HBC donor. In this complex, H is mainly bonded to the Si atom, then the Si and Ga atoms reach their “natural” valence of four and three, respectively. Similarly, an (As) – SiGa – HAB complex is stable in the case of a SiGa donor in hydrogenated GaAs, because it involves a H acceptor and a SiGa donor. In this case, the As atom has a weak interaction with Si, thus reaching its valence of three. Clearly, these simple models based on the formation of acceptor –donor pairs cannot hold in the case of an isoelectronic impurity like, e.g. NAs in GaAsN. In InGaNAs alloys, the observed reduction of the InGaAs energy gap has been accounted for by a “band anticrossing” model where a strong interaction between the InGaAs conduction band and an N resonant level results in a splitting of the conduction band and a reduction of the InGaAs band gap [18]. Other theoretical studies have

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explained the effects of N on the electronic structure of the host semiconductor by proposing models based on perturbed host states (N exerts a large perturbation that mixes host crystal states forming new low-energy states) [19,20] and localized cluster states (states due to small N aggregates) [21]. These studies were focussed on the band structure of the alloys with N and were performed by using empirically corrected atomic pseudopotentials in order to correctly reproduce energy band gaps. Here, the attention is instead focused on the properties of N – H complexes in III – V-N alloys. Thus, results of different theoretical studies on this subject [11,22 – 30] will be reviewed and discussed together with experimental findings in order to achieve a coherent theoretical picture accounting for the H passivation of the N effects. The reviewed results will concern the structure and stability of the N – H complexes, their formation, chemical bonding, vibrational properties and electronic structure. In general, these results have been achieved by using first-principles Density Functional Theory –Local Density Approximation (DFT – LDA) methods in a supercell approach. These methods have been extensively and successfully used to investigate the energetics of complexes formed by H and defects in semiconductors [14]. Moreover, they have provided indications on the electronic properties of the H-complexes, which have permitted to clarify the mechanisms of the H passivation of shallow impurities. We can anticipate that the theoretical studies cited above generally agree on the properties of the N – H complexes. Thus, we report here only representative theoretical results and explicitly mention cases where the findings are in disagreement. Moreover, quite similar results have been found for different III– V-N alloys. We have chosen, therefore, the most investigated case, the GaAsN one, as a representative of the other III –V-N alloys and analyzed in detail the corresponding theoretical and experimental findings. Then, the results achieved in the case of the other alloys have been briefly discussed by stressing the differences with GaAsN. In the case of GaAsN, the discussion of results has been developed as described in the following. (i) Results on the structure and relative stability of N – H complexes have been considered first. They give general information on what complexes could be formed in a III –V-N alloy. (ii) The formation energy of the N –H complexes as a function of the Fermi energy position have then been considered. Formation energies permit to identify which N – H complexes are formed under different doping conditions. (iii) The electronic levels induced in the energy gap by the N –H complexes have been discussed and related to H passivation mechanisms. The H passivation of the structural effects of N have also been discussed. These results indicate what complexes could be responsible of the passivation of all of the N effects (both electronic and structural effects). (iv) Formation mechanisms of the N – H complexes have been discussed in order to identify the most likely complexes formed in a given alloy. (v) The vibrational properties calculated for several N –H complexes have been compared with the experimental counterparts in order to check the theoretical predictions about the complexes formed in a hydrogenated III –V-N alloy.

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Finally, in the conclusions, a theoretical picture including simple models has been proposed to explain the H passivation of the N effects in all of the investigated III –V-N alloys.

13.2. THEORETICAL METHODS

In general, the results reported here have been achieved by using DFT – LDA methods in a supercell approach, atomic pseudopotentials and plane-wave basis sets [31]. These methods give total energy values of supercells simulating, e.g. a GaAs lattice containing an N – H complex. The geometry of such a system has been optimized by minimizing the atomic forces of all of the atoms in the supercell. The chemical bonding and the nature of the electronic states in the N – H complexes have been investigated by analyzing (i) the plots of the total (valence) electronic charge density; (ii) the plots of the lCn;0 l2 densities, which show the distribution of the electronic charge induced by a particular electronic state described by the Cn;0 wavefunction; (iii) the atomic distances and the atomic displacements in the N – H complexes. Some calculations were also performed by using ab initio cluster density functional methods, where clusters and localized basis are used in place of supercells and plane-wave basis sets [32]. For what concerns the formation energy of an N – H complex, by analogy with the case of defects [33], in a supercell approach the formation energy per H atom V½N – nHq of a N – nH complex involving n H atoms and a q charge can be written as 1 V½N – nHq ¼ ½E½N – nHq 2 E½N 2 nmH þ qme  n q where E[N– n H] is the total energy of the simulation supercell containing one N atom and n H atoms (e.g. a 64-atom GaAs supercell), mH is the chemical potential of hydrogen, which is generally assumed equal to half of the energy of the H2 molecule in the vacuum, and q is the positive (negative) charge on the complex, namely, the number of electrons transferred from (to) the complex to (from) an electron reservoir with a chemical potential (or Fermi level) me (me ¼ 0 corresponds to a Fermi level at the top of the valence band). The formation energy of the defect depends, therefore, on the charge of the defect itself which may change with the position of the Fermi energy. The charge of the defect depends on the position of the defect electronic-states in the energy gap. Such a position can be investigated by calculating the transition energy of the defect electronic state, that is, the Fermi energy value 1n=nþ1 for which the occupation number of the defect state in the energy gap changes from n to n þ 1: In turn, 1n=nþ1 can be estimated by the Fermi energy position where the formation energies of the n and n þ 1 charge-states of the defect are equal [34]. As an example, in the GaAs0.97N0.03 alloy, (i.e. the alloy simulated by 64-atom supercells), isolated N atoms and N –H complexes have been considered as isolated defects and the corresponding 1n=nþ1 values have been calculated.

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The 1n=nþ1 values should be compared with the GaAs energy gap, which is generally underestimated in LDA. In some cases, 1n=nþ1 values have been compared with the experimental band gap. Here, we report results where the energy gap has been estimated by calculating the 10=2 value in the N-free compound material. Moreover, this value has been checked by calculating the 1þ=0 value for the Si shallow-donor (i.e. a substitutional Si atom at a Ga site, SiGa). This shallow donor induces a level close to the bottom of the GaAs conduction band, the corresponding 1þ=0 value provides, therefore, a state of reference to locate the N and N –H levels in the energy gap by permitting to compare consistent results obtained within the same approach. In the present case, transition energies play a significant role. They can be used indeed to determine the position of the electronic levels induced by N and N – H complexes in the energy gap, thus permitting to follow the evolution of the band gap of a host material induced by the incorporation of N and the subsequent formation of N – H complexes. About the theoretical results reported here, we would like to stress that they are representative of the results achieved in different theoretical studies. In detail, the reported total energies have been calculated by using separable ab initio pseudopotentials [35], plane-wave basis sets, the special-points technique for k-space integration, and the exchange-correlation functional of Ceperley – Alder as implemented in the PWscf package [36]. Ultrasoft pseudopotentials have been used in the case of nitrogen [37]. Geometry optimizations have been performed by fully relaxing the positions of all the atoms of a supercell by minimizing the atomic forces. The results concerning the geometries, the formation energies and the transition energies of the N – H complexes have been achieved by using 64-atom supercells, the ð4; 4; 4Þ k-point Monkhorst – Pack mesh, and cutoffs of 22 Ry. Vibrational frequency values have been calculated by performing a full vibrational analysis via Lanczos diagonalization of the Hessian matrix [38], exploiting the variational formalism of density functional perturbation theory [39]. This procedure has required further geometry optimizations of the N –H complexes. In detail, these calculations have been performed in the LDA by using the exchange-correlation functional through Pade´ approximation [40], as implemented in the CPMD code [41]. Separable ab initio relativistic pseudopotentials of the Goedecker –Hutter– Hartwigsen type have been used for Ga and As [42], a Von Barth –Car type pseudopotential has been used for H, and a norm conserving Martins – Troullier pseudopotential has been used in the case of N [43]. In this case, the results have been achieved by using 64-atom supercells, energy and frequency values at the G point and cut-off of 50 Ry in plane-wave basis sets. No appreciable differences have been found between the geometries of the N –H complexes calculated by using the above two geometry-optimization procedures. A rough estimate of dipole moments corresponding to the N –H bonds in the N – H complexes has been achieved by calculating the Lo¨wdin atomic charges.

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13.3. N – H COMPLEXES IN GaAsN ALLOYS

The theoretical studies cited above [11,22 – 30] have investigated the properties of both mono-hydrogen and di-hydrogen N – H complexes, like those shown in Figures 13.1 and 13.2, respectively. These studies have found very similar results for what concerns the structure, chemical bonding, relative stability, and electronic properties

Figure 13.2. Atomic configurations of some di-hydrogen complexes in GaAsyN12y: BC and AB indicate a bond centered and an antibonding site of H, respectively. The configurations of the N – Hp2 ðaÞ – ðdÞ complexes are shown in the (a)–(d) figures, respectively. (e) shows the C2v configuration of the N – 2Hþ2 BC complex.

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of the N –H complexes formed in different alloys, like GaPN, GaAsN, InGaAsN. Thus, we discuss first the results achieved in the case of GaAsN, which is the most investigated and representative III –V-N alloy. 13.3.1 Structure and Energetics of Mono-hydrogen Complexes The mono-hydrogen complexes investigated in GaAsN involve the Hþ, H0, and H2 species, one N atom and its Ga neighbors. Two different cases have been considered for the H sites, which correspond to a H atom located close to the N atom and to the Ga atom of a Ga –N bond, respectively. In the former case, a H atom (ion) has been located at (i) a site close to the bond-centered site of a Ga – N bond, see Figure 13.1(a); (ii) an antibonding site on the N side, see Figure 13.1(b); (iii) a tetrahedral site (Td) [17]; (iv) some lower symmetry sites not aligned with the Ga – N bond axis. These complexes have been identified, e.g. with the notation N – Hþ BC ð – GaÞ; see Figure 13.1(a), in order to stress the main atoms involved in the complex. In the case of a H atom close to the Ga atom, the BC, AB, and Td sites are located on the side of the Ga atom of a Ga –N bond. These complexes, characterized by a Ga –H interaction, are unstable or higher in energy than those involving a H atom located next to the N atom. Thus, only the latter complexes will be discussed here. Atomic distances and displacements calculated for these mono-hydrogen complexes are reported in Table 13.1 together with the total energy values relative to the energy of the most stable complex for each H species, that is taken equal to zero. A comparison of the calculated atomic distances with the corresponding values estimated by using the atomic covalent radii [44] gives clear indications about the chemical bonding in the N – H complexes. As an example, the geometry of the N – Hþ BC ð – GaÞ complex of Figure 13.1(a) (the most stable complex formed by the Hþ ion) is characterized by an on line N – Hþ BC – Ga þ ˚, configuration where the N – Hþ and Ga – H distances are equal to 1.05 and 2.43 A BC BC Table 13.1. Atomic distances, atomic displacements with respect to ideal positions (DX values), and total energy values of mono-hydrogen complexes in GaAsN Complex

N –H

Ga –H

Ga– N

DGa

DN

E

½N – Hþ BC ð – GaÞ ½ðGa – ÞN – Hþ AB  ½As – Hþ BC – Ga

1.05 1.06 1.55

2.43 4.80 1.82

3.48 3.74 3.37

0.63 0.53 0.53

0.45 0.81 0.44

0.00 0.24

½N – H0BC ð – GaÞ ½ðGa – ÞN – H0AB 

1.08 1.07

2.11 4.40

3.18 3.34

0.29 0.07

0.49 0.87

0.00 0.32

½N – H2 BC ð – GaÞ ½ðGa – ÞN – H2 AB 

1.09 1.07

1.95 4.14

3.04 3.07

0.04 20.34

0.63 1.01

0.00 0.10

Positive (negative) DX values indicate an outward (inward) atomic displacement with respect to the Ga– N chemical bond. Total energy values are relative to the energy of the most stable complex (for each H species) that is taken equal to zero. Distances are given in angstroms, total energies in eV. In the case of the As – Hþ BC – Ga complex, the DAs and As –X values are reported in the DN and N–X columns (X ¼ Ga, H), respectively. The upper, middle, and lower parts of the table report results for the Hþ, H0, and H2 species, respectively.

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˚ , respectively, when respectively. The N – H and Ga – H distances are equal to 1.07, 1.58 A þ estimated by using the atomic covalent radii. The N – HBC and Ga – Hþ BC distances in the complex are 3% smaller and 54% larger than those calculated by covalent radii, thus clearly indicating the formation of a strong N –H bond and the existence of a weak Ga – H ˚ have been calculated interaction. It should also be noted that the values of 2.05 and 2.41 A for the Ga –N and Ga –As bond lengths in the case of an isolated N atom and of pure GaAs, respectively. These values permit one, e.g. to appreciate the large increase in the Ga –N ˚ distance in the N – Hþ BC ð – GaÞ complex (3.48 A, see Table 13.1). The results achieved for this complex can also be compared with the geometry of the As – Hþ BC – Ga complex þ þ formed by a H ion in GaAs, see Table 13.1. In this complex, the As – Hþ BC and Ga – HBC ˚, distances are 2 and 15% larger than those estimated by the covalent radii, 1.52 and 1.58 A respectively, which indicates the existence of a bonding interaction of the Hþ ion with BC both the As and Ga atoms. Thus, the three-center bond formed by Hþ in the As – Hþ BC – Ga complex is replaced by a two-center N – H bond plus a dangling bond of the Ga atom in the þ N – Hþ BC ð – GaÞ complex. The deep difference between the chemical bonding of H in the two above complexes is confirmed by the plots of the total (valence) charge density shown in Figure 13.3. This figure shows that the considerable electronic charge piled up on an isolated N atom (see Figure 13.3(a)) is used to screen the Hþ BC ion (see Figure 13.3(b)), thus resulting in a piling up of the charge on the N – H pair and in the formation of a strong N – H bond. A quite different charge distribution is shown in Figure 13.3(c)), that suggests

Figure 13.3. Contour plots in the (110) plane of the total (valence) charge density corresponding to (a) an þ þ isolated N atom, (b) the N – Hþ BC complex, (c) the As – HBC – Ga complex in pure GaAs, and (d) the N – HAB complex. The As, Ga, and N atoms are indicated by black, gray, and white full dots, respectively. Small crosses represent the H atoms.

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instead the formation of a three-center As – Hþ BC – Ga bond in pure GaAs. In agreement with this picture, the total energy values calculated for the above complexes show that the N – H bond in the N – Hþ BC ð – GaÞ complex is 1.2 eV more stable than the As –H bond formed in the corresponding As – Hþ BC – Ga complex. The tendency of nitrogen to form strong N –H bonds is confirmed by the existence of a ðGa – ÞN – Hþ AB complex (see Figure 13.1(b)) only 0.24 eV higher in energy than the N – Hþ ð – GaÞ complex, see Table 13.1. The ðGa – ÞN – Hþ BC AB complex is characterized by a ˚ ˚ that is 86% larger than the N – H distance of 1.06 A and by a Ga – N distance of 3.74 A ˚ value given by the covalent radii (2.01 A). Furthermore, both Ga and N atoms relax outward (see Table 13.1). The geometry of this complex indicates, therefore, the formation of a strong N –H bond and a negligible Ga –N interaction. This picture is confirmed by the corresponding charge density distribution, see Figure 13.3(d), that shows a charge piling up on the N –H pair very similar to that of Figure 13.3(b). Even the N – H bond in the ðGa – ÞN – Hþ AB complex results to be 1.2 eV more stable than the As –H bond formed in the corresponding complex in GaAs, where an As atom replaces the N atom. A similar analysis of the atomic geometries of the other complexes reported in Table 13.1 indicates that all of those mono-hydrogen complexes are characterized by the formation of strong N – H bonds. Three further important indications can be derived from the data of Table 13.1 when the details of the complex geometries are analyzed together with the corresponding total energy values. First, the formation of strong N – H bonds has significant effects on the behavior of the Hþ, H0, and H2 species which results to be quite different in GaAs and GaAsN. Second, a weak Ga – H bonding interaction exists in the N – HBC ð – GaÞ complexes with different charges. Third, the N atom in GaAsN suffers a lacking of electronic charge. These results will be carefully discussed in the following because they are related to the passivating effects of H which will be presented in the following sections. For what concerns the behavior of the Hþ, H0, and H2 species in GaAsN and GaAs, we have already noted that Hþ forms a strong N – Hþ BC bond in the former material and a threecenter As – H –Ga bond in the latter one. In the case of H0, the N – H0BC ð – GaÞ complex is the most stable complex at variance with the case of GaAs, where the most stable complex corresponds to a H atom located at the AB site on the side of the As atom [45]. In the case of H2, the complex formed by the H2 ion located at the BC site close to the N site, N – H2 BC ð – GaÞ; is once more the most stable one. This last result is rather surprising for two reasons: (i) it is very different from that achieved in GaAs, where a Td site is the most stable site for H2 [45]; (ii) it does not agree with the simple model described in Section 13.1, where an acceptor behavior of H is related to the formation of an isolated H2 ion with the electronic configuration of He, stable at the Td site and not interacting with its neighboring atoms [15]. About the existence of a weak Ga – H bonding interaction in the N – HBC ð – GaÞ complexes, this is suggested by an analysis of the local lattice relaxations occurring in

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these complexes with different charges. In fact, in these complexes, the Ga –H distance and the Ga atomic displacement appreciably decrease on going from the Hþ to the H0 and H2 species. In detail, the Ga – H distances and the Ga displacements decrease from 2.43 to ˚ and from 0.63 to 0.04 A ˚ , respectively, see Table 13.1. 1.95 A Finally, the fact that N in GaAsN suffers a lacking of electronic charge can be deduced from the above two considerations. In fact, in the N – Hþ BC ð – GaÞ complex, N forms a strong N – H bond by hindering the formation of a three-center N –H –Ga bond, that is, it subtracts the H ion to a possible Ga – Hþ BC interaction and induces a dangling bond on the Ga atom. A small Ga – H interaction becomes possible only by satisfying the needs of the N atom, that is, by adding some electronic charge to the complex. Furthermore, H2 is not stable at the Td site because the N atom needs more electronic charge than the As atom it substitutes. The N atom forms, therefore, a strong bond with the negative H2 ion at variance with the As atom in GaAs. A consequence of the above results is that the acceptor character of H0 in GaAs should be weakened in GaAsN because the negative charge of H2 is shared with the N atom. In turn, this should affect the negative-U behavior of H, that is, the existence of an H acceptor level in the gap lower than the donor level [46]. An estimate of the negative-U character of H is given by the energy released in the reaction 2H0 ! Hþ þ H2. As a matter of fact, this energy has the value of 0.6 eV in GaAs [46] and of 0.1 eV in GaAsN, in agreement with the results of the above discussion. 13.3.2 Structure and Energetics of Di-hydrogen Complexes The configurations of some di-hydrogen complexes are shown in Figure 13.2. The Ga –HBC – N – HAB complex shown in Figure 13.2(a) is the most stable di-hydrogen complex in GaAsN. This complex is also referred to as N – Hp2 ðaÞ because it is characterized by an “on-line” Hp2 -like configuration [15], where the two H atoms are bonded to a Ga and an N atom of a Ga – N bond, respectively. Three further dihydrogen complexes with a similar on line configuration have been investigated, N – Hp2 ðbÞ; N – Hp2 ðcÞ; and N – Hp2 ðdÞ; whose geometries are shown in Figure 13.2(b) – (d), respectively. Finally, the Ga – HBC – N –HBC – Gaþ2 complex shown in Figure 13.2(e) (also referred to as N – 2Hþ2 BC ) has been considered, which represents a charged dihydrogen complex involving two Hþ BC ions both bonded to the N atom. In this case, þ each H ion is almost aligned with its neighboring N and Ga atoms, thus leading to a C2v symmetry for the complex quite different from the C1v symmetry of the above Hp2 di-hydrogen complexes. Details of the geometries of the above complexes and the corresponding total energy values are given in Table 13.2. An analysis of the data in this table shows that the properties of these complexes are dominated by the formation of strong N – H bonds, as in the case of mono-hydrogen complexes. For instance, in the N – Hp2 ðaÞ complex, the N –HAB and Ga –HBC bond lengths are equal ˚ , respectively, equal and 3% smaller than the corresponding values to 1.07 and 1.54 A

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Table 13.2. Atomic distances, atomic displacements with respect to ideal positions (DX values), and total energy values of di-hydrogen complexes in GaAsN Complex [Ga– H1(BC) – N– H2(AB)](a) [H1(AB) –Ga–H2(BC) –N](b) [H1(AB) –Ga–N–H2(AB)](c) [Ga– H1(BC) – As– H2(AB)] [Ga– H1(BC) – N– H2(BC) –Gaþ2]

N –H1

N–H2

Ga–H1

Ga– H2

Ga –N

DN

DGa

E

2.06 5.35 5.75 1.92 1.05

1.07 1.06 1.06 1.58 1.05

1.54 1.59 1.60 1.65 2.43

4.67 2.70 5.20 5.05

3.60 3.76 4.14 3.47 3.47

1.04 0.43 0.84 0.84 0.66

0.16 0.93 0.90 0.23 0.64

0.0 0.13 0.53

Positive (negative) DX values indicate an outward (inward) atomic displacement with respect to the Ga– N chemical bond. Total energy values are relative to the energy of the most stable complex that is taken equal to zero. Distances are given in angstroms, total energies in eV. In the case of the Ga– H1(BC) – As–H2(AB) complex, the DAs and As–X values are reported in the DN and N–X columns (X ¼ Ga, H), respectively.

˚ , that is 92% larger than estimated from covalent radii. The N – HBC distance is 2.06 A ˚ the 1.07 A value estimated from the atomic covalent radii. This complex is, therefore, characterized by the formation of two strong N – HAB and Ga – HBC bonds and by a negligible N – HBC interaction. This chemical bonding is confirmed by the total charge-density distributions shown in Figure 13.4(a). One should note the similarity between the charge density distributions around the N –HAB bond shown in Figures 13.3(d) and 13.4(a). The geometry of the N – Hp2 ðaÞ complex can also be compared with that of the Hp2 complex in GaAs (i.e. the Ga –HBC – As –HAB complex) also reported in Table 13.2. In the latter complex, the As –HAB, Ga – HBC, and As – HBC bond lengths are 4% larger, equal and 26% larger than the values estimated by using the covalent radii, respectively, thus suggesting the existence of some As – HBC bonding interaction (similarly to that found in the case of the As – Hþ BC – Ga complex, see Section 13.3.1) at variance with the case of the N – Hp2 ðaÞ complex. This picture seems confirmed by a comparison of the total charge-density distribution of Figure 13.4(a) with that of Figure 13.4(c). Finally, it can be noted that the displacement of the As atom in the Hp2 complex leads this atom on the plane formed by its three nearest neighboring Ga atoms, whereas the corresponding displacement of the N atom in the N – Hp2 ðaÞ complex leads to an inversion of the tetrahedral umbrella centered on the N atom, in agreement with the above differences between the As –HBC and N – HBC interactions. A further confirmation of the quite different chemical bonding occurring in the above two complexes is given by the energies corresponding to the dissociation of the N – Hp2 ðHp2 Þ complexes which leads to the formation of an isolated N(As) atom and an interstitial H2 molecule in the GaAs lattice. These dissociation energies are equal to þ 1.22 eV (a positive value indicates that some energy is required to dissociate the complex) and 2 0.71 eV in the case of the N – Hp2 ðaÞ and Hp2 complexes, respectively, thus showing that only the former complex is more stable than the H2 molecule in GaAs. The HAB – Ga – HBC – N complex shown in Figure 13.2(b) has also a Hp2 -like configuration. It will be also referred to as N – Hp2 ðbÞ: This complex is only 0.13 eV

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Figure 13.4. Contour plots in the (110) plane of the total (valence) charge density corresponding to (a) the N – Hp2 ðaÞ complex, (b) the N – Hp2 ðbÞ complex, and (c) the Ga –HBC –As–HAB complex. The As, Ga, and N atoms are indicated by black, gray, and white full dots, respectively. Small black or white crosses represent the H atoms.

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higher in energy than the N – Hp2 ðaÞ complex and presents a quite similar chemical bonding. The geometry of the N – Hp2 ðbÞ complex and the corresponding total charge-density distributions (see Figure 13.4(b)) show indeed that this complex is characterized by two strong Ga – HAB and N – HBC bonds and by a negligible Ga – HBC interaction. The di-hydrogen complex of Figure 13.2(c) is further higher in energy. The complex of Figure 13.2(d) is unstable, together with the corresponding one having the two H atoms bonded to a Ga atom of the Ga –N bond (not shown in the figure). These two complexes evolve without barriers towards the geometries of the N – Hp2 ðaÞ and N – Hp2 ðbÞ complexes, respectively. þ Finally, the geometry of the C2v complex, N – 2Hþ2 BC ; is characterized by N – HBC bondþ lengths equal to the N – H bond length in the N – HBC ð – GaÞ complex. The charge states þ 1, 0 and 2 1 of this complex have also been investigated. The corresponding geometries (not reported in Table 13.2) differ from that of the complex with charge þ 2 mainly for the atomic displacements of the Ga atoms and the Ga – H atomic distances. In detail, the Ga ˚ and from 2.43 to displacements and the Ga –H distances decrease from 0.64 to 0.28 A ˚ , respectively, on going from þ 2 to 2 1 charge of the complex, in agreement with 2.00 A the local relaxations found in the case of the mono-hydrogen N – Hþ BC ð – GaÞ complex (see Table 13.1). The above results show that even the H pairs behave quite differently in GaAs and GaAsN. Two different Hp2 -like complexes more stable than the H2 molecules can be formed indeed in GaAsN at variance with the case of GaAs where Hp2 -like complexes are metastable [15]. Moreover, an As – 2Hþ2 BC complex with a C2v symmetry like that of the N – 2Hþ2 complex is not stable in pure GaAs, thus further confirming that the strength of BC the N – H bonds has significant effects on the properties of di-hydrogen complexes. 13.3.3 Formation Energies and Stability of N – H Complexes The above theoretical results concerning the structure and relative total energies of N – H complexes suggest that different mono-hydrogen and di-hydrogen complexes are stabilized by the formation of strong N –H bonds and may exist in hydrogenated GaAsN. We can now enrich this theoretical picture by analyzing the formation energies of the above N – H complexes. These formation energies depend on the position of the Fermi energy in the energy gap. Thus, the results achieved for the GaAs and GaAsN energy gaps will be preliminarily discussed. The 1 0/2 [GaAs] value calculated for pure GaAs is 1.85 eV, 22% higher than the experimental value of the energy gap (1.52 eV). An 1þ=0 value of 1.84 eV has also been estimated for the electronic level induced in the energy gap by a Si donor (SiGa) in GaAs. In agreement with the shallow character of this dopant, the 1þ=0 ½SiGa  value is close to the 10=2 ½GaAs value, thus indicating the consistency of the present approach. The value of 1.85 eV is assumed, therefore, as our estimate of the GaAs energy gap. The 10=2 ½N value calculated for an isolated N atom in GaAs is 1.51 eV from the top of the valence band. This value is assumed as the energy gap

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Table 13.3. Formation energies per H atom (in eV) of H complexes and molecules in GaAs0.97N0.03 calculated for Fermi energy ðme Þ values equal to 0 (top of the valence band), Eg =2 and Eg ; where Eg is the calculated GaAsN energy gap (1.51 eV) Complex [N–Hþ BC(–Ga)] [N–H0BC(–Ga)] [N–H2 BC(–Ga)] [(Ga–)N –Hþ AB] [(Ga–)N –H0AB] [(Ga–)N –H2 AB] [N–Hp2(a)þ1] [N–Hp2(a)] [N–Hp2(a)21] [N–Hp2(b)] [N–2Hþ2 BC] [N–2Hþ1 BC] [N–2H0BC] [N–2H21 BC] [H2(N)] [H2(Ga)] [Hþ BC] [Hp2] [H2(Ga)]

0

Eg/2

Eg

21.01 0.07 1.31 20.85 0.39 1.43 20.23 20.28 0.81 20.21 20.94 20.48 20.03 0.92 0.41 0.23

20.25 0.07 0.55 20.09 0.39 0.67 0.15 20.28 0.43 20.21 20.18 20.10 20.03 0.54 0.41 0.23

0.51 20.07 20.21 0.67 0.39 20.09 0.53 20.28 0.05 20.21 0.58 0.28 20.03 0.16 0.41 0.23

0.05 0.56 0.20

0.81 0.56 0.20

1.57 0.56 0.20

Formation energies per H atom of several H complexes and molecules in GaAs are given in the last three rows of the table.

of the GaAs0.97N0.03 alloy (the alloy simulated by a 64-atom supercell), thus corresponding to a reduction of 340 meV of the calculated GaAs energy gap, close to the experimental value of 400 meV [47]. The formation energies per H atom of the most interesting mono- and di-hydrogen complexes corresponding to Fermi energy values equal to 0 (top of the valence band), Eg =2; and Eg ; where Eg is the calculated GaAsN energy gap (1.51 eV), are given in Table 13.3. This table also reports the formation energies of H2 molecules in GaAsN as p well as of Hþ BC ; H2 ; and H2 molecules in GaAs. In the case of the H2 molecules, H2(Ga) indicates a molecule located close to a Td site that has Ga atoms as nearest neighbors. The formation energies of Table 13.3 permit one to identify the most stable N – H complex at a given Fermi energy value provided that the charge state of each complex corresponding to that Fermi energy is known. In the cases of the N – HBC and N – Hp2 ðaÞ complexes, this information is given in Figure 13.5. This figure reports the formation energies of these complexes in different charge states as a function of the Fermi energy, thus indicating, for each complex, the charge state corresponding to the lowest energy at a given value of the Fermi energy. Moreover, in the same figure, the crossing points of the formation energies corresponding to different charge-states of the complexes permit one to estimate

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Figure 13.5. Formation energy as a function of the Fermi energy me for the N–HBC and N – Hp2 ((a) and (b)) complexes in GaAs0.97N0.03. The vertical short-dashed and long-dashed lines correspond to the 10=2 ½N and 10=2 ½GaAs values, respectively, namely to the energy gaps of GaAs0.97N0.03 and GaAs (1.51 and 1.85 eV, respectively). The line segments represent the charge states of the complexes and the dots indicate the transition energies.

the transition energy values. The formation energies of the N –HAB complex in different charge states are not shown in Figure 13.5, since they are almost identical to those corresponding to the N –HBC complex. The formation energies of the N –2HBC complexes as a function of the Fermi energy are shown in Figure 13.6.

Figure 13.6. Formation energy as a function of the Fermi energy me for the N–2HBC complexes in GaAs0.97N0.03. The vertical short-dashed and long-dashed lines correspond to the 10=2 ½N and 10=2 ½GaAs values, respectively, namely to the energy gaps of GaAs0.97N0.03 and GaAs (1.51 and 1.85 eV, respectively). The line segments represent the charge states of the complexes and the dots indicate the transition energies.

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An analysis of the results given in Table 13.3 can now be performed by taking into account the formation energy graphs shown in Figures 13.5 and 13.6. Preliminarily, it can be observed that, in GaAs, the H2 molecule is the most stable species for almost all the me values in the energy gap (see the last three rows in Table 13.3). In GaAsN, the N – Hp2 complexes (the (a) and (b) complexes in the table) and the N –HBC complexes (in the various charge states) are instead more stable than the H2 molecules. These results confirm, therefore, that the formation of strong N –H bonds stabilize both the HBC and Hp2 complexes with respect to the case of GaAs. The results in Table 13.3 also indicate that p- and n-type doping have significant effects on the formation of the N – H complexes. When the Fermi level is close to the valence band maximum (VBM) (p-type doping), Figures 13.5 and 13.6 indicate that the N – HBC, N – HAB, N – Hp2 ðaÞ; and the N – 2HBC complexes have the þ 1, þ 1, 0 and þ 2 charge states, respectively. Then, the values in Table 13.3 show that the N – Hþ1 BC complex is the most þ favored one and that the N – 2Hþ2 and N – H complexes have also small formation BC AB energies. In the case of semi-intrinsic GaAsN (Fermi energy value equal to Eg =2), Figures 13.5 and 13.6 indicate the charge states of þ 1, þ 1, and 0 for the N – HBC, N –HAB and N – Hp2 complexes, respectively, while the charge state of the N – 2HBC complex could be p þ 2 or þ 1. The formation energies of the N – Hþ BC and N – H2 complexes are very close, thus implying that they could coexist at that Fermi energy location. The formation of the þ1 N – 2Hþ2 BC and N – 2HBC complexes is less certain because they have formation energies 200 and 360 meV larger than that of the N – Hp2 ðaÞ complex, respectively. N – Hþ AB complexes p should not be formed. A similar analysis shows that the N – H2 BC and N – H2 complexes should prevail when the Fermi level is close to the CBM (n-type doping). It also has to be taken into account that hydrogenation changes the position of the Fermi level in a given semiconductor because H passivates the shallow impurities. Thus, e.g. in p-type GaAsN, þ þ2 the N – Hþ BC ; N – HAB ; and N – 2HBC complexes are favored at the beginning of hydrogenation. Then, the Fermi level raises due to the H passivation of the shallow acceptors and the two N – Hp2 complexes should be also formed. When the Fermi level reaches the midgap, the N – Hp2 ðaÞ; N – Hp2 ðbÞ; and N – Hþ BC complexes are the most favored þ2 complexes. The N – Hþ and N – 2H complexes previously formed are likely still AB BC present. One should expect, therefore, that all of the above five complexes can be observed in hydrogenated p-type GaAsN. In the case of hydrogenated n-type GaAsN, the neutral 21 N – Hp2 and the N – H21 BC complexes start to form. The formation of the N – HAB and N – 2 0 HBC complexes is instead uncertain due to their higher formation energies. Then, hydrogen passivates the shallow donors, thus lowering the Fermi level. When me is close to midgap, the N – Hp2 and N – Hþ1 BC complexes should be present, while the presence of N – HAB and N – 2HBC complexes remains uncertain. In summary, the above results indicate that (i) after hydrogenation, the Fermi level is located close to the midgap independent on the initial doping conditions. This implies that the N – Hp2 complexes should be formed both in p- and n-type GaAsN. In turn, this is a significant result, because the N – Hp2 complexes

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play a significant role in the N passivation, as will be explained in the following section. (ii) Different hydrogen complexes should be formed in the case of p- and n-type GaAsN. 13.3.4 Transition Energies and H Passivation of N Electronic Effects First, let us consider the N passivation in the case of p-type GaAsN. In this case, it has been shown in the previous section that the most stable complex, N – Hþ BC ; starts to form at the þ2 beginning of hydrogenation together with the N – Hþ and the N – 2H AB BC complexes. Then, p the Fermi level raises and the N – H2 complexes ((a) and (b)) should be formed. As observed above, in Figure 13.5 the crossing points of the formation energies corresponding to the different charge-states of the N –HBC and N – Hp2 ðaÞ complexes permit one to estimate the transition energy values. Figure 13.5 shows that the 1 þ/0[N –HBC] is about 0.4 eV lower than the energy gap estimated for the GaAs0.97N0.03 alloy. The 1 0/2 [N – HBC] is about 0.2 eV higher than the 1 þ/0[N –HBC] value and still lower than the GaAsN energy gap. Similar results have been achieved in the case of the N –HAB complexes. For what concerns the N – Hp2 ðaÞ complex, the 1þ=0 ½N – Hp2 ðaÞ value is located inside the valence band, close to the VBM of GaAsN (out of scale and not shown in Figure 13.5). The 10=2 ½N – Hp2 ðaÞ value is instead about 0.3 eV higher than the energy gap estimated for pure GaAs. Similar results are obtained in the case of the N – Hp2 ðbÞ complex. Although the above 1n=nþ1 values are affected by the well-known LDA band gap error, they clearly show that the effects of N on the GaAs energy gap can be neutralized by the formation of the N – Hp2 ðaÞ complex, while mono-hydrogen complexes do not restore the GaAs band gap. Similarly, in the case of the N –2HBC complexes, an analysis of the transition energies shown in Figure 13.6 indicates that the GaAs energy gap could be restored by the formation of the neutral N – 2H0BC complex. A value of 1.91 eV can be estimated indeed for the 1 0/2 1[N – 2HBC] transition energy level close to the value of the energy gap estimated for pure GaAs. On the basis of the above results, it can be concluded that, in the case of p-type GaAsN, the N – Hp2 complexes have the strongest effects on the band gap and are, therefore, the main responsible of N passivation. The N – 2HBC complexes can also neutralize the N effects on the GaAs band gap. In the case of n-type GaAsN, the N – 2HBC complexes should not be formed. The N passivation is achieved, therefore, only through the formation of the N – Hp2 complexes. For what concerns the models for the N passivation by H, basically, two models have been proposed to explain why the lowering of the GaAs conduction band minimum (CBM) induced by N in GaAsN is not neutralized by forming the mono-hydrogen N – HBC complexes, while the formation of the N – Hp2 complexes pushes the CBM back up completely [25 – 28]. The first model is based on a three-step process schematically shown in Figure 13.7 [25]. First, the bonding of a HBC atom to N leads to a large atomic displacement, breaking the involved Ga – N bond. This eliminates one of the nitrogenderived GaAsN CBM states, creating a N dangling bond (DB)-like state in the valence

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Figure 13.7. A schematic plot of the effect of the N – Hp2 ðaÞ complexes on the band gap of GaAsN. In step one, one of the Ga– N bonds is broken. A Ga DB-state and a N DB-state emerge at the expense of one GaAsN CBM state. In step two, H(1) is added to the AB side of N, forming the N– H(1)B and N– H(1)A states. In step three, H(2) is added next to the Ga, forming the Ga –H(2)B and Ga –H(2)A states. Figure reprinted with permission from Ref. [25]. Copyright (2002) by American Physical Society.

band and a Ga DB-like state near the GaAsN CBM. Second, the binding of H(1) to the N DB-state creates an N – H(1)B bonding state deep in the valence band and an N –H(1)A antibonding state in the GaAs conduction band. Third, the binding of H(2) to the Ga DB-like state creates a bonding Ga – H(2)B state in the valence band and an antibonding Ga –H(2)A state inside the conduction band of GaAs. The net results of this process is that one GaAsN CBM state is completely removed.

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The second model is based on an analysis of (i) the bonding or antibonding character of p the electronic states induced by the N – Hþ BC and N – H2 complexes, and (ii) the local lattice relaxations occurring in the N – HBC complexes with different electronic charge [26,28]. Contour plots in the (110) plane of the charge densities lCn;0 l2 corresponding to the lowest unoccupied molecular orbitals (LUMO) induced by an isolated N atom and its N – Hþ BC and N – Hp2 complexes are shown in Figure 13.8. The LUMO of the isolated N (i.e. the conduction band minimum of GaAsN) is characterized by a strong localization of the electronic charge on the N atom, see Figure 13.8(a). The formation of the N – Hþ BC complex gives rise to an occupied level in valence band corresponding to the formation of a strong N – H bond and to the LUMO of Figure 13.8(b). Three main features characterize the latter state: (a) the electronic charge is still strongly localized on the N atom as in the case of isolated N, although polarized toward the Hþ ion; (b) the charge distribution of Figure 13.8(b) clearly shows the existence of a dangling bond of the Ga neighboring the H ion that points toward the H itself; (c) the LUMO of Figure 13.8(b) does not have an antibonding character. It can induce instead a weak bonding Ga – HBC interaction. In detail, the point (a) can be explained in terms of a Hþ ion taking the place of the Ga atom no longer bonded to the N atom. The N atom forms indeed a stable N – H bond and still keeps all of its five electrons to form four chemical bonds, i.e. three N electrons are involved in three Ga – N bonds and the remaining two electrons bind the Hþ BC ion instead of the fourth Ga atom. Thus, the Hþ insertion in the Ga –N bond does not affect the main characteristic of the original nitrogen LUMO, that is, the strong charge localization on N. On the other hand, the fact that the Ga dangling bond can induce a Ga – HBC bonding interaction, points (b) and (c) above, is supported by the previous discussion of the atomic relaxations occurring in the N – HBC complexes with different electronic charges, see Section 13.3.1. Those atomic relaxations show indeed that, when occupied by one or two electrons, the LUMO of Figure 13.8(b) induces a progressive reduction of the Ga – HBC distance as shown by the 0 2 geometries of the N – Hþ BC ; N – HBC and N – HBC complexes, see Table 13.1. The þ characteristics of the LUMO of the N – HBC complex (i.e. its similarities with the LUMO of the isolated N and the absence of any antibonding character) account, therefore, for the fact that this state is not higher in energy than the LUMO of the isolated N. In turn, this implies that the formation of a mono-hydrogen complex cannot lead to the N passivation. In the case of the N – Hp2 ðaÞ complex, two N electrons and the two electrons of the H atoms are involved in the formation of the Ga –H and N –H bonds. The occupied electronic levels corresponding to these stable bonds are located in and close to the top of the valence band. The latter bonding state has its antibonding counterpart in the LUMO shown in Figure 13.8(c). In this state, the charge is still localized on the N atom but polarized towards the HBC atom, that is, towards the atom bonded to the Ga atom. Furthermore, there is some charge localization between the same two non-bonded H and N atoms. This charge localization reveals a strong antibonding character of this electronic state, that accounts for an 10=2 ½N – Hp2 ðaÞ higher than 1 0/2 [N] and 1 0/2 [N– HBC] and also higher than the value

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Figure 13.8. Contour plots in the (110) plane of the charge density lCn;0 l2 corresponding to the lowest p unoccupied molecular orbital (LUMO) of (a) an isolated N atom, (b) the N – Hþ BC complex, and (c) the N – H2 ðaÞ complex, in GaAs0.97N0.03. The Ga, As and N atoms are indicated by black, gray, and white full dots, respectively. Small crosses represent the H atoms.

estimated for the bottom of the GaAs conduction band. The formation of the N – Hp2 ðaÞ complex can lead, therefore, to the neutralization of the N effects on the GaAs energy gap. There is a substantial good agreement between the above two models of N passivation. Moreover, it has to be noted that the second model reveals interesting relationships between the H passivation of the electronic effects of N, the nature of the electronic states p induced by the N – Hþ BC and N – H2 complexes, and the local lattice relaxations occurring in

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the N – HBC complexes with different electronic charge. These indications are also related to the H passivation of the effects N has on the structure of GaAs in GaAsN, as will be explained in the following sections. While different theoretical studies agree on the values of the transition energies corresponding to the N – HBC and N – Hp2 complexes and the N passivation models [23, 25 –28], one theoretical study has suggested that mono-atomic H in GaAsN exists only in a donor charge state [25]. In that study, the (þ /2 ) transition energy corresponding to the N – HBC complexes has been found indeed above the CBM estimated for GaAsN, see Figure 13.9 and compare with Figure 13.5. This different result may be related to peculiar LDA corrections applied to the defect electronic states in that theoretical study [25]. In Figure 13.9, the (þ /2 ) transition energy is located about 0.2 eV above the GaAsN CBM. Such a small energy difference makes this theoretical prediction less firm. However, a more pronounced donor behavior of H is expected in the case of InGaAsN where the CBM is lower than that of GaAsN. As a matter of fact, in the InGaAsN alloy, a different study has confirmed a H donor behavior as will be discussed in a following section [28].

Figure 13.9. Formation energies of monatomic H in GaAsN as a function of the Fermi energy 1F : Only the lowest energy BCN configuration (i.e. N –HBC) is shown for each charge state: (þ), (0), and (2). The vertical dashed line indicates the calculated band gap of GaAsN. Figure reprinted with permission from Ref. [25]. Copyright (2002) by American Physical Society.

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Previous results concern the H passivation of the most important effect of N in GaAsN, that is the dramatic reduction of the GaAs energy gap. However, N also induces a strong modification in the conduction band curvature which results in an increase in the electron effective mass and a lowering of the exciton localization. These effects are also neutralized by H incorporation. Theoretical results have accounted for these experimental findings [11]. Figure 13.10(a) depicts the difference of the total charge densities calculated with and without an excess electron, namely, the charge density of an added electron in a H-free GaAsN crystal. The excess electron in the conduction band is clearly localized along the Ga –N bonds. Figure 13.10(b) shows the same quantities calculated for a GaAsN alloy containing the N – Hp2 ðaÞ complex. A delocalization of the excess electron can be observed in this case consistently with the increase in the exciton radius and a decrease in the electron effective mass. These findings are confirmed by the similar effective masses calculated for hydrogenated GaAsN and GaAs, and by the almost identical band structures in the two cases. Thus, the formation of N – Hp2 ðaÞ complexes can also account for the H passivation of fine N effects on the GaAs band structure. 13.3.5 H Passivation of N Structural Effects In GaAsN, small percents of N affect not only the band structure of the host material but also its lattice structure [10]. In detail, in the case of the GaAsyN12y ðy ¼ 0:0081Þ alloy grown on a GaAs (001) surface, high-resolution X-ray diffraction measurements have  shown a reduction of the lattice constant along the growth direction ða’ GaAsN ¼ 5:636 AÞ ˚ with respect to that of the GaAs substrate (aGaAs ¼ 5.653 A). Moreover, it has been shown that H can neutralize these structural effects of N by restoring the value of aGaAs for a’ GaAsNþH : The same effects of N and H on the lattice properties were clearly observed in

Figure 13.10. (a) Calculated charge isosurfaces for an electron added to a neutral 64-atom GaAsN supercell without H. Light and dark gray balls indicate As and Ga atoms, respectively. (b) Same as (a) for a GaAsN lattice in which a N – Hp2 (see the text) complex is formed. H atoms are indicated by pale gray balls in the figure center. Figure reprinted with permission from Ref. [11]. Copyright (2004) by American Physical Society.

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the GaAsyN12y ðy ¼ 0:0013Þ and InxGa12xAsyN12y ðx ¼ 0:36; y ¼ 0:052Þ alloys. The effects of the formation of different N –H complexes on a’ of the GaAsN alloy were also theoretically investigated [10]. In detail, preliminary theoretical calculations concerned p the structural effects induced by the formation of the N – Hþ BC and N – H2 ðaÞ complexes. The geometries of both the complexes are characterized by large local-lattice relaxations, ˚ for an isolated N to as shown by an increase in the Ga –N distance from the value of 2.05 A þ p ˚ for the N – H and N – H2 complexes, respectively, see the values of 3.48 and 3.60 A BC Table 13.3. However, surprisingly, these quite similar local relaxations have completely different effects on the a’ of hydrogenated GaAsN. The formation of N – Hp2 complexes ˚ leads to a value of a’ GaAsNþH equal to 5.51 A, almost coincident with that theoretically ˚ . On the other hand, in the case of the N – Hþ estimated for aGaAs, that is equal to 5.56 A BC complexes, not only there is no recovering of the aGaAs value, but the value found for the ’ ˚ ˚ a’ GaAsNþH ; 5.37 A, results to be slightly smaller than that estimated for aGaAsN ; 5.41 A. In a þ different study, the theoretical investigations have been extended to the N – HAB and þ N – 2Hþ2 BC complexes [30]. The geometry of the N – HAB complex is characterized by a p Ga – N distance larger than that estimated for N – H2 ðaÞ; that is the complex recovering the GaAs lattice structure, see Table 13.1. In the N – 2Hþ2 BC complex, the Ga –N distance is instead almost coincident with that of the N – Hþ complex. Notwithstanding, these two BC ˚ , slightly smaller than the value of a’ complexes lead to a same a’ value of 5.39 A GaAsN : Even these results confirm, therefore, that only the N – Hp2 ðaÞ complex neutralizes the structural effects of N. In order to clarify this puzzling result, the geometries of the N – HBC, N – HAB and N – Hp2 complexes were carefully analyzed (the N – 2Hþ2 BC complex was not considered because it behaves like the N – Hþ complex). In detail, this analysis concerned (i) the geometries of BC the two mono-hydrogen complexes in different states of charge, see Table 13.1; and (ii) the ˚ , that geometries of the three above N – H complexes calculated for an a’ value of 5.34 A ’ is, smaller than the aGaAsN ; see Table 13.4. Preliminarily, we would recall the results discussed in Sections 13.3.1 and 13.3.4 concerning the geometries of the N – HBC complex with different charge states and the models proposed for the N passivation. First, the geometries of the N – HBC complex with charge states of þ 1, 0, and 2 1 show that the Ga – HBC and Ga – N distances and the Ga atomic displacements (DGa) decrease by Table 13.4. Atomic distances and atomic displacements with respect to ideal positions (DX values) of some ˚ , see the text mono- and di-hydrogen complexes in a contracted lattice of GaAsN with a’ equal to 5.34 A Complex

N –HBC

[N –Hþ BC( –Ga)] [(Ga–)N –Hþ AB]

1.04

[Ga– HBC –N–HAB]

2.00

N–HAB 1.04 1.05

Ga –HBC

Ga– N

DGa

DN

2.29

3.33 3.55 3.51

0.50 0.38 0.20

0.49 0.83 1.07

1.51

Positive (negative) DX values indicate an outward (inward) atomic displacement with respect to the Ga– N chemical bond. Distances and displacements are given in angstroms.

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increasing the electronic charge on the complex. This suggests the existence of a Ga – HBC bonding interaction that increases with the electronic charge on the complex. In turn, this result perfectly agrees with the features of the LUMO induced by the N – Hþ BC complex, which becomes occupied by one and two electrons when the complex has charge 0 and 2 1, respectively. This electronic level is characterized indeed by a Ga dangling bond pointing toward the HBC atom, which can account for the existence of a Ga – HBC bonding interaction, and by a location deep in the GaAs energy gap which agrees with its bonding character. Second, the geometry of the N – Hþ AB complex is characterized by the formation of a strong N – H bond and negligible Ga – N interactions. Notwithstanding, even in this complex, the Ga – N distances and DGa values decrease by increasing the electronic charge on the complex. This can be related to the beginning of a Ga – N bonding interaction favored by an increase in the charge on the Ga dangling bond pointing toward the N atom. Finally, at variance with the cases of the above mono-hydrogen complexes, in the N – Hp2 complex, an increase in the electronic charge (i.e. a change in the charge of the complex from 0 to 2 1) does not favor an N – HBC bonding interaction. In fact, there is no reduction of the N –HBC and Ga –N distances in the negatively charged complex. This result is also supported by the antibonding character of the LUMO of the neutral complex discussed in Section 13.3.4. The different evolution of the N – HBC, N –HAB, and N – Hp2 ðaÞ geometries with the electronic charge of the complex can account for the different effects of these complexes on the structure of the crystal lattice. As an example, in the case of the N – Hþ BC complex, the evolution of the complex geometry with increasing electronic charge indicates the existence of some Ga – HBC bonding interaction. This interaction can also be favored by a reduction of the Ga –HBC distance caused by a contracted a’ : In turn, this interaction can lower the total energy of a contracted lattice configuration, thus leading to an a’ not larger (and actually slightly smaller) than the a’ GaAsN : In other words, the chemical bonding in the N – Hþ complex can neutralize the effects of the local lattice relaxations suggested by the BC atomic displacements reported in Table 13.1. Similar considerations can apply to the case of the N – Hþ AB complex. Thus, in the above two complexes, the effects of a contraction of the Ga –N distances should be similar to those induced by an increase in the electronic charge of the complex. On the other hand, in the case of the N – Hp2 complex, similar effects stabilizing a contracted geometry of the complex do not exist. The above considerations are supported by a comparison between the geometries of the above three complexes in GaAsN, see Tables 13.1 and 13.2, and in the case of a small contraction of the GaAsN lattice corresponding to a reduction of about 1% of a’ ˚ ), see Table 13.4. In the contracted lattice, the DGa values in the (i.e. a’ equal to 5.34 A þ N – Hþ and N – H complexes are reduced by 21 and 28%, respectively, with respect to BC AB their corresponding values in the non-contracted lattice, see Table 13.1. On the other hand, in the case of the N – Hp2 complex, the DGa value increases by 20% in the contracted lattice with respect to the corresponding value in the non-contracted one, see Table 13.2.

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These results clearly show that the mono-hydrogen complexes and the N – Hp2 complexes have opposite reactions to a lattice contraction in agreement with the different characteristics of their chemical bonding. The above results lead to some interesting suggestions. First, only the N – Hp2 ðaÞ complexes neutralize both the electronic and structural effects induced by the presence of N in GaAs. Second, the origin of the different behavior of the N – Hp2 ðaÞ and mono-hydrogen complexes is the same, that is, the different chemical bonding characterizing these complexes. Third, the model proposed to explain the passivation of the electronic effects of N gives also useful indications to account for the neutralization of the structural effects. 13.3.6 Formation Mechanism of N – Hp2 and N – 2HBC Complexes in p-type GaAsN Here, results are reported about a mechanism recently proposed for the formation of the N – Hp2 ðaÞ and N – 2Hþ2 BC ðC2v Þ complexes in the p-type GaPN, which holds in the case of GaAsN as well [29]. In GaAsN, the formation of N –H complexes is related to the formation of a H species (Hþ, H0, or H2) and its diffusion in the lattice of the host material (GaAs) until it binds to a N atom. In pure GaAs, the BC site of a Ga –As bond is the stable site of Hþ, the AB site on the anion side is the stable site for H0 and the AB site (close to a Td site) on the cation side is the stable site for H2 [29,45]. Moreover, the formation energies of the different H species as a function of the Fermi level show that the neutral H is never stable [29,45,46]. In detail, Hþ BC is the stable species for a Fermi level ranging from the VBM to a 60% of Eg ; whereas, for higher Fermi levels, the stable species p becomes H2 AB : Let us consider now the formation of the N – H2 ðaÞ complexes in semiintrinsic or slightly p-type GaAsN, which corresponds to the material experimentally investigated [4,8,13]. In GaAsN, a Fermi level located between the VBM and Eg =2 induces the formation of the Hþ BC species in the GaAs lattice. Moreover, it is assumed that the N atoms, due to their higher electronegativity, carry a fraction of negative charge larger than that carried by the As atoms, as also suggested by the charge density plot of Figure 13.3(a). This extra charge can give rise to a driving force which attracts the Hþ BC ions towards the N þ atoms. The N – Hþ complexes are then formed. A second H ion can then be attracted by BC the negative charge that still piles up on the N atom in the N – Hþ complex, see Figure BC 13.3(b). The second Hþ ion should approach the N atom on the side of the AB site, see Figure 13.1. This seems quite reasonable because the formation of an N – Hþ AB bond does not require any local lattice relaxation. The insertion of the second Hþ ion at a neighbor BC site, which would lead to the C2v complex of Figure 13.2(e), requires instead a sizeable ˚ (see Table 13.2 and the atomic relaxation of the involved Ga –N bond from 2.05 to 3.47 A displacements sketched in Figure 13.11, path II). Thus, the formation of an N – Hp2 ðdÞþ2 complex having the geometry of the N – Hp2 ðdÞ complex shown in Figure 13.2(d) þ and involving a Hþ BC and a HAB ions both bonded to the N atom has been investigated, see Figure 13.11. Very interestingly, the configuration of the N – Hp2 ðdÞ

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Figure 13.11. Sketch diagram showing the possible evolution of the N – Hp2 ðdÞþ2 complex along the paths (I) and (II) leading to the N – Hp2 ðaÞ and the N – 2Hþ2 BC complexes, respectively. Main atomic displacements are indicated by dashed arrows.

complex shown in Figure 13.2(d), unstable when formed by neutral H atoms, is metastable when involving two Hþ ions. The formation of the N – Hp2 ðdÞþ2 complex can have interesting consequences. It can represent indeed an intermediate complex preceding the formation of both the N – Hp2 ðaÞ and N – 2Hþ2 BC complexes, as it will be shown in the following. Preliminarily, we observe that the N – Hp2 ðdÞþ1 complex is also metastable. The formation energies (per H atom) of the N – Hp2 ðdÞþ2 and N – Hp2 ðdÞþ1 complexes are equal to 0.22 and 0.20 eV, respectively, for the Fermi level at the VBM. A formation energy of 0.50 eV has also been estimated for the neutral N – Hp2 ðdÞ complex with the atoms fixed to the positions they have in the N – Hp2 ðdÞþ1 complex. The above formation energies permit to estimate the values of 0.86 and 0.64 eV for the 1þ2=þ1 ½N – Hp2 ðdÞ and 1þ1=0 ½N – Hp2 ðdÞ transition levels. These transition levels are, therefore, located below the position of Eg =2 estimated for the GaAsN alloy. Thus, the following mechanism has been proposed for the formation of the N – Hp2 ðaÞ complex in p-type GaAsN: Hþ BC ions diffuse in the GaAs lattice and bind to the N atoms by forming first the N – Hþ complexes and then the N – Hp2 ðdÞþ2 BC ones. H ions also bind to charged shallow acceptors and passivate their effects by raising the Fermi level. When the Fermi level reaches Eg =2 the charged N – Hp2 ðdÞ complexes become neutral (due to the location of the 1þ2=þ1 ½N – Hp2 ðdÞ and 1þ1=0 ½N – Hp2 ðdÞ below Eg =2) and, as discussed in Section 13.3.2, they spontaneously transform into the N – Hp2 ðaÞ

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complexes, see path (I) in Figure 13.11. Alternatively, path (II) of Figure 13.11 can p þ2 be considered. The Hþ complex can move at a BC site of a close AB ion of an N – H2 ðdÞ Ga – N bond (likely by involving a local vibration mode), thus forming the N – 2Hþ2 BC ðC2v Þ p þ2 complex. Interestingly, the evolution of the intermediate N – H2 ðdÞ complex along path (I) or (II) of Figure 13.11 depends on the position of the Fermi energy. When the Fermi energy is close to VBM, the charged N – Hp2 ðdÞþ2 complex may only evolve along path (II). On the other hand, for a Fermi energy close to Eg =2; the same complex becomes neutral and evolves toward path (I) leading to the formation of the most stable neutral complex. The Fermi energy works, therefore, as a “switch” between the above two paths. The above mechanism has significant consequences on the N –H complexes which can be formed in p-type GaAsN. The analysis of the formation energies reported in Section 13.3.3 would suggest indeed the formation of five complexes in that alloy: the N – Hþ BC ; þ þ2 p N – HAB ; N – 2HBC ; and the two N – H2 complexes. The above formation mechanism implies instead that in p-type GaAsN the formation of the N – Hþ BC complexes is followed first by that of the N – 2Hþ2 ðC Þ complex. Then, for a raised Fermi level, the N – Hp2 ðaÞ 2v BC þ complexes are formed. The N – HBC complexes initially formed are largely involved in the formation of the above two di-hydrogen complexes, thus their final concentrations should be quite low. Moreover, the N – Hp2 ðbÞ complexes, although characterized by a small formation energy, should not be formed. N – Hþ AB complexes may be formed but with low concentrations due to their higher formation energies. Thus, the above results lead to the p conclusion that only two complexes, i.e. the N – 2Hþ2 BC and N – H2 ðaÞ; out of five are formed in hydrogenated p-doped GaAsN. 13.3.7 Vibrational Properties of N –H Complexes Generally, experimental investigations of the local vibrational modes in hydrogenated semiconductors give significant information on the structural properties of complexes formed by H and impurities or defects, thus representing a severe test for theoretical predictions [14]. In this concern, the results of a recent infrared (IR) absorption spectroscopy investigation of the N- and H-related vibrational modes in hydrogenated, slightly p-type GaAsyN12y alloys [12] will be compared here with the corresponding theoretical results [48]. Preliminarily, it should be observed that while the theoretical studies generally agree on the existence of the N – Hp2 ðaÞ complex in GaAsN and its crucial role in the passivation of the N effects [11,23,25,26,28,30], the IR spectroscopy study cited above has challenged those theoretical results by suggesting the formation of an N – H complex where both the H atoms are bonded to the N atom, which is inconsistent with the structure of the N – Hp2 ðaÞ complex [12]. In the cited IR spectroscopy study, different vibrational frequencies have been measured in hydrogenated or deuterated slightly p-doped GaAsyN12y epilayers with y ¼ 0:008; see Table 13.5. In this table, the high frequencies of the absorption lines at 3195 and 2967 cm21 are characteristic of the stretching modes of H strongly bonded to a light

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Table 13.5. Vibrational frequencies (in cm21) for the H and D modes measured in hydrogenated and deuterated GaAsN [12]

nH nD

3195 2376

– 2233(w)

2967 2216

2868(w) 2137(w)

2015 –

1447 1076

798

Weak lines are indicated by “w”.

element like N and are much higher than those expected for Ga – H stretching (which has a typical frequency near 1800 cm21). The line at 1447 cm21 has a frequency characteristic of an N – H bending mode in an ammonia molecule (1627 cm21) suggesting an assignment to an N – H wagging mode. Similarly, the vibrational lines at 2376 and 2216 cm21 for a deuterated sample have frequencies characteristic of N – D stretching, and the 1076 cm21 line has a frequency near that of N – D bending in ammonia. The frequency ratio for the modes corresponding to the H and D lines is close to 1.34 similar to that observed previously for N –H modes. For a sample containing H and D, two additional D-stretching lines appear at 2366 and 2221 cm21 in addition to the lines observed in the sample containing only D. A new H-stretching line at 3192 cm21 that is the isotopically shifted partner of the 2366 cm21 line was also observed. All of these results suggested that the D-stretching lines at 2376 and 2216 cm21 were due to a single defect complex containing two coupled D atoms. In fact, for the corresponding defects containing both H and D, the stretching modes are dynamically decoupled to produce the new lines shifted toward the average position of the coupled modes. Similar considerations were presumed to apply to the corresponding H-stretching modes at 3195 and 2967 cm21. The weak line at a frequency of 2137 cm21 in the D-spectrum was suggested to be caused by a Fermi resonance interaction between the second harmonic of the 1076 cm21 line and the 2216 cm21 line. Similar considerations would apply to the H-stretching spectra where the lines at 1447 and 2967 cm21 would be related to the weak line at 2868 cm21. A vibrational band at 471 cm21 was also observed in GaAsN without H and assigned to N local modes. When the 471 cm21 band was removed by deuteration, a weak new absorption band at 505 cm21 appeared. A weak low-frequency mode in the hydrogenated sample at 495 cm21 was possibly present. Finally, series of anneals showed that the appearance of the above H and D lines were correlated with the changes in the band gap energy caused by H and with the changes of the N modes. On the ground of the above results, it was concluded that the principal D modes at 2376, 2216, and 1076 cm21 all belong to a single defect and similarly for the corresponding H modes at 3195, 2967, and 1447 cm21. This implies that two high frequency N –H modes are related to a same complex, which agrees with two H atoms bonded to a same N atom and is inconsistent with the structures of the N – Hp2 ðaÞ and N – Hp2 ðbÞ complexes suggested by theoretical studies [23,25 –28]. On the side of theory, the results discussed in the previous sections suggest that the p N – 2Hþ2 BC and N – H2 ðaÞ complexes are the most likely complexes formed in þ1 hydrogenated p-type GaAsN, while the presence of N – Hþ1 BC and N – HAB complexes

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443

is uncertain. The vibrational frequency values of N and H local modes calculated for the above four complexes, the N – Hp2 ðbÞ complex and an isolated N atom in the GaAs lattice are given in Table 13.6 [48]. The values of 3213, 3089 and 1442 cm21 estimated for the N – 2Hþ2 BC complex are in a very good agreement with the two high stretching frequencies of 3195 and 2967 cm21 as well as with the 1447 cm21 wagging frequency experimentally observed, respectively. The last values also agree with an estimate of 1578 cm21 for a wagging mode in the N – H3 molecule, see Table 13.6. Furthermore, 21 for a N local mode only the N – 2Hþ2 BC complex shows a frequency value of 532 cm 21 which is significantly higher than the values close to 430 cm found for an isolated N atom in GaAsN. This agrees with the increase in the N vibrational frequencies experimentally observed upon hydrogenation. The 2233 cm21 N –D mode and the 2015 cm21 N – H mode of Table 13.5 were not assigned by the experiment. The former mode would correspond to an N –H mode of 3003 cm21 (estimated on the ground of an N – H and N – D frequency ratio of 1.34). In this way, we would have two N – H local modes of 3003 and 2015 cm21 which favorably compare with the 2980 and 2003 cm21 frequency values calculated for the N – Hp2 ðaÞ complex. Further, a value of 1073 cm21 can be estimated for an N –H mode corresponding to the 798 cm21 N – D mode of Table 13.5. These two modes not previously assigned by the experiment could correspond to a wagging mode of the HAB in the N – Hp2 ðaÞ complexes as we will explain later. The above results strongly suggest the existence of both the N – Hp2 ðaÞ and N – 2Hþ2 BC complexes in p-type GaAsN. Two further arguments support that suggestion. The first one concerns the wagging frequency values estimated around 450 Table 13.6. Frequency values (in cm21) calculated for the H local vibration modes in several N–H complexes and for an isolated N atom in GaAsN are reported in the upper part of the table Complex

Bond

n (st)

n (wa)

n (wa)

n (wa)

n (N)

n (N)

n (N)

[N –Hþ BC( –Ga)] [N –Hp2(a)] [N –Hp2(a)] [N –Hp2(b)] [N –Hp2(b)] [(Ga–)N –Hþ AB] [N –2Hþ2 BC] [N –2Hþ2 BC]

N –HBC Ga –HBC N –HAB Ga –HAB N –HBC N–HAB N–HBC N–HBC

3156 2003 2980 1690 3121 3094 3213 3089

– – – – – – 1442 –

887 450 992 710 934 987 977 –

889 455 990 713 937 987 885 –

392 397 397 409 409 430 378 –

404 407 407 413 413 430 415 –

410 408 408 414 414 430 532 –

[N] [N –H3] [N –H3] [N –H3]

N –H N –H N –H

– 3428(3414) 3428(3414) 3294(3336)

– 1578(1627) – –

– 1578(1627) – –

– 978(968) – –

430 – – –

434 – – –

437 – – –

Frequency values calculated for the N–H3 molecule are reported in the lower part of the table together with the corresponding experimental values (in parentheses) taken from Ref. [51]. Stretching and wagging frequencies of the H-related modes are indicated by (st) and (wa), respectively. Frequencies corresponding to N-related modes are indicated by (N).

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and 900 cm21 for the Ga –HBC bonds in the N – Hp2 ðaÞ complex and for the N – HBC bonds in the N – 2Hþ2 BC complex, respectively. These wagging modes have not been observed experimentally. However, their invisibility seems to be an intrinsic feature of the bonds formed by a H atom located at the BC site of a covalent bond in both IV and III– V semiconductors. As an example, no wagging modes have been observed in the IR spectroscopy investigation of B –HBC – Si bonds in B-doped crystalline silicon (Si:B), of SiAs – HBC –Ga bonds in p-doped GaAs:Si and of CAs – HBC –Ga bonds in p-doped GaAs:C [14]. In the last case, the invisibility of the HBC wagging modes has also been accounted for in terms of reduced effective charges [49]. On the contrary, wagging modes are generally observed for a H atom located at an AB site, as in the case of the P –Si – HAB complex in Si:P or As – SiGa – HAB complex in n-doped GaAs:Si [14]. These last results support the assignment of the above 1073 cm21 N – H mode to a wagging mode close to 990 cm21 calculated for the N –HAB bond in the N – Hp2 ðaÞ complex. The second argument concerns the different strength of the vibrational lines p we would assign to the N – 2Hþ2 BC and N – H2 ðaÞ complexes. Experiment shows that two strong N – H vibrational lines at 3195 and 2967 cm21 are observed for the N – HBC bonds of the former complex whereas only a weak 2233 cm21 N –D line should be related to the N – HAB bond in the latter complex. This result could be caused by a p concentration of N – 2Hþ2 BC complex much higher than that of the N – H2 ðaÞ complex. Alternatively, the N –H modes could have a different IR activity in the two complexes. An estimate of the dipole moments corresponding to the N – H bonds in the above two complexes has been achieved by calculating the Lo¨wdin atomic charges of the involved atoms. Although this gives a rough estimate of dipole moments, a ratio of 1.5 is calculated between the dipole moments in the two complexes which strongly suggests p an IR activity of the N – 2Hþ2 BC complex higher than that of the N – H2 ðaÞ complex. In that case, both the complexes could be present with appreciable concentrations in hydrogenated GaAsN. As a final remark, the vibrational frequencies calculated for the þ p other, less likely N – H complexes (the N – Hþ BC , N – HAB ; and N – H2 ðbÞ complexes) are different from those of the N – Hp2 ðaÞ and C2v complexes (see Tables 13.5 and 13.6) and actually they are not experimentally observed, thus further confirming the good agreement between theory and experiment in the case of hydrogenated GaAsN alloys.

13.4. INTRINSIC N AND H IMPURITIES IN GaP AND GaAs

The results discussed in the previous sections concern GaAsN alloys containing N intentionally introduced in different concentrations (up to some percent) and exposed to hydrogenation treatments. Some pioneering experimental and theoretical studies concerned instead GaAs and GaP samples grown by liquid encapsulated Czochralski (LEC) technique, which implies the presence of very low concentrations of intrinsic

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N and H [2,3,22,23,50]. In the case of GaP, the local vibrations related to N and H where investigated by performing IR spectroscopy measurements [2,3,50]. Absorption lines at 2885.5 and 2054.1 cm21 and weaker lines at 2879.7 and 2052.4 cm21 were observed whose intensity ratio matched precisely the expected relative abundance of 15 N/14N. The higher frequencies are close to the N – H stretching frequencies found in molecules, thus suggesting the formation of a N – H defect. Moreover, uniaxial stress measurements showed that this defect possessed a trigonal symmetry. Then, a di-hydrogen model for that N –H defect having the configuration of the N – Hp2 ðdÞ complex was suggested as shown in Figure 13.2(d), where two H atoms are attached to a same substitutional N atom [2,3,50]. The observed N – H defect is also electrically active as photo-illumination results in a decrease in the intensity of the 2885.5 and 2054.1 cm21 bands and at the same time an increase in the intensity of two other bands at 2728.8 and 2102.2 cm21. The new bands are associated with the same defect in a different charge state. A bend mode at 1049.8 cm21 was also connected to the defect [2]. These experimental results are quite different from those previously discussed for hydrogenated GaAsN and were accounted for by different theoretical models which, however, are somewhat in contradiction with each other. A first theoretical study found that the N – Hp2 ðdÞ complex is unstable in GaPN as it is in GaAsN [22] (independently confirmed by two other studies [24,29]). This study also showed that the N – Hp2 ðdÞ complex is electrically inactive, that is, it does not induce electronic levels in the GaP energy gap, in conflict with the experimental results. The vibrational properties of the N –HAB complex with the charge state of þ 1, 0, and 2 1 were then investigated. This complex induces indeed an electronic level in the energy gap and can be optically active. The experimental results were then accounted for assigning the 2885.5 and 1049.8 cm21 lines to the stretching and wagging modes of the N – HAB complex and the 2054.1 cm21 line to an overtone of the 1049.8 cm21 line. Moreover, the different lines observed under photoillumination were related to a different charge of the N – HAB complex. A different theoretical study investigated the H vibration modes in GaPN [24]. The results of this work parallel those concerning the structure and formation energies of the N – H complexes in GaAsN, already discussed in the previous sections [23,25 – 29]. However, it assigns the two experimental high-frequency vibrational lines to the local modes related to the Ga –HBC and N –HAB bonds in the N – Hp2 ðaÞ complex. Such an assignment seems quite questionable, due to the observed relationship between the intensity ratio of the two observed lines and the relative abundance of 15N/14N suggesting that both the lines are to be ascribed to N –H modes. Finally, in LEC GaAs, the vibrational lines observed are quite similar to those found in the case of LEC GaP [3,50]. In GaAs, a further theoretical study has investigated the vibrational properties of the N –HBC and N –HAB complexes in different charge states as well as those of the N – Hp2 ðaÞ complex [23]. That study assigns the experimental lines to the stretching and wagging modes of the N –HBC complex, at variance with the two theoretical studies cited

446

Dilute Nitride Semiconductors

above. However, even this assignment seems questionable because, as observed in Section 13.3.7, the wagging modes related to the HBC atom are generally invisible. Instead, the experimental results found in the cases of LEC GaP and GaAs could be accounted for by the vibrational properties of the N – HAB complex, which is optically active and related to stretching and wagging H modes compatible with the measured frequencies.

13.5. N – H COMPLEXES IN InGaAsN

The theoretical results achieved in the case of the InGaAsN alloys and concerning the energetics, formation energies and passivation mechanisms of the N – H complexes closely parallel those found in the case of the GaAsN alloys [28]. An exception is represented by the case of monoatomic H, which behaves as a donor as anticipated in a previous section. This is shown by the transition energies reported in Figure 13.12 to be compared with those of Figures 13.5 and 13.9.

13.6. N – H COMPLEXES IN GaPN

The introduction of atomic H in GaPN alloys has almost the same effects observed in the case of GaAsN when high H doses are used in the hydrogenation treatments.

Figure 13.12. Formation energy as a function of the Fermi energy me for the N–HBC and N – Hp2 complexes in In0.25Ga0.75As0.97N0.03. The vertical short-dashed and long-dashed lines correspond to the 10=2 ½InGaAsN and 10=2 ½InGaAs values, respectively, namely to the energy gaps of In0.25Ga0.75As0.97N0.03 and In0.25Ga0.75As (0.82 and 1.62 eV, respectively). The line segments represent the charge states of the complexes and the dots indicate the transition energies.

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Some differences are observed instead in the optical behavior of hydrogenated GaPN and GaAsN, when using low H doses [8]. Theoretical investigations have found that the structure, the formation energies, passivating effects and electronic properties of the N – H complexes in the GaPN alloys are very similar to those found in the case of GaAsN alloys [29]. Thus, the different optical behavior of hydrogenated GaPN and GaAsN cannot be ascribed to different properties of the N –H complexes formed in the two materials. On the other hand, these investigations have found that the bonds formed by Hþ BC ions in the GaP lattice are stronger than those formed in GaAs, thus inducing a slower motion of these ions in GaP with respect to GaAs. This suggests that different actual H doses could be present in GaPN and GaAsN samples after the same hydrogenation treatment, thus explaining the different optical behavior observed in the two hydrogenated materials [29].

13.7. CONCLUSIONS

The results achieved in the case of hydrogenated GaAsN dilute alloys, the most investigated ones, lead to a clear and consistent theoretical picture, which can be schematically described as follows: (i) The results concerning the structure and relative stability of the N – H complexes identify some complexes which could be potentially formed in the hydrogenated alloy. (ii) The formation energies of these complexes show that different complexes can be formed depending on the doping conditions. Moreover, they permit to estimate the location of the electronic states induced in the energy gap by the N –H complexes. (iii) The above information, the nature of the electronic states induced by the complexes and the characteristics of the chemical bonding in the N – H complexes lead to models accounting for the different effectiveness of these complexes in determining the passivation of the electronic and structural effects of N on the properties of the host GaAs. (iv) Mechanisms suggested for the formation of the N –H complexes lead to a strict selection of the complexes which can exist in the lattice resulting in two complexes in the case of p-type GaAsN. (v) The above two complexes can account for the H neutralization of both the electronic and structural effects of N on the host GaAs. Moreover, the corresponding vibrational frequencies are in a very good agreement with the measured values. Thus, in the case of GaAsN, the theoretical findings perfectly match the experiment. Moreover, the conclusions achieved in the case of GaAsN hold to a large extent in the cases of InGaAsN and GaPN alloys.

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REFERENCES [1] Buyanova, I.A., Chen, W.M. & Monemar, B. (2001) Electronic properties of Ga(In)NAs alloys. MRS Internet J. Nitride Semicond. Res., 6, 2. [2] Clerjaud, B., Coˆte, D., Hahn, W.-S., Lebkiri, A., Ulrici, W. & Wasik, D. (1996) Nitrogen – dihydrogen complex in GaP. Phys. Rev. Lett., 77, 4930. [3] Hahn, W.-S., Clerjaud, B., Coˆte, D., Gendron, F., Porte, C., Ulrici, W., Wasik, D. & Wilkening, W. (1994) Nitrogen – hydrogen complexes in GaP and GaAs. Mater. Sci. Forum, 277, 143– 147. [4] Baldassarri Ho¨ger von Ho¨gersthal, G., Bissiri, M., Polimeni, A., Capizzi, M., Fischer, M., Reinhardt, M. & Forchel, A. (2001) Hydrogen-induced band gap tuning of (InGa)(AsN)/GaAs single quantum wells. Appl. Phys. Lett., 78, 3472. [5] Polimeni, A., Capizzi, M., Geddo, M., Fischer, M., Reinhardt, M. & Forchel, A. (2001) Effect of nitrogen on the temperature dependence of the energy gap in InxGa12xAs12yNy/GaAs single quantum wells. Phys. Rev. B, 63, 195320. [6] Bissiri, M., Baldassarri Ho¨ger von Ho¨gersthal, G., Polimeni, A., Gaspari, V., Ranalli, F., Capizzi, M., Amore Bonapasta, A., Jiang, F., Stavola, M., Gollub, D., Fischer, M., Reinhardt, M. & Forchel, A. (2001) Hydrogen-induced passivation of nitrogen in GaAs12yNy. Phys. Rev. B, 65, 235210. [7] Bissiri, M., Baldassarri Ho¨ger von Ho¨gersthal, G., Polimeni, A., Capizzi, M., Gollub, D., Fischer, M., Reinhardt, M. & Forchel, A. (2002) Role of N clusters in InxGa12xAs12yNy band gap reduction. Phys. Rev. B, 66, 033311. [8] Polimeni, A., Bissiri, M., Felici, M., Capizzi, M., Buyanova, I., Chen, W.M., Xin, H.P. & Tu, C.W. (2003) Nitrogen passivation induced by atomic hydrogen: the GaP1 2 yNy case. Phys. Rev. B, 67, 201303(R). [9] Masia, F., Polimeni, A., Baldassarri Ho¨ger von Ho¨gersthal, B., Bissiri, M., Capizzi, M., Klar, P.J. & Stolz, W. (2003) Early manifestation of localization effects in diluted Ga(AsN). Appl. Phys. Lett., 82, 4474. [10] Polimeni, A., Ciatto, G., Ortega, L., Jiang, F., Boscherini, F., Filippone, F., Amore Bonapasta, A., Stavola, M. & Capizzi, M. (2003) Lattice relaxation by atomic hydrogen irradiation of III-N-V semiconductor alloys. Phys. Rev. B, 68, 085204. [11] Polimeni, A., Baldassarri Ho¨ger von Ho¨gersthal, G., Masia, F., Frova, A., Capizzi, M., Sanna, S., Fiorentini, V., Klar, P.J. & Stolz, W. (2004) Tunable variation of the electron effective mass and exciton radius in hydrogenated GaAs12xNx. Phys. Rev. B, 69, 041201(R). [12] Jiang, F., Stavola, M., Capizzi, M., Polimeni, A., Amore Bonapasta, A. & Filippone, F. (2004) Vibrational spectroscopy of hydrogenated GaAs1 2 yNy: a structure-sensitive test of an Hp2(N) model. Phys. Rev. B, 69, 041309(R). [13] Polimeni, A., von Ho¨gersthal, G.B.H., Bissiri, M., Capizzi, M., Frova, A., Fischer, M., Reinhardt, M. & Forchel, A. (2002) Role of hydrogen in III-N-V compound semiconductors. Semicond. Sci. Technol., 17, 797. [14] Pankove, J.I. & Johnson, N.M. Eds. (1991) Hydrogen in Semiconductors, Semiconductors and Semimetals, vol. 34, Academic Press, New York. [15] Amore Bonapasta, A. & Pavesi, L. (1996) Hydrogen interaction with shallow and deep centers in GaAs. Int. J. Quantum Chem., 57, 823. [16] Figure 13.1 shows the locations of BC and AB sites in the case of Ga – N bond, where a N atom has taken the place of an As atom.

Theory of Nitrogen – Hydrogen Complexes in N-Containing III– V Alloys

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[17] The Td site is close to the AB site of Figure 13.1(b), and located along the axis of the Ga– N ˚ far from the N (As) atom. (Ga – As) bond, about 2.40 A [18] Shan, W., Walukiewicz, W., Ager, J.W., III, Haller, E.E., Geisz, J.F., Friedman, D.J., Olson, J.M. & Kurtz, S.R. (1999) Band anticrossing in GaInNAs alloys. Phys. Rev. Lett., 82, 1221. [19] Mattila, T. & Zunger, A. (1998) Deep electronic gap levels induced by isovalent P and As impurities in GaN. Phys. Rev. B, 58, 1367. [20] Mattila, T., Wei, S.H. & Zunger, A. (1999) Localization and anticrossing of electron levels in GaAs12xNx alloys. Phys. Rev. B, 60, R11245. [21] Kent, P.R.C. & Zunger, A. (2001) Theory of electronic structure evolution in GaAsN and GaPN alloys. Phys. Rev. B, 64, 115208. ¨ berg, S., Torres, V.J.B. & Briddon, P.R. [22] Dixon, P., Richardson, D., Jones, R., Latham, C.D., O (1998) Nitrogen – hydrogen defects in GaP. Phys. Stat. Sol. (b), 210, 321. [23] Kim, Y.-S. & Chang, K. (2002) Nitrogen-monohydride versus nitrogen-dihydride complexes in GaAs and GaAs12xNx alloys. Phys. Rev. B, 66, 073313. [24] Janotti, A., Zhang, S.B. & Wei, S.-H. (2002) Hydrogen vibration modes in GaP:N: the pivotal role of nitrogen in stabilizing the Hp2 complex. Phys. Rev. Lett., 88, 125506. [25] Janotti, A., Zhang, S.B., Wei, S.-H. & de Walle, C.V. (2002) Effects of hydrogen on the electronic properties of dilute GaAsN alloys. Phys. Rev. Lett., 89, 086403. [26] Amore Bonapasta, A., Filippone, F., Giannozzi, P., Capizzi, M. & Polimeni, A. (2002) Structure and passivation effects of mono- and dihydrogen complexes in GaAs12yNy alloys. Phys. Rev. Lett., 89, 216401. [27] Orellana, W. & Ferraz, A.C. (2002) Stability and electronic structure of hydrogen – nitrogen complexes in GaAs. Appl. Phys. Lett., 81, 3816. [28] Amore Bonapasta, A., Filippone, F. & Giannozzi, P. (2003) Nitrogen passivation by hydrogen in GaAs12yNy and InxGa12xAs12yNy alloys. Phys. Rev. B, 68, 115202. [29] Amore Bonapasta, A., Filippone, F. & Giannozzi, P. (2004) Structure, electronic properties and formation mechanisms of hydrogen –nitrogen complexes in GaP12yNy alloys. Phys. Rev. B., 69, 115– 207. [30] Amore Bonapasta, A. & Filippone, F. (2003) Local and lattice relaxation in hydrogenated GaAs12yNy alloys. Phys. Rev. B, 68, 073202. [31] Marx, D. & Hutter, J. (2000) Ab Initio Molecular Dynamics: Theory and Implementation, vol. 1, John von Neumann Institute for Computing, Ju¨lich, p. 301. [32] Jones, R. & Briddon, P.R. (1998) Identification of Defects in Semiconductors, Semiconductors and Semimetals, vol. 51, Academic Press, Boston, p. 287. [33] Amore Bonapasta, A. & Giannozzi, P. (2000) Effects of strain and local charge on the formation of deep defects in III –V ternary alloys. Phys. Rev. Lett., 84, 3923. [34] de Walle, C.G.V., Limpijumnong, S. & Neugebauer, J. (2001) First-principles studies of beryllium doping of GaN. Phys. Rev. B, 63, 245205. [35] Gonze, X., Stumpf, R. & Scheffler, M. (1991) Analysis of separable potentials. Phys. Rev. B, 44, 8503. [36] Baroni, S., Corso, A.D., de Gironcoli, S. & Giannozzi, P., PWscf, http://www.pwscf.org. [37] Vanderbilt, D. (1990) Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. Phys. Rev. B, 41, 7892. [38] Filippone, F. & Parrinello, M. (2001) Vibrational analysis from linear response theory. Chem. Phys. Lett., 345, 179. [39] Putrino, A., Sebastiani, D. & Parrinello, M. (2000) Generalized variational density functional perturbation theory. J. Chem. Phys., 113, 7102.

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[40] Goedecker, S., Huetter, J. & Teter, M. (1996) Separable dual-space Gaussian pseudopotentials. Phys. Rev. B, 54, 1703. [41] CPMD V 3.7, Copyright IBM Corp 1990– 2003, Copyright MPI fuer Festkoerperforschung, Stuttgart 1997– 2001, http://www.cpmd.org. [42] Hartwigsen, C., Goedecker, S. & Hutter, J. (1998) Relativistic separable dual-space gaussian pseudopotentials from H to Rn. Phys. Rev. B, 58, 3641. [43] Troullier, N. & Martins, J. (1991) Efficient pseudopotentials for plane-wave calculations. Phys. Rev. B, 43, 1993. [44] The values of the H, Ga, As, and N atomic covalent radii used here are 0.32, 1.26, 1.20, and ˚ , respectivelyPhillips, J.C. (1973) Bonds and Bands in Semiconductors, Academic Press, 0.75 A New York, These covalent radii give N– H, Ga– H, Ga– N, and Ga– As distances equal to 1.07, ˚ , respectively. 1.58, 2.01, and 2.46 A [45] Pavesi, L. & Giannozzi, P. (1991) H passivation of Si impurities in GaAs. Phys. Rev. B, 43, 2446. [46] Amore Bonapasta, A. (1998) Evidence of the negative-U behavior of H in GaAs from an investigation of H and As antisites. Phys. Rev. B, 58, 10378. [47] Francoeur, S., Sivaraman, G., Qiu, Y., Nikishin, S. & Temkin, H. (1998) Luminescence of as-grown and thermally annealed GaAsN/GaAs. Appl. Phys. Lett., 72, 1857. [48] Amore Bonapasta, A., Filippone, F., Jiang, F., Stavola, M., Capizzi, M. & Polimeni, A. Energetics and vibrational properties of nitrogen– hydrogen complexes in GaAs12yNy alloys, Phys. Rev. B, submitted for publication. ¨ berg, S. (1991) Theory of the structure and dynamics of the C impurity and C –H [49] Jones, R. & O complex in GaAs. Phys. Rev. B, 44, 3673. [50] Clerjaud, B., Coˆte, D., Hahn, W.-S., Lebkiri, A., Ulrici, W. & Wasik, D. (1997) On the way to the investigation of hydrogen in GaN: hydrogen in nitrogen doped GaP and GaAs. Phys. Stat. Sol. (a), 159, 121. [51] Herzberg, G. (1945) Infrared and Raman Spectra of Polyatomic Molecules, Van Nostrand Reinhold Company, New York.

Dilute Nitride Semiconductors M. Henini (Ed.) q 2005 Elsevier Ltd. All rights reserved.

Chapter 14

Dislocation-free III – V-N Alloy Layers on Si Substrates and Their Device Applications Hiroo Yonezu Department of Electrical and Electronic Engineering, Toyohashi University of Technology, 1-1 Hibarigaoka, Tempaku-cho, Toyohashi, Aichi 441-8580, Japan

ABSTRACT

The generation mechanisms of structural defects such as dislocations, stacking faults and anti-phase domains (APDs) are described in the growth of III –V compound semiconductors on Si substrates. Structural defect-free III –V-N alloy layers as well as a Si layer were grown on the Si substrate, where the lattice constant of the III – V-N alloy layers was matched to that of Si by adjusting N compositions. Possible applications are discussed on light emitting diodes (LED), lasers, solar cells and novel optoelectronic integrated circuits. It is noticed that massively parallel information processing, which is ultimately hard in electronic systems, could be performed in single-chip optoelectronic integrated circuits. 14.1. INTRODUCTION

Combining III –V compound semiconductors with Si has been a dream for the evolution of semiconductor devices since their specific features of both the materials are utilized. However, the difficulty in the growth of III – V compound semiconductors on Si had prevented the development of high-performance devices. The main problem was the generation of structural defects such as dislocations and stacking faults. This problem has been overcome by growing III– V-N alloys called dilute nitrides on Si, which were lattice-matched to Si. A dislocation-free GaPN layer was grown on a Si substrate for the first time by molecular beam epitaxy (MBE) [1,2]. The generation of stacking faults was suppressed as well by growing a thin GaP initial layer on the Si substrate. Then, dislocation-free GaPAsN layers were grown on the Si substrate [3,4]. It would be a starting point for the evolution of optoelectronic devices with superior performances in the near future. In this chapter, the causes of difficulties and countermeasures are firstly described for the growth of III– V compound semiconductors on a Si substrate. Then, possible applications to the optoelectronic devices and integrated circuits (OEICs) are described. Finally, key issues for future progress are discussed. 451

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14.2. DISLOCATION GENERATION MECHANISMS IN LATTICE-MISMATCHED HETEROEPITAXY

Dislocations are generated during lattice-relaxation process in lattice-mismatched heteroepitaxy. Epitaxial growth modes depend on the amount of lattice mismatch. Twodimensional (2D) growth mode is generally kept in the growth with a lattice mismatch smaller than about 2% [5]. When the thickness of an epitaxial layer is over a critical thickness, misfit dislocations are introduced at a growing surface for releasing lattice strain, as shown in Figure 14.1(a). The misfit dislocations (MDs) glide to a heterointerface. The number of MDs is increased with the increase in the thickness of epitaxial layers. The critical thickness decreases with the increase in lattice mismatch. Stransky – Krastanov (S-K) mode, in which the 2D growth mode is changed to the 3D growth mode during growth, is generally observed at an initial growth stage in heteroepitaxy with a lattice mismatch larger than about 2% [5,6]. This mode means that lattice strain is firstly relaxed by enlarging a surface and then by introducing misfit dislocations at the surface of grown islands. Some of the misfit dislocations are bent at the edge of the islands. The bent misfit dislocation forms a threading dislocation in continuing growth, as shown in Figure 14.1(b). It should be also noted that stacking faults could be generated at the coalescence of grown islands.

Figure 14.1. Lattice-relaxation process: (a) two-dimensional (2D) growth mode and (b) Stransky–Krastanov mode.

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The lattice-relaxation process in the S-K mode is clearly shown in Figure 14.2, in which a thin InAs layer is sandwiched between GaAs layers [6]. The thickness of the InAs layer was varied from 1 to 9 monolayers (ML). The 2D growth mode was kept for the 1 ML thick InAs layer. Islands were formed in the 2 ML thick InAs layer. The island grew according to the increase in deposition. Threading dislocations were generated from grown islands. The tilted cross-sectional transmission electron microscopy (TEM) images, named tilted cross-sectional TEM (X-TEM) images, show more clearly the generation process of threading dislocations compared with conventional X-TEM images.

Figure 14.2. TEM observation of the generation of threading dislocations in Stransky–Krastanov mode [6].

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Thus, it is apparent that dislocation-free epitaxial layers are obtained for the thickness smaller than the critical thickness in lattice-mismatched heteroepitaxy. The thickness of dislocation-free strained layers is decreased with the increase in the lattice mismatch. In the growth of III –V compound semiconductors on a Si(100) substrate, however, no 2D growth mode is generally observed. It is due to specific problems mentioned in Section 14.4. Then, high-density threading dislocations and stacking faults are generated.

14.3. LATTICE-MATCHED HETEROEPITAXY OF III –V-N ALLOYS ON III – V COMPOUND SEMICONDUCTORS

Lattice-matching is ideal for obtaining dislocation-free epitaxial layers in heteroepitaxy. A lattice constant is decreased by adding a small amount of nitrogen (N) atoms to III – V compound semiconductors, while a band gap ðEg Þ is decreased [7 – 9]. Figure 14.3 shows the range of lattice constants and band gaps which could be covered by III –V-N alloys [10]. Thus, III –V-N alloys are candidates for lattice-matching to conventional substrates such as Si, Ge, GaP, GaAs and InP. Possible III – V-N alloys, which lattice-match to the conventional substrates, are listed in Table 14.1. The lattice constant of III– V-N alloys follows Vegard’s law. Dislocation-free III– V-N alloy layers can be grown on the conventional substrates.

Figure 14.3. Map of lattice constants and band gaps [10].

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Table 14.1. III –V-N alloys lattice-matched to conventional substrates Substrate Si GaP Ge GaAs InP

III– V-N alloys GaP0.98N0.02, GaP12x 2 yAsxNy, InxGa12xP12yNy GaP12x 2 yAsxNy, InxGa12xP12yNy GaAs12xNx InxGa12xAs12yNy, InxGa12xP12yNy, GaAs12x 2 ySbxNy InP12x 2 yAsxNy, InxGa12xAs12yNy

For InGaPN, the lattice constant is increased by increasing In compositions and is decreased by increasing N compositions. Thus, InxGa12xP12yNy can be lattice-matched to Si and GaP substrates. Lattice-matching lines are shown in Figure 14.4(a), where x ¼ 2:28ðy 2 2Þ for Si and x ¼ 2:28y for GaP. GaP0.98N0.02 lattice-matched to Si [2]. Latticematched InGaPN layers have been grown on a GaP substrate in the range of In and N compositions below 17.6 and 7.4%, respectively [11]. For GaPAsN, the lattice parameter is increased by increasing As compositions and is decreased by increasing N compositions. Thus, GaP12x 2 yAsxNy can be lattice-matched to Si and GaP substrates. The lattice-matching lines are shown in Figure 14.4(b), where x ¼ 4:6ðy 2 2Þ for Si and x ¼ 4:6y for GaP. A dislocation-free GaP0.92As0.05N0.03 layer was grown on the Si substrate [3]. Lattice-matched GaPAsN layers have been grown on a GaP substrate in the range of As and N compositions below 33 and 7%, respectively [4,12]. The band gap of GaP0.65As0.3N0.05 was 1.58 eV at 18 K. For InGaAsN, which is usually written as GaInNAs, the lattice constant is increased by increasing In compositions and is decreased by increasing N compositions. Thus, InxGa12xAs12yNy can be lattice-matched to GaAs and Ge substrates. The line

Figure 14.4. Alloy compositions lattice-matched to Si and GaP: (a) InGaPN and (b) GaPAsN.

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Figure 14.5. Alloy compositions lattice-matched to GaAs and InP: (a) InGaAsN and (b) InPAsN.

lattice-matched to GaAs is shown in Figure 14.5(a), which is represented by x ¼ 2:8y: Lattice-matched InGaAsN layers have been grown on a GaAs substrate in the range of In and N compositions smaller than 3 and 1.6%, respectively [13]. The deterioration of crystalline quality is avoided in the range of small N compositions. InPAsN and InGaAsN can be lattice-matched to InP substrates. The lattice-matching line of InP12x 2 yAsxNy is shown in Figure 14.5(b), which is represented by y ¼ 0:21x [14].

14.4. GROWTH OF DISLOCATION-FREE III – V-N ALLOY LAYERS ON Si SUBSTRATES

The epitaxial growth of III –V compound semiconductors on Si substrates contains the specific following problems due to the difference of material parameters in Table 14.2 [15,16].

Table 14.2. Material parameters of conventional semiconductors Semiconductors

Si Ge GaP GaAs InP GaN InN

Lattice constant ˚) (A

Thermal expansion coefficient ( £ 1026/K)

Eg (eV)

Type

Thermal conductivity (W/mK)

5.43 5.66 5.45 5.65 5.87 3.19 5.75

2.6 5.8 5.3– 5.8 6.8 4.5 5.6 3.8– 4.2

1.12 0.66 2.26 1.42 1.35 3.36 0.8 –0.9

Indirect Indirect Indirect Direct Direct Direct Direct

151 58 110 46 70 130 –

Dislocation-free III– V-N Alloy Layers on Si Substrates

457

Figure 14.6. Comparison of initial surface coverage between MBE and MEE at low-temperature growth [18].

(1) The difference in the number of valence electrons, (2) the difference in lattice constants, (3) the difference in thermal expansion coefficients. Problem (1), which is the most essential problem, is closely related to the interface formation at an initial growth stage. The problem causes the generation of threading dislocations and stacking faults as well as anti-phase domains. Group V atoms such as P and As are adsorbed on the topmost surface of a Si substrate in conventional MBE or metalorganic vapor phase epitaxy (MOVPE). Then the surface is chemically stabilized by forming P – P and As – As dimmers on the Si(100) surface [17]. The stabilized surface makes it difficult to form a chemical bonding with group III atoms. This leads to the 3D growth mode nucleated probably at defects (Figure 14.6(a)). Thus, threading dislocations as well as stacking faults are generated during the lattice relaxation process of grown islands due to a large lattice mismatch of about 4%. It was clarified that a part of P and As atoms is desorbed on the Si surface in a conventional growth temperature of 5908C in MBE. This effect could enhance the formation of stacking faults at the coalescence of grown islands [18]. These problems were solved by growing a thin GaP initial layer with a small lattice mismatch of 0.4% by migration-enhanced epitaxy (MEE) at relatively low temperatures. The desorption of P atoms on the Si surface was suppressed by lowering the growth temperature from 590 to 4508C. MEE solves the problem of a small surface migration of Ga atoms at low temperatures. A quasi-2D growth mode was realized from the initial growth stage at 4508C by MEE, as shown in Figure 14.6(b). As a result, dislocation-free and stacking fault-free GaP layers were obtained when the thickness of the GaP initial layer was less than a critical thickness of about 50 nm [19]. Problem (1) causes the generation of anti-phase domains as well. A Si(100) surface forms monolayer steps covered with P atoms, as shown in Figure 14.7(a). Then continuing

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Figure 14.7. Anti-phase domains: (a) generation and (b) annihilation mechanisms [15,16,20].

atomic layers form different domains called anti-phase domains (APDs). P and Ga layers are shifted by 1 ML between adjacent domains. Wrong bonds of P – P and Ga –Ga, called anti-phase boundaries, are formed at a boundary between adjacent domains. This problem is solved by using a vicinal Si(100) surface in low-temperature MEE. APDs can be annihilated at an early growth stage when the terrace length is short, as shown in Figure 14.7(b) [20]. Thus, the Si substrate with a vicinal surface is effective for the annihilation of APDs. In addition, 2 ML steps can be partially expected since step bunching occurs locally at the high-temperature treatment of Si substrates. It is apparent that no APDs are formed on the 2 ML-step surface. The growth temperature dependence on the annihilation effect was examined in the MEE growth of GaP by using a Si(100) substrate misoriented by 48 towards the [001] direction. APDs were investigated with a dark-field image by TEM. APDs were annihilated at an early growth stage within 10 nm thickness in the growth at 4508C. However, APDs grew to over 100 nm at 5808C. The growth of APDs could be enhanced at high growth temperatures by a long surface diffusion length and an increased area of P-desorbed surfaces. The initial formation of APDs would be related to the charge imbalance at the hetero-interface which could principally cause the mixture of group III and V atoms and Si [21,22]. A 20 nm thick GaP initial layer was grown on the Si(100) substrate misoriented by 48 towards [011] at 4508C by MEE. There were no structural defects of misfit dislocations and threading dislocations as well as stacking faults in the GaP initial layer and the heterointerface between the GaP initial layer and Si substrate. Thus, a Si surface is converted to a GaP surface without the structural defects. It is noted that the lateral lattice constant of the GaP initial layer is the same as that of Si.

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459

Figure 14.8. Tilted X-TEM images: (a) 200 nm GaP0.98N0.02 and (b) GaP grown on the Si substrate [1,2].

Problem (2) causes the generation of misfit dislocations and threading dislocations in the lattice relaxation process. This problem is solved by lattice-matched growth using GaPN, GaAsPN and InGaPN. The GaP12xNx layers were grown at 5908C by MBE. Radical nitrogen was supplied with an rf plasma source flowing N2 gas. N compositions were controlled by varying rf power from 270 to 390 W. Ga and P2 fluxes were supplied by, respectively, evaporating elemental Ga and InP polycrystals with conventional thermal effusion cells. The substrate was a Si(100) misoriented by 48 towards the [011] direction. The thickness of the GaPN layer was typically 300 nm. The lattice constants and N compositions x of the GaP12xNx layer were estimated with peak angles measured by (400) and (511) X-ray diffraction (XRD), lattice parameters of GaP and cubic GaN, elastic parameters of GaP and Vegard’s law. The lattice constants of the GaP12xNx layers were decreased with the increase in N compositions x: The threading and misfit dislocations were investigated with a tilted X-TEM image. Neither threading dislocations nor misfit dislocations were observed in the 200 nm thick GaP0.98N0.02 layer grown on the Si(100) substrate covered with the 20 nm thick GaP initial layer, as shown in Figure 14.8(a) [1,2]. On the other hand, misfit dislocations were observed in a 200 nm thick GaP layer grown on the Si substrate, as shown in Figure 14.8(b). A dislocation-free III – V-N alloy layer was grown for the first time on a Si substrate [1,2]. Thus, it was clarified that the dislocation-free GaAsPN and InGaPN layers can be grown on the Si substrate covered with the GaP initial layer.

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Figure 14.9. Thermal strain at grown surface: (a) with a Si capping layer and (b) without a Si capping layer.

Problem (3) causes a tensile strain in III– V compound semiconductors grown on Si substrates during the cooling process since the thermal expansion coefficients of the III– V compound semiconductors are larger than those of Si (Table 14.2). In the GaP0.98N0.02 layer grown on Si substrates at 5908C, the tensile strain of the order of 108 Pa/cm2 is contained, as shown in Figure 14.9(b). When the tensile strain is increased above a critical value at a relatively higher temperature, edge dislocations are introduced from a grown surface. The edge dislocations glide on a (111) glide plane and remain at the hetero-interface along the k110l directions. The tensile strain can be compensated by growing a III –V compound semiconductors with compressive strain. This was tried with an InGaAs layer [23]. However, the etch pit density was still of the order of 106 cm22. A Si capping layer is ideal since its lattice constant is almost the same as that of the Si substrate. No edge dislocation could be introduced from the surface of the Si capping layer since the strain is very small. In the Si capping layer grown on the GaP0.98N0.02 layer on Si substrates, the tensile strain is negligibly small theoretically, as shown in Figure 14.9(a). Thus, a dislocation-free structure could be composed of the III– V-N alloy layers latticematched to the Si substrate and the Si capping layer when the growth temperature is relatively high as in MOVPE. A Si/GaPN/Si structure is a representative of the Si/III – V-N alloy/Si structure. A 100 nm thick Si capping layer following a 400 nm thick GaP12xNx layer was grown on the Si substrate covered with a 20 nm thick GaP initial layer [24]. Growth conditions were the same as those of the GaPN layer lattice-matched to Si in Figure 14.8. For Si epitaxy, a Si flux was supplied by evaporating a polycrystalline Si with an electron beam evaporator. In order to suppress the desorption of P atoms, the substrate temperature was decreased down to 4508C while P2 and N radical fluxes were shut off. Then the Si layer was grown at 5908C. The growth process was investigated with reflection high-energy election

Dislocation-free III– V-N Alloy Layers on Si Substrates

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Figure 14.10. PHEED patterns for each growth step of the Si/GaP0.971N0.029/Si structure [24].

diffraction (RHEED). Streak RHEED patterns were kept during the growth of the GaP12xNx and Si capping layers, as shown in Figure 14.10, which means that each layer was grown two-dimensionally. The lattice mismatch of 0.13% was obtained between the GaP12xNx layers and Si substrate, which is almost the same as that between AlAs and GaAs. The N composition x was estimated to be 2.9%. The (400) X-ray rocking curves were shown in Figure 14.11. The FWHMs of the GaP0.971N0.029 layer and Si substrate were 14 and 13 arcsec, respectively. Thus, it has been clarified that the GaP0.971N0.029 and Si capping layers have structurally high crystalline quality comparable to a bulk Si. No threading dislocations and no misfit dislocations were observed in any of the epitaxial layers and hetero-interfaces, as shown in Figure 14.12. No stacking faults or APDs were observed either. Thus, a structural defect-free Si/GaPN/Si structure was realized.

14.5. DEVICE APPLICATIONS

The dislocation-free III –V-N alloys grown on Si substrates can be applied to conventional optoelectronic devices as well as novel OEICs. Si has the specific features of high thermal conductivity (Table 14.2) and a large wafer size. Thus, conventional devices such as light emitting diodes (LEDs), lasers and solar cells can operate at high efficiency and high temperatures, and can be produced with low costs.

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Figure 14.11. XRD profiles of the Si/GaP12xNx/Si structure ðx ¼ 0:029Þ: (a) experimental and (b) simulation results [24].

Figure 14.12. TEM images of the Si/GaP12xNx/Si structure: (a) X-TEM and (b) tilted X-TEM images [24].

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14.5.1 Double Heterostructure LED It has been argued that GaPN contains a factor of direct transition since the absorption edge is steep while GaP with an indirect band gap shows a gradual absorption edge [25 – 27]. A GaPN homojunction LED was fabricated by a gas source MBE [28]. Then a GaPN/GaP double heterosturucture (DH) LED was fabricated by gas-source MBE [29] and solidsource MBE [30]. A 100 nm thick GaP12xNx active layer was sandwiched between p-GaP and n-GaP layers on an n-type GaP substrate, as shown in Figure 14.13(a). The N compositions of the active layer were varied from 1.8 to 2.6%. The thickness of the active layer was smaller than the critical thickness. It should be noted that the critical thicknesses of GaPN and GaAsN are larger than those of GaP and GaAs, respectively [19]. The peak wavelength for a GaP0.98N0.02 active layer was about 650 nm at room temperature. The spectrum was relatively broad with a long low-energy tail, as shown in Figure 14.13(b). The low-energy tail was also observed in the active layers by photoluminescence (PL). Cathodoluminescence (CL) and electroluminescence (EL) intensity was increased by rapid thermal annealing (RTA) in N2 ambient at around 9008C for 10 s [31]. The reduction of the energy tail and blue shift of the peak wavelength were observed after RTA. These effects could be caused by the reduction of spatial inhomogeneity of N atoms. InGaPN/GaPN and GaPAsN/GaPN DH LEDs can be formed on a Si substrate. Cladding layers are composed of p- and n-GaP0.98N0.02 layers lattice-matched to Si grown on the Si substrate covered with the GaP initial layer as mentioned in Section 14.4. An active layer should be InGaPN or GaPAsN lattice-matched to Si, whose band gap energy is smaller than that of the GaP0.98N0.02 cladding layers by about 0.3 eV or more. A peak wavelength of around 720 nm is expected. Another candidate of the active layer is a strained GaPN

Figure 14.13. GaPN/GaP DH LED: (a) layer structure and (b) emission spectrum [30].

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layer with a thickness smaller than the critical thickness. It has been reported that the electron concentration in Si-doped InGaPN layers was reduced for N compositions larger than 1% [32]. GaPN has a similar problem. These LEDs are possibly realized after the doping of the GaPN layer is controlled. PL and CL peak wavelengths of InGaPN were extended to 1.0 mm at 77 K by increasing the N composition up to 7%. Thus, the wide variation of peak wavelengths is expected in the InGaPN/GaPN or GaAsPN/GaPN DH LEDs grown on the Si substrate. However, it should be noted that the PL intensity of III– V-N alloys is generally decreased with the increase in N compositions. This effect could be attributed to N-related point defects. The reduction of carrier concentration is possibly related to the N-related point defects, as well. Thus, the reduction of the point defects is essential for bright and long-wavelength LEDs grown on the Si substrate. 14.5.2

III – V-N Alloy Lasers

III– V-N alloy lasers are attractive for high-power operation and combination with Si LSIs. A quantum well (QW) laser structure was grown on the Si substrate covered with the thin GaP initial layer by MBE, as shown in Figure 14.14 [3]. A 5 nm thick strained GaP0.31As0.66N0.03 QW layer was sandwiched between 100 nm thick GaP0.92As0.05N0.03 guiding layers. The strained GaP0.31As0.66N0.03 QW layer has probably a direct band gap since GaP0.34As0.66 has a direct band gap. The outer GaP0.92As0.05N0.03 guiding layers and GaP0.98N0.02 cladding layers were lattice-matched to Si. A lattice mismatch between these III– V-N alloy layers and Si substrate was about 0.09%, which is smaller than a lattice mismatch of 0.13% between AlAs and GaAs. No threading dislocations and no misfit dislocations were observed in any of the epitaxial layers and hetero-interfaces. For DH lasers, a GaP12x 2 yAsxNy active layer should be designed to lattice-match to Si. InGaPN is another candidate for lasers. A possible layer structure consists of InxGa12xP12yNy strained QW layer, Inx0 Ga12x0 P12y0 Ny0 guiding layers and GaP0.98N0.02 cladding layers, which are lattice-matched to Si. A dislocation-free InxGa12xP12yNy/ Inx0 Ga12x0 P12y0 Ny0 DH laser structure is possibly grown on the Si substrate. These III –V-N alloy layers should be designed to lattice-match to Si. Lasing wavelengths increase with

Figure 14.14. Dislocation-free GaPAsN/GaPN quantum well laser structure grown on the Si substrate [3].

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the increase in N composition of the QW and active layer for GaPAsN and InGaPN lasers, as seen in Figure 14.3. Lasing has not been reported since the GaPAsN or InGaPN lasers has not been realized. Direct transition is essential for lasers. Thus, a large N composition is required for the QW or active layer, as in Figure 14.3. In addition, a large conduction-band offset is needed for carrier confinement, which leads to high performances. This requires high-quality GaPAsN and InGaPN QW or active layers with large N compositions. The doping control of GaPN, GaPAsN and InGaPN is essential for fabricating the lasers. Thus, N-related point defects must be reduced more effectively in lasers rather than LEDs. More studies have been done for InGaAsN lasers lattice-matched to GaAs substrates. High performance is expected at high-temperature operation since the conduction-band offset is large compared with that of conventional InGaAsP lasers [33]. A typical lasing wavelength is 1.3 mm for optical fiber communication. In and N compositions of strained QW layers are about 30 –40% and less than 1%, respectively [8]. A low threshold current density of about 250 A/cm2 has been achieved at room temperature [34]. N compositions have been limited to small values in order to avoid the deterioration of the InGaAsN QW layer. 14.5.3 Solar Cells The band gap of III– V-N alloys is controlled by varying In and N compositions. Large absorption coefficients are obtained in GaPAsN and InGaPN near the band gap since the absorption edge is steep, compared with GaPAs and InGaP with an indirect band gap, as shown in Figure 14.15 [10]. Thus, highly efficient solar cells are expected to be realized. A multijunction solar cell is particularly expected, which is composed of a GaPAsN or InGaPN solar cell and a Si or Ge solar cell. The use of Si substrates leads to remarkable cost reduction and improvement in mechanical strength. A multijunction solar cells composed of GaPAsN and Si solar cells were evaluated theoretically since the doping of GaPN is not controlled at that time [12]. High conversion efficiencies were estimated. A two-junction solar cell of GaPAsN(Eg ¼ 1:7 eV)/Si(1.1 eV) projects maximum efficiencies of 33.8% for AM0 and 37.4% for AM1.5 G. A threejunction solar cell of GaPAsN(1.8 eV)/GaPAsN(1.4 eV)/Si(1.1 eV) projects maximum efficiencies of 36.6% for AM0 and 40.6% for AM1.5G. Similar multijunction solar cells composed of InGaPN and Si solar cells could realize high conversion efficiency. Another multijunction solar cell, composed of InGaAsN and Ge solar cells, is also attractive for high efficiency. A four-junction solar cell of InGaP(1.8 eV)/GaAs(1.4 eV)/ InGaAsN(1.0 eV)/Ge(0.7 eV)projectsmaximumefficienciesof39.1%forAM0and40.5%for AM1.5G [12]. It should be noticed that the increase in the minority carrier diffusion length is essential for high conversion efficiency. The reduction of N-related point defects could increase the diffusion length.

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Figure 14.15. Absorption coefficients of some semiconductors [10].

14.5.4

Opto-electronic Integrated Circuits

Novel OEICs can be constructed based on the Si/GaPN/Si structure in Figure 14.12. The GaPN layer can be replaced with an optoelectronic device layer formed with III –V-N alloy layers lattice-matched to Si, as shown in Figure 14.16 [16]. Electronic circuits can be formed in the Si capping layer. Novel multichip processors could be evolved, in which adjacent chips are interconnected with parallel optical beams. Particularly, massively parallel information processing is valuable, as in biological neural systems. The information processing is performed in an electronic circuit formed in the Si capping layer and parallel optical outputs are emitted from LEDs or lasers formed in the III– V-N alloy layers. In this system, ultra-high speed processing is expected. It should be noticed that massively parallel information processing is hardly possible in present electronic processing systems. Small lasers such as VCSELs or small LEDs are preferred for being driven with LSIs in the Si layer since operating currents are small. They can be installed into a large number of unit circuits in LSIs. In order to fabricate the OEICs, new fabrication processes should be developed since group V atoms (P and As) and Si are impurities in Si and III– V-N alloy layers, respectively. The temperature of Si LSI fabrication processes has been continuing to be lowered. The low-temperature processes for Si LSIs could meet to the requirement for suppressing mutual contamination in the fabrication process.

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Figure 14.16. Idea of a novel optoelectronic integrated circuit (OEIC) [16].

14.6. SUMMARY

The generation of structural defects such as dislocations, stacking faults and anti-phase domains has been suppressed by overcoming the three problems in the growth of III – V compound semiconductors on Si substrates. Dislocation-free GaPN, GaPAsN and InGaPN layers as well as Si layers have been obtained on a Si substrate. Alloy compositions are adjusted to lattice-match to Si. These III –V-N alloys with small N compositions lattice-matched to Si show specific features of efficient light emission and a large absorption coefficient near a band gap although the III– V compound semiconductors without nitrogen show poor electroluminescence and a small absorption coefficient near a band gap due to an indirect band gap. Thus, highly efficient optoelectronic devices have been expected such as LEDs, lasers and solar cells. A more attractive device is a novel OEIC, in which optoelectronic devices and LSIs are formed in III – V-N alloy and Si layers, respectively. However, III –V-N alloys contain N-related point defects. The defect density is increased with the increase in N compositions. It has been commonly clarified in III – V-N alloys that the defect density is decreased by RTA. However, the defects are still

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contained, which degrade the performances of optoelectronic devices. The evolution of III– V-N alloys and Si is expected when the defects density is reduced to that of conventional III –V compound semiconductors. ACKNOWLEDGEMENTS

This chapter is composed of the results of several research subjects. The author would like to thank Y. Furukawa, A. Utsumi, S.-M. Kim, S.-Y. Moon, K. Momose, Y. Fujimoto, K. Samonji, Y. Takagi, T. Kawai and N. Ohshima for their contributions. This work was partially supported by the Ministry of Education, Science, Sports and Culture under a Grant-in-Aid for Scientific Research in Japan (Specially Promoted Research and the 21st Century COE Program).

REFERENCES [1] Samonji, K., Yonezu, H., Ojima, K., Fujimoto, Y. & Ohshima, N. (1998) Proceedings of the Second International Symposium on Blue Laser and Light Emitting Diodes, Tu-P58, p. 314. [2] Furukawa, Y., Yonezu, H., Ojima, K., Samonji, K., Fujimoto, Y., Momose, K. & Aiki, K. (2002) Jpn. J. Appl. Phys., 41, 528. [3] Fujimoto, Y., Yonezu, H., Utsumi, A., Momose, K. & Furukawa, Y. (2001) Appl. Phys. Lett., 79, 1306. [4] Momose, K., Yonezu, H., Furukawa, Y., Utsumi, A., Yoshizumi, Y. & Shinohara, S. (2003) J. Cryst. Growth, 251, 443. [5] Kawai, T., Yonezu, H., Ogasawara, Y., Saito, D. & Pak, K. (1993) Appl. Phys. Lett., 63, 2067. [6] Kawai, T., Yonezu, H., Saito, D., Yokozeki, M. & Pak, K. (1994) Jpn. J. Appl. Phys., 33, L1740. [7] Kondow, M., Uomi, K., Hosomi, K. & Mozume, T. (1994) Jpn. J. Appl. Phys., 33, L1056. [8] Kondow, M., Uomi, K., Kitatani, T., Watahiki, S. & Yazawa, Y. (1996) J. Cryst. Growth, 164, 175. [9] Bi, W.G. & Tu, C.W. (1996) Appl. Phys. Lett., 69, 3710. [10] Ceisz, J.F. & Freidman, D.J. (2002) Semicond. Sci. Technol., 17, 769. [11] Sanorpim, S., Nakajima, F., Katayama, R., Nakadan, N., Kimura, T., Onabe, K. & Shiraki, Y. (2003) Phys. Stat. Sol. (c), 0, 2773. [12] Geisz, J.F., Freidman, D.J., McMahon, W.E., Ptak, A.J., Kibble, A.E., Olson, J.M., Kurtz, S., Kramer, C., Young, M., Duda, A., Reedy, R.C., Keyes, B.M., Dippo, P. & Metzger, W.K. (2003) Presented at the National Center for Photovoltaics and Solar Program Review Meeting, Denver, CO, NREL/CP-520-33545. [13] Li, W. & Pessa, M. (2001) Phys. Rev. B, 64, 113308. [14] Bi, W.G. & Tu, C.W. (1998) Appl. Phys. Lett., 72, 1161. [15] Encyclopedia of Materials: Science and Technology, Elsevier Science, 2001, pp. 5785– 5793. [16] Yonezu, H. (2002) Semicond. Sci. Technol., 17, 762. [17] Uhrberg, R.I.G., Bringans, R.D., Bachrach, R.Z. & Northrup, J. (1986) Phys. Rev. Lett., 56, 520.

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[18] Takagi, Y., Yonezu, H., Samonji, K., Tsuji, T. & Ohshima, N. (1998) J. Cryst. Growth, 187, 42. [19] Momose, K., Yonezu, H., Fujimoto, Y., Ojima, K., Furukawa, Y., Utsumi, A. & Aiki, K. (2002) Jpn. J. Appl. Phys., 41, 7301. [20] Kawabe, M. & Ueda, T. (1987) Jpn. J. Appl. Phys., 26, L944. [21] Harrison, W.A., Kraut, E.A., Waldrop, J.R. & Grant, R.W. (1978) Phys. Rev., B18, 4402. [22] Kroemer, H. (1987) J. Cryst. Growth, 81, 193. [23] Takano, Y., Kanaya, Y., Kawai, T., Torihata, T., Pak, K. & Yonezu, H. (1990) Appl. Phys. Lett., 56, 1664. [24] Momose, K., Yonezu, H., Fujimoto, Y., Furukawa, Y., Motomura, Y. & Aiki, K. (2001) Appl. Phys. Lett., 79, 4151. [25] Xin, H.P., Tu, C.W., Zhang, Y. & Mascarenhas, A. (2000) Appl. Phys. Lett., 76, 1267. [26] Bellaiche, L., Wei, S.-H. & Zunger, A. (1997) Appl. Phys. Lett., 70, 3558. [27] Vurgaftman, I., Meyer, J.R. & Ram-Mohan, L.R. (2001) J. Appl. Phys., 89, 5815. [28] Xin, H.P., Welty, R.J. & Tu, C.W. (2000) Appl. Phys. Lett., 77, 1946. [29] Xin, H.P., Welty, R.J. & Tu, C.W. (2000) IEEE Photon Tech. Lett., 12, 960. [30] Moon, S.-Y., Utsumi, A., Yonezu, H., Furukawa, Y. & Ikeda, T. (2003) The Fifth International Symposium on Blue Laser and Light Emitting Diodes, Abstracts, p. 262. [31] Utsumi, A., Yonezu, H., Furukawa, Y., Momose, K. & Kuroki, K. (2003) Phys. Stat. Sol. (c), 0, 2741. [32] Hong, Y.G., Juang, F.S., Kim, M.H. & Tu, C.W. (2003) J. Cryst. Growth, 251, 437. [33] Kondow, M., Uomi, K., Niwa, A., Kitatani, T., Wataniki, S. & Yazawa, Y. (1996) Jpn. J. Appl. Phys., 35, 1273. [34] Tansu, N., Yeh, J.-Ya. & Mawst, L.J. (2003) Appl. Phys. Lett., 83, 2512.

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Dilute Nitride Semiconductors M. Henini (Ed.) q 2005 Elsevier Ltd. All rights reserved.

Chapter 15

GaNAsSb Alloy and Its Potential for Device Applications J-C. Harmanda, L. Lia, R. Mouilleta, G. Ungaroa, V. Salleta, L. Traversa, G. Patriarchea, L. Largeaua, R. Kudrawiecb, G. Se¸kb and J. Misiewiczb a

Laboratoire de Photonique et de Nanostructures, CNRS, Route de Nozay, 91460 Marcoussis, France Institute of Physics, Wrocław University of Technology, Wybrzez˙e Wyspian´skiego 27, 50-370 Wrocław, Poland

b

ABSTRACT

Growth and properties of GaNAsSb alloy are investigated, and compared with those of other dilute III– N-V alloys. This alloy is an alternative candidate to GaInNAs to elaborate low band gap strained or lattice-matched layers on GaAs. Basic characteristics such as band gap bowing, band gap offsets or band gap shift under annealing are examined. Some unforeseen results are reported and discussed. Then we prospect potential applications that could take advantage of this alloy. The GaInNAsSb quinary alloy is also considered. GaAs-based telecommunication lasers (1.5 mm) and reduced turn-on voltage heterojunction bipolar transistors (HBTs) are demonstrated, but some limitations are pointed out.

15.1. INTRODUCTION

The earliest studies on dilute III– V-nitrides were initiated a long time ago on N-doped GaP [1]. In the early 1990s, research activities on wide band gap nitrides have promoted the development of efficient nitrogen sources for epitaxy. As a consequence, a renewed interest has emerged for mixed III –V-N compounds. GaNAs was particularly investigated [2]. The anomalous large band gap bowing observed in this alloy offers a unique feature: the band gap and the lattice parameter can be reduced simultaneously by the introduction of a small amount of nitrogen. It appeared that this characteristic was of great interest to extend the range of GaAs-based materials, with interesting potential for device applications. Initially proposed by Kondow, GaInNAs is the most popular III – V-N today. In the past decade, the development of GaInNAs has been mainly driven by the need of low-cost sources for optical fiber networks. Compressively strained GaInNAs/ GaAs quantum wells (QW) appeared as challenging candidates to replace the GaInPAs/ InP system for emission at 1.3 mm wavelength. Successful realizations of edge emitting lasers and vertical cavity surface emitting lasers have been reported [3,4]. This GaInNAs 471

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compound was also investigated for solar cells in order to improve their efficiency [5], and for HBTs in order to reduce their turn-on voltage [6]. Besides this attractive alloy, little work has been devoted to other possible compounds. This chapter introduces an alternative GaAs-based quaternary, GaNAsSb, as well as a quinary, GaInNAsSb. We show that these compounds can be grown by molecular beam epitaxy (MBE), and we pay attention to the incorporation rates of the different alloy constituents. This is an important step to achieve a good control of composition, which is more critical than for GaInNAs. As observed in other dilute III– V-Ns, nitrogen incorporation in GaAsSb results in band gap reduction and lattice contraction. A significant difference is expected in the band offsets with GaAs because Sb plays an important role in the valence band offset. We point out that this band configuration is attractive for the HBT application, and we report some recent experimental measurements on GaNAsSb HBTs. Another important characteristic in which GaNAsSb differs from GaInNAs is that this quaternary has a single cation. The consequence on the electronic properties is discussed, and experimental work shows unforeseen results on the metastable band gap of this alloy. The GaInNAsSb quinary is also examined, and we illustrate the surfactant role of Sb during the growth of this alloy. This is a determinant advantage to extend the emission wavelength of GaAs-based QW to the 1.55 mm range. Laser characteristics will be presented.

15.2. MBE OF THE GaNAsSb ALLOY

All the samples reported in this work were grown by MBE. The N source was a radio frequency (RF) plasma cell, with RF power ranging from 250 to 550 W. Growth temperature of nitrogen-containing layers was systematically lower than 4808C, and the typical value was 4208C. Arsenic and antimony sources included a cracking zone. First investigations were carried out to study the incorporation of nitrogen in different III – V matrix. In particular, an open question was to know if the nitrogen incorporation rate was sensitive to the presence of antimony. For this purpose, four samples were grown. Each sample included a reference 0.1-mm thick GaNAs layer. Then, the samples were topped with a 15 nm layer of GaInAs, GaInNAs, GaAsSb, or GaNAsSb, respectively. The nitrogen plasma conditions were 0.2 sccm flow and an effective RF power of 300 W for all the N-containing layers. The same In flux was used for the first two samples and the same Sb flux was used for the two latter samples. Figures 15.1 and 15.2 show high-resolution X-ray diffraction (XRD) rocking curves for these four samples, together with calculations based on dynamical theory. The ternary layer compositions were deduced from the best calculated fits. As can be seen on the rocking curves, the nitrogen compositions of the GaAsN reference layers are very similar (0.011 –0.012) in all the four samples. This indicates a good

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Figure 15.1. X-ray diffraction rocking curves on GaInAs (curve a) and GaInAsN (curve b). Curves (a0 ) and (b0 ) are calculated. The peak corresponding to the experimental quaternary layer (shown by arrow Q) is observed at the angle expected if In and N compositions are those of the ternary reference layers.

Figure 15.2. X-ray diffraction rocking curves on GaAsSb (curve a) and GaAsSbN (curve b) topped samples. Curves (a0 ) and (b0 ) are calculated. The peak corresponding to the experimental quaternary layer (shown by arrow Q) is not observed at the angle expected if Sb and N compositions are those of the ternary reference layers.

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reproducibility of the nitrogen source. The In composition in the reference GaInAs top layer was found to be 0.177. Now, we consider the GaInNAs sample. It is reasonable to assume that the In composition is the same as for GaInAs (0.177). If we suppose that the N incorporation is inversely proportional to the growth rate, and not affected by the chemical interaction with In, then the N composition should be 0.009. The rocking curve of the GaInNAs sample was calculated with these composition values. Figure 15.1 shows that the experimental curve is in very good agreement with this calculation, and this tends to validate our assumptions. The same approach was carried out for the Sb-containing samples. Figure 15.2 shows that we found a Sb composition of 0.144 in the GaAsSb reference ternary layer, and a N composition of 0.012 in the GaNAs reference layer. We first assumed that Sb and N compositions were unchanged in the GaNAsSb layer, and calculated the corresponding rocking curve. In this case, the comparison of calculated and experimental curves indicates a clear disagreement. A good fit of the intensity diffracted by the GaAsSbN layer (this fit is not shown here) can be obtained by increasing the N composition to 0.029, or decreasing the Sb composition to 0.10. The XRD analysis cannot discriminate between these two extreme cases. A complementary analysis by secondary ion mass spectroscopy (SIMS) was performed on a dedicated sample consisting of a succession of GaAsN, GaInAsN and GaAsSbN layers. The same conditions were applied to the nitrogen source for all the layers. The Ga-related growth rate was 1 mm/h. Different In compositions of GaInAsN layers were obtained with variable In flux, and different Sb compositions of GaAsSbN layers were obtained with constant Sb flux and variable As flux. SIMS analysis was performed and the nitrogen concentration was found to vary between 2 and 4.5% depending on the other constituents of the layers. We calculated the N incorporation rates (ratio between nitrogen concentration and growth rate) and we normalized the results to the case of GaAsN. These data are plotted as a function of In or Sb concentration in the layers (Figure 15.3). These results confirm the conclusions of XRD analyses: (i) the presence of indium does not significantly affect the incorporation of nitrogen; and (ii) on the other hand, the nitrogen incorporation is enhanced in the GaAsSbN layers. We measured a 60% increase for a Sb composition of 0.35. This can be understood as a result of competition between the As, Sb, and N incoming species involved in the growth reaction. The substitution of arsenic by antimony in the gas phase favors the formation of GaN. In this section, we have shown that the MBE growth of GaNAsSb does not present any particular problem. On the contrary, N is found to be more easily incorporated than in GaNAs or GaInNAs. However, the composition control of this alloy is more critical than that of GaInNAs, because of a dependence of N composition on the Sb/As ratio. It is worth noting that this interdependence of group V incorporations generates a serious ambiguity to the determination of the actual compositions of GaNAsSb layers.

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Figure 15.3. Incorporation rate of nitrogen in GaInAsN layers (circles), or GaAsSbN layers (triangles) as a function of In or Sb composition. The values are normalized to the GaAsN case at equivalent growth rate.

15.3. BANDS

Band gap and band discontinuities are of major importance to evaluate the potential of a particular material system for a particular application. In this section, we examine the potential of GaNAsSb for long-wavelength emission on GaAs, and discuss the band discontinuities values. For this objective, we draw a very simple picture of GaNAsSb/GaAs bands assuming that, in the quaternary alloy, the band structure results from the superposition of Sb-related and N-related effects. The same simple picture is applied to GaInNAs/GaAs, in order to compare these systems. With this aim, we first consider the GaAsSb and GaInAs ternary alloys. They have regular behaviors, i.e. the introduction of large-size (Sb or In) substitutional atoms, results in band gap narrowing, and lattice parameter extension. GaAsSb has a higher bowing coefficient than GaInAs. As a consequence, for 0 , y , 0:4; GaAs(12y)Sby has a lower band gap than Ga(12y)InyAs. On the other hand, the compressive strain in these ternaries is almost equivalent for layers coherently grown on GaAs. These characteristics are shown in Figure 15.4 where the band gaps of the two ternaries, EGaInAs and EGaAsSb , are plotted as a function of the compressive g g strain in the layers. A more drastic difference concerns the band discontinuities of the two ternaries with GaAs. Strained GaInAs has large conduction band discontinuity with GaAs ðDEc ¼ 0:7DEg Þ; while the GaAsSb/GaAs interface is slightly type II with a deep potential well in the valence band of GaAsSb ðDEv ¼ 1:05DEg Þ [7]. The combination of these characteristics allows the GaAsSb QWs to emit at longer wavelength than GaInAs QWs, for the same compressive strain. This is shown in Figure 15.5 which depicts a calculation of the fundamental transition energy in the both types of ternary strained QWs. For each

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Figure 15.4. Band gap energy of GaInAs and GaAsSb alloys coherently grown on GaAs as a function of strain.

In or Sb composition y, the QW thickness was considered equal to the critical thickness before the onset of dislocations. In this calculation, we have used a phenomenological expression of the critical thickness. (This expression fits experimental data of GaInAs critical thickness grown with standard MBE conditions. Note that this critical thickness can be exceeded with modified growth conditions). Assuming this expression is valid for GaInAs and GaAsSb, the calculation shown in Figure 15.5 indicates that GaAsSb QWs have a transition energy minimum of 150 meV lower than GaInAs QWs minimum. This emission at longer wavelength is at the expense of electron confinement, which is absent in GaAsSb/GaAs QWs as mentioned earlier. Now, let us consider the quaternary materials.

Figure 15.5. Calculated transition energy in GaInAs/GaAs or GaAsSb/GaAs quantum wells. For each In or Sb composition, the quantum well width is designed at the critical thickness.

GaNAsSb Alloy and Its Potential for Device Applications

477

In both cases, the addition of nitrogen can exactly or partially compensate the compressive strain, and the N-related band gap bowing effect produces a further reduction of the band gap. As a direct consequence of Figures 15.4 and 15.5, at a given N composition and at a given strain, GaNAsSb is certainly more favorable than GaInNAs to achieve a minimal transition energy on GaAs. This characteristic of GaNAsSb QWs is illustrated in Figure 15.6 showing room temperature (RT) photoluminescence (PL) spectra. A GaAs0.843Sb0.15N0.007 QW emits at 1.15 mm, and a GaAs0.729Sb0.26N0.011 QW emits at 1.35 mm. It is important to note that this PL spectra were obtained after annealing the samples (see Section 15.4). Emission at the same wavelengths with GaInNAs QWs would certainly require higher compressive strain or higher N composition. The band offsets at the GaNAsSb/GaAs interface can be estimated as follows: N in GaAs is known to essentially lower the conduction band minimum, with negligible interaction with the valence band states. This is complementary to the Sb effect, which mainly raises the valence band minimum. In this respect, GaNAsSb/GaAs is an interesting system where DEc and DEc can be tuned independently, by adjusting the N and Sb concentrations, respectively. However, at a given N content, the electron confinement is necessarily lower than in GaInNAs/GaAs. For that reason, the GaNAsSb/GaAs QWs are not very attractive for 1.3 mm lasers: adequate electron confinement can be obtained, but with a higher N concentration than in a GaInNAs/GaAs QW. This is not a likely direction to follow. As a matter of fact, the best strategy for 1.3 mm GaInNAs QWs, has been to minimize the amount of nitrogen in order to reduce the degradation of optical properties.

Figure 15.6.

Room temperature photoluminescence spectra of GaNAsSb quantum wells. Sample A: GaAs0.843Sb0.15N0.007, sample B: GaAs0.729Sb0.26N0.011 (samples were annealed).

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Nevertheless, we will see in Section 15.5 how the III –N – As – Sb compounds can be useful in designing GaAs-based long-wavelength lasers. On the other hand, GaNAsSb is a promising alternative to GaInNAs for solar cell or HBT applications. Because low band gap can be obtained more easily, for a given band gap, GaNAsSb can be less strained or its N content can be minimized as compared to GaInNAs. This is certainly favorable to the two applications considered earlier. In addition, GaNAsSb has a particular interest for the base layer of a N – p– n HBT. Sb composition can be increased to improve the injection efficiency at the emitter– base interface of this device: a higher barrier to the hole diffusion can be designed. This type of HBT will be examined in Section 15.8 of this chapter.

15.4. ANNEALING EFFECT

Annealing of GaInNAs is known to produce a significant blue shift of its band gap. The origin of this band gap shift has been widely discussed. In this section, we re-examine this phenomenon, and we compare the behavior of GaNAs, GaInNAs and GaNAsSb. For this purpose, we have grown a set of samples consisting of 0.1-mm thick layers of each alloy. To determine their compositions, the samples were analyzed by SIMS to measure the N concentrations, and XRD to measure the lattice parameters. The N levels measured by SIMS were calibrated from the determination of GaNAs composition by XRD, assuming Vegard law. The nitrogen compositions were found to be very close to 2% for the three samples. The In and Sb concentrations of the quaternary layers were found to be 5 and 8.1%, respectively, as deduced from the lattice parameters. The GaNAs layer was tensely strained, the GaInNAs was almost lattice-matched to GaAs, and the GaNAsSb was slightly compressively strained. PL and photoreflectance (PR) spectra of the III– V-N layers are shown in Figure 15.7, for as-grown and annealed (7508C, 10 min) samples. Details of the PR optical characterization can be found in the present book, as presented in the chapter by Misiewicz and Kudrawiec. The three alloys show a significant blue shift of their emission (PL) and their absorption (PR), after annealing. At RT, the tensely strained GaN0.02As0.98 layer has light hole band gap of 1.103 eV, which is shifted to 1.115 eV after annealing. In the almost lattice-matched Ga0.95In0.05N0.02As0.98 layer, heavy and light hole transitions are not resolved, and the band gap shifts from 1.077 to 1.104 eV. The compressively strained GaN0.02As0.90Sb0.08 layer has a heavy hole band gap of 0.941 eV, shifted to 0.985 eV by thermal annealing. Table 15.1 summarizes these results. The band gap blue shift is thus observed in GaNAs, GaInNAs and GaNAsSb alloys, but with different values, 12, 27, and 44 meV, respectively. The quaternary alloys are more sensitive to the anneal than the ternary. It is worth noting that the largest shift is observed in GaNAsSb. In the following, we review the possible reasons for this blue shift. Annealing may induce interdiffusion of the constituents at each side of a heterointerface. The optical

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Figure 15.7. Photoluminescence and photoreflectance (solid line: experimental, dashed line: calculated) of (a) GaNAs, (b) GaInNAs, (c) GaNAsSb samples, before and after annealing.

transitions in QW structures are particularly sensitive to this interdiffusion between wells and barriers. However, the present study is based on relatively thick layers (0.1 mm). Therefore, in this case, a short interdiffusion of constituents across the interfaces cannot induce a significant transition energy shift. It was also suggested that annealing could

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Table 15.1. Characteristics of three layers with similar N concentrations: GaNAs, GaInNAs, and GaNAsSb Alloy N composition (%) In composition (%) Sb composition (%) Egap before annealing (eV) Egap after annealing (eV) Anneal-induced band gap shift (meV) EGaAs –Egap before annealing (meV) EGaAs –Egap after annealing (meV) Biaxial strain contribution to (EGaAs –Egap) (meV) In or Sb contribution to (EGaAs –Egap) (meV) N contribution to (EGaAs –Egap) before annealing (meV) normalized to N ¼ 1% N contribution to (EGaAs 2 Egap) after annealing (meV) normalized to N ¼ 1%

GaNAs

GaInNAs

GaNAsSb

2.05 0 0 1.103 (e-lh) 1.115 þ12 þ322 þ310 þ49 0 þ133

1.9 5.0 0 1.077 1.104 þ 27 þ 348 þ 321 þ6 þ 80 þ 138

2.0 0 8.1 0.941 (e-hh) 0.985 þ 44 þ 484 þ 440 215 þ 153 þ 173

þ127

þ 124

þ 151

Experimental band gaps are given for as-grown and annealed samples. The contributions to the band gap are evaluated for the different alloys.

activate nitrogen out-diffusion from the III – V-N layers [8], resulting in a decrease of N composition. We have checked by XRD whether the lattice parameters of the three III– V-N layers were changed upon annealing at 7508C for 10 min. This is shown in Figure 15.8 for the GaNAsSb sample. After sample annealing, the X-ray rocking curve is essentially unchanged. The GaNAsSb diffraction peak is neither shifted nor widened. Therefore, it can be concluded that the average layer composition did not change. More particularly, there was no nitrogen out-diffusion from these samples. We further investigate possible anneal-induced structural modifications of the layers by transmission

Figure 15.8. X-ray diffraction rocking curves of a GaNAsSb layer before and after annealing.

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Figure 15.9. Transmission electron microscopy of a GaNAsSb layer before and after annealing; (002) images.

electron microscopy (TEM). Figure 15.9 shows (002) images of the GaNAsSb layer, before and after annealing. Annealing did not produce any significant change. The layer contrast is uniform, and there is no evidence of clustering or phase separation. Similar observations were done, by TEM, as well as by XRD, on the GaNAs and GaInNAs samples: no structural change was identified by these analyses. Therefore, in these layers, the emission blue shift cannot be due to N out-diffusion, or strong compositional fluctuations. Only very short-distance interactions between the constituents of the alloys can explain such a huge effect on the optical properties, without any sign of structural change detected by XRD or TEM. As a matter of fact, a recent experimental work [9] by X-ray absorption fine structure spectroscopy (XAFS) has clearly evidenced in GaInNAs that a local rearrangement of N nearest neighbors was induced by annealing. As-grown GaInNAs was found to have a nearly random distribution of cations, Ga or In, around N, and annealed samples showed a redistribution where the number of In – N bonds had significantly increased. This tendency to separate the alloy into In – N þ Ga –As is driven by strain energy minimization, as explained by Kim and Zunger [10]. In addition, their empirical pseudopotential calculations showed that this local rearrangement of N first neighbors can explain the band gap blue shift. This explanation is now widely adopted and prevails over other interpretations. The relative number of cations Ga/In which are bonded to N is crucial in this model. The situation is very different in GaNAsSb. Like GaNAs, it has a single type of cation, and substitutional N can only bond to Ga. Local atomic rearrangements are also expected to occur in GaNAsSb, since Sb can play an important role to balance the local strain induced by N. However, the N first neighbor shell will not be concerned by these rearrangements, and consequently the effect on the electronic states is expected to be weaker. Surprisingly, our experimental results indicate that GaNAsSb presents a larger band gap blue shift than GaInNAs. To explain this behavior, we speculate that for comparable annealing conditions, the atomic rearrangement is much more drastic in GaNAsSb than in GaInNAs. One good reason for that would be that the total cohesive energy of GaNAsSb crystal will not change with the anion redistribution (the absolute numbers of Ga – N, Ga – As, and Ga – Sb bonds are unchanged). This is not the case with GaInNAs, where the cohesive energy minimization will tend to form (In –As) þ (Ga – N), and the elastic energy is minimized for the opposite (In – N) þ (Ga– As) configuration.

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In addition, we should not forget that even for the GaNAs layer, a band gap blue shift was observed. It shows that there is a group V sublattice rearrangement, even without Sb. In that case, we believe that the tendency to N pairing which results from growth is minimized by annealing. Such N pairing is expected to decrease the material band gap as compared to ideally isolated N [11]. Hence, the GaNAs anneal-induced blue shift can also be understood. Because it is well established that annealing improves the spectral characteristics of dilute III– V-Ns, the previous observations are of practical importance. In GaNAsSb, we have measured a large anneal-induced blue shift which is, indeed, not favorable to longwavelength emission. This is, however, balanced by another interesting feature of GaNAsSb, which is drawn out in Table 15.1. This table shows that the simple picture of III– V-N band gaps given in Section 15.3 is not accurate. We consider the band gap values of the three alloys measured before or after annealing, and their differences with GaAs band gap. The contributions due to alloying with In or Sb are estimated from bulk GaInAs or GaAsSb band gap variations. The biaxial strain contribution is also evaluated. The rest of the band gap difference is attributed to N alloying effect, and divided by the N concentration for each layer. We observe that, even for the annealed samples, this procedure leads to a stronger contribution of nitrogen to the band gap reduction in GaNAsSb (2 151 meV for xN ¼ 1%Þ; than for the other alloys (2 127 meV for GaNAs, and 2 124 meV for GaInNAs). This is again the sign that the effect of N on electronic and optical properties of these alloys depends on its local environment—first neighbor and second neighbor shells, at least. In this section, we have pointed out two experimental features of GaNAsSb, which have fundamental as well as practical interests. Annealing of GaNAsSb results in a stronger blue shift of its band gap as compared to the case of GaInNAs. Nevertheless, even for the annealed samples, the N-related band gap bowing is larger in GaNAsSb than in GaInNAs or GaNAs.

15.5. QUINARY ALLOY

We have mentioned that the GaAs/GaNAsSb system has a lower electron confinement than GaAs/GaInNAs system. For 1.3 mm laser application, the latter system has already proven a high potential, and there is no strong argument to develop GaNAsSb lasers at this wavelength. However, GaNAsSb QWs can be considered for emission beyond 1.3 mm. Moreover, the five elements combination, i.e. the GaInNAsSb quinary alloy, is particularly interesting to reach a good compromise between electron confinement and long emission wavelength. This quinary material has been already investigated by few groups. The first reported studies focused on the improvement of optical and structural quality of GaInNAs by the introduction of Sb [12]. It was suggested that Sb acts

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Figure 15.10. PL peak energy of different types of QWs as a function of Sb flux. Circles: GaNAs(Sb); triangles: GaInAs(Sb); squares: GaInNAs(Sb).

as a surfactant. In the following, we explain and illustrate how this surfactant effect takes place. For this purpose, we have grown GaNAs(Sb), GaInAs(Sb) and GaInNAs(Sb) QWs with various Sb flux. Figure 15.10 shows the PL peak energies of this series of QWs. The PL peaks are red-shifted as a result of Sb incorporation in these different QWs. The shifts are quantitatively very similar in GaInAs(Sb) and GaInNAs(Sb) QWs, suggesting that, at given Sb flux, comparable amount of Sb was incorporated in these two materials. On the other hand, the shift is much larger for the GaNAs(Sb) QWs. This indicates that more Sb was incorporated in this material. At the highest Sb flux, the PL shifts are consistent with an Sb composition of 0.085 in GaNAs(Sb), and only 0.02 in GaInAs(Sb) and 0.016 in GaInNAs(Sb). We have to mention here that, according to the results of Section 15.1, N incorporation is sensitive to Sb, and according to Section 15.4, the band gap bowing is stronger in GaNAsSb. These effects contribute to the PL shifts observed in GaNAs(Sb) and GaInNAs(Sb), and they were taken into account to estimate the Sb compositions given above. The higher Sb incorporation rate in GaNAs(Sb) is essentially due to the absence of In-related compressive strain in this compound. The present GaInAs(Sb) and GaInNAs(Sb) QWs have an indium concentration of 0.36. The related strain is very high and not favorable the incorporation of large-size Sb atoms. Hence, a large part of incoming Sb segregates at the surface before re-evaporation. As a consequence, the Sb surface coverage is very high during GaInAs(Sb) or GaInNAs(Sb) growth. This high Sb coverage is at the origin of the surfactant effect, which is independent of the presence of N in the layer. As a matter of fact, we have found that Sb is beneficial to reduce the surface faceting and to delay the formation of dislocations in highly strained GaInAs

484

Figure 15.11.

Dilute Nitride Semiconductors

Experimental XRD rocking curves of the three-QWs samples: (a) GaInNAs/GaAs; (b) GaInNAsSb/GaAs.

growth [13]. Here, we will focus on the GaInNAs(Sb) results. Two samples with three QWs of GaInNAs or GaInNAs(Sb), were compared by XRD and TEM. Both samples have the same structure, the only difference being the additional Sb flux during the growth of the quinary QWs. The QWs are 8-nm-thick, separated by 20 nm GaAs barriers. The structures also include a 100 nm reference GaNAs layer. Figure 15.11 shows the XRD rocking curves of these two samples. The diffraction peaks at the largest angle correspond to the GaNAs reference layers. At the shortest angles, a group of satellites is due to the periodicity of the three QWs. The comparison of the satellite intensities in the two samples is striking. Satellites are clearly resolved for the quinary QWs, whereas they are very weak for the quaternary QWs. Pendellosung fringes are also clearly distinguishable for the quinary QW sample. In addition, the maxima of the envelopes indicate that the compressive strain is higher in the quinary QW structure compared to the quaternary QW structure. This confirms that a small fraction of Sb, estimated here as 0.01, is effectively incorporated in the quinary QWs. TEM views of these two samples can be seen in Figure 15.12. These views confirm the strong contrast between the structural quality of the two samples. The GaInNAs QW interfaces are not flat. More particularly, the top interfaces have developed a strong roughness. In addition, extended defects can be observed. On the opposite, interface faceting, generation and propagation of extended defects are prevented in the GaInNAsSb QWs. These observations evidence that Sb has a very beneficial effect on the structural quality of highly strained layers: the strain relaxation mechanisms can be delayed. Laser characteristics have been found to be improved consistently [14].

GaNAsSb Alloy and Its Potential for Device Applications

Figure 15.12.

485

Transmission electron microscopy of the three-QWs samples: (a) GaInNAs/GaAs; (b) GaInNAsSb/GaAs.

15.6. LONG-WAVELENGTH GaAs-BASED LASER

As stated before, GaInNAs QWs have demonstrated a high potential for 1.3 mm GaAsbased lasers. However, a rapid increase of their threshold current density with emitting wavelength has been observed. This is likely due to the increasing concentration of nitrogen that is required to extend the wavelength. Nitrogen (5%) was necessary to demonstrate GaInNAs QW lasing at 1.5 mm [15]. Such a relatively high concentration is detrimental to the optical quality of the QWs. Therefore, the use of Sb becomes particularly relevant to achieve emission above 1.3 mm: (i) we have shown that it allows to obtain low band gap with less nitrogen, (ii) the Sb surfactant effect allows to accumulate more strain in the QW, (iii) Sb can bring some flexibility to design QW barriers. This last point is interesting since another strategy to extend the emission wavelength has been to design QWs with intermediate barrier height [16,17]. This allows to lower the QW confinement energies, as shown in Figure 15.13. In this figure, different QW designs are shown including GaAs/GaNAs/GaInNAs and GaAs/GaNAsSb/GaInNAsSb double-step QWs. PL of such QWs are reported in Figure 15.14. The same growth conditions were used for these four samples, except that material sources were switched with different sequences. The inner part of the QWs is 8-nm thick with 0.36 indium concentration. Two samples have 5 nm intermediate barriers (GaNAs or GaNAsSb) surrounding the QW (GaInNAs or GaInNAsSb). The GaNAs intermediate barriers lower the GaInNAs QW transition energy by 27 meV, and the GaNAsSb intermediate barriers lower the GaInNAsSb QW transition energy by 63 meV. It is also interesting to note that the PL red shift between GaInNAs and GaInNAsSb QWs is 23 meV, whereas it is 59 meV between GaInNAs/GaNAs and GaInNAsSb/GaNAsSb, although the same Sb flux was used for the growth of the single- or double-step barrier QWs. As shown before, the Sb

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Figure 15.13. Different types of QWs designed to extend their emission wavelength.

Figure 15.14. PL spectra corresponding to the QW design of Figure 15.13.

GaNAsSb Alloy and Its Potential for Device Applications

487

Figure 15.15. RT PL spectra of as-grown (dotted line) and annealed (solid line) Ga0.61In0.39N0.015As0.975Sb0.01/ GaN0.02As0.88Sb0.1/GaAs SQW.

incorporation in GaNAsSb is more efficient than in GaInNAsSb. This is the main reason why the Sb-related PL shift is stronger in the double-step design, than in the single-step design. Figure 15.15 shows that, with a relatively low N content, the 1.5-mm range can be covered with this type of QW: an 8 nm Ga0.61In0.39N0.015As0.975Sb0.01 QW with two 5 nm GaN0.02As0.88Sb0.1 intermediate barriers emits around 1.58 mm at RT, with a PL linewidth of 42 meV. The spectral characteristics of this as-grown sample were improved with a 5-min anneal at 7008C. An inconveniently large PL shift to 1.48 mm was observed, and has already been discussed in the previous section. However, the PL efficiency was improved by more than a factor of 10, and the linewidth was narrowed to 35 meV. This linewidth value is at the state of the art for 1.5 mm emission on GaAs, although 10 meV larger than the linewidth observed for 1.3 mm GaInNAs QWs. Increased alloy disorder is a possible reason for this larger linewidth. Nevertheless, it is interesting to note that even though this QW is extremely strained, there is no sign of relaxation which could be induced by annealing, since the PL characteristics were improved. The same single QW as described earlier was inserted in a standard AlGaAs/GaAs waveguide structure with n and p type electrodes. A 20 mm £ 1120 mm stripe with cleaved facets was tested under pulsed operation at 208C. The laser spectrum and output power versus current characteristics are shown in Figure 15.16. The threshold current density is 3.5 kA/cm2, and the emission wavelength is centered at 1.50 mm. In a more recent work by Bank and coworkers, a 1.1 kA/cm2 threshold current density at 1.49 mm was demonstrated with a GaInNAsSb SQW laser [18]. They also achieved a 1.46 mm GaAs-based VCSEL with GaInNAsSb QWs [19]. These results, which are the best today, confirm that Sb can be determinant to transpose the very attractive performance of 1.3 mm GaInNAs lasers to the 1.55 mm region.

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Figure 15.16. L(I) characteristics of a quinary GaInNAsSb SQW laser. The inset is a laser emission spectrum for a driving current equal to 1.15 times the threshold current.

15.7. HBT

The turn-on voltage of HBTs, Vbe-on, is largely related to the band gap energy of their base layer. Therefore, the use of low band gap base materials is attractive to lower Vbe-on, and thereby to reduce the power supply voltage and power consumption of HBT circuits. As a matter of fact, the InP HBTs exhibit much lower Vbe-on than conventional GaAs HBTs because their base layer material (Ga0.47In0.53As or GaAs0.51Sb0.49) have lower band gap than GaAs. The use of GaInNAs in the base layer has been proposed to minimize this disadvantage of GaAs HBTs [4,20]. As expected, a reduction of Vbe-on was demonstrated by several groups. We emphasize that same, or even larger (see Sections 15.3 and 15.4) benefit on band gap reduction of the base layer can obtained with GaNAsSb. Moreover, if the band offsets of GaInNAs/GaAs interface are well suited to P –n – P HBTs, they are not favorable to N – p– N structures. The large conduction band offset, DEc ; impedes electron collection at the base –collector interface, and reduces electron injection from emitter to base. These effects can be attenuated by grading these interfaces, however, the small valence band offset, DEv, generates a detrimental hole diffusion from the highly doped base to the emitter. The band offsets at the GaNAsSb/GaAs interface are much more favorable to N – p– N HBT application because Sb essentially increases the valence band offset. We now report our first experimental investigations to implement GaNAsSb in the base of a N – p –N HBT. First, we want to stress that all the previous reports on GaInNAs

GaNAsSb Alloy and Its Potential for Device Applications

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HBTs have used metal organic vapor phase epitaxy (MOVPE) to grow the HBT structures. The HBT structures reported hereafter were grown by MBE. We selected a lattice-matched GaNAsSb compound with 2% of nitrogen, and 6% of Sb. With these compositions, the band offsets relative to GaAs are about DEc ¼ 300 meV; and DEv ¼ 100 meV: These values are not optimal, but this first attempt was targeting the Vbe-on reduction. Preliminarily, we checked that high Be doping of GaNAsSb was achievable in GaNAsSb. In a calibration sample, Hall measurement indicated a hole concentration of 5.7 £ 1019 cm23 and a hole mobility of 27 cm2/V s. For the HBT structures, an Al0.25Ga0.75As(Si) emitter was used. This choice allowed to grow reference structures with GaAs base for comparison. The Al composition was graded over 50 nm at the emitter– base interface, in order to reduce the barrier to electron injection into the base. From its interface with the base layer, the collector region consisted of a graded GaNAs(Si) followed by GaAs(Si). The complete design is shown in Table 15.2. Large devices (120 £ 120 mm2 sized emitters) with a double mesa design were obtained with standard process steps. Figure 15.17 shows the variation of current injected in the base layer, as a function of emitter –base voltage for the GaNAsSb and the reference HBTs. For a given current, the GaNAsSb HBT exhibited a clear reduction of the Vbe voltage as compared with the reference HBT (reduction of 240 meV for an injected current of 1 £ 1024 A). The expected effect was therefore, evidenced although a parasitic serial resistance appeared at higher injected current in the GaNAsSb HBT. However, a serious counterpart to this improvement was a catastrophic collapse of the current gain. The reference structure had a current gain of 80, whereas the gain fell down to 0.14 in the GaNAsSb HBT, meaning that Ic was smaller than Ib in this transistor. We tried to evaluate the contribution of growth conditions, which had to be modified to grow the GaNAsSb base. For this purpose, another reference structure was grown with a GaAs base, but we

Table 15.2. Layers of a GaNAsSb HBT structure Layer Contact Al grading ð0:3 ! 0Þ Emitter Al grading ð0 ! 0:3Þ Spacer Spacer Base Spacer N Grading N ð0 ! xÞ Collector Contact Substrate

Material GaAs:Si AlGaAs:Si Al0.3GaAs:Si AlGaAs:Si GaAs GaAs12x 2 ySbyNx GaAsSbN:Be GaAs12x 2 ySbyNx GaAsNx:Si GaAs:Si GaAs:Si S.I. GaAs

Doping (cm23) 19

1.4 £ 10 2 £ 1017 2 £ 1017 2 £ 1017 n.i.d. n.i.d. 1019

1017 1017 1.4 £ 1019

Thickness (nm)

Growth temperature (8C)

100 50 100 50 3 2 100 5 50 200 200 200

545 545 545 545 545 450 450 450 450 585 545 585

490

Dilute Nitride Semiconductors

Figure 15.17. Current in the base layer as a function of Vbe for two types of HBT. Full line: reference HBT with a GaAs base layer; dotted line: HBT with a GaNAsSb base.

applied the same growth conditions as for GaNAsSb HBT, to this structure. The gain was observed to decrease to 65. This means that the modification of growth conditions had a minor contribution to the drop in current gain. The Gummel plots of these HBTs revealed that regular behaviors were measured in the reference structure: Ic(Vbe) ideality factor of 1.02, and Ib(Vbe) ideality factor of 2.0. These characteristics drastically changed in the GaNAsSb transistor, which showed values of Ic(Vbe) and Ib(Vbe) ideality factors close to each other: 1.25 and 1.32, respectively. In fact, most of electrons injected into the base layer recombined inside this layer, without being collected. The very poor collection was not due to a residual barrier at the base –collector interface: we checked that the application of a Vbc voltage did not improve Ic. A second GaNAsSb HBT structure was grown with a similar structure, but the base thickness, Wb, twice smaller (50 nm). In that case, the current gain was 0.54. This represents an improvement by a factor of about 4, for a reduction of the base thickness by a factor of 2. This is a strong indication that the base current is essentially due to carrier recombination in the volume of the base layer, since in that case the current gain is, in a first approximation, proportional to Wb22 : From these results, the minority carrier diffusion length in the base layer was estimated to 36 nm. Obviously, this value is smaller than the base thickness. This particularly low diffusion length is a symptom of a drastic degradation of electron lifetime. This lifetime is shortened by non-radiative recombination induced by

GaNAsSb Alloy and Its Potential for Device Applications

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N cluster states. This limitation of III –V-N alloys seems particularly detrimental to carrier transport. It is also responsible for a significant degradation of GaInNAs laser performances, observed when N concentration is increased. Gain degradation in GaInNAs HBTs was also reported by other groups. However, it was not as severe as in the present case. To some extent, this can be explained by the relatively high N composition in the present work. The difference in growth techniques is yet another reason to consider. The typical growth temperature of III –V-nitrides is about 1008C higher by MOVPE as compared with MBE growth. In consequence, one can predict that N distribution in the III –V matrix, and thereby the density of non-radiative recombination centers, are quite different in MBE or MOVPE material. For electronic transport, it seems that MOVPE-grown III –V-Ns are more suitable. To conclude, it is thought that GaNAsSb is a good candidate for the base layer of a HBT. The band offsets relative to GaAs are more favorable to N – p– n structures than those of GaInNAs. The reduction of Vbe-on was demonstrated in such a GaNAsSb HBT. However, our investigations by MBE showed that, at present, the limitation of electron transport in the GaNAsSb base rules out the possibility to get sufficient current gain.

15.8. CONCLUSIONS

The GaNAsSb study is an interesting way to deepen the fundamental knowledge of III –V-N alloys, as well as to widen their application field. GaNAsSb grown on GaAs is an alternative to the extensively studied GaInNAs alloy. The comparison of these two alloys was of particular interest in several respects: (i) Our growth investigations, by MBE equipped with a N plasma source, revealed that N is more easily incorporated when a fraction of As is replaced by Sb. Consequently, it means that the sticking coefficient of N plasma active species is lower than unity, in particular in GaNAs or GaInNAs growth. (ii) In opposition to GaInNAs, GaNAsSb has a single type of cation. It was expected that this characteristic would make GaNAsSb less sensitive to thermal anneal. Surprisingly, the band gap blue shift, which is commonly observed after annealing III –V-N alloys, is larger in the case of GaNAsSb. This tends to show that the annealinduced atomic rearrangement is more drastic in this alloy, and that the III –V-N band gap value is also sensitive to the composition of the second neighbor shells around N atoms. (iii) We found that the N-related band gap bowing is stronger in GaNAsSb than in GaNAs or GaInNAs. This characteristic remains true even after annealing. This observation is of fundamental and practical interest. In particular, GaNAsSb is more favorable to obtain low band gap on GaAs.

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(iv) The band offsets of GaNAsSb/GaAs interface significantly differs from those of GaInNAs/GaAs. An independent adjustment of DEc and DEv can be achieved by varying N and Sb compositions, respectively. This characteristic can be very attractive in a device like N – p –N HBT. Moreover, due to this offset configuration and to the stronger band gap bowing, GaNAsSb/GaAs QWs are much more favorable than GaInNAs QWs to achieve emission at long wavelengths. However, this is at the expense of electron confinement, which must be high enough to achieve lasers insensitive to temperature. A compromise can be found by elaborating GaInNAsSb quinary alloys. We have tested the potential of these alloys in laser and HBT devices. N –p –N HBTs with a GaNAsSb base layer were fabricated. The reduction of Vbe-on was demonstrated as a result of the low band gap base. However, we have observed that N is highly detrimental to carrier transport. Referring to other studies, the degradation of transport properties seems to be more severe in MBE as compared to MOVPE-grown III –V-N materials. GaAsbased laser structures were realized with GaInNAsSb QWs. Here, the major role of Sb was a surfactant effect during growth. Lasing was demonstrated at 1.5 mm. To date, this quinary system is the most successful approach to demonstrate GaAs-based in the 1.55 mm region.

ACKNOWLEDGEMENTS

The authors are grateful to Jean-Luc Pelouard and Fabrice Pardo for their help and expertise in HBT characterization, Sophie Bouchoule and Kamel Mergem for their effort in laser fabrication and measurements. This work was financially supported by “Re´gion Ile de France,” “Conseil Ge´ne´ral de l’Essone,” RNRT-SINTROP’S project, RMNTREGINAL, and European IST-GIFT project.

REFERENCES [1] [2] [3] [4]

Thomas, D. & Hopfield, J. (1966) Phys. Rev. B, 25, 3828. Weyers, M., Sato, M. & Ando, H. (1992) Jpn. J. Appl. Phys., 31, L853. Friedman, D.J., Geisz, J.F., Kurtz, S.R. & Olson, J.M. (1998) J. Cryst. Growth, 195, 409. Chang, P.C., Baca, A.G., Li, N.Y., Sharps, P.R., Hou, H.Q., Laroche, J.R. & Ren, F. (2000) Appl. Phys. Lett., 76, 2262. [5] Livshits, D.A., Egorov, A.Y. & Riechert, H. (2000) Electron. Lett., 36, 1381. [6] Reinhardt, M., Fischer, M., Kamp, M. & Forchel, A. (2000) Electron. Lett., 36, 1025. [7] Teissier, R., Sicault, D., Harmand, J.C., Ungaro, G., Le Roux, G. & Largeau, L. (2001) J. Appl. Phys., 89, 5473.

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[8] Spruytte, S.G., Larson, M.C., Wampler, W., Coldren, C.W., Petersen, H.E. & Harris, J.S. (2001) J. Cryst. Growth, 227– 228, 506. [9] Ciatto, G., D’Acapito, F., Grenouillet, L., Mariette, H., De Salvador, D., Bisognin, G., Carboni, R., Floreano, L., Gotter, R., Mobilio, S. & Boscherini, F. (2003) Phys. Rev. B, 68, 161210. [10] Kim, K. & Zunger, A. (2001) Phys. Rev. Lett., 86, 2609. [11] Bellaiche, L. & Zunger, A. (1998) Phys. Rev. B, 57, 4425. [12] Yang, X., Heroux, J.B., Mei, L.F. & Wang, W.I. (2001) Appl. Phys. Lett., 78, 4068. [13] Harmand, J.C., Li, L.H., Patriarche, G. & Travers, L. (2004) Appl. Phys. Lett., 84, 20. [14] Yang, X., Jurlovic, M.J., Heroux, J.B. & Wang, W.I. (1999) Appl. Phys. Lett., 75, 178. [15] Fischer, M., Reinhardt, M. & Forchel, A. (2000) Electron. Lett., 36, 1208. [16] Miyamoto, T., Takeuchi, K., Koyama, F. & Iga, K. (1997) IEEE Photonics Technol. Lett., 9, 11. [17] Ha, W., Gambin, V., Bank, S., Wistey, M., Yuen, H., Kim, S. & Harris, J.S., Jr. (2002) IEEE J. Quantum Electron., 38 (9), 1260. [18] Bank, S.R., Wistey, M.A., Yuen, H.B., Goddard, L.L., Ha, W. & Harris, J.S. (2003) Electron. Lett., 39, 1445. [19] Wistey, M.A., Bank, S.R., Yuen, H.B., Goddard, L.L. & Harris, J.S. (2003) Electron. Lett., 39 (25), 1822. [20] Welser, R.E., DeLuca, P.M. & Pan, N. (2000) IEEE Electron. Dev. Lett., 21, 554.

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Dilute Nitride Semiconductors M. Henini (Ed.) q 2005 Elsevier Ltd. All rights reserved.

Chapter 16

A Comparative Look at 1.3 mm InGaAsN-based VCSELs for Fiber-optical Communication Systems H. Riechert and G. Steinle Infineon Technologies, D-81730 Munich, Germany

ABSTRACT

Optical data transmission will greatly benefit from vertical cavity surface emitting lasers (VCSELs) by taking the step from the transmission wavelength of 0.85 –1.3 mm, since this will allow a much extended transmission distance at high data rates as well as greatly enhanced eye safety. VCSELs are key components for low-cost systems (such as Gb Ethernet). This review therefore addresses the status of VCSELs emitting around 1.3 mm. The various approaches based on both GaAs- and InP-based active regions will be outlined and their respective advantages and drawbacks will be discussed. At present, devices based on InGaAsN – GaAs quantum wells offer the highest promise due to their superior optical output powers at both room temperature and at elevated temperatures. We will give an overview of the performance achieved with these devices and illustrate their application in low-cost transceivers which can cover distances up to 10 km with data rates of up to 10 Gb/s. 16.1. INTRODUCTION: 0.85 mm VERSUS 1.3 mm VCSELs

Optical data communication relies on semiconductor lasers which can be modulated at high frequencies and can be fabricated at low cost. Ideally, such lasers should be available as monolithic linear arrays for multichannel parallel transmission (as supplied in the parallel optical link Parolie by Infineon). A crucial issue for both cost and efficiency of the entire system is the ease of coupling of the lasers’ optical output into a standard silica fiber. In this respect, vertical cavity surface emitting lasers (VCSELs) are ideally suited (Figure 16.1). Whereas in conventional “edge-emitting lasers” the resonator is obtained by cleaving the semiconductor structure, the resonator of a VCSEL is created in the epitaxial crystal growth by growing two stacks of mirrors consisting of alternate layers with as high a difference in refractive index as possible (“distributed Bragg reflectors” ¼ DBR mirrors). Centered between these reflectors is the cavity containing 495

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Figure 16.1. Schematic of VCSEL cross-section.

the active layers as the laser medium. Thus, the laser resonator does not lie in the plane of the wafer surface but is perpendicular to it and the VCSELs can be formed by structuring the entire wafer into circular mesas. Therefore, their emission cone is also circular and ideally matches the acceptance cone of the fiber. Moreover, the parallel processing of VCSELs on wafer and the on-wafer testing of completed devices greatly reduce production cost. Typical requirements for VCSELs to be employed in data communication systems are single-mode operation and an output power of about 1 mW over the whole range of operating temperatures up to 858C. This high-temperature operation in particular is one of the main technical challenges for VCSEL development. Presently, all commercially available VCSELs are epitaxially grown on GaAs substrates, where the almost lattice-matched material AlxGa(12x)As serves to constitute the DBR mirrors. The standardized wavelength for these devices is 0.85 mm and the output is transverse multimode. Although these first-generation devices can be readily created within the class of GaAs-based materials (InGaAs/AlGaAs) and are now well established, transmission systems will greatly benefit in several ways if their emission wavelength can be shifted into the 1.3 mm region and the output can be constrained to a single transverse mode for coupling into single-mode fibers: †

† †

Most evidently, at this wavelength the dispersion (more precisely: group velocity dispersion) in the silica fiber is zero, such that light pulses experience no spreading in time as they travel along the fiber. Therefore, 1.3 mm are obviously ideal for high-bit rate data transmission, which is their main advantage over 1.55 mm. The absorption of fibers is significantly lower for 1.3 mm than for 0.85 mm, such that longer distances can be covered. Additionally at 1.3 mm much higher optical power may be transmitted without surpassing the power limit imposed by eye-safety regulations, since the human eye is by a factor of about 20 less sensitive at 1.3 mm compared to 0.85 mm. This allows the installation of more parallel lines in one fiber bundle (also for multimode systems) or to increase the present transmission distance from about 300 m to more

A Comparative Look at 1.3 mm InGaAsN-based VCSELs

† †

497

than 10 km. The voltage of a 1.3 mm laser can be reduced to about two-third of that for a 0.85 mm device, which is a significant advantage for the driving electronics. Manufacturing of true single-mode VCSELs is easier for 1.3 mm emission than for 0.85 mm due to the mode diameter, which is about 1.5 times larger.

On the other hand, going to longer wavelength has some fundamental drawbacks: One lies in the greatly increased optical absorption in p-type doped material which requires a much more refined device design. The other is that smaller band gap materials tend to have significantly higher Auger recombination which leads to nonradiative losses in the laser.

16.2. APPROACHES TO ACHIEVE 1.3 mm VCSELs

The advantages listed above have spurred a large body of work and various approaches to realize long-wavelength VCSELs. Some recent reviews can be found in Refs. [1,2]. The following overview is structured by the most important choice to take: on the one hand one might adhere to the well-established GaAs VCSEL technology and try to find a way to extend the wavelength from InGaAs quantum wells beyond the strain-induced limit, which lies at about 1.2 mm. On the other hand one might choose the commonly used InP-based materials for the active region, in this case facing the need to find an effective technological realization for the DBR mirrors. 16.2.1 InP-Based Active Region InP-based materials are not well suited to form DBR mirror stacks, since they offer only a small change in index of refraction and, more importantly, suffer from the very poor heat conductivity of quaternary materials. To overcome this problem, InP-based active regions have been fused with separately grown, GaAs-based DBR mirrors [3] or—in addition to that—even with GaAs-based short-wavelength lasers [4] which serve to optically pump the 1.3 or 1.55 mm active region. Promising results have been obtained in this way, in particular a cw-output power of 1.6 and . 0.5 mW was achieved at 20 and 858C [4], which up to now was the benchmark for 1.3 mm VCSELs. However, the process of fusing is not considered very amenable to large-scale production and devices have so far not become commercially available. Another possibility is the growth of monolithic structures on InP with lattice-matched AlGaAsSb based mirrors, which has been demonstrated for the 1.55 mm wavelength range (l ¼ 1560 nm; aperture diameter 8 mm, cw-output power . 1 mW at 208C, . 100 mW at 808C [5]). After the growth of the DBRs and a process for creating a current aperture by lateral oxidation appear to have been mastered, this approach still suffers from the need to

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have sufficiently thick InP layers in the cavity to spread the heat away from the active region. For 1.3 mm devices, the InP/antimonide approach is in principle suitable, but has not yet been employed. Recently, a novel approach using very high reflectivity InP/air DBRs has been used to realize both 1.3 and 1.55 mm VCSELs [6]. For room temperature operation, very promising results have been obtained, but apparently the problem of heat spreading is particularly severe in this case. Consequently, the cw-output power so far achieved at 808C is limited to less than 100 mW. The best performance for VCSELs with InP-based active regions has been achieved for emission at 1.55 mm, using a structure consisting of an epitaxial quaternary In(Ga)AlAs mirror on one side and a short dielectric mirror on the other side, which is mounted on a heat sink-like metal contact. In this structure the lateral current confinement is achieved by a laterally structured, buried tunnel junction, which is overgrown in a second epitaxial step (l ¼ 1550 nm; aperture diameter 6 mm, cw-output power q 1 mW at 208C, 0.5 mW at 808C [7]). This approach has also been used for 1.3 mm emission, where more DBR mirror layers are needed. In this case, the performance falls short of the 1.55 mm devices. In summary, it should be mentioned that InP-based long-wavelength VCSELs show large promise for the 1.55 mm range. However, no similar performance has been shown for 1.3 mm. Moreover, in all cases discussed above, the manufacturing process is clearly more complicated than the established monolithic VCSEL technology based on GaAs. 16.2.2 GaAs-Based Active Region The other alternative is to adhere to the well-established technology of GaAs VCSELs, which allows a monolithic growth of the whole VCSEL structure, but requires to overcome the long-wavelength emission limit of InGaAs quantum wells. Due to strain limitations, this limit lies at about 1.15 –1.2 mm [8]. To push the light emission of GaAsbased structures to longer wavelengths, several alternative approaches are being studied in research labs worldwide. The emission wavelength of VCSELs may be extended beyond the peak gain wavelength by extensive gain – cavity detuning. By this approach, single-mode operation up to 1.27 mm has been achieved with InGaAs-QWs [9]. The output power at 908C was as high as 0.6 mW due to the optimum matching of gain and cavity wavelength at the highest operating temperatures, however this design results in high laser threshold at room temperature and has a high risk to obtain good long-term reliability. One uses InAs-based quantum dots created by self-organization effects during growth. Despite the problem of gain saturation in quantum dots, 1.3 mm VCSELs have been successfully fabricated [10], using fully oxidized AlAs/GaAs DBRs with an active region of only three layers of InAs quantum dots. The lasing threshold of such structures with an 8 £ 8 mm2 current aperture is about 2 mA. At present, the best results for such structures

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are 0.65 mW of output power at room temperature in cw operation, with a low threshold of 1.3 mA ([11] also 8 £ 8 mm2), but with a poor high-temperature performance. Another approach applies GaAsSb/GaAs quantum wells. In order to achieve emission at 1.3 mm, it requires very highly strained GaAsSb layers, but by embedding them in straincompensating layers of GaAsP, electrically pumped VCSELs emitting at 1.3 mm could be realized [12]. They also exhibit a low threshold current of only 1.2 mA for a 6 mm diameter current path, but so far only very low output powers (below 100 mW cw at 300 K) have been reported. More recently, GaAsSb-based VCSELs emitting 0.3 mW at 108C and 0.1 mW at 708C (single mode at 1266 nm) have also been reported [13]. Finally, the utilization of InGaAsN, which is the route we have chosen, was spurred by early work of Weyers et al. [14] on the band gap narrowing in GaAs due to nitrogen incorporation and by pioneering laser work of Kondow et al. [15] in the mid-1990s. The approach of incorporating N into InGaAs has the advantage of being only a minor change to an otherwise well-established material system. Due to their high electronegativity, N atoms strongly change the band structure of (In)GaAs and at low nitrogen concentrations, each percent of N reduces the band edge by about 150 meV. Thus, the addition of only about 2% of N is sufficient to achieve 1.3 mm emission from InGaAsN. However, compared to InGaAs, the optical quality of the N-containing alloy degrades significantly with increasing N content. Therefore, the first VCSELs with an active region consisting of InGaAsN/GaAs QWs [16], realized in 1998, were limited to an emission wavelength of 1.2 mm. The first such devices emitting at 1.28 mm and beyond were made in 2000 [17,18] and as will be shown in the next section, this approach now has a clear lead in the performance of 1.3 mm VCSEL technology [19 –21].

16.3. 1.3 mm VCSELs BASED ON InGaAsN

All the early VCSEL results mentioned above were obtained with structures grown by molecular beam epitaxy (MBE), where a plasma source is employed to generate reactive nitrogen from N2. More recently the first MOVPE-grown VCSELs emitting at or beyond 1.26 mm have been reported [22 – 24]. In this technique, 1,1-dimethyl hydrazine (uDMHy) is used as a nitrogen precursor. The active regions of the VCSEL structures typically consist of two or three about 6 nm thick InGaAsN-QWs containing about 30 – 35% indium and 1 – 1.8% nitrogen, separated by 20– 25 nm barrier layers. A key issue in the design of long-wavelength VCSELs is to avoid optical losses in p-doped material, which are much more severe at 1.3 mm than at 0.85 mm [25]. We have therefore chosen an intracavity-contacted configuration with undoped AlGaAs mirrors and a conventional p – i –n doping sequence inside the cavity. A thin AlAs layer, which is laterally oxidized after mesa formation, serves as a current-confinement aperture and

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constricts the active volume. For top-emitting structures, the top mirror generally consists of about 26 –28 pairs of Al0.8Ga0.2As/GaAs or a sufficient combination of semiconductor and dielectric mirror pairs, the bottom mirror is made by using about 32– 34 pairs of AlGaAs/GaAs. To contact the p- and n-type regions, a double mesa structure is created by a combination of wet and dry etching. The dopant profiles in the doped layers must be adjusted very carefully in order to avoid optical losses. One drawback of intra-cavity contacts is the high lateral series resistance for the current flow in the p-GaAs layer due to the low hole mobility. Another approach, avoiding this problem, has been taken in Ref. [16], where both DBR mirrors are n-type doped and a tunnel junction is positioned in a minimum of the optical field in the cavity in order to convert electrons into holes. Thus, in such a structure, the current can be injected through the DBRs. However, the absorption losses are still higher than with undoped DBRs. For application in current data transmission systems, typically 2 4 dBm (0.4 mW) coupled average power is needed for 2.5 Gbps performance up to 15 km (OC-48 IR) and 10 Gbps performance up to 10 km (10 GbE). Since coupling efficiencies are typically 50% and higher, about 1 mW output power from the VCSEL is enough to satisfy the power demands. The data presented in the following paragraphs are all taken from production type devices and represent the present state of the art. In order to achieve single-mode emission, the oxide aperture is close to a diameter of about 6 mm (^ 1 mm). Devices with this geometry exhibit single-mode output powers of about 1 mW with side-mode suppression ratio better than 30 dB in a large temperature range between 0 and 858C (measured on wafer). In Figure 16.2 a typical device is shown with a single-mode output power of about 1.1 mW at 858C and even at 1058C about 750 mW SM output power is obtained (with a threshold of about 2 mA), which gives

Figure 16.2. LIV diagram of 1300 nm VCSEL chip at 0, 25, 55, 85 and 1058C.

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Figure 16.3. Spectral properties of 1300 nm VCSEL chip at 258C.

enough margin for uncooled operation in high temperature environments. Due to the aperture size of nearly 7 mm, the side-mode suppression ratio drops below 30 dB for output powers above 1.2 mW, which is shown in Figure 16.3 for room temperature. Accelerated lifetime tests have been performed at 858C 7 mA (12.4 Mio cumulated equivalent device hours without any failures), 858C 14 mA (325 Mio cumulated equivalent device hours with four failures) as well as 1258C 7 mA (43.6 Mio equivalent device hours without any failures). These data allow to extrapolate an average failure rate in time of less than 20 FIT (1 FIT corresponding to one failure in 109 operating hours) during 15 years of operation at 558C. Additionally no failures out of 339 unpackaged devices have been observed during 1000 h in an 858C/85% damp heat environment. The 1300 nm VCSELs have been packaged in a TSSOP10 package which is a surfacemountable plastic housing with a plane lead frame, suitable for 10 Gb/s and very small

Figure 16.4. Packaging for single-mode fiber coupling (LC-receptacle) and electrical high-frequency connection (flexboard).

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Figure 16.5. 10 Gbps eye of packaged 1300 nm VCSEL chips with single-mode fiber coupling.

(3 mm £ 3 mm £ 1 mm). A metal die pad is used for optimum heat sinking. The packaged TSSOP10 devices are automatically mounted on a batch of flexboards for mechanically flexible electrical connection, which in turn are being welded to LC receptacles for SMF coupling. The basic structure of the finished “Transceiver Optical Sub Assembly” ( ¼ TOSA) is shown in Figure 16.4. To illustrate the potential of InGaAsN VCSELs for high-bandwidth data transmission, an eye diagram of 1300 nm VCSELs in a TSSOP10 package at 10 Gbps is shown in Figure 16.5. This early prototype of a high speed 1300 nm VCSEL is packaged in the same TSSOP10 housing with flexboard and LC receptacle as the productive 2.5 Gbps chips. Based on this, Infineon has prototyped innovative intelligent small form factor (iSFP) transceiver modules which operate at 2.5 Gb/s and will be available for low-cost data transmission over about 10 km of standard single-mode fiber.

16.4. OUTLOOK

Spurred by the recent success of growing InGaAsN with the addition of Sb which has yielded low-threshold edge-emitting lasers with wavelengths well beyond 1.3 mm (Harris et al., this volume, Chapter 1), it is to be expected that InGaAsNSb-based VCSELs with

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improved performance and extended wavelength range can be achieved. First results in this respect are given in Ref. [26], where improved VCSELs incorporating this novel alloy were reported, as well as the report of the so far longest wavelength GaAs-based VCSEL, emitting up to 1.46 mm [27].

16.5. CONCLUSION

In the past few years significant progress has been made towards 1.3 mm VCSEL devices which are suitable for use in optical data transmission systems. At present, GaAs-based monolithic approaches appear to be closest to this goal, with devices based on InGaAsN/GaAs showing clearly the best performance. Based on such devices, prototypes of transceiver modules for operation at 2.5 Gb/s have been demonstrated.

ACKNOWLEDGEMENTS

Work at Infineon was partly funded by the EU under BriteEuram BRPR-CT98-0721 (OPTIVAN) and by the Bundesministerium fu¨r Bildung und Forschung (BMBF), Contract No. 01BC911/1. The authors gratefully acknowledge the collaboration with A. Yu. Egorov, S. Illek, G. Kristen, D. Supper, Gh. Dumitras, F. Mederer and M. Kicherer. REFERENCES [1] A review of long-wavelength VCSELs up to the introduction of InGaAsN is given in Karim, A., Bjo¨rlin;, S., Piprek, J. & Bowers, J.E. (2000) Long-wavelength vertical-cavity lasers and amplifiers. IEEE Sel. Top. Quantum Electron., 6, 1244–1253. [2] Riechert, H., Ramakrishnan, A., & Steinle, G. (2002) Development of InGaAsN-based 1.3 mm VCSELs, Semicond. Sci. Technol., 17, 892– 897. [3] Karim, A., Abraham, P., Lofgreen, D., Chiu, Y.J., Piprek, J. & Bowers, J. (2001) Wafer bonded 1.55 mm vertical-cavity lasers with continuous operation up to 1058C. Appl. Phys. Lett., 78, 2632– 2633. [4] Jayaraman, V., Goodnough, T.J., Beam, T.L., Ahedo, F.M. & Maurice, R.A. (2000) Continuous-wave operation of single-transverse-mode 1310 nm VCSELs up to 1158C. IEEE Photonics Tech. Lett., 12, 1595– 1597. [5] Hall, E., Nakagawa, S., Almuneau, G., Kim, J.K. & Coldren, L.A. (2000) Room-temperature, CW operation of lattice-matched long-wavelength VCSELs. Electron. Lett., 36, 1465– 1467. [6] Lin, C.-K., Bour, D.P., Zhu, J., Perez, W., Leary, M.H., Tandon, A., Corzine, S.W. & Tan, M.R. (2002) High-temperature continuous-wave operation of 1.3– 1.55 mm VCSELs with InP/air-gap DBRs, IEEE 18th International Semiconductor Laser Conference, Garmisch, paper ThA6.

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[7] Ortsiefer, M., Shau, R., Bo¨hm, G., Ko¨hler, F., Rosskopf, J., Steinle, G., Borchert, B. & Amann, M.-C. (2001) High-temperature 2.5 Gb/s vertical-cavity surface-emitting lasers at 1.55 mm wavelength, 27th European Conference on Optical Communication (ECOC 2001). [8] Sato, S. & Satoh, S. (1999) 1.21 mm continuous-wave operation of highly strained GaInAs quantum well lasers on GaAs substrates. Jpn. J. Appl. Phys., 38, L990 – L992. [9] Sundgren, P., Marcks von Wu¨rtemberg, R., Berggren, J., Hammar, M., Ghisoni, M., Oscarson, ¨ dling, E. & Malmquist, J. (2003) High-performance 1.3 mm InGaAs vertical cavity V., O surface emitting lasers. Electron. Lett., 39, 1128– 1129. [10] Lott, J.A., Ledentsov, N.N., Ustinov, V.M., Maleev, N.A., Zhukov, A.E., Kovsh, A.R., Maximov, M.V., Volovik, B.V., Alferov, Zh.I. & Bimberg, D. (2000) InAs – InGaAs quantum dot VCSELs on GaAs substrates emitting at 1.3 mm. Electron. Lett., 36, 1384– 1385. [11] Lott, J.A., Ledentsov, N.N., Ustinov, V.M., Alferov, Zh.I. & Bimberg, D. (2001) Continuous wave 1.3 mm InAs– InGaAs quantum dot VCSELs on GaAs substrates, CLEO 2001 Technical Digest, paper CTuH5, p. 137. [12] Anan, T., Yamada, M., Nishi, K., Kurihara, K., Tokutome, K., Kamei, A. & Sugou, S. (2001) Continuous wave operation of 1.30 mm GaAsSb/GaAs VCSELs. Electron. Lett., 37, 566– 567. [13] Dowd, P., Johnson, S.R., Feld, S.A., Adamcyk, M., Chaparro, S.A., Joseph, J., Hilgers, K., Horning, M.P., Shiralagi, K. & Zhang, Y.-H. (2003) Long wavelength GaAsP/GaAs/ GaAsSb VCSELs on GaAs substrates for communications applications. Electron. Lett., 39, 987– 988. [14] Weyers, M., Sato, M. & Ando, H. (1992) Jpn. J. Appl. Phys., 31, L853. [15] Kondow, M., Uomi, K., Niwa, A., Kitatani, T., Watahiki, S. & Yazawa, Y. (1996) GaInNAs: a novel material for long-wavelength-range laser diodes with excellent high-temperature performance. Jpn. J. Appl. Phys., 35, 1273– 1275. [16] Larson, M.C., Kondow, M., Kitatani, T., Nakahara, K., Tamura, K., Inoue, H. & Uomi, K. (1998) GaInNAs –GaAs long-wavelength vertical-cavity surface-emitting laser diodes. IEEE Photonics Tech. Lett., 10, 188– 190. [17] Choquette, K.D., Klem, J.F., Fischer, A.J., Blum, O., Allerman, A.A., Fritz, I.J., Kurtz, S.R., Breiland, W.G., Sieg, R., Geib, K.M., Scott, J.W. & Naone, R.L. (2000) Room temperature continuous wave InGaAsN quantum well vertical-cavity lasers emitting at 1.3 mm. Electron. Lett., 36, 1388– 1390. [18] Steinle, G., Egorov, A.Y. & Riechert, H. (2001) Monolithic VCSEL with InGaAsN active region emitting at 1.28 mm and cw output power exceeding 500 mW at room temperature. Electron. Lett., 37, 93 – 95. [19] Steinle, G., Mederer, F., Kicherer, M., Michalzik, R., Kristen, G., Egorov, A.Y., Riechert, H., Wolf, H.D. & Ebeling, K.J. (2001) Data transmission up to 10 Gbit/s with 1.3 mm wavelength InGaAsN VCSELs. Electron. Lett., 37, 632–634. [20] Jackson, A.W., Naone, R.L., Dalberth, M.J., Smith, J.M., Malone, K.J., Kisker, D.W., Klem, J.F., Choquette, K.D., Serkland, D.K. & Geib, K.M. (2001) OC-48 capable InGaAsN vertical cavity lasers. Electron. Lett., 37, 355– 356. [21] Naone, R.L., Jackson, A.W., Feld, S.A., Galt, D., Malone, K.J. & Hindi, J.J. (2001) Monolithic GaAs-based 1.3 mm VCSEL directly-modulated at 10 Gb/s, CLEO 2001 post deadline paper CPD 13-1. [22] Sato, S., Nishiyama, N., Miyamoto, T., Takahashi, T., Jikutani, N., Arai, M., Matsutani, A., Koyama, F. & Iga, N. (2000) Continuous wave operation of 1.26 mm GaInNAs/GaAs vertical

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[24]

[25]

[26]

[27]

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cavity surface emitting lasers grown by metalorganic chemical vapor deposition. Electron. Lett., 36, 2018– 2019. Takeuchi, T., Chang, Y.-L., Leary, M., Tandon, A., Luan, H.-C., Bour, D., Corzine, S., Twist, R. & Tan, M. (2001) Low threshold 1.3 mm InGaAsN vertical cavity surface emitting lasers grown by metalorganic chemical vapor deposition, LEOS 2001, late news proc. PD 1.2. Ramakrishnan, A., Steinle, G., Supper, D., Degen, C. & Ebbinghaus, G. (2002) Electrically pumped 10 Gbit/s MOVPE grown monolithical 1.3 mm VCSEL with GaInNAs active region. Electron. Lett., 38, 322. Babic, D.I., Piprek, J., Streubel, K., Mirin, R.P., Margalit, N.M., Mars, D.E., Bowers, J.E. & Hu, E. (1997) Design and analysis of double-fused 1.55-mm vertical-cavity lasers. IEEE J. Quantum Electron., 33, 1369– 1383. Shimizu, H., Setiagung, C., Ikenaga, Y., Ariga, M., Kumada, K., Hama, T., Iwai, N. & Kasukawa, A. (2003) 1.3 mm-GaInNAsSb based material and its application to VCSELs. Proc. IPRM, 263. Wistey, M.A., Bank, S.R., Yuan, H.B., Goddard, L.L. & Harris, J.S. (2003) Monolithic GaInNAsSb VCSELs at 1.46 mm on GaAs by MBE. Electron. Lett., 39, 1822– 1823.

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Dilute Nitride Semiconductors M. Henini (Ed.) q 2005 Elsevier Ltd. All rights reserved.

Chapter 17

Long-wavelength Dilute Nitride –Antimonide Lasers J.S. Harris Jr., M. Wistey, S. Bank, L. Goddard, V. Lordi, H. Bae and H. Yuen Solid State and Photonics Lab, Stanford University Stanford, CA, USA

17.1. INTRODUCTION

17.1.1 Applications: The Driving Force for Long-wavelength Devices The incredible growth of the Internet and data transmission is pushing the bandwidth requirements for metro (MAN), local (LAN) and storage (SAN) area networks to unprecedented performance levels. In spite of the rapid increase in capacity of current optical communications networks, it should come as little surprise that the information highway is now limited by the same problems of all mature, high-speed transportation systems such as airlines, trains or automobiles. All are limited by the switching hub from the main high-speed/capacity backbone through the traffic jams in the on/off ramps and slow feeder lines to the final destination, as illustrated in Figure 17.1. This bottleneck on the information highway is often referred to as the “last mile” problem and is now the focus of considerable effort to create truly high-speed MAN, LAN and SAN area networks [1 – 4]. This is the driving force behind the development of low cost, 1.3 –1.6 mm, directly modulated, un-cooled VCSELs; in contrast to the backbone networks, for which high performance is far more important than low cost, high-speed direct access will require hundreds of millions of lasers. Thus, laser cost and ultimately integration are the major issues, which must be addressed before widespread adoption will occur. Compared to current generation lasers, the cost will have to be reduced by at least 100 times. While this might seem to be a daunting challenge, first generation LANs based on low cost 850 nm GaAs VCSELs have demonstrated that they can meet the cost, reliability, speed and thermal requirements for such lasers. However, they operate at a wavelength for which 10 Gbps transmission is only possible over about 50 m (not km)! as illustrated in Figure 17.2 [1 – 3]. Thus, longer wavelength lasers are absolutely essential to achieve useful transmission distances at this data rate. In addition to the primary focus on low-cost VCSELs, there are additional devices (Raman and semiconductor optical amplifiers, detectors, modulators, switches, routers, etc.) and higher levels of device integration that will also be required to make full use of the available optical fiber bandwidth and enable high-bandwidth networks to the desktop 507

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Figure 17.1. Cartoon illustrating the on/off ramp bottlenecks for both highway and “information highway” transportation systems.

to become a reality [4]. While the focus of this chapter is on long-wavelength lasers, both VCSELs and high-power edge-emitting lasers, progress toward realizing modulators and saturable absorbers in GaInNAs(Sb) that can be monolithically integrated with these lasers is also described. 17.1.2 Candidate Long-wavelength Materials Systems The above opportunities have certainly not gone unnoticed to device and materials scientists. There has been an intense effort over the past decade to realize both low-cost,

Figure 17.2. Transmission distance versus laser modulation frequency for a variety of optical fiber/laser diode sources utilized in optical networks.

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Figure 17.3. Bandgap versus lattice constant for III-arsenide alloys showing lines of lattice match to GaAs for nitride–arsenide alloys and to InP for arsenide-phosphide alloys in the region applicable to long wavelength fiber systems.

long-wavelength VCSELs and high-power pump lasers between 1.3 and 1.6 mm [2,3]. Semiconductor lasers operating in the 1.3 – 1.6 mm region require materials with band gaps between 0.95 and 0.78 eV. The potential candidate alloys are shown in Figure 17.3. One of the requirements for alloy semiconductors is that they must be reasonably closely lattice matched to readily available binary substrates (GaAs or InP). The potential choices are thus defined by the intersection of the horizontal lines defining wavelength with the vertical lines below GaAs and InP defining lattice match. For many years it was believed that there was no suitable alloy adequately lattice matched to GaAs that would emit at . 1.1 mm, so InGaAsP on InP was the only materials system that met the perceived criteria. As a result, virtually all of the long-wavelength communications lasers today are fabricated from this system. InGaAsP/InP-based Bragg grating and distributed feedback (DFB) lasers at 1.55 mm have been extensively developed for the fiber backbone, however, they are prohibitively expensive for high volume MAN, LAN and SAN systems. Despite sizeable efforts to realize low-cost, long-wavelength VCSELs, limitations in the InGaAsP alloy system have made this an extremely difficult challenge [2,3]. The search for new options has led to multiple choices of materials combinations and device structures [2,3] to either avoid or accommodate the physical properties limitations of the InGaAsP/InP materials system. The major limitations of the InP-based system

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include (a) lack of alloys which are lattice matched and produce a large difference in the index of refraction for the distributed Bragg reflectors (DBRs) required for VCSELs, (b) T0 ; the temperature coefficient of the laser threshold, is quite low compared to InGaAs/ GaAs, the dominant technology for high power EDFA pump lasers, and (c) the thermal conductivity of the DBR mirror or cladding layers is inferior to GaAs-based structures, resulting in a greater junction heating under operation. The InGaAsP limitations pushed exploration of several approaches, which can be divided into two “camps” [2,3]: (1) those using InGaAsP/InP quantum well active regions, but alternative non-epitaxial approaches for the DBR mirrors and (2) those based upon GaAs/AlAs DBR mirror technology, but a new active gain region of materials closely lattice matched to GaAs. InGaAsP QW-based VCSELs have been fabricated using metal mirrors [5], wafer bonded AlAs/GaAs mirrors [6], combined InGaAsP/InP and AlAs/GaAs metamorphic mirrors [7], AlGaAsSb/AlAsSb mirrors [8], dielectric mirrors [9] and InP/air mirrors [10,11]. GaAs-based VCSEL approaches include InAs quantum dot active regions [12], GaAsSb/InGaAs Type II quantum wells [13] and GaInNAs closely lattice matched to GaAs [14,15]. The GaInNAs work started with the discovery by Kondow et al. [14] that small additions of N to InGaAs dramatically reduced the band gap of the resulting alloy and made GaInNAs a very attractive long-wavelength material. This discovery was far from obvious, given the known properties of all other III –V ternary and quaternary alloys, where the general rule was that alloys with a smaller lattice constant had an increased rather than decreased band gap as illustrated in Figure 17.3. The large electronegativity of N and its small covalent radius cause a very strong negative bowing parameter and the addition of N to GaAs or GaInAs dramatically decreases the band gap far more rapidly with alloy composition than other III –V alloys illustrated in Figure 17.3 [16 – 18]. The success of these materials systems has catapulted them into the lead for the development of a broad range of VCSELs and high-power edge-emitting lasers. We believe they will be the foundation of lower cost optical networks. GaNas and GaInNAs not only produce low-cost VCSELs, which have been a key focus, but they enable both Raman and semiconductor optical amplifiers (SOAs), which will provide gain throughout the 1.3 – 1.6 mm wavelength region. This will enable use of the full low-loss fiber bandwidth [4]. Additionally, it will be crucial to employ lasers that are un-cooled and directly modulated. Research on GaInNAs has revealed several additional factors vis-a`-vis InGaAsP/InP that could prove decisive in the race to produce low-cost, long-wavelength VCSELs and high-power Raman pump lasers. First, for the same band gap material, quantum well in the conduction band is deeper [14,15,19, Chapters 8– 10], the electron effective mass is larger in GaInNAs [19,20, Chapter 7], thus providing better confinement for electrons and better match of the valence and conduction band densities of states. This leads to a higher T0 ; higher operating temperature, higher efficiency and higher output power [15]. Second, most of the energy band engineering used to minimize heterojunction voltage drops use intermediate graded layers of AlxGa(12x)As or AlAs/GaAs superlattices, all of which are

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lattice matched to GaAs and do not require difficult compositional control over both column III and column V constituents in a quaternary layer to maintain lattice match, unlike InGaAsP [2,3]. Third, compositional control and uniformity of GaInNAs grown by MBE [2,21 – 26] is relatively easy compared to MOVPE [27 –35] or to AsP control in InGaAsP [36,37]. This will translate into better yield and far easier scale up to larger wafers for lower cost. Fourth, VCSELs can be straightforwardly fabricated using the welldeveloped GaAs/AlAs mirror and AlAs oxidation for current and optical aperture confinement technologies. Fifth, and we believe most important in the long term, this quinary alloy provides a single materials system for growth and processing which can produce not only the entire range of active devices (lasers, detectors, optical amplifiers, modulators, saturable absorbers, etc.), but enables significant integration of these devices with photonic crystal waveguides, resonators and GaAs electronics that will provide a truly revolutionary foundation technology for low-cost, ultra-fast photonic integrated circuits that will eliminate the current access limitations and produce ubiquitous highspeed networks to and from the desktop. 17.2. EPITAXIAL GROWTH SYSTEMS: MOVPE AND MBE

While the preceding discussion highlights the advantages of the GaInNAs(Sb)/GaAs system over the InGaAsP/InP or GaAsSb/GaAs systems, there are still very significant challenges for GaInNAs to produce useful, reliable lasers at 1.3– 1.6 mm [2,3,14,15, 19 –26]. The growth conditions for dilute nitrides are considerably more complex and challenging than in previous III – V semiconductor epitaxy. The primary technologies for growing GaInNAs(Sb) are molecular beam epitaxy (MBE) [2,3,14,15,19 –26] and metalorganic vapor phase epitaxy (MOVPE) [27 – 35]. MBE can be thought of as an elaborate thermal evaporation system under ultrahigh vacuum, with a specific furnace to evaporate (or sublimate) each element, which chemically react to form a compound only on the surface of the substrate. MOVPE is a gas-source deposition system, using heat at the wafer to crack precursor gases that chemically react within a boundary layer above the substrate and deposit the desired molecules onto the surface. As a result, MBE is kinetically dominated while MOVPE is closer to equilibrium and is thermodynamically dominated. Although MOVPE has historically been the preferred production technology for optoelectronic devices, MBE offers several distinct advantages for growing GaInNAs(Sb), for reasons which we will explain shortly. MOVPE was the primary choice for GaAs-based systems for 850 nm VCSELs, InGaAs for 980 nm EDFA pump lasers, and 1.55 mm InP-based DFB lasers, which made sense at the time. MOVPE for GaAs-based 850 nm VCSELs allowed higher growth rates and a high throughput, allowing dozens or even hundreds of wafers to be grown in a single day. Also, due to the inherently analog nature of gas flow in MOVPE, it

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was far easier to grow graded interfaces in AlAs/GaAs DBR mirrors for efficient VCSELs. While similar chirp grading can be mimicked in MBE by using hundreds of Al/Ga shutter operations, this approach was not regarded as “production worthy” and so, until recently, MBE was relegated to a research and development tool [2,3,33]. However, newer generations of MBE machines are capable of growing with a dozen or more sources, so multiple-step grading is possible with nearly the same effectiveness as linear or parabolic grading in MOVPE [33]. Also, the newer MBE machines are capable of growing on platens of multiple wafers (7 £ 6 in.), greatly increasing the manufacturing throughput, so the production advantages of MOVPE have been somewhat reduced. In a similar fashion, InP-based systems for producing edge-emitting lasers were almost entirely based on MOVPE. Valved phosphorous sources did not yet exist in MBE, and InP-based materials presented severe fire hazards whenever the MBE systems were opened and exposed to air. In MOVPE, on the other hand, the growth temperature, gas flow control, doping, etc. were all within a range that was compatible with readily available chemical precursors and growth parameters for MOVPE. Thus MOVPE became the dominant optoelectronic epitaxial technology. The situation for growth of GaInNAs (Sb) is significantly different [2,3,14,15]. In order to incorporate a sufficient amount of nitrogen into the material, the growth has to be done at much lower growth temperatures. The GaInNAs(Sb) alloy is not stable, but only metastable; it tends to segregate rather than forming an alloy, so the growth conditions must be carefully controlled to prevent this segregation. This is due to the different basic crystal structures of the constituent alloys and their regions of growth compatibility; InGaN is a hexagonal (wurtzite) crystal while InGaAs is cubic (zincblende), so there is a miscibility gap in which the alloys cannot be mixed under thermodynamically stable conditions [22 – 27]. Hence, as one increases either the fraction of nitrogen or the growth temperature, phase segregation occurs and the material breaks up into microscopic regions of InGaAs and InGaN [22 –27]. Because growth must be at much lower temperatures than earlier GaAs and InP-based systems, growth by MOVPE is far more challenging. Compared to MOVPE growth of N-based wide band gap systems which use ammonia as the N source, the growth temperature for GaInNAs is too low to achieve reasonable cracking of either ammonia or arsine [31 –35]. New sources with difficult precursor reactions and highly non-linear incorporation ratios greatly complicate the growth compared to work on earlier III – V materials systems. There are also strong precursor reactions between N and Al, so MOVPE growth is either done in two separate reactors [33, 34], by a two-step growth process [35] or by avoiding use of Al containing materials entirely by using InGaP for the wide band gap materials [38,39]. The aluminum-free approach has worked acceptably well for edge-emitting lasers, but is not well suited for the DBR mirrors or oxide confining regions which are critical for VCSEL fabrication. In addition, the higher growth temperatures limit the N incorporation where micro-phase

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segregation [26,32] begins and makes it extremely challenging to reach the N compositions needed to produce lasers beyond 1.3 mm. An illustration of this challenge is to look at the early literature on GaInNAs lasers and note how many results were reported between 1.25 and 1.28 mm, even though the minimum fiber dispersion occurs at 1.31 mm. Only Fischer’s early result stands in contrast to this with GaInNAs lasers at 1.52 mm [40]. However, MOVPE is not to be entirely ruled out, and several other chapters in this book discuss more recent, successful VCSELs and edge-emitting lasers in the range from 1.3 to 1.5 mm [24,41 – 43]. The most recent work by Tansu [44] reports exceptionally good quality film and some of the lowest threshold lasers to date from 1.2 to 1.38 mm. The key to good growth appears to be to optimize the growth of InGaAs under conditions of low temperature and extremely low arsine flow, similar to the partial pressure of arsine during GaInNAs growth by MBE. A growth pause at the quantum well interface increases PL dramatically, and the use of GaAsP barriers around the QW gives a large current characteristic temperature T0 ; in other words, the threshold current is fairly stable even if the temperature changes somewhat. MBE is certainly not without its challenges in growing these metastable alloys, but it also has significant advantages. Kondow’s first work [14,15] utilized a N plasma source added to a gas source MBE system. This system provided the insight into the potential for GaInNAs. However, the issues of H incorporation and its effect on the material [45 – 48] are described by Bonapasta and Filippone in Chapter 13. In a gas source MBE system, the composition is also very sensitive to growth temperatures [31 –35] due to the low arsine cracking efficiency. Solid source MBE with an atomic N plasma source has proven to be the simplest and most effective system to enable growth at the lowest temperatures and over the largest range of N and In compositions [2,3,14 –26,40,49]. Growth temperature is the single most critical parameter controlling growth [22,23]. When growth temperature exceeds a critical value, MBE growth begins to change from 2D, layer-by-layer growth to 3D island growth with microphase-segregation [26,32]. Figure 17.4 is a TEM micrograph showing successful growth of two GaInNAs QWs, followed by a third which has segregated, resulting in terrible surface morphology and luminescence, which does not recover even after anneal. All of these regions of terrible morphology are In-rich, and occur only above the QW, which indicates that some type of In surface segregation is occurring during GaInNAs growth. When this region becomes sufficiently In-rich, phase segregation occurs. Such observations are very common and the window for good epitaxial growth is quite narrow compared to other III– V alloys. There is a small N composition dependence on optimum growth temperature, however, 420 , T , 4608C maintains 2D epitaxial growth over the greatest range of small N compositions. Antimony raises the temperature at which this segregation occurs by about 108C. The ratio of Group V elements to Group III elements also affects the growth, but less so than temperature. The issue of strain and surface structure is discussed extensively in Chapter 1 on MBE growth with Sb.

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Figure 17.4. TEM cross-section image of 3-QW 35% In GaInNAs-GaAs barrier sample where 3D growth and phase segregation have occurred in the third QW.

There are several clear advantages for MBE over MOVPE for growth of high quality GaInNAs(Sb) for long-wavelength lasers. Perhaps the most fundamental is the absence of hydrogen and carbon-containing precursors from MBE systems. Hydrogen has been implicated in the formation of N – H clusters and gallium vacancies [49], leading to dramatically short laser lifetimes, in the order of hours. Hydrogen-free, solid source MBE has produced lasers with expected lifetimes of years [50]. Second, Volz et al. have observed a clear dependence of Jth for l . 1:2 mm lasers on carbon concentration [51] rather than on N or In composition to reach this wavelength. The combination of low growth temperature and MOVPE carbon-based precursor sources make growth very difficult, particularly for wavelengths . 1.3 mm. Finally, the relatively weak interaction between elements in MBE compared to MOVPE when composition changes are made such that changing fluxes or digital alloying is approximately linear and not difficult to control, even for a quinary alloy like GaInNAsSb. We have observed many differences in defects, impurity incorporation, annealing, etc. in GaInNAs and GaInNAsSb alloys compared to other III– V alloy systems [2,21 – 23,47 –53]; these are described in Chapter 1. The particularities of annealing are unique to the GaInNAs and GaInNAsSb systems and play a significant role in laser performance. The main issues are summarized in Section 17.3; their incorporation into our MBE growth has produced the dramatic improvements in material quality that have led to the exciting devices described in Sections 17.4 –17.6. They now cover the full range of low-loss fiber wavelengths.

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17.3. ION DAMAGE AND ANNEALING BEHAVIOR

One of the most critical parameters for good lasers is low non-radiative recombination. This has been one of the biggest challenges for all of the dilute nitrides because of the low growth temperature and requirement in MBE to use some type of plasma source to produce atomic N that is sufficiently reactive to be incorporated into the alloy. As a result of the low temperature growth and ion damage from the source, the luminescence properties of GaInNAs deteriorate incredibly rapidly with increasing nitrogen concentration [2,3,21 – 35]. We have undertaken a number of investigations of GaInNAs quantum wells to try to understand the luminescence problems. Thermal annealing increases the PL of GaInNAs QWs by 30 –75 times over as-grown QWs as well as blue shifting the luminescence peak by 50– 80 nm. Typical PL spectra before and after annealing are illustrated in Figure 17.5 [22,23]. The increase in intensity is presumably due to both the out-diffusion of point defects and an increase in the crystalline quality of the quantum well material. The wavelength shift was long thought to be due to either or both nitrogen out-diffusion and group III interdiffusion (GaIn) [21 – 26,52]; however, as reviewed in Chapter 1, this now appears to be due almost entirely to local atomic rearrangement of the N nearest-neighbors (NN) from largely Ga in as-grown material to largely In in annealed material [54,55]. One of the issues long suspected in this luminescence issue was the possibility of either ion or electron damage from the N plasma source. Such damage was reported by Pan et al. at the 2000 International MBE Conference [56 – 58]; however, they were using a dc plasma

Figure 17.5. Photoluminescence of as-grown and annealed GaInNAsSb illustrating both the increase in intensity and blue shift with anneal.

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source while almost all other MBE groups who were using rf sources. We sought to see if any similar effect could be observed with the rf source by having bias deflection plates installed in our rf plasma source. Based upon their results and thinking that a high bias would deflect all ions or electrons, we applied 800 V bias to the plates and grew several QW structures and observed no improvement. In fact, if anything, we observed a slight decrease in PL from tested QW structures. Hence, we grew for a 3-year period with no deflection plate bias. As described in detail in Chapter 1 on MBE Growth, we re-examined this result with more care in first measuring the ion and electron currents in the MBE system using the nude beam flux gauge as a Langmuir probe and discovered that low voltages were not only sufficient to deflect the ions and electrons, but that the high voltage may have caused a dc plasma in front of the source which created even more energetic ions or caused sputtering of the deflection plates, resulting in undesired impurities being incorporated into the epitaxial layers [59,60]. Following the successful mapping of the electron and ion distributions with deflection plate bias, we found that minimizing the ion current and hence damage resulted in significantly better material, not only as-grown, but particularly after anneal. The results of these experiments are shown in Figure 17.6. The PL not only shows very clear improvement with deflection bias, but that improvement appears to keep rising to higher anneal temperatures or times. At high anneal temperatures, the sample with þ 18 V deflection had more than five times greater PL intensity compared to the no-deflection sample. At low pump powers, the relatively narrow PL linewidth was reduced even further with deflection bias and PL linewidth of 32 meV was observed after an 8008C 1 minute

Figure 17.6. Photoluminescence for samples grown with different voltages applied to one deflection plate. The other plate was grounded. Note the higher luminescence over all annealing conditions, and the higher anneal temperatures reachable before the PL is quenched.

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anneal [60]. We have also shown the first clear, room temperature exciton peak in the 1.5 mm wavelength range, offering further evidence that removing plasma damage provided significantly better quality material [153]. This discovery has been one of the keys to our successful realization of low threshold, long wavelength GaInNAsSb lasers, described in the following four sections.

17.4. GaInNAsSb EDGE-EMITTING LASERS

This section reviews the recent developments in GaInNAsSb edge-emitting lasers. Progress on both 1.3 and 1.55 mm GaInNAsSb lasers has advanced dramatically since the first demonstrations in 2000 [62,63]. As with any emerging technology, it is difficult to predict the full impact the antimony containing devices will play in commercial applications; however, the substantial improvements due to the addition of antimony are quite promising and it provides a single materials technology base for all active layers in the full communications band and enables fabrication/integration of these active devices with photonic crystals because of the high index contrast one can realize with the oxidation of AlAs [2]. Initial work on GaInNAsSb was in the 1.3 mm range, as it was found that antimony allowed the extension of the lasing wavelength. While GaInNAsSb devices have thus far not exceeded GaInNAs lasers in the 1.3 mm range, they have demonstrated vastly improved performance , 1.55 mm [63,64]. At the present time more work is required before an accurate assessment of each approach can be made. The development of dilute nitride lasers (primarily GaInNAs) has been reviewed recently by Harris [2,3]; the remainder of this chapter thus focuses primarily on GaInNAsSb edge-emitting and VCSEL lasers grown on GaAs. 17.4.1 Initial Results Wang and co-workers at Columbia University reported the first GaInNAsSb laser [61]. The active layer was a single GAInNAsSb quantum well (QW) surrounded by GaAs and was embedded in an Al0.3Ga0.7As waveguide. The device was grown by solid-source MBE and lased under pulsed conditions at 1.295 mm with a threshold current density, Jth ; of 1.02 kA/cm2. The external efficiency, he ; and characteristic temperatures, T0 ; were quite low, 12.5% and 64 K, respectively. This was, however, a great validation of the potential of the GaInNAsSb system. This report was quickly followed by a group at Furukawa Electric who demonstrated higher performance CW lasers, grown by gas-source MBE (GS-MBE), but at a shorter wavelength of 1.26 mm [62]. The active layer was a single Ga0.61In0.39As0.9807N0.0033Sb0.016 QW surrounded by GaAs and embedded within an InGaP waveguide. A Jth of 700 A/cm2 was demonstrated at room temperature and a high T0 of 126 K was observed. The he was only , 21%, but was due to the highly reflective

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(HR) coatings applied to both facets (78%/95%). The devices also showed both high peak gain coefficient, g0 ; of 1700 cm21 and differential gain of 1.5 £ 10215 cm2, despite containing only a single QW [64]. More recently, the Furukawa group demonstrated high performance multiple quantum well lasers, under pulsed conditions, using three-step MOVPE/GS-MBE/MOVPE growth [65]. To obtain thicker active regions, Spruytte et al. utilized strain compensating GaNAs barrier layers [22,23,66]. The compositions were Ga0.68In0.34As0.972Sb0.016/ GaN0.019As0.981. It was noted that while the gain-per-well was slightly lower for these structures than for a SQW grown in a single-step, the other laser parameters were comparable. The triple and quintuple well devices showed similar performance in terms of threshold-per-well, gain-per-well, and efficiency. Therefore, the reduction in gain-per-well is likely not a reduction in the material quality associated with thick highly strained active regions. This is consistent with observations of PL intensity scaling of GaInNAs(Sb), where luminescence is relatively unchanged from one to three QWs, but then scales linearly for more wells [66,67]. Moreover, the constant gain coefficient-per-well, transparency current density, and internal efficiency ($ 95% for all structures) indicate that the carriers (electrons and holes) are evenly distributed between the QWs. This is likely due to the weak band offsets expected when utilizing GaNAs barriers and is discussed in Ref. [68]. Excellent temperature stability, T0 ¼ 105 K (900 mm long device), was obtained with the triple QW devices, but lower values (, 80 K) were observed for the single and quintuple lasers. 17.4.2 Pushing Beyond 1.3 mm While the Furukawa group has continued to improve GaInNAsSb lasers in the 1.3 mm regime, other groups began incorporating antimony in an effort to push to 1.55 mm. Harris and co-workers demonstrated a 1.38 mm GaInNAs/GaNAs laser using solid-source MBE, but were unable to extend the wavelength further without severe degradation of performance [69,70]. Addition of antimony allowed the demonstration of a triple QW GaInNAsSb/GaNAsSb 1.46 mm laser with maximum pulsed power exceeding 70 mW from a 5 mm wide stripe. The minimum threshold current density was 2.8 kA/cm2 with an he of 35%, at room temperature. A single QW 1.49 mm laser, containing slightly more antimony, was also demonstrated but with extremely high threshold current density of 18.8 kA/cm2 [66]. While quite high, performance was vastly improved over the first report of lasing at 1.52 mm with a GaInNAs active layer [40]. The group of Harmand and co-workers at CNRS demonstrated vastly improved 1.5 mm lasers shortly thereafter [72]. Using a single Ga0.6In0.4N0.01As0.075Sb0.015 QW surrounded by GaN0.02As0.88Sb0.1 barriers, embedded in an Al0.8Ga0.2As/GaAs waveguide, they demonstrated a 1.50 mm laser with pulsed Jth of 3.5 kA/cm2, he of 24%, and up to 44 mW of output power. The lasers operated up to 408C, with a T0 of 83 K. The growth technique was solid-source MBE.

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With improved growth techniques to mitigate plasma-related damage, Harris and coworkers demonstrated the first low-threshold CW GaInNAsSb devices in the 1.5 mm regime using solid-source MBE [59,60,63,73,74]. The lasers oscillated at 1.49 mm with threshold current densities of 1.1 kA/cm2 and 910 A/cm2 under CW and pulsed operation, respectively [63]. CW output powers as high as 30 mW were observed with he ¼ 40%: The initially observed T0 value of 65 K was caused by insufficient thickness of the p-side ohmic contact. Improved T0 and peak output power were subsequently obtained [75]. As of this writing, these are the highest performance devices reported. These have been the most widely investigated devices and will, therefore, be the focus of results and discussion in the following sections. 17.4.3 Device Structures The lasers reported were of the separate confinement heterostructure ridge-waveguide type. A schematic diagram of the device structure is shown in Figure 17.7. The active layer was a single 7.5 nm Ga0.62In0.38N0.023As0.95Sb0.027 quantum well surrounded on either side by 22 nm GaN0.025As0.975 barriers. Compositions were determined as discussed in Chapter 1 on MBE growth of GaInNAs(Sb), using prior measurements of similar structures, through a combination of HR-XRD, Rutherford backscattering, and nuclear reaction analysis [76]. GaNAs barriers exhibit improved low temperature growth morphology, as compared to GaNAsSb, while also providing strain compensation [73]. It is important to note that this has only been examined over the narrow window of barrier growth conditions dictated by these QW compositions. Work is currently underway to

Figure 17.7. Schematic diagram of the edge-emitting lasers used in this study.

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investigate this further. Moreover, the removal of antimony from the barriers may provide superior hole confinement due to a larger valence band offset between the QW and barrier. Details of the MBE growth of the QW were discussed in Chapter 1. The single quantum well active layer was symmetrically embedded in a GaAs waveguide with a total thickness of , 460 nm. The n-type cladding of the laser was 1.8 mm of Al0.33Ga0.67As with the outer 900 nm doped at 3 £ 1018 cm23 and the inner 900 nm doped at 7 £ 1017 cm23. The p-type cladding was a similar structure, with the inner 900 nm doped at 5 £ 1017 cm23 and the outer 900 nm was doped at 3 £ 1018 cm23. The regions nearest to the core were doped more lightly to minimize free carrier absorption (FCA) losses. A 50 nm top p-type GaAs cap layer was doped at , 1 £ 1020 cm23 to facilitate low resistance ohmic contacts. The sample was ex situ annealed at 8008C for 1 min in a rapid thermal annealing furnace where arsenic outdiffusion was minimized with a GaAs proximity cap. Ridge widths of 5, 10, and 20 mm were defined using a combination of lift-off of evaporated Ti/Pt/Au and a self-aligned dry etch to the top of the GaAs waveguide. The wafer was then thinned to , 120 mm and backside metal (Au/Ge/Ni/Au) was evaporated. To reduce contact resistance, the structure was sintered at 4108C for 1 min. Fabry –Perot cavities of multiple lengths were defined by cleaving. 17.4.4 Laser Characterization Testing was performed epitaxial-side up on a temperature controlled copper heatsink. Unless otherwise specified, all parameters were measured at room temperature (208C), under CW operation, on as-cleaved facets. Figure 17.8 shows the light output and voltage versus current input ðL – I – VÞ curves for a 20 mm £ 2450 mm device. The threshold current density, Jth ; was measured to be 1.06 kA/cm2. Lasing occurred at 1.498 mm as shown in Figure 17.9. The slope efficiency above threshold was 0.26 W/A corresponding to he of 31%. Efficiencies as high as 40% were observed in shorter devices. While this is a record in performance at 1.5 mm as shown in Figure 17.10 [63,75], there is still significant room for improvement and realization of lasers with , 500 A/cm2 thresholds. These low efficiency values and high threshold current are attributed to carrier leakage from the well and poor material quality of the barriers. These effects will be discussed in detail later in the chapter. 17.4.4.1 Temperature Dependence. The effects of device temperature were also explored. The threshold current density is plotted versus heatsink temperature in Figure 17.11. The characteristic temperature, T0 ; was found to be 139 K measured over the range of temperatures from 10 to 608C and 43 K from 60 to 708C. This sharp kink in the Jth ðTÞ curve is due to the rapid onset of processes, which scale with the cube and/or higher power of the carrier density, and strongly increase the temperature sensitivity. Experimental evidence of this non-radiative recombination in Z-parameter measurements

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Figure 17.8. CW light output and voltage versus current ðL – I – VÞ characteristic for 20 mm £ 2450 mm ridge waveguide laser.

is presented later in the chapter. CW lasing was not observed above 708C. The loss of laser action is also attributed to the onset of Auger recombination and/or carrier leakage [68,77]. Spontaneous emission (Z-parameter) measurements performed on these lasers revealed that Auger recombination dominates laser operation when the current density rises

Figure 17.9. Lasing spectrum of the 20 mm £ 2450 mm device showing oscillation at 1.498 mm.

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Figure 17.10. Recent trends in GaInNAs(Sb) lasers. Squares indicate 1.3 mm range lasers with linear fit (solid line), circles indicate previous 1.5 mm range lasers with linear fit (solid line), and the star represents this datum. Adapted from Ref. [63].

above , 1.5– 2 kA/cm2, in agreement with Figure 17.11 [77]. The Z-parameter technique has shown similar evidence of Auger recombination in 1.3 mm GaInNAs lasers [78]. Moreover, the kink in Jth ðTÞ was always observed at the temperature where Jth reached , 1.5 –2 kA/cm2, regardless of device length. As will be shown later, this appears to be

Figure 17.11. Plot of lnðJth Þ with temperature (squares) and the fits to an Arrhenius relation (lines). The T0 value for each temperature range is indicated.

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a commonality among all GaInNAs(Sb) devices reported in this wavelength regime. Onset of Auger recombination was also found to be independent of temperature over the range studied, likely indicating a low activation energy of Auger processes, Ea # 27 eV [68,77,79]. The lasing wavelength shifted with temperature by 0.58 nm/K, or 0.32 meV/K. The shift with temperature is consistent with temperature dependent PL measurements discussed in Chapter 2 [80,81]. The shift agrees with those observed for GaInNAs-based lasers at 1.3 mm [82] and is similar to that of InGaAsP lasers at 1.5 mm [83]. Due to this temperature dependence, CW laser action was observed at 1.52 mm at a heatsink temperature of 708C. This was the first report of CW GaAs-based laser operation at 1.5 mm and beyond. 17.4.4.2 Cavity Length Studies. Cavity length studies of Jth and he were employed to determine various device parameters. The results of the cavity length study are summarized for each stripe width in Table 17.1. Figure 17.12 plots 1=he as a function of cavity length, L; for 10 mm wide stripes. The internal loss was found to be quite low, in the range of 1.91– 4.7 cm21 for 5, 10, and 20 mm stripes. The loss for 5 mm wide stripes, 1.91 cm21, is comparable to some of the best results for InP waveguides [84] and lower than 1.5 mm InAs quantum dot lasers grown on GaAs [85]. The internal quantum efficiency, hi ; was found to be between 42 and 50%. This low value may be due to short carrier residency in the QW in conjunction with non-radiative centers within the GaNAs barriers. While GaNAs barriers are of superior optical quality to GaNAsSb, under these growth conditions, they likely possess large numbers of non-radiative centers. DLTS measurements show extremely high defect densities, even in low nitrogen content GaNAs [86]. An additional mechanism for the low hi may be poor interfaces between the QW and barriers, however, no evidence currently supports such a mechanism. More work is needed to identify and remedy the cause(s) for the low hi : A plot of lnðJth Þ; with 1=L; for 10 mm stripes is shown in Figure 17.13. Using conventional methods of plotting lnðJth Þ versus 1=L; the gain overlap product, Gg0 ; was

Table 17.1. Summary of cavity length study Parameter

hi (%) ai (cm21) G·g0 (cm21) g0 (cm21) Jtr (A/cm2) b0 (cm/A) Rth (K/W) (L ¼ 983 mm)

5 mm stripe

10 mm stripe

20 mm stripe

42 1.91 25.0 1786 635 2.81 41.5

49 4.69 25.7 1836 658 2.79 37.8

46 3.00 26.2 1871 479 3.91 30.8

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Dilute Nitride Semiconductors

Figure 17.12. Plot of 1=he with cavity length (squares) and the fit to theory (line) for 10 mm wide lasers.

determined to be , 25– 26 cm21 and the transparency current density, Jtr ; was found to be , 0.5 –0.65 kA/cm2. From finite difference simulations, a 2D overlap of the fundamental mode with the active region, G ¼ 1:4% was calculated, yielding a gain coefficient, g0 ; in the range 1786– 1871 cm21. This is higher than for GaInNAs/GaNAs lasers at 1.3 mm [87] and InGaAsP lasers at 1.5 mm [88,89]. With continued improvements in hi and Jth ; GaInNAsSb will become quite promising for high power laser applications, including Raman pump lasers. Based on these data, the peak differential gain at transparency, b0 ¼ g0 =Jtr , was quite low, 2.79– 3.91 cm/A, and predicts poor current modulation response. This is attributed

Figure 17.13. Plot of lnðJth Þ with the inverse of cavity length (squares) and fit to theory (line) for 10 mm wide lasers.

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mainly to the large number of non-radiative recombination sites; improved results are expected through advances in growth techniques. It is also expected that the actual differential gain with respect to carrier density, dg=dn; will be significantly higher than predicted by b0 due to the low hi and Jtr : 17.4.4.3 Temperature Sensitivity. The temperature dependence of laser performance is a critical motivation for the use of dilute nitride alloys over conventional InP-based approaches. This section will examine recent work on 1.5 mm GaInNAsSb devices to determine the causes of the temperature sensitivity [68]. It is expected that non-radiative recombination can be minimized through further improvements in growth technology, similar to the steady improvement of GaInNAs lasers at 1.3 mm [2,3,55]. The inherent temperature sensitivity of the alloy is, therefore, of great interest as it will likely determine the ultimate viability of GaInNAsSb lasers. This section begins with a description of the method of Tansu and co-workers for examining the temperature behavior of lasers. First applied to InGaAs lasers emitting , 1.2 mm [90], it has also been used to characterize GaInNAs lasers at 1.3 mm [91]. Typical cavity laser studies have consisted of measuring the threshold current density, Jth ; and the external differential quantum efficiency, he ; with for several cavity lengths to obtain the important device parameters, at room temperature. Through variation of cavity length, L; and temperature, T; a characteristic temperature for each device parameter is obtained. This temperature dependent information allows greater understanding of the physical mechanisms governing laser operation. In conjunction with other techniques such as spontaneous emission [92] and Z-parameter [93] measurements that are discussed subsequently, a full understanding of the relevant physics is obtained. The lasers studied were identical to those discussed in the previous section except a highly reflective coating of reflectivity , 98.7% was applied to one facet while the output facet was left as-cleaved. Devices were mounted on a temperature controlled copper chuck and measured under low duty cycle pulsed (1 ms, 1% duty cycle) conditions from 15 to 758C in 58C steps. Output power was measured with an InGaAs amplified photodiode mounted on an integrating sphere. The sphere and detector were calibrated together for diverging laser sources. Care was taken to ensure maximal Fermi level pinning in the device structure by extracting the threshold and efficiency from output powers in the range of 5– 10 mW [94]. This corresponds to a range of J=Jth < 1:2 – 1:4 at 158C. At 758C, the ratio is reduced slightly to 1.1 –1.25. This may cause a slight reduction in the measured ai and an increase in hi at elevated temperatures [94]. Data points were rejected if the linearity of the light output with current input ðL – IÞ had R , 0:999: Most measurements showed R . 0:9995; but degradation in the R value was observed at elevated temperatures, consistent with softer Fermi level pinning due to carrier leakage from the QW. Figures 17.14 and 17.15 show the compiled behavior of Jth and he with temperature, respectively, for a representative 10 mm £ 983 mm device. The T0 of the device is seen to

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Dilute Nitride Semiconductors

Figure 17.14. Variation of Jth with temperature over the range 15–758C.

be 106 K from 15 to 608C (288 –333 K) and 91 K from 60 to 758C (333 – 348 K). The threshold current density at 608C is 2 kA/cm2 and is consistent with the observed turn-on of Auger recombination and/or carrier leakage near , 1.5– 2 kA/cm2 in these lasers [77]. The external efficiency shows a similar “kink” at 608C, where T1 drops from 208 to 104 K. This result is inconsistent with conventional laser physics that requires that the carrier density pin within the QW at threshold. Consequently, it is expected that Auger recombination would not affect he due to its dependence on the cube of the carrier density, which is fixed. It is believed that this is either evidence of carrier leakage or an artifact caused by the thin p-metal contact and the resulting spreading resistance. Some comparably performing devices do not show a kink in he ðTÞ over the 15– 758C

Figure 17.15. Variation of he with temperature over the range 15–758C.

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Figure 17.16. Degradation of Gg0 with temperature. The strong temperature dependence at room temperature, Tg0 ¼ 113 K, indicates strong carrier leakage effects.

temperature range, consistent with the conclusion that this is an artifact of the device structure. The threshold current density with temperature was measured for several cavity lengths and were used to extract the gain parameters g0 and Jtr : Similar to the he ðTÞ measurements, Jth ðTÞ was fitted to local Arrhenius relations to reduce the propagation of measurement error. Under the assumption of a logarithmic gain model, the fitted data were used in the cavity length calculations to calculate g0 ðTÞ and Jtr ðTÞ: The values of hi ðTÞ and ai ðTÞ found in the previous section were used in the calculations. Figure 17.16 is a plot of Gg0 versus T: The gain coefficient is an extremely insightful parameter due to its strong sensitivity to the effects of both carrier leakage and Auger recombination. It is seen to degrade rapidly, even at low temperatures, and Gg0 decreased from 23 to 16 cm21 before Auger recombination/carrier leakage begins to dominate at current densities above 2 kA/cm2. A dramatic reduction in Tg0 to 45 K is observed when these processes become significant. The low characteristic temperature Tg0 ¼ 113 K (15 – 608C) is indicative of carrier leakage. Tansu and Mawst have shown strong evidence of hole leakage in 1.3 mm GaInNAs lasers [95]. Through the use of GaAsP barriers surrounding the QW to suppress hole leakage, they have shown a simultaneous reduction in Jth and improvement in T0 : Moreover, device performance improves monotonically with phosphorous concentration (increasing band offsets surrounding the QW). The dramatically reduced Tg0 observed at 1.5 mm, as compared to , 350 K for GaInNAs at 1.3 mm, is a strong evidence of increased carrier leakage at 1.5 mm. The enhanced temperature sensitivity is an unexpected result at longer wavelengths as the valence band offset is expected to be larger due to the addition of antimony into the QW. However, the valence band offsets between GaInNAsSb/GaNAs and GaNAs/GaAs for 1.5 mm QWs is small and imply substantially increased leakage as compared to GaInNAs at 1.3 mm

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(, 100 meV valence band offset). This effect, in conjunction with the poor crystal quality of the GaNAs barriers and Auger recombination, creates a complex loss mechanism that degrades the temperature stability. At relevant operating temperatures, carriers in the QW continually escape into the GaNAs barriers. Electrons are quickly reabsorbed due to the short transit time in the GaNAs barriers and large (200 –300 meV) barrier to the GaAs, in conjunction with any concentration and potential gradients. For holes, there is a smaller barrier and carriers are virtually free to diffuse through the barriers and GaAs core. The recapture time, however, is finite and leads to a small probability that the carriers will recombine within the GaNAs barriers or the GaAs waveguide. This is exacerbated if a large population of non-radiative sites and traps exist in the barriers. The hole thermionic escape time is sufficiently small and carriers escape and are recaptured repeatedly, thereby increasing the overall probability that each carrier is lost to leakage. This is also likely the cause not only of the low Tg0 ; but also the low hi in the lasers studied here and in Refs. [71,72]. As the operating temperature is increased, the probability of thermionic escape increases super exponentially, while the trap capture probability remains roughly constant. Detailed theoretical analysis is currently underway, but the internal efficiency reduction due to leakage can be roughly estimated to agree with the observed values using a modified rate equation model based upon the work of Nagarajan and Bowers [96]. These findings are supported by measurements of the spontaneous emission, under pulsed excitation, performed on these devices and discussed later in the chapter. The most salient point that validates the role of carrier leakage is that non-lasing transitions do not pin strongly at threshold. The ratio of the spontaneous emission efficiency for non-lasing transitions is , 40%, while , 10% ratios are typical in AlGaAs/GaAs semiconductor lasers where carrier leakage is not a significant issue [96]. 17.4.4.4 Above Threshold Parameters. External efficiency was extracted for several cavity lengths. Short cavity effects were removed by only considering devices ranging in length from 533 to 983 mm (effective cavity lengths 1050 –1950 mm). To reduce propagation of measurement error, he ðTÞ was fitted to local Arrhenius relations, from 288 to 328 K and 333 to 348 K. The fitted data were used in the cavity length calculations, at each temperature, to extract ai ðTÞ and hi ðTÞ: Figure 17.17 is a plot of ai ðTÞ: A clear increase is observed with temperature and is consistent with the observations of IVBA in ai ðTÞ for unstrained InGaAs lasers on InP [93,97,98]. The low temperature Tai value of 306 K is consistent with the measurements of Henry et al. that measured IVBA with temperature in GaAs (calculated to be 307 K from Figure 7) [99]. The magnitude of ai ; however, was found to be somewhat higher. Internal loss is the sum of IVBA and other mechanisms including unavoidable waveguide roughness due to processing. Waveguide roughness and similar losses are

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Figure 17.17. Increase of ai with temperature, indicating the presence of IVBA.

expected to be temperature independent. The internal loss was extrapolated to be 1.66 cm21 at 0 K. Removing this term, gives a room temperature loss of 2.73 cm21, which is similar in magnitude to the measurements of Henry and co-workers. Due to the lack of strain in the AlGaAs system, it is expected that free carrier processes should be approximately independent of the aluminum mole fraction [100]. Accounting for the doping level of 5 £ 1017 cm23 and the overlap of the optical wave to the p-AlGaAs layer of 10.5%, the Henry data predicts ai of 1.84 cm21, at room temperature. The difference between the calculations and the measured data is likely due to holes injected into the GaAs waveguide, electron related free carrier losses, and absorption in the GaInNAsSb/ GaNAs active region. It should be noted that although IVBA is a significant loss mechanism, it reduces T0 by only , 5 K. The effects of Auger recombination/carrier leakage are also evident in Figure 17.17 for temperatures above 608C. As internal loss is extracted above threshold, this is an artifact of the device structure caused by the thin p-type ohmic contact and should be neglected. Figure 17.18 shows the measured hi as a function of temperature. The value of hi degrades from 57 to 47% over the temperature range studied, corresponding to a Thi of 291 K. As expected, no kink is present in hi ðTÞ: Simply, the same fraction of carriers is injected into the QW regardless of whether or not Auger recombination is significant. While more carriers recombine non-radiatively when Auger is significant, the efficiency of injection is unchanged. Moreover, the lack of a kink is an evidence that Auger recombination occurs in the QW and not, as expected, in other areas of the device. The moderate decrease observed in hi when Auger recombination becomes significant is simply measurement noise.

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Figure 17.18. Dependence of hi upon temperature. Both the low value of hi at room temperature and its low characteristic temperature indicate carrier leakage.

17.4.4.5 Comparison of QW and Barrier Designs. Through comparison with other published dilute nitride lasers, it is now possible, to some extent, to evaluate the effects of QW and barrier material design on device performance [75]. We conclude from the analysis that recombination/carrier leakage is significant in all the approaches at wavelengths , 1.5 mm. Additionally, GaNAs and GaAs may have a weak type-II band lineup with GaInNAs(Sb) for light-holes, due to the large QW compressive strain. Several different approaches have been reported in the literature to reach 1.5 mm including GaInNAs with GaAs barriers (termed GaInNAs/GaAs) [71] and GaInNAsSb with GaNAsSb barriers (GaInNAsSb/GaNAsSb) [72]. It is noted that the lasers reported here (GaInNAsSb/GaNAs) have both a reduced Jth and higher T0 than the approaches by Harmand [72] and Forchel [71]. As a result, we can conclude that any improvement in T0 reported here is due to improved device structure and not simply an artifact of temperature insensitive non-radiative centers. We may similarly rule out Auger recombination as the cause for reduced room temperature T0 ; spontaneous emission measurements show that Auger recombination only becomes significant when the threshold current density is elevated above , 2– 4 kA/cm2 (i.e. those necessary at higher temperatures) [78]. Each reported laser structure shows a kink in Jth ðTÞ at a current density of , 1.5 – 2 kA/cm2-per-well, similar to that in Figure 17.11 [71,72]. Additionally, the T0 above this point is similar in each case: 69 K in Ref. [71], 68 K in Ref. [72] (estimated from the figure), and 43 K here. The 43 K is smaller than the others; and is believed to be due to error extracting T0 from only two data points in Figure 17.11. It should be noted that Auger recombination is not the dominant loss

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531

mechanism at room temperature, but it does dominate at elevated threshold current densities. Based upon the preceding discussion, Auger recombination appears to be a universal characteristic of the nitride – arsenide alloys reported thus far beyond , 1.4 mm. Neither changes in barrier material nor presence of antimony have mitigated these effects to date. In pushing to 1.55 mm, the choice of additional indium or antimony, to red shift the alloy, will likely be determined by the Auger coefficient of the resulting quantum wells, as well as the band offsets. The dominant mechanism affecting T0 at room temperature in the lasers reported here is likely hole leakage from the QW due to weak valence band confinement [75, 90]. This is likely also the case for 1.3 mm GaInNAs/GaAs lasers [87]. In light of the improvements in T0 reported here, 139 K compared to 111 K, we conclude that the addition of nitrogen into the barriers increases the QW valence band offset—leading to the conclusion of type II confinement. This observation is in agreement with band offset measurements and laser studies by Tansu et al. at shorter wavelengths [87]. Tansu and co-workers found a simultaneous reduction in Jth and enhancement in T0 when they changed from GaAs to GaNAs barriers surrounding a GaInNAs QW. They attributed this improvement to a reduction in hole leakage due to the increased valence band offset between the QW and barrier due to the type-II nature of GaNAs/GaAs. This is in contrast, however, to capacitance –voltage measurements of p- and n-type GaNAs/GaAs (N% < 3%) that have found the band offset to be type-I [100]. The valence band offset was found to be 11 ^ 2 meV. The difference may lie in the strain ˚ ) GaNAs layer is in contact with a highly strained GaInNAs effects when a thin (35 A layer [87]. It is, however, difficult to determine whether the difference in valence band offset, in the case of , 1.5 mm lasers, is due to the presence of nitrogen in the barriers or antimony in the QW. Band offset measurements of GaAsSb with GaAs show that band gap reduction takes place primarily in the valence band up to , 40% antimony [101]. However, recent measurements discussed earlier on the GaInNAsSb/GaNAs structures used by this group show the band offset ratio to be 80/20. This corresponds to a relatively small band offset between GaInNAsSb and GaNAs [74]. The improvement in T0 reported by the Stanford group is likely due to the reduced carrier density in the QW from reduced non-radiative recombination and higher material gain. The reduced, but still substantial, carrier overflow into the confinement regions, thereby increased T0 [91]. Similarly, a T0 of 83 K was reported in Ref. [72] for GaInNAsSb/GaNAsSb devices. While the difference in T0 may also be due to reduced threshold carrier density, the valence band offset is likely further reduced through the addition of antimony into the barriers. This is compounded by the growth morphology problems of GaNAsSb grown at low temperatures [73]. We conclude, therefore, that GaNAs is likely a superior barrier material for 1.5 mm lasers. Moreover, increasing the antimony content in the QW would further improve hole confinement, thereby increasing both T0 and hi :

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Dilute Nitride Semiconductors

17.5. SPONTANEOUS EMISSION STUDIES

Analysis of the spontaneous emission spectrum is a useful technique for investigating carrier recombination and internal efficiency in edge-emitting lasers. This is difficult to do in VCSELs because of their very small gain region and very strong cavity effects. Even with edge-emitters, but one must still be careful to minimize effects of amplification of the spontaneously emitted photons as one nears threshold. We modify our edge-emitting laser structures by etching a hole in the top ohmic contact region using a focused ion beam system to define and etch the pattern [78]. The vertically emitted, unamplified, true spontaneous emission (TSE) of the laser device is the observed. This spontaneous light was collimated using a lens with moderate numerical aperture (NA ¼ 0.31), which limits the collection angle inside the active region to , 58 due to refraction. The light was focused onto a multi-mode fiber for measurement with an optical spectrum analyzer (OSA). The TSE escaped the device structure vertically around the ridge waveguide metal edges in one set-up, labeled (EDGE) in Figure 17.19, and through a 5 £ 10 mm window that was etched in the top p-metal and slightly into the p-AlGaAs cladding layer using a focused ion beam in another set-up, labeled (WINDOW) also shown in Figure 17.19. In WINDOW mode, some of the EDGE light will also be detected. The lasers are highly reflective coated ðR ¼ 98:7%Þ on one facet and cleaved on the other ðR ¼ 30%Þ: By design, the polarization of the collected light in this vertical configuration is transverse electric (TE). Transverse magnetic (TM) can only be emitted in the QW plane. Since the GaInNAsSb quantum well is compressively strained , 2.5%, the main interband transition is between the ground states of the electron and heavy hole (E1 – HH1)QW, which has non-zero transition matrix elements at k ¼ 0 for TE

Figure 17.19. EDGE and WINDOW measurement configurations for TSE measurements.

Long-wavelength Dilute Nitride – Antimonide Lasers

533

polarization only. Therefore, a fixed fraction of all of the emission of the main transition is collected in this configuration. Since the GaNAs barriers are tensilely strained, the lowest interband transition in the barriers is between the ground states of the electron and light hole (E1 – LH1)Barrier, so both TE&TM polarized emission exist but only the TE portion is detected. The small collection angle of , 58 produced low signal levels so the data was collected in CW and pulsed (1 ms width, 10% duty cycle) modes. Unfortunately, this leads to device heating of about 308C in CW and 38C in pulsed mode at 3 kA/cm2. Due to chromatic aberration of the lenses and the wavelength dependence of the refractive index nðlÞ of the active region, the collection efficiency is wavelength dependent because of refraction and Fresnel transmission. These effects are estimated to affect the overall measurement accuracy by , 5%. 17.5.1 Features of the Spectrum The TSE-EDGE spectrum with the background noise floor subtracted is plotted in Figure 17.20. The data was taken at 158C in CW mode for a 20 £ 533 mm device at

Figure 17.20. 158C TSE-EDGE without background and multi peak Gaussian fit for a 20 £ 533 mm device at 1.72 kA/cm2, just below threshold.

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1.72 kA/cm2 just below threshold (JthCW ¼ 1:80 kA/cm2). The peaks at 0.853, 0.926, and 1.016 eV are attributed to overlapping peaks of the dominant QW transitions: from the estimated two electron levels to the three heavy hole levels and continuum of light holes in the barrier, namely, E1 – HH1, E1 – LH1, E1 –HH3, E1 –LHbarrier, E2 – HH2 and E2 –LHbarrier, while the peak at 1.110 eV is believed to be from barrier emission. The 0.778 eV peak is 20 meV below the estimated band gap of the QW region and is thought to be the exciton peak or due to a (N –N)As interstitial defect level or a variation in the local potential, possibly due to slight N clustering. The TSE-EDGE spectrum was measured on a similar adjacent 20 £ 533 mm device, CW (Jth ¼ 1:80 kA/cm2 at 158C), at 15, 45 and 758C at 1.72 kA/cm2, without background subtraction, and plotted in Figure 17.21. The four peaks are slightly higher than the previous figure because the noise floor was not subtracted. At low biases, the main QW peak red-shifted the usual 0.58 nm/K or 0.34 meV/K due to the band gap reduction with temperature. The other QW peaks blue-shifted slightly probably because of increased contributions from higher energy transitions due to the increased occupancy of the higher states with temperature. The total QW emission rate decreased as expected by the T 21 dependence of the radiative coefficient B [102]. The emission rate from the barrier remained constant because

Figure 17.21. 15, 45, 758C TSE-EDGE with background for a 20 £ 533 mm device at 1.72 kA/cm2.

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the decrease in BBarrier is compensated for by an increase in barrier occupancy due to thermionic emission of carriers from the QW into the barrier [103]. The emission rate for the 0.778 eV peak increased and became broader, which might be an artifact due to a more prominent low energy tail edge of the main transition. 17.5.2 Fermi-level Pinning In pulsed mode, at 158C, the TSE-EDGE spectra were collected for various current densities on the device of Figure 17.21 (JthPUL ¼ 1:70 kA/cm2 at 158C). The emission rate at various wavelengths spaced by 25 nm was extracted and plotted versus the current in Figure 17.22. In the figure, the spontaneous emission at each wavelength increases significantly, both below and above threshold. Above threshold, the Fermi levels should pin strongly because stimulated emission should consume every additional injected carrier [94]. The spontaneous emission should saturate for wavelengths close to lasing wavelength. However, Figure 17.22 shows that the spontaneous emission is only weakly clamped. The emission efficiency (slope) above threshold is still about 40% of the below threshold value, indicating that the Fermi levels are not pinned throughout the entire structure. The optics in this EDGE configuration primarily image the section of the active region near the ridge waveguide edge where lateral current/carrier spreading provide fewer

Figure 17.22. 158C TSE-EDGE at various wavelengths spaced by 25 nm versus current in pulsed mode.

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Dilute Nitride Semiconductors

carriers and the optical field is weaker than in the direct center of the ridge. There would be lower gain and weaker stimulated emission at the edge and this could explain the continued spontaneous emission above threshold. Also, the top metal contact is only ˚ thick, which led to some non-uniform injection along the cavity length. 2000 A These two non-uniform spreading effects would reduce the device’s quantum efficiency by the factor hds ; described in Refs. [94,104] and may partially explain the device’s low internal efficiency of 40– 50%. Another explanation of the low efficiency is non-radiative carrier recombination in the barriers after the carriers escape the QW through thermionic emission. 17.5.3 Local Z-parameter Analysis of radiative and non-radiative recombination can be made by measurements of the local Z-parameter. The Z-parameter describes the dominant process for recombination in semiconductor lasers [105,106]. Below threshold, where stimulated emission can be neglected, the injected current balances the net recombination in steady state I ¼ eVa RðnÞ;

RðnÞ ¼ An þ Bn2 þ Cn3

ð17:1Þ

where e is the electronic charge, Va is the active volume, RðnÞ is the net recombination rate, and A; B; and C are the monomolecular, radiative, and Auger coefficients, respectively. The total spontaneous emission rate is proportional to the radiative current, Irad Irad ¼ eVa Bn2 ;

TSE / Irad / n2

ð17:2Þ

If one of the recombination processes dominates the current, Equation (17.1) can be approximated by I / nZ

ð17:3Þ

where Z ¼ 1; 2, or 3 if the current is dominated by monomolecular, radiative, or Auger recombination, respectively. This interpretation is valid for a limited range of current. From Eqs. (17.2) and (17.3), Z can be solved for as the derivative of the lnðIÞ versus lnðTSE1=2 Þ relationship. Defining the local Z-parameter as this derivative, and assuming A; B; and C are independent of n; Eqs. (17.1) and (17.2) yield [77] Z;

IAug dðlnðIÞÞ I ¼ 1 þ rad þ 2 1=2 Itot Itot dðlnðSPE ÞÞ

ð17:4Þ

where IAug and Itot ; are the Auger and total current. This extends the previous interpretation of Z to range continuously from one where monomolecular dominates to three where Auger recombination dominates. Any departure from two indicates the presence of non-radiative recombination, but Z ¼ 2 only implies equal amounts of monomolecular

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and Auger recombination since Z can be re-expressed, using Irad ¼ Itot 2 IAug 2 Imono ; as Z ¼2þ

IAug 2 Imono Itot

ð17:5Þ

where Imono is the monomolecular current. In real devices, two non-ideal effects complicate the Z-parameter analysis. First, there can be significant carrier leakage at high injection levels, especially in devices with low barrier heights. Recombination due to carrier leakage is expected to depend on carrier concentration anywhere from n3 to n7 depending on whether the drift or diffusion leakage current dominates [107]. Thus, Z . 3 would be a good evidence of carrier leakage. Second, the radiative coefficient decreases slowly with carrier concentration due to band filling and other non-ideal effects [107,108], BðnÞ < B0 2 B1 n; so the interpretation of Z is valid only for small values of n: The first-order correction, DZ $ 0; is given by
 IAug s I Bn 1 2 rad þ 2 DZ ¼ ð17:6Þ ; s¼ 1 2 2 3s B0 Itot Itot where s is the fractional reduction in the radiative coefficient, estimated to be , 10% at threshold, so DZ , 0:18 even in the worst case scenario: s ¼ 10% and IAug < Itot : Notice that DZ ¼ 0 if and only if Irad ¼ Itot or s ¼ 0: To measure the Z-parameter at various currents and temperatures in a reasonable amount of time, the integrated TSE was measured with an InGaAs PIN detector instead of collecting the spectra with the OSA and integrating numerically. Since the integrated TSE rate is the desired quantity, the InGaAs detector will do the integration electrically provided the detector’s quantum efficiency is independent of wavelength. The detector used had a quantum efficiency that was flat to within 5% over the 200 nm range of the two dominant emission peaks of Figure 17.19 and so the overall accuracy is only slightly deteriorated using this shortcut. The WINDOW configuration in CW mode, at 158C, was used on a 10 £ 750 mm device CW (Jth ¼ 1:0 kA/cm2). The data is plotted in Figure 17.23. As the current density is increased, Z increases gradually from 1.1 to above 2.0 just below threshold. At low currents, the device is clearly dominated by monomolecular recombination. Near threshold, Z exceeds 2, indicating some Auger recombination or carrier leakage. A possible distribution of the threshold current that is consistent with Eqs. (17.4) – (17.6) is 40% monomolecular, 20% radiative, and 40% Auger or carrier leakage. The temperature dependence of the local Z-parameter of an adjacent 10 £ 750 mm device is plotted in Figure 17.24. At low current densities, the Z-parameter appears to be independent of temperature and increases almost linearly with current density. At threshold, the TSE weakly clamps as described in Section 17.5.2 so the Z-parameter diverges to þ 1. The sudden rise in Z provides a surprisingly good indicator of lasing threshold. From thermal resistance measurements of other sized devices and theory,

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Dilute Nitride Semiconductors

Figure 17.23. Z-Parameter at 158C versus current from 10 £ 750 mm device using WINDOW configuration in CW mode (JthCW ¼ 1:0 kA/cm2).

Figure 17.24. Z-Parameter at 158C versus current from 10 £ 750 mm device using WINDOW configuration in CW mode (JthCW ¼ 1:0 kA/cm2).

Long-wavelength Dilute Nitride – Antimonide Lasers

539

a thermal resistance of 45 K/W was calculated. In CW mode, this produces a slight 6 – 138C temperature rise in the active region when the threshold ranges from 1 to 2 kA/cm2, which obscures the exact dependence of Zth on temperature. As the temperature is increased, the threshold density increases exponentially Jth ¼ J0 expðT=T0 Þ: At threshold, Zth increases from 1.90 to 2.05 to 2.25 to 2.50 as the stage temperature is increased from 15 to 458C in 108C steps. For comparison, Fehse et al. [78] report that Zth increases from 2.1 to 2.4 in GaInNAs/GaAs at 1.3 mm and is roughly saturated at 2.9 in InGaAs/InP at 1.3 mm over the same 15 –458C temperature range. The temperature dependence of the recombination coefficients A; B; and C is expected to be [78,104,109]
 E A < T 1=2 ; B < T 21 ; C < exp 2 a ð17:7Þ kB T where Ea is the activation energy for the Auger process. C is a rapidly varying function of temperature; it is nearly zero for kB T p Ea and then increases swiftly for kB T , Ea before saturating for kB T q Ea : Near room temperature, the monomolecular coefficient A; was observed to saturate [78], so A is approximately constant. At low densities, monomolecular and radiative recombination dominate, and since A is temperature insensitive and B decreases by , 15% over the limited temperature range of the measurement, the low current density Z – J curves in Figure 17.24 appear to be temperature independent. At and above 358C, where the threshold current density is above 1.5 kA/cm2 and Zth exceeds 2.25, Auger recombination begins to dominate and the high current density part of the Z – J curves should begin to separate with temperature due to the strong temperature dependence of C: This predicted feature is not visible in Figure 17.24, because the data in this region is limited to a small temperature range DT ¼ 208C. A device with two anti-reflective (AR) coated facets to prevent lasing is needed to investigate this feature further. At low temperatures, it is expected that Z should continue to increase with J above 1.5 kA/cm2, but not as rapidly as it does at high temperatures.

17.6. GaInNAsSb VCSELs

Vertical cavity surface emitting lasers (VCSELs) are of great commercial interest for optical networking and dense, fast interconnects because of their much lower cost and ease of fiber coupling [1,2]. A schematic diagram of a VCSEL structure is shown in Figure 17.25. The top DBR in a top emitting VCSEL, such as in Figure 17.25, will typically have a reflectivity of 99.5% or better; the bottom DBR may have a nominal reflectivity of 99.99%, where the loss is mostly due to FCA. Typical VCSEL mesas range from 8 to 30 mm in diameter. The DBR mirrors offer some immunity to feedback and some

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Dilute Nitride Semiconductors

Figure 17.25. Schematic diagram of simplified structure of a top-emitting VCSEL. Light is emitted through the hole in top ring contact.

degree of temperature stability compared to edge-emitting lasers. In contrast to edgeemitting lasers, which are easy to grow but difficult to test or package, VCSELs are easy to test and package, but they can be quite difficult to grow, especially with a new material system. Since Kondow’s discovery in 1995 that GaInNAs reduced the band gap sufficiently to reach wavelengths beyond1.2 mm, there has been intense activity to develop such VCSELs [1 – 4]. Larson et al. [110] demonstrated the first GaInNAs VCSEL, which was optically pumped and lased at 1.27 mm. The first electrically pumped VCSELs were realized by Coldren et al. [111] at 1.2 mm and Choquette et al. at 1.3 mm [112] and recently Wistey et al. [161] reported the first GaAs-based VCSEL beyond 1.31 mm, operating at 1.46 mm.

17.6.1

GaInNAsSb VCSEL Design

The successful growth of VCSELs requires several key ingredients. Some of these are important to edge-emitting lasers as well, and have already been mentioned in the previous section. For example, nearly all semiconductor lasers require very high material quality, with few defects, which will efficiently emit light. The role of plasma damage, oxygen contamination, and antimony were mentioned in Section 17.3 and described in more detail in Chapter 1 on MBE growth of dilute nitrides. Also, several material and device parameters can be extracted from edge-emitting lasers grown from the desired material. These parameters include lasing wavelength, threshold current density, and gain per unit length, were discussed in the preceding section on edge-emitting lasers. The key

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541

ingredients which are specifically important for VCSELs include; QW selection, DBR design, cavity correction, accurate refractive indices, and low thermal impedance. The choice of quantum wells and barriers is determined primarily by the desired wavelength. It is difficult to reach wavelengths beyond 1.1 mm using only GaNAs in the quantum well, or beyond 1.2 mm using only InGaAs, or beyond 1.3 mm using only GaInNAs. The longest wavelengths appear to be reached using GaInNAs or GaInNAsSb quantum wells surrounded by GaNAs barriers [63,71] or GaAs barriers [40]. The GaNAs decreases the quantum confinement in the QW and provides strain compensation for the QW [22]. Compressive strain in a quantum well leads to higher gain, due to improved overlap of the electron and hole wavefunctions, so most InGaAs lasers on GaAs or InP are grown with some amount of compressive strain built in. However, compressive strain by itself tends to promote phase segregation and dislocations in GaInNAs, leading to early device failure. GaNAs, on the other hand, is tensilely strained on GaAs, so by growing GaNAs barriers below and above the QW, the total strain is reduced. Additional compressive strain from multiple quantum wells can be compensated by making the GaNAs layers either thicker or with more nitrogen. However, even with tensile GaNAs barriers for strain compensation, strain sets an upper limit of roughly 3 –4 QWs for VCSELs at 1.5 mm. With more than three QWs, the compensating layers of GaNAs must either be very thick or contain a large fraction of nitrogen. Large nitrogen concentrations lead to defects and degraded growth, while thick layers push the QWs so far apart that they no longer overlap with the peak of the standing wave in the VCSEL cavity. It is also possible for highly strained GaInNAsSb to reach the critical thickness within a single QW, if the strain is not already partially compensated by layers below it. Beyond the QW design, the DBR mirror design is particularly critical for longer wavelength VCSELs because FCA increases with l2 ; hence is four times greater at 1.55 mm compared to 850 nm. Even at 1.3 mm, this problem was sufficient that the first three groups to realize l . 1:2 mm VCSELs in GaInNAs used different approaches to fabricate the mirrors. These are illustrated in Figure 17.26, where (a) is a conventionally doped mirror with top and bottom contacts and current driven through the mirrors used by Coldren et al. [111,113], (b) is the double n-type mirror with Nþ þ /Pþ þ tunnel junction and current driven though the mirrors adopted by Choquette et al. [112] and (c) is the lateral intracavity contact with undoped mirrors used by Riechert et al. [114]. The best approach is still unclear since there is a broad range of requirements for different systems. At this point, it seems reasonable that the lateral intracavity contact with undoped mirror approach is the easiest one to realize, particularly by MBE and produces good single mode VCSELs with up to , 1.5 mW of power at room temperature. However, at higher power, current crowding becomes a significant factor and the lasers jump transverse modes. The only way to combat this is with more uniform current injection or even increasing the gain in the center by using optical pumping. Optical pumping is an attractive possibility if higher powers are desired because this also eliminates the FCA problem in the mirrors,

542

Dilute Nitride Semiconductors

Figure 17.26. Schematic diagrams of (a) conventional n- and p-doped DBR mirrors with current passing through the mirror layers, (b) double n-type DBR mirrors, nþþ =pþþ tunnel junction and current passing through the mirror layers and (c) intracavity contact with lateral current flow and undoped DBR mirrors.

although this approach has not been widely pursued because of the greater complexity and cost of making two lasers. However, if the two VCSELs can be grown monolithically, this may not be as difficult as the separate pump approaches attempted before [115 – 117]. The most critical factor in fabricating VCSELs is realizing the quite precise thicknesses of the various layers, beginning with the cavity. Because of the short distance between the mirrors, it is critically important that the cavity be the correct optical thickness. There must be an integer number of wavelengths in one round trip between the mirrors for the VCSEL to begin lasing. One method of guaranteeing this condition is to stop the growth after a few DBR pairs, cool the wafer to room temperature (or lasing temperature), and measure the spectrum reflected from a white light source [118]. Any error in the cavity length can be detected by matching the reflectivity spectrum to a simulation. If the cavity is too short or too long, the subsequent layer of the DBR can be made longer or shorter, respectively, to pull the cavity mode in the correct direction. The use of a cavity correction at the beginning of the top DBR can save a growth even if the sources have drifted somewhat from the intended growth rates. This cavity correction, as with the choice of all layer thicknesses in the VCSEL, requires accurate refractive index data. Although Adachi’s method [119,120] is almost universally used for GaAs and AlGaAs refractive indices, and is quite accurate near the band gap, its accuracy decreases in the near infrared. Gehrsitz [121] has provided an improved, semiempirical model from 1 to 3 mm, in good agreement with experimental data from our group and others [122]. Gehrsitz’ semi-empirical model offers an added feature in terms of being able to predict the refractive index at elevated temperatures, up to , 1508C. Fewer studies have been performed on the dilute nitrides, but model dielectric functions are available for GaNAs [123] and GaInNAs [124,125]. (The refractive index plot in an earlier

Long-wavelength Dilute Nitride – Antimonide Lasers

543

paper from this group appears to have suffered a publishing misprint in the axes.) No systematic studies of GaInNAsSb refractive index have been performed to date, so the refractive index for GaInNAsSb quantum wells can only be estimated from GaInNAs at correspondingly shorter wavelengths. It should be noted that doping changes the refractive index, so some slight correction may be necessary. Growth of a calibration sample of a desired doping of GaAs or AlGaAs can fix the actual refractive index and eliminate possible errors between theory and practice. Typically VCSELs utilize an AlAs oxide aperture placed both above and below the QWs to prevent current spreading [126,127]. This necessitates growth of a $ 97% AlAs layer as the last AlGaAs layer of the bottom mirror and first AlGaAs layer in the top mirror and that the other AlGaAs DBR layers be , 90% AlAs to prevent their oxidation. We have observed that our dilute nitride lasers seem to suffer from reliability issues when the mesa is etched all the way through the QW. Although oxide confined VCSELs have occasionally met with disfavor in industry due to reliability issues, oxide confinement is still very important for GaInNAs(Sb) VCSELs due to the high current densities it offers. There are significant challenges for VCSELs as the wavelength is extended: first, the crystallinity of GaInNAs(Sb) is worse at longer wavelengths; second, the DBRs have more loss due to FCA; and third, GaAs/AlGaAs have lower index contrast, necessitating more quarterwave layers in the DBR. All of this translates into higher current densities required to overcome these losses and reach laser threshold. The last of the DBR layers is a phase matching layer at the top surface. At the surface of the VCSEL, the top contact can be used as part of the top mirror, even for a top-emitting VCSEL, where the ring contact or patterned surface can be used to suppress higher order transverse modes [128]. But metals are lossy reflectors with a complex refractive index, so they introduce some phase delay in the incident wave. The top surface of the DBR, then, needs to be phase matched to the gold. Because DBRs have lower refractive index contrast at 1.5 mm than 1.0 mm, more mirror pairs are required to reach high enough reflectivity. But a thicker stack leads to more optical losses, and worse, more Joule heating from increased resistance. It is, therefore, quite important for long-wavelength lasers that the DBR be optimized for low resistance. Yechuri has provided a straightforward method of optimizing DBR band structure for minimal electrical resistance [129,130] using graded regions at each interface, as well as careful doping. Growth of these graded regions is fairly straightforward to perform by MOVPE, because variable gas flows are available, but MBE offers only discrete shutter operations. The usual solution is to perform step grading and/or digital alloying, in which a shutter is opened and closed with a , 2 nm period and successively longer or shorter duty cycles. Particular attention should be paid to the p-doped DBR, because FCA is worse for holes than electrons, and the absorption increases at longer wavelengths, roughly increasing with the square of the wavelength in the mid-IR region. By performing digital alloying with at least one intermediate step, using multiple group III sources, a reasonable

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Dilute Nitride Semiconductors

approximation to the Yechuri method above can be made, and with a reasonable number of total shutter operations. The electrical resistance is not the only issue in a DBR. Because the DBR is so thick and sits between the QWs and the substrate or heat sink, the thermal impedance of the DBR is significant as well. The temperature of the QW will generally be higher than in an edgeemitting laser with the same QW design; this may change the operating wavelength, leading to a gain/cavity mismatch. This leads to a decrease in output power, and aggravates the heat-related drop in internal quantum efficiency. Generally, the best results are produced by mounting bottom-emitting VCSELs with the epitaxial side (top side) down on a heat sink, but reasonable top emitters can also be made. Binary materials, such as GaAs and AlAs, have better thermal conductivity than alloys, which in turn are significantly better than dielectric DBRs. The worst-case thermal impedance is an air gap DBR, and thick heat spreading layers are necessary for such devices to lase at all [11]. Ideally, the DBRs should be made with as few pairs as possible, and very highly doped at the interfaces to minimize both ohmic heating from electrical resistance and thermal impedance without greatly increasing free carrier optical absorption. For VCSELs formed by etching a mesa, etching through the cavity increases the thermal impedance, although this may be offset by the increased quantum efficiency from having a second oxide aperture below the QWs. Early devices also showed poor lifetime when the quantum well was etched through, possibly due to high non-radiative recombination and heating. Planarization can also help remove heat from the VCSEL mesa and may help with device reliability. The Stanford GaInNAsSb VCSELs were grown before the corresponding edgeemitting lasers had been fully tested. The VCSELs were designed rather conservatively, as hard numbers for gain had not yet been established. In addition, long-wavelength lasers tend to suffer from Auger recombination and low quantum efficiency, conditions which could be improved by cooling, so the VCSELs were designed to operate at temperatures of 08C or below. This meant that the VCSELs were intended to lase at a wavelength near 1470 nm, while the edge-emitting lasers lased at 1495 nm at room temperature. This is consistent with the 0.6 nm/8C shift in the edge-emitting lasers, and similar to the usual shift with temperature in InGaAs lasers. A PL sample was grown immediately before the VCSEL QWs to ensure that the wavelength of emission would be correct. The sample was immediately unloaded from the chamber, then annealed at 7608C for 1 min. PL showed peak emission at 1.508 mm, far longer than the 1.465 mm from amplified spontaneous emission, and also longer than the 1.463 mm from the original PL sample on which these growths were based. Part of the difference may have been due to an unexpected increase in antimony flux from our unvalved Sb cracker: the desired Sb flux was 1.11 £ 1027 but remained constant at 1.0 £ 1027 even after the temperature was raised several times, but we suspect the actual Sb flux then rose soon after the growth began. It is more likely that the longer wavelength was due to excess

Long-wavelength Dilute Nitride – Antimonide Lasers

545

damage to the wafer from lighting the plasma multiple times. We have established through other experiments that plasma damage causes a shift to longer wavelengths, even though it decreases nitrogen composition [131]. The VCSEL consisted of a bottom mirror, cavity, and top mirror, all epitaxially grown on n-doped GaAs. The bottom mirror was composed of 29 alternating pairs of silicon-doped Al0.92Ga0.08As and GaAs for the DBR. The cavity was a one-wavelength ð1lÞ thick layer of GaAs, designed for 1.485 mm, with three quantum wells (QWs) at the center of the cavity. The QWs were based on emitting lasers which operated at wavelengths from 1.49 to 1.51 mm. The QWs were 7 nm Ga0.62In0.38N0.016As0.958Sb0.026 with 20 nm GaNAs barriers below, between, and above the QWs. The composition reported here was determined from calculations by Volz based on SIMS, XRD, RBS, and NRA-RBS [76]. The top DBR was p-doped with carbon, and 24 pairs thick. A thin, digital alloy of 98% aluminum was included as part of the second AlGaAs layer from the cavity for use as the oxide confinement layer. Nitrogen was supplied by an SVT Associates rf plasma cell at 300 W and 0.5 sccm. The Sb flux was 1.15 £ 1027 Torr, and the arsenic overpressure was 20 times the Group-III flux in the quantum wells and 15 times elsewhere. Because the nitride MBE system did not have enough ports for multiple AlGaAs compositions, the DBRs were grown in a separate MBE machine and transferred under ultrahigh vacuum. Plasma conditions were optimized to minimize plasma damage during growth [58,132,133]. A conventional liftoff process was used to define metal rings for the top contacts, and top and bottom metal were deposited in an evaporator. Unfortunately, there were a number of processing difficulties which produced rough sidewalls and surfaces, adding significant scattering loss and no mesas smaller than 62 mm in diameter survived the liftoff process. Also, because the selective oxidation layer was too thin, it did not significantly oxidize, so rather than a single layer oxidizing, the top DBR oxidized uniformly about 10 mm inwards. This added optical scattering losses and series resistance to the top DBR. The VCSELs were mounted epi-side up on a copper chuck, cooled by a thermoelectric cooler (TEC), for testing. Despite the above difficulties, the VCSELs lased in pulsed mode when cooled to a chuck temperature of 2 108C. Figure 17.27 shows the fiber-coupled optical spectrum at 500 mA and 800 mA of peak current, showing the onset of stimulated emission. The VCSELs were pulsed at 0.1% duty cycle, with 2 ms pulses at a 500 Hz repetition rate. The VCSELs lased at 1458 – 1460 nm from 2 58C down to 2 308C, which was as low as the TEC stage could reach. Multiple transverse modes were visible above threshold, due to the large 66 mm current aperture size of the VCSELs. Several L – I curves for a VCSEL with a 66 mm diameter aperture are shown in Figure 17.28. The threshold current Ith was 229 mA (pulsed) at 2 258C, 248 mA at 2 208C, and 283 mA at 2 158C, corresponding to current densities Jth of 6.7, 7.3, and 8.3 kA/cm2, respectively. The thermal mounting was improved for this measurement, resulting in lower threshold currents. The VCSELs QWs

546

Dilute Nitride Semiconductors

Figure 17.27. Fiber-coupled spectrum of VCSEL pulsed at 500 mA (lower curve) and 800 mA (upper curve), showing onset of stimulated emission and multiple transverse modes above threshold. Operated at 0.1% duty cycle and 2108C, with 66 mm current aperture.

Figure 17.28. Fiber-coupled, pulsed power versus current setpoint, at various temperatures. The threshold current for each temperature is listed. The kink at 2258C, 400 mA is due to overshoot by the current source.

Long-wavelength Dilute Nitride – Antimonide Lasers

547

were identical to the single quantum well from the equivalent cw 1.49 mm edge-emitting lasers. Due to the lower operating temperature and a short cavity, the VCSELs lased at 1.46 mm, a significantly shorter wavelength. Microcavity emission from a similar structure showed that the growth of the top DBR only partially annealed the active region, but an additional rapid thermal anneal was required for peak photoluminescence. A peak power of 0.77 mW was achieved, which was surprisingly high given the problems outlined above. In spite of all the processing problems, these GaInNAsSb VCSELs operated at 1.46 mm and there is no reason to believe that properly processed devices could not reach 1.5 or 1.55 mm, given that cw edge-emitting lasers have already been demonstrated beyond 1.5 mm. At these long-wavelengths, extra care must be given to optimal DBR design, both electrical and optical. Accurate refractive index data are vital for the design and characterization of the VCSEL structure, as well as any corrections to the cavity during the growth. Heating is another issue, especially with weak gain and thicker DBRs, but this can be minimized by regrowth, planarizing, or careful packaging. These are engineering problems that have been reasonably solved, thus it seems reasonable that GaInNAsSb VCSELs will soon operate cw at 1.55 mm and provide a low-cost source to enable high speed access to the optical fiber network.

17.7. HIGH POWER LASERS BASED ON GaInNAs(Sb)

High power semiconductor lasers are compact, highly efficient and durable light sources for several critical components needed to achieve widespread high-bandwidth optical networks. They are the energy source for EDFA, OPA, or Raman amplifiers required to provide gain in optical communications networks. High power laser diodes operating at wavelengths longer than 1.3 mm are especially important for optical communications and inband-pumping of solid-state Er lasers. It has been difficult to achieve temperature-stable, high-power lasers in InGaAsP/InP active layer-based devices due to the disadvantageous band alignment in the conduction band. The introduction of GaInNAs active layers opens up new possibilities for these applications due to better band alignment, higher gain and better thermal conductivity, all leading to more favorable high-temperature and highpower characteristics. 17.7.1 High-power Laser Design Issues Single-stripe, edge-emitting structures are usually employed for high-power laser diodes. Some applications require the laser to be single-mode. Unfortunately, single-mode operation requires the stripe width to be small. It is difficult to get more than , 1 W from narrow stripe lasers, but this power level can still be useful for applications such as Raman amplifiers [134]. For higher power single-mode output, various approaches such as

548

Dilute Nitride Semiconductors

phase-locked laser arrays, master oscillator power amplifiers, external-cavity lasers, and antiguided arrays have been tried with some success to broaden the laser aperture while maintaining single-mode operation. When a multi-mode astigmatic beam output is acceptable, simply using wider stripes leads to higher output power. As high as 10 W has been achieved from a 100 mm wide stripe. The output power of high power diode lasers is limited either by catastrophic optical damage (COD) or thermal rollover. Typical L– I curves for COD and thermal rollover are shown in Figure 17.29(a) and (b), respectively. 17.7.1.1 Catastrophic Optical Damage (COD). COD, also referred to as catastrophic optical mirror damage, COMD, is irreversible damage at the laser facet caused by heating due to high optical power. There is a higher density of recombination centers at the cleaved

Figure 17.29. Schematic L – I curves illustrating (a) catastrophic optical damage and (b) thermal rollover.

Long-wavelength Dilute Nitride – Antimonide Lasers

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interface and the associated depletion of carriers makes the active layer near the facet highly absorbing at the lasing wavelength. Excited carriers diffuse to the interface and recombine there, increasing local temperature and thus shrinking the band gap, which leads to more absorption. As the output intensity is increased, this positive feedback eventually causes permanent damage to the laser facet. COD manifests itself as a sudden drop in output power when current is increased, after which the laser ceases to operate [135]. Surface passivation can improve COD threshold by reducing the surface defect densities. Various materials (SiO2, SiN, amorphous Si, sulfur, etc.) have been used to passivate the cleaved facet surface and achieve COD limit of 10 , 30 MW/cm2 for various materials as compared to less than 5 MW/cm2 before passivation. COD limit of 30 MW/cm2 has been demonstrated for 1.3 mm GaInNAs lasers [136]. One of the facets of high power lasers is usually HR (high reflectivity) coated to get maximum output power from the other, low reflectivity facet. Facet coating can also passivate the facet interface and provide greater protection from heating due to nonradiative recombination at the interface. The relation between the COD threshold and the maximum output power is shown to be [137] Pmax ðCWÞ ¼

dwð1 2 RÞ I Gð1 þ RÞ COD

ð17:8Þ

where d is the thickness of the active layer, G is the optical confinement factor of the active layer, w is the laser width, and R is the front facet reflectivity, and ICOD is the intensity of catastrophic damage. Even with the same COD threshold intensity, maximum output power can be increased by decreasing front facet reflectivity. Equation (17.8) also indicates that the maximum output power can be increased by increasing d=G: This can be achieved by employing a broader waveguide, i.e. thicker waveguide core. With this, the optical field becomes less concentrated at the waveguide center where the active region is usually placed, allowing higher output power for a given COD intensity limit. Use of a thicker waveguide also decreases the divergence of the output beam and reduces internal loss due to absorption in the highly doped cladding layers. However, lower G leads to lower modal gain, so an optimal value must be found. In addition to this trade-off, the waveguide thickness should be less than the single-mode cutoff thickness in the vertical direction. The maximum allowable thickness is limited by the onset of the third mode, rather than the second mode, because the second mode has a very small overlap with the active layer. Rapid heat removal away from the interface is also important to defer the onset of catastrophic damage. COD thresholds as high as 40 MW/cm2 have been demonstrated by very careful mounting and aggressive heat-sinking [138].

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17.7.1.2 Thermal Rollover. Thermal rollover refers to the gradual decrease of laser efficiency with increased current injection and eventual decrease in the output power itself. Thermal rollover effect is more pronounced in CW than pulsed operation. It has many causes. Examples include gain reduction due to thermal broadening of the Fermi distribution of carriers and carrier leakage out of the active region, as higher injection current increases the temperature through ohmic loss. Sufficiently large conduction and valence band offsets at the quantum well/barrier heterointerface are essential to have a high thermal rollover limit. Temperature performance of lasers is often characterized by T0 ; the characteristic temperature, which is a measure of the threshold current dependence on the temperature, as expressed in the equation Ith ðT þ dTÞ ¼ Ith ðTÞedT=T0

ð17:9Þ

Use of GaInNAs on GaAs as the active layer material can be very beneficial in this respect, because it has higher T0 than the incumbent InGaAsP/InP technology due to a larger conduction band offset. It has been reported that the valence band offset of GaInNAs/GaAs interface may be small, leading to large hole leakage [95], but it can be solved by employing larger band gap materials as a barrier against hole leakage. Efficient heat sinking is also very important to minimize thermal rollover. Epi-down mounting is mandatory to ensure low thermal resistance. Use of longer cavity length also helps with reducing thermal resistance, but at the cost of reduced external quantum efficiency. Reduced external quantum efficiency can be compensated for by reducing the front facet reflectivity, which also increases the COD-limited maximum output power. Wide stripe cavities also have lower thermal resistance, but a maximum width may exist due to the single transverse mode requirement. In addition to temperature insensitivity and heat removal efficiency, it is also important to generate less heat in the first place. Serial (electrical) resistance through the laser structure is an important parameter to be minimized by careful design of the laser structure, doping, and contacts. Non-radiative recombination is another important factor to consider. While the energy of radiatively recombining electron –hole pairs is emitted as photons from the laser, nonradiative recombination only contributes to heat generation. Monomolecular recombination due to defects has been problematic in GaInNAs especially for wavelengths over 1.5 mm, but this problem is being solved by incorporation of antimony as surfactant and other improvements in growth techniques [59,60,133,135,162]. Auger recombination is also a serious problem, because the Auger coefficient tends to increase with wavelength. More detailed descriptions about the radiative and non-radiative recombination can be found in Section 17.5.3 on Z-parameter measurement. Internal loss should be minimized for higher efficiency and less heat generation. Lower internal loss allows the cavity length to be increased without degrading the external quantum efficiency or threshold current; a longer cavity decreases serial resistance and

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increases its thermal footprint. The doping of the cladding layers is a tradeoff parameter, because lower doping decreases free carrier absorption losses at the cost of increased series resistance. 17.7.2 Current GaInNAs(Sb) Laser Results High power laser diodes for wavelengths shorter than 1.3 mm have been reported with CW output power as high as , 10 W CW [138,139] from 100 mm wide broad area stripes. For 1.3 mm, high power GaInNAs lasers have already been demonstrated (8 W multi-mode CW output from 100 mm wide aperture [136] and 200 mW single-mode CW output from 2.7 mm wide aperture [140]. For 1.5 mm, InGaAsP has reached pulsed output level of 16 W [141]. Although comparable results for GaInNAs-based 1.5 mm lasers have not been achieved yet, a promising GaInNAs(Sb) 1.5 mm laser result is reported in Ref. [75]. A highly reflective coating (, 98.7%) was applied to one facet and the other was left ascleaved. The laser is mounted epi-side up for the measurement. Figure 17.30 shows representative L – I curves for 10 mm £ 983 mm devices, under pulsed (1 ms, 1% duty cycle) and CW operation. Under pulsed conditions, the peak output power was substantially higher than under CW operation, 527 mW versus 100 mW. The difference in output power is attributed to the high thermal resistance associated with mounting devices epitaxial-side up during testing. Measurements of the thermal resistance show it to be , 38 K/W for a 10 mm £ 983 mm device, which agrees well with theory [142]. Calculations indicate a 2– 3-fold reduction in CW device heating if devices are mounted epitaxial-side down. Moreover, the sharp decrease of the peak CW output power with chuck temperature (Figure 17.31) indicates that ohmic heating and the temperature sensitivity of threshold are important issues for achieving high CW output power.

Figure 17.30. L – I curves under pulsed and CW operation for HR coated 10 mm £ 983 mm laser.

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Figure 17.31. Peak CW output power versus temperature for HR coated 10 mm £ 983 mm laser (square) and its linear fit (line).

If thermal management is improved, CW output powers , 500 mW are considered feasible from a SQW laser with minimal added packaging and processing. The rapid degradation in pulsed output power shown in Figure 17.30 is attributed to catastrophic optical mirror damage (COD) and/or burnout of the p-side contact directly under the probe tip. The optical power density was calculated to be , 4.9 MW/cm2 at the onset of failure, which can be significantly improved by facet passivation. In addition, the p-side contact was rather thin after the self-aligned etch and , 30% of the ohmic heating in the device occurred along the contact. This parasitic heating mechanism can be eliminated without substantially more complex processing.

17.8. RELATIVE INTENSITY NOISE

Many intrinsic laser properties can be investigated through measurement of the relative intensity noise (RIN) and it is a particularly important parameter for analog communications and spectroscopy or fluorescence where intensity is measured as a function of time. 17.8.1 Definition of RIN The definition of laser RIN is the ratio of the mean square optical intensity deviation, in a 1 Hz frequency bandwidth, at a specified frequency f and average optical power Pavg to the square of the average optical power RINðdB=HzÞ ;

kDP2 l P2avg

ð17:10Þ

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Detector noise, such as thermal, shot or amplifier noise, is not included in the definition of laser RIN. Low RIN is needed for a high signal-to-noise ratio for data transceivers. The signal-tonoise ratio at the detector is inversely proportional to the amount of noise in the detector bandwidth. The signal-to-noise ratio is given approximately by [143] SNRdetector ¼

m2 1 ; 2B RIN

m;

Pon 2 Poff Pon þ Poff

ð17:11Þ

where m is the on-off modulation index, B is the detector bandwidth, the RIN is expressed in linear units per Hz, and Pon and Poff are the high and low optical power levels. 17.8.2 Theoretical Expression for RIN The RIN spectrum can be derived from the carrier and photon rate equations, with Langevin noise sources [144], and expressed in the following form [145]: RINðW=HzÞ ¼

4 f 2 þ ðgp =2pÞ2 dfST 2 p ðfr 2 f 2 Þ2 þ f 2 ðg=2pÞ2

ð17:12Þ

where dfST is the Schawlow – Townes linewidth, fr is the resonance frequency, g is the damping factor, while gp in the numerator is the exact damping factor including the nonlinear gain. The RIN spectrum is roughly centered at the resonance frequency, the damping coefficient g affects the width, and Schawlow – Townes linewidth sets the amplitude. 17.8.3 Measurement of RIN The set-up for measuring RIN, shown in Figure 17.32, consists of collimation of the laser beam with a short focus high NA lens and focusing onto a single mode fiber with a longer focus lower NA lens. The optical power was received with an Agilent 11982A lightwave converter. A bias tee used in reverse separated the AC and DC electrical components. The AC component was sent to preamplifier and then measured with an electrical spectrum analyzer, while the DC power was measured with an oscilloscope.

Figure 17.32. Experimental set-up for RIN measurements.

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After measurement of the RIN spectrum, the data was converted to a linear scale and the thermal noise was subtracted by measuring the spectrum with the laser off, while the shot noise was subtracted by measuring a comparable power LED, which produces a flat noise spectrum. Figure 17.33 shows the RIN spectrum at 1.3 kA/cm2 (JthCW ¼ 1:0 kA/cm2) of a 10 £ 750 mm cleaved/HR device at 158C in CW mode and its fit to Eq. (17.12). Of the four intrinsic parameters which are extracted, the least accurately determined is gp because of its weak effect on the RIN spectrum. RIN was measured at various other currents and displayed in Figure 17.34. As expected, the overall RIN level decreased and the frequency of the RIN peak increased with current or output power. The resonance frequency is expected to increase linearly with the square root of the output optical power and the D parameter is defined as the slope of this relationship [64,147] pffiffi fr ¼ D P;

dg "
sffiffiffiffiffi# vg a þ a 1 2 Rr Rf i m dn D ¼ 1þ 1 2 Rf Rr 4p2 Va ðhnÞ am 2

G

ð17:13Þ

where P is the front facet output power, G is the optical confinement factor, dg=dn is the differential gain, vg is the group velocity, Va is the active volume, hn is the photon energy, ai and am are the internal and mirror losses, Rr and Rf are the rear and front mirror reflectivities. The last term in square brackets is approximately one for cleaved/HR devices. Large D values are desired for high-speed devices. From Figure 17.35, a value of 1.0 GHz/mW1/2 was obtained, which is pretty good considering the large device size. Notice that the one parameter fit must pass through the origin. By inverting Eq. (17.13), a more intrinsic material parameter, the differential gain, can be obtained from the D parameter if the other factors are known. These factors are tabulated for the device in Table 17.2. The differential gain of GaInNAsSb at 1.5 mm was calculated to be 1.5 £ 10215 cm2. This value is two to three times that observed of InP-based devices at 1.3 and 1.5 mm [144 – 146], about 50% higher than GaInNAsSb/GaAs and GaInAsSb/GaAs at 1.3 mm [64], and is approaching the enormous differential gain observed in non-gain-saturated, InGaAs/ GaAs multiple quantum well lasers at 0.9 –1.1 mm [147]. The huge differential gain of GaInNAsSb at 1.5 mm is attributed to the increased compressive strain (, 2.5%) in the QW. Large differential gain is a crucial element in achieving low threshold, high T0 ; and high power lasers. For equal confinement factors and total losses, threshold can be reached at lower values of carrier concentration. This reduces Auger recombination, which scales as n3 ; and may reduce the temperature sensitivity of the threshold current. Or, a larger waveguide with a smaller optical confinement factor G; but the same total gain can be fabricated. This increases the power limitations of catastrophic optical mirror damage (COMD) and thereby allows higher output powers. Two other intrinsic parameters that can be extracted from the RIN analysis are the K factor and the threshold damping coefficient g0 : The damping coefficient g increases with

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Figure 17.33. RIN spectrum, linear scale, at 1:3JthCW for a 10 £ 750 mm cleaved/HR device at 158C in CW mode and its fit to Eq. (17.12).

Figure 17.34. RIN spectra, log scale, at 1.2, 1.3, 1.6, and 1:9JthCW for a 10 £ 750 mm cleaved/HR device at 158C in CW mode.

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Figure 17.35. Resonance frequency fr versus square root of output optical power and the linear fit passing through the origin to yield D ¼ 1:0 GHz/mW1/2. High biases were excluded from the fit because thermal rollover significantly reduces the differential gain.

Table 17.2. Various parameters for the 10 £ 750 mm device Symbol

Name

Value

he hi Rf Rr am ai vg G Va hn tp D D2 dg/dn K f3dB, max dg/dN 1 g0 te

External differential quantum efficiency Internal differential quantum efficiency Reflectivity of front facet Reflectivity of rear facet Mirror loss Internal loss Group velocity Optical confinement factor Active volume Photon energy Average photon lifetime in cavity

0.36 0.60 0.30 0.987 8.03 cm21 5.35 cm21 9.1 £ 109 cm s21 0.014 6 £ 10211 cm3 1.36 £ 10£19 J 8.2 £ 10212 s 1.0 GHz/(mW1/2) 1 £ 1021 J21 s21 1.5 £ 10215 cm2 0.75 ns 11.8 GHz 21.4 £ 10213 cm2 1.5 £ 10216 cm3 1.25 GHz 0.8 ns

Differential gain Maximum 3 dB bandwidth for amplitude modulation Nonlinear gain Nonlinear gain coefficient Damping coefficient at threshold Differential carrier lifetime at threshold

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557

Figure 17.36. Damping coefficient g versus the square of the resonance frequency fr2 and its linear fit to give K ¼ 0:75 ns and g0 ¼ 1:25 GHz.

a square of the resonance frequency as plotted in Figure 17.36; the K factor and g0 are defined as the slope and intercept, respectively [144].

g ¼ Kfr2 þ g0

ð17:14Þ

The maximum optical modulation 3 dB laser bandwidth is inversely proportional to K [144]. pffiffi 2p 8:9 f30 dB;max ¼ 2 < K K

ð17:15Þ

Thus, high-speed transceivers require small values of K: We find that the K factor is 0.75 ns, which leads to a maximum 3 dB bandwidth of 11.8 GHz. The K factor increases with the average photon lifetime in the cavity tp 1 0 dg B dN C C K ¼ 2p2 tph B @1 2 G dg A dn ›g 1 ¼ 2vg tph G ›N 1 tp ¼ v g ð ai þ am Þ ð17:16Þ

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where N is the photon density, dg=dN is the non-linear gain, and 1 is the non-linear gain coefficient. With the values of Table 8.1, this device has a non-linear gain of 2 1.4 £ 10213 cm2, and a non-linear gain coefficient 1 of 1.5 £ 10216 cm3. The threshold damping coefficient g0 in Eq. (17.14) is given by [107,144]

g0 ¼

GRsp d RðnÞ; þ dn Va N

1 dR ¼ dn te

ð17:17Þ

where Rsp is the spontaneous emission rate, n is the carrier concentration, and te is the differential carrier lifetime. The portion of the linear fit used to obtain K and g0 is sufficiently above threshold that we can neglect spontaneous emission and so te < 1=g0 : Thus, with a measured g0 ¼ 1:25 GHz value, the differential carrier lifetime at threshold is estimated at 0.8 ns. In conclusion, the large differential gain observed in highly strained GaInNAsSb/GaAs is another advantage over InP-based lasers. With a lower carrier concentration at threshold, one could expect to see lower non-radiative Auger recombination, which scales as n3 : This has been observed through Z-parameter measurements at room temperature and was described in Section 17.5.3. Higher CW output powers before the onset of COMD, such as the reported 8 W from GaInNAs/ GaAs at 1.3 mm [136,148] should also be possible in future GaInNAsSb/GaAs lasers at 1.5 mm.

17.9. GaInNAsSb ELECTROABSORPTION MODULATORS AND SATURABLE ABSORBERS

For very high speed optical communications systems, direct modulation of the laser source is often not feasible or practical and external modulators are required. The use of an external modulator decouples the high-speed electrical circuit from the laser drive circuit and greatly reduces chirp in the system. Saturable absorbers are also important elements in high-speed systems to provide a gain modulating medium for mode locking lasers. Both modulators and saturable absorbers may become important components of future highspeed optical interconnects used to overcome the limiting RC delays in microprocessor back-ends. Operation at long-wavelengths promotes lower drive voltage, as well as the possibility for seamless integration of the network with the processor. We have examined the use of GaInNAsSb active layers in electroabsorption modulators operating in the 1500 –1600 nm wavelength range. Two practical configurations for the modulator are feasible. In a reflection configuration, the electroabsorptive properties of the QWs are used to modulate the amplitude of light reflecting off the device’s surface by applying a voltage across the device. Alternatively, a waveguide configuration can be used, where a voltage applied to the device changes

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559

the absorption of the QWs in the waveguide and modulates the light propagating through the waveguide. The reflection configuration is especially attractive for optical interconnect and other optical computing applications, and can be made into 2D arrays. The waveguide approach may be more conducive to use in integrated optical circuits. Some disadvantages of the waveguide approach are polarization-sensitivity, larger wafer real estate required, inability to form 2D arrays, and more difficult input/output coupling. Incidentally, a transmission configuration, where light passing through the QWs at normal incidence is modulated by voltage-control of the absorption, is also feasible, although such devices have been shown to always operate non-optimally compared to reflective devices [149]. However, in some integrated device architectures, a transmission modulator might still be desired; its operation is similar to the reflective device. The mechanism of optical modulation employed in these electroabsorption modulators is the quantum confined Stark effect (QCSE) [150]. Essentially, the QCSE refers to the red shift of the QW band gap or absorption edge upon application of an electric field perpendicular to the wells. The band gap redshift arises from modification of the QW potential by the electric field to induce shifts in the quantized energy levels within the well. Since the carriers are confined by the quantum well barriers, exciton ionization and consequent broadening of the absorption edge is suppressed when the field is applied, leading to a sharp shift of the edge. Recent work in our group has shown that GaInNAsSb QWs show very large absorption swings due to the QCSE and have much potential for use in optical modulators in the 1.3 –1.6 mm wavelength range [151]. Figure 17.37 shows representative absorption data from GaInNAsSb/GaNAs QWs grown on GaAs, with various voltages (electric fields) applied across the QWs, demonstrating the QCSE. The QWs contained approximately

Figure 17.37. Quantum confined Stark effect measured for GaInNAsSb/GaNAs QWs grown on GaAs, showing sharp excitons (FWHM , 25 meV) at room temperature. The spectra correspond to applied voltages of 1–6 V; the values of electric field indicated on the figure were calculated using the depletion approximation and account for the built-in field of the diode.

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˚ 40% In, 2.5% N, and 2.7% Sb, with about 2.7% N in the barriers. The QWs were 80 A ˚ -thick barriers. The data shown in Figure 17.37 were taken from triple thick, with 200 A QW structures grown in the center of the 0.5 mm intrinsic region of a GaAs p – i –n diode. The n-type region was 1.38 mm thick and doped 1 £ 1018 cm23 with Si, while the p-type region was 1.0 mm thick and doped 5 £ 1017 cm23 with Be, with a 50 nm 1 £ 1019 cm23 Be-doped capping contact layer. Circular mesa devices were fabricated, and gold contacts were evaporated on the n and p layers, for testing. The QCSE is clearly exemplified in Figure 17.37. The absorption of the QWs is nearly zero below the band gap (wavelengths longer than , 1550 nm) and rises sharply at the band edge, following the step-like 2D density of states. The sharp peak at the band edge is the excitonic resonance arising from strong electron –hole interaction in the well. As the electric field is increased across the QWs, the bandedge is seen to shift to longer wavelengths without a significant change in spectral shape. This leads to a spectral range between 1500 and 1600 nm where the absorption coefficient can be modulated dramatically by varying the voltage across the device. The voltage modulation of the absorption coefficient is shown more clearly in Figure 17.38, where the difference of the spectra in Figure 17.37 with respect to the 0 V spectrum are shown. Two possible regions for modulator operation are evident. For wavelengths above , 1540 nm, the absorption coefficient is seen to rise with the application of external bias, for “normally on” operation; below , 1540 nm, the absorption coefficient is lowered by the bias, for “normally off” operation. In general, it is desirable to operate in the long-wavelength “normally on” region to minimize device insertion loss and maximize contrast ratio. By examining Figures 17.37 and 17.38, we can see that in the “normally on” region, a large absolute absorption change Da is

Figure 17.38. Change in absorption coefficient relative to 0 V for GaInNAsSb/GaNAs QWs from Figure 17.37.

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accompanied by a large ratio of amax =amin because of the very small amin : In addition, the small absorption in the “on” or 0 V state minimizes the insertion loss. On the other hand, in the “normally off” region, although a slightly larger Da can be achieved by operating at the wavelength of the 0 V exciton peak, the amax =amin ratio is low due to considerable absorption in the “on” state. Additionally, a large fraction of the input optical power is absorbed by the device even in the “on” state of the “normally off” modulator. Using the data shown in Figures 17.37 and 17.38, we can choose a modulator device architecture and calculate estimated device performance. For illustration, the case of an asymmetric Fabry – Perot reflection modulator [149,152], shown schematically in Figure 17.39, is discussed here. This architecture takes advantage of the absorption changes from the QCSE to modulate the intensity of reflected light from the device, but also utilizes a resonant cavity to enhance the contrast ratio. Optimization of the front mirror reflectivity Rf and back mirror reflectivity Rb to the absorption characteristics of the QWs in the cavity allows the realization of high contrast ratio devices. Normally, we wish to design the bottom mirror reflectivity to be near unity, so that the loss from reflection off the back mirror is small compared to the minimum absorptive loss in the cavity from the QWs. Then, for a chosen operating wavelength and voltage swing, the front mirror reflectivity is the main design degree of freedom. Generally, the optimum choice for Rf would be to match ð1 2 amax Þ in the cavity, so that in the “off” state the cavity is on resonance and the reflectivity is zero (i.e. infinite contrast ratio). This condition requires that Rf ¼ Rb expð22amax LÞ

ð17:18Þ

where L is the interaction length through the QWs and Rb is assumed to be one. Generally, a higher Rf will lead to a higher contrast ratio, but also a higher cavity finesse which undesirably reduces the optical bandwidth of the device. For the characteristics shown in

Figure 17.39. Schematic of asymmetric Fabry–Perot reflection modulator, adapted from Ref. [149].

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Figures 17.37 and 17.38, and choosing to operate at 1550 nm, we have amax ¼ 15,062 cm 21 and amin ¼ 5868 cm21 ; which gives Da ¼ 9194 cm21 and X ¼ amax =amin ¼ 2:6: From these values, we calculate a required Rf ¼ 0:73 for the matching condition. Using the formulae derived in Ref. [149], we then calculate an expected insertion loss of , 7 dB and maximum modulation ratio of over 20 dB. The expected optical bandwidth of the device is at least 20 nm full-width at half-maximum (assuming the use of AlAs/GaAs DBRs for the mirrors and a 0.25 mm i-region). Progress is being made in our group toward fabrication and demonstration of such high performance modulators based on GaInNAsSb on GaAs. We note that the required Rf for the case above is fairly high due to the short interaction length imposed by the ability to only grow a few GaInNAsSb QWs. However, the device performance (aside from insertion loss) is not strongly affected, because this material exhibits very high values of absorption coefficient. Device performance is largely determined by the product of absorption coefficient and interaction length; the GaInNAsSb material system wins with its large absorption coefficient, but the interaction length is small due to strain-limited growth. Compared to current InGaAs(P)/InP-based devices, which suffer from a much smaller absorption coefficient, but which can be fabricated with a longer interaction length, similar performance is expected from a similar overall product of a·L: Further discussion of this point is presented below. In the general case, the “matching condition” of Eq. (17.18) is not exactly satisfied, and there is a trade-off between modulation ratio and insertion loss, and also the optical bandwidth of the device. Furthermore, optimization of the QW absorption characteristics and choice of operating wavelength affects this trade-off. By maximizing the ratio amax =amin ; the modulation ratio is improved while reducing the insertion loss. However, a large Da and/or a shorter cavity leads to higher optical bandwidth as well as lower operating voltage. No attempt has been made thus far to optimize the QWs used for this illustration, and better performance is expected in the future by improving the absorption characteristics in Figure 17.37 using techniques found in the literature [153,154]. The results and calculations of expected device performance presented above are very encouraging and motivate a continued effort to optimize our GaInNAsSb QWs and fabricate a high-performance modulator. A modulation ratio of 20 dB, if realized, would be useful for either analog or digital application, comparable to current devices fabricated in InGaAsP on InP [155]. Indeed, the electroabsorption characteristics of our unoptimized GaInNAsSb QWs shown in Figure 17.37, particularly the peak absorption coefficient, are superior to those reported for InGaAs(P) on InP [156 –158]. The quality of our material, indicated by the 25 meV FWHM of the low-field exciton peak at room temperature, is only slightly worse than 1.55 mm InGaAsP on InP (15 meV FWHM at 295 K) [158]. A main issue would be to reduce the operating voltage to 1.0 – 1.5 V. A key issue, alluded to above, with the use of GaInNAsSb QWs for modulator applications is the presence of highly strained QW layers. The strain imposes a maximum

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(critical) thickness of material that can be grown pseudomorphically before large numbers of dislocations spontaneously nucleate. With GaNAs barriers, we can currently grow only up to 4 QWs for operation around 1.5 mm (the results above are for a 3 QW growth). In the reflection configuration, this translates into a very short interaction length and consequent requirement of a high finesse cavity (large insertion loss and relatively low optical bandwidth). As illustrated above, the problem of low optical bandwidth is largely overcome by the high absolute value of absorption coefficient for the GaInNAsSb QWs, which also allows the use of a short cavity length with few QWs. Use of a short cavity also promotes lower voltage operation, although a major hurdle for GaInNAsSb modulator devices might still be a relatively high voltage requirement. The high voltage requirement is partly a consequence of the high electron effective mass in the material (due mainly to the N content), which reduces the rate of shift of the absorption edge with applied voltage.

17.10. LASER RELIABILITY

While the dilute nitrides are a rapidly evolving field, there have been several reports of reliability for MBE-grown GaInNAs lasers. These investigations have shown that, at least for MBE-grown GaInNAs devices, reliability is more than sufficient for commercial deployment. Kondow et al. at Hitachi reported the first reliability data on a GS-MBE grown edge-emitting laser in 1999 [159]. The single QW 1.3 mm laser mounted epi-side up survived 1000 h at 248C under constant current conditions , 4.5 kA/cm 2. The 3.6 £ 800 mm device was coated with HR coatings on both sides (70 and 95%). During the initial , 200 h burn-in process, the threshold improved 14% (3.7 –3.2 kA/cm2) while the external efficiency fell 9% (0.066 – 0.060 W/A) and the overall output power improved from 1.3 to 1.7 mW. The output power and other parameters were constant over the subsequent 800 h. Over the course of testing, the lasing wavelength shifted 0.9 nm, from 1.323 to 1.322 mm. This report was the first to show the potential reliability of GaAsbased 1.3 mm lasers. The following year, Livshits and co-workers at Infineon and Ioffe Institute demonstrated . 2500 h of operation at a temperature of 1248C and 1.5 W of pulsed (1% duty cycle) output power, corresponding to a current density of 30 kA/cm2 [136] and upwards of 1000 h at 1.5 W of CW output power at 358C. The high performance device showed no noticeable degradation after thermal stressing. The active layer was a Ga0.64In0.36N0.0154As0.9846/GaN0.0224As0.9776 QW/barrier grown by solid-source MBE and lased at 1.3 mm. The mirrors were AR (5%) and HR (99%) coated. These results indicated not only the potential for GaInNAs as an active material for reliable high power lasers, but also that GaInNAs-based devices could reliably meet the operating temperature ranges required for commercial deployment.

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More recently, workers at Optical Communication Products (OCP, formerly Cielo Communications) demonstrated excellent reliability of high-performance 1.25 –1.3 mm GaInNAs VCSELs grown by MBE [50,160]. The aging process is similar to those of conventional 850 nm VCSELs and are well characterized by the three stages of aging (i) burn-in and infant mortality (, 100– 150 h), (ii) operating life with low random failure, and (iii) the wearout regime. During the burn-in phase, an improvement in output power (fixed bias current) was observed and is consistent with the behavior observed by Kondow et al. [159]. Failure of devices with fabrication and other short-lived defects were observed. After burn-in, few random failures were observed before the wearout phase. The results after . 106 device hours of testing was a lifetime of , 27 years for 0.1% unreliability with 90% confidence for devices biased at 6 mA (, 1 – 1.5 mW) 408C [50]. The thermal activation energy of wearout was 0.77 eV, which is quite high (typically , 0.2 –0.7 eV), indicating that the degradation depends weakly on operating temperature. The current density acceleration factor, n; was found to be 2.4 and is typically , 2 for most devices and material systems. Under high stress conditions, no failures were observed at a current density of 28 kA/cm2 at 1108C (0.8 –1 mW) for 8000 h. At 30 kA/cm2 at 1248C (0.8 – 1 mW) devices began to fail after , 2500 h. It should be noted that failure was referenced to the preburn-in output powers. The authors also investigated the wearout mechanisms using electroluminescence and cross-sectional TEM [160]. Dark line defects (DLD) and dark spot defects (DSD) were both observed in devices that failed. DLDs along the k100l directions were observed in (and confined to) the active region. The authors postulated that DSDs correspond to point defect from which DLDs grow during operation. This is consistent with the defects expected from low temperature growth of a highly strained metastable alloy. Additionally, failed devices became multi-mode during failure, consistent with degradation associated with DLDs. It was also observed that the output wavelength of failed devices blue shifted more (1.2 nm) than those of devices that survived life testing (, 0.8 nm). Based upon this discussion, reliability does not appear to present any fundamental limits to the viability of the GaInNAs alloy. It is expected that the addition of antimony to GaInNAs should improve material quality further, thereby improving device reliability once the device structure has been fully optimized. Since fabricating the first low threshold, long wavelength laser, we have undertaken at least a preliminary look at their reliability. The first CW GaInNAsSb lasers at 1.5 mm used GaNAs barriers, which being a random alloy, did not have as high of a crystalline quality as typical GaAs barriers used in 1.3 mm GaInNAs lasers. Also, due to the small QW valence band offset, there is a large amount of carrier leakage, primarily holes, from the QW to the n-type barrier. This large carrier leakage and poorer material quality leads to greater non-radiative recombination, which increases the threshold and operating currents, causing device degradation and short lifetimes, typically on the order of 1 –100 h.

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17.10.1 Constant Current Life-testing Although lifetime testing of research devices is not particularly definitive, it does serve to provide some insight into potential problems for the basic materials and device technology. We have tested some of our devices in constant current mode, at 2.0 kA/cm2, with the stage at 158C. The output power of a 10 £ 983 mm device decreased rapidly from 10.8 mW during the first hour, before failing to lase CW at 158C and 2.0 kA/cm2 after 3.5 h. The time evolution of output power and voltage are shown in Figure 17.40. The kink in output power at t ¼ 3:5 h is the device dropping below lasing threshold. Notice that device degradation continues to occur below threshold. The overall duration of current stress at 2.0 kA/cm2 was 12.8 h. After life testing, there was no significant observable change in the I – V curve, but the L – I curve exhibited a large jump in the threshold current, but no major change in the efficiency. These pre/post life test CW I – V and L – I curves are displayed in Figure 17.41. 17.10.2 Constant Power Life-testing A nearby 10 £ 983 mm device was measured in constant power mode, just barely above threshold, at 1.15 mW, with the stage at 158C. The percentage increase in drive current

Figure 17.40. First 4 h of life testing data at a constant current density of 2 kA/cm2 for a 10 £ 983 mm device at 158C (12.8 h total stress). The output power, plotted on a log scale, dropped from 10.8 mW to below 0.5 mW when it stopped lasing after 3.5 h. The voltage, plotted on a linear scale, remained roughly constant.

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Figure 17.41. Pre and post life test L – I and I – V characteristics. There is a strong increase in threshold, but a weak change in efficiency after one accounts for heating. The I – V curve showed a negligible increase in voltage.

and voltage to maintain constant power are plotted versus time on a log –log scale in Figure 17.42. The drive current increased rapidly during the first hour and leveled off somewhat after initial burn-in. Since the bias is just barely above threshold, this measurement accurately monitors changes to the threshold density with life testing. The overall duration of constant power stress was 85.4 h and during that time, the current doubled, while the voltage rose by 40% due to the series resistance. Drastic changes, possibly creation of additional recombination paths, occurred after 40 h as evidenced by the sudden decrease and then renewed increase in voltage and to a lesser extent the same pattern in drive current. After life testing, there is a small, but significant decrease in the voltage of the I – V curve, while the L – I curve showed a very large increase, nearly a factor of two, in the threshold current, but almost no change in the differential quantum efficiency. The pre/post life test curves are shown in Figure 17.43. The rise in Ith and decrease in voltage suggest an increase in leakage current as the major source of the degradation. 17.10.3

Accelerated Degradation

There is an avalanche process in constant power mode that leads to rapid device degradation. A slight increase in the non-radiative recombination will increase the

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Figure 17.42. Eighty-five-hour lifetest at a constant output power of 1.15 mW of a 10 £ 983 mm device at 158C. The percentage increase in drive current and voltage are plotted versus time on a log–log scale.

Figure 17.43. Pre and post life test L – I and I – V characteristics. The L – I curve shows a 2-fold increase in the threshold current but no major change in the efficiency after one accounts for heating. There is a significant decrease in voltage, possibly indicative of increased leakage current.

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required current to operate a constant power. This increase in current produces an increase in the voltage applied because of the series resistance and increases the dissipated electrical power, which results in a rise in junction temperature because of the thermal resistance. The rise in temperature increases the threshold current because of the exponential dependence of the threshold current on temperature. Thus, an even larger value of current is needed and the process repeats until a new steady-state, constant output power equilibrium is reached. The new current is usually much larger than indicated by the simple small increase in non-radiative current. It is believed that the device’s accelerated failure rate AF increases rapidly with current density and temperature as [160]
n
 J Ea AF ¼ a exp ð17:19Þ Ju kB T where Ja is the applied current density, Ju is a reference current density, and Ea is the activation energy for the degradation process, and n < 2 is an empirical factor. The operation at higher overall current causes a quadratic increase in the device damage rate. Also, operation at higher temperature activates more device degradation mechanisms. By mounting the devices epi-side down, the thermal resistance can easily be reduced by 2 to 3-fold for ridge waveguide devices and 4 to 6-fold for broad area devices. Combined with a lower series resistance design, this avalanche effect can be mitigated. Also, by reducing non-radiative recombination in barrier traps, i.e. using GaAs barriers or improving the material quality of GaNAs barriers or increasing the barrier height, longer device lifetimes can be expected.

17.11. SUMMARY

The discovery of 1.3 – 1.6 mm active quantum well material that can be grown on GaAs to capitalize on the superior AlAs/GaAs materials and processing technology has been a real breakthrough and has fuelled a complete re-evaluation of long wavelength lasers. We believe that GaInNAsSb on GaAs will be the fundamental technology for wide bandwidth MAN/LAN/SAN optical switches, routers and high power Raman and solid-state laser pumps. The major challenge of this materials system has been to understand the differences compared to other III –V alloys systems and to produce low threshold lasers at any desired wavelength between 1.3 and 1.6 mm. The most recent results incorporating Sb to form a quinary alloy, GaInNAsSb appear to overcome many of the prior problems with phase segregation. We believe that GaInNAsSb will be the active gain material of choice because it has significantly higher gain for VCSELs, is closer to the existing QW technologies than InAs QDs, and has fundamental energy band advantages over its other competitors. GaInNAsSb also has an inherent lateral uniformity advantage over other

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active QW materials choices; however, this is only realized by solid-source MBE. As illustrated from the TEM strain maps, recent ion damage results, DLTS, etc., there are still challenges to realize truly low laser thresholds with GaInNAsSb. However, recent improvements based upon these observations suggest that with proper feedback and control during QW growth, these problems can be overcome by MBE. I believe the newest versions of production MBE systems, with their greater versatility in number of liquid metal sources, could easily change the role of MBE. As described in Chapter 1, the advantages are not only the large wafer capability, (but most importantly for VCSELs) also the vertical configuration of effusion cells, which allows up to 8 or even 10 column III metal sources. This enables very simple step grading of the mirrors and higher growth rates without oval defects, eliminating the greatest challenges of MBE production of VCSELs. The advances in equipment combined with the significantly easier growth of GaInNAsSb by MBE will likely make MBE the choice for production of both VCSELs and high power edge emitting lasers. Progress has been fast and furious and the future for this materials system and the potential for its inclusion as a major part of the optical networks are indeed bright. ACKNOWLEDGEMENTS

The work at Stanford has been the result of efforts by a number of current and former graduate students, including Wonill Ha, Vincent Gambin, Sylvia Spruytte, Chris Coldren, Mike Larson, Evan Pickett, Tihomir Gugov, postdocs Dr Kerstin Volz and Dr Seongsin Kim and Dr Danielle Chamberlin of Agilent Technologies. The authors acknowledge many useful discussions on device physics with Prof. A.R. Adams of the University of Surrey, Prof. N. Tansu of Lehigh University, and D.P. Bour of Agilent Technologies.

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[74] Yuen, H.B., Bank, S.R., Wistey, M.A., Harris, J.S., Jr. & Moto, A., Comparison of GaNAsSb and GaNAs as quantum well barriers for GaInNAsSb optoelectronic devices operating at 1.3– 1.55 mm, J. Appl. Phys., submitted for publication. [75] Bank, S.R., Wistey, M.A., Goddard, L.L., Yuen, H.B., Lordi, V. & Harris, J.S. (2004) Low threshold, continuous wave, 1.5 mm GaInNAsSb lasers grown on GaAs. IEEE J. Quantum Electron., 40, 656– 664. [76] Volz, K., Gambin, V., Ha, W., Wistey, M.A., Yuen, H., Bank, S. & Harris, J.S. (2003) The role of Sb in the MBE growth of (GaIn)(NAsSb). J. Cryst. Growth, 251, 360– 366. [77] Goddard, L.L., Bank, S.R., Wistey, M.A., Yuen, H.B., Harris, J.S., Jr. (2004) Measurements of intrinsic properties of high power CW single quantum well GaInNAsSb/GaAs lasers at 1.5 mm. CLEO/QELS and PhAST Technical Digest on CD-ROM (The Optical Society of America, Washington, DC, 2004), CTuP22. [78] Fehse, R., Tomic, S., Adams, A.R., Sweeney, S.J., O’Reilly, E.P., Andreev, A. & Riechert, H. (2002) A quantitative study of radiative, Auger, and defect related recombination processes in 1.3 mm GaInNAs-based quantum-well lasers. IEEE J. Sel. Top. Quantum Electron., 8, 801–810. [79] O’Reilly, E.P. & Silver, M. (1993) Temperature sensitivity and high temperature operation of long wavelength semiconductor lasers. Appl. Phys. Lett., 63, 3318– 3320. [80] Bank, S.R., Lordi, V., Wistey, M.A., Yuen, H.B., Harris, J.S., Jr. (2004) Temperature dependent behavior of GaInNAs(Sb) alloys grown on GaAs, 46th Electronic Materials Conference, Notre Dame, IN, AA7. [81] Bank, S.R., Wistey, M.A., Yuen, H.B., Lordi, V. & Harris, J.S., Jr. Effects of antimony and ion damage on carrier localization in GaInNAs on GaAs, submitted for publication. [82] Katsuyama, T., Yamada, T., Iguchi, Y., Takagishi, S., Murata, M., Hashimoto, J. & Ishida, A. (2003) Very low threshold current GaInNAs quantum well lasers operating at 1.30 mm, CLEO/QELS Conference, Baltimore, MD. [83] Piprek, J. (2003) Semiconductor Optoelectronic Devices: Introduction to Physics and Simulation, Academic Press, San Diego, CA, p. 158. [84] Angenent, J.H., Erman, M., Auger, J.M., Gamonal, R. & Thijs, P.J.A. (1989) Extremely low loss InP/GaInAsP rib waveguides. Electron. Lett., 25, 628– 629. [85] Ledentsov, N.N., Kovsh, A.R., Zhukov, A.E., Maleev, N.A., Mikhrin, S.S., Vasil’ev, A.P., Semenova, E.S., Maximov, M.V., Ustinov, V.M. & Bimberg, D. (2003) High performance quantum dot lasers on GaAs substrates operating in the 1.5 mm range. Electron. Lett., 39, 1126 –1128. [86] Krispin, P., Gambin, V., Harris, J.S. & Ploog, K.H. (2003) Nitrogen-related electron traps in Ga(As,N) layers (#3% N). J. Appl. Phys., 93, 6095– 6099. [87] Tansu, N., Yeh, J.Y. & Mawst, L.J. (2003) Low-threshold 1317-nm InGaAsN quantum-well lasers with GaAsN barriers. Appl. Phys. Lett., 83, 2512– 2514. [88] Thijs, P.J.A. (1994) Strained-layer InGaAs(P)/InP quantum well semiconductor lasers grown by organometallic vapour phase epitaxy, PhD Dissertation, Technische Universiteit Delft. [89] Thijs, P.J.A., Binsma, J.J.M., Tiemeijer, L.F. & Van Dongen, T. (1992) Submilliamp threshold current (0.62 mA at 08C) and high output power (220 mW) 1.5 mm tensile strained InGaAs single quantum well lasers. Electron. Lett., 28, 829– 830. [90] Tansu, N., Chang, Y.L., Takeuchi, T., Bour, D.P., Corzing, S.W., Tan, M.R.T. & Mawst, L.J. (2002) Temperature analysis and characteristics of highly strained InGaAs – GaAsP – GaAs (lambda . 1.17 mm) quantum-well lasers. IEEE J. Quantum Electron., 38, 640– 651. [91] Tansu, N. & Mawst, L.J. (2002) Low-threshold strain-compensated InGaAs(N) (l ¼ 1:19 – 1:31 m) quantum-well lasers. IEEE Photon. Technol. Lett., 14, 444– 446.

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Dilute Nitride Semiconductors M. Henini (Ed.) q 2005 Elsevier Ltd. All rights reserved.

Chapter 18

Application of Dilute Nitride Materials to Heterojunction Bipolar Transistors Rebecca J. Weltya, Roger E. Welserb, Charles W. Tuc and Peter M. Asbeckc a

Lawrence Livermore National Laboratory, Livermore, CA, USA Kopin Corporation, 695 Myles Standish Blvd, Taunton, MA, USA c University of California at San Diego, La Jolla, CA, USA b

ABSTRACT

The application of GaInNAs to heterojunction bipolar transistors (HBTs) enables re-engineering the band structure of these devices to provide a variety of benefits. Conventional GaAs-based HBTs have emitters of GaInP (or AlGaAs), base and collector regions of GaAs and are grown on a GaAs substrate. GaInNAs is used to replace the GaAs in the base region of the transistors. The lower band gap of GaInNAs leads to devices which have lower input turn-on voltages ðVBE Þ than those of conventional devices, which is highly beneficial for battery-operated powerefficient circuits. The difference in band gap between the GaInNAs base and GaAs collector also contributes to reducing the offset voltage ðVoffset Þ and lowering the knee voltage of the transistors, which leads to enhanced efficiency in microwave power amplifiers. Although the material transport characteristics of GaInNAs are not as favorable as those of GaAs due to lower electron and hole mobilities, and higher recombination rates, it has been shown that the HBT dc current gain, current gain cutoff frequency ð fT Þ; and maximum frequency of oscillation ð fmax Þ can be as good as (or better than) those of conventional devices by proper engineering—for example, by grading of the composition of the GaInNAs material across the base region. It is also critical to compensate for the discontinuities of the conduction band at the base – emitter and base – collector junctions. This chapter outlines the key strategies to improve HBT characteristics, and describes device design and fabrication with GaInNAs base regions. It also summarizes reported HBT characteristics and circuit performance with these devices. 18.1. INTRODUCTION

One of the devices that can be expected to benefit from the band gap engineering of GaInNAs alloys is the heterojunction bipolar transistor (HBT) implemented with GaAs substrates. GaAs HBTs are in widespread use, particularly in microwave power amplifiers 579

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for wireless applications. The use of GaInNAs in the base region of HBTs allows the turnon voltage VBE applied between base and emitter to be lowered, which improves HBT performance in battery-powered operation. The structure of representative GaAs HBTs manufactured at present is shown in Figure 18.1(a). With a substrate of semi-insulating GaAs, the devices comprise of epitaxial layers corresponding to a collector of n-type GaAs, a base of p-type GaAs and an n-type emitter of a material whose band gap is wider than that of the base (typically AlxGa12xAs with x , 0:25 or GaInP). This is followed by a cap layer of GaAs or InGaAs to assist in forming the emitter ohmic contact. An associated band diagram is shown in Figure 18.1(b). With the wide band gap of the emitter, high emitter injection efficiency is maintained independent of the emitter and base doping levels, so that it is possible to achieve high current gain (. 40 for microwave applications, . 100 for digital and mixedsignal applications) even with very heavily doped base regions (with hole concentration in the range of 1 – 5 £ 1019 cm23). The transistors achieve very high microwave power gain because of the low base resistance and short base transit time. They also can achieve high values of breakdown voltages (. 25 V BVcbo, . 15 V BVceo), as required for robust operation in power amplifiers. As a result of these advantages, GaAs-based HBTs have become the devices of choice for the power amplifiers used in many cellular phone handsets, particularly those with high linearity requirements (for example, phones that

Figure 18.1.

(a) Representative GaAs HBT layer structure. From Ref. [2]. (b) Corresponding HBT energy band diagram.

Application of Dilute Nitride Materials to Heterojunction Bipolar Transistors 581 follow the CDMA standard and use filtered QPSK modulation). The manufacturing volume of the GaAs HBT amplifiers is estimated to easily exceed 500 million units per year. Substantial attention has been given to low cost production, with several GaAs HBT fabrication lines now using 6 in. diameter wafers [1]. While the GaAs HBT characteristics are closely matched to the needs of linear, efficient power amplifiers operated with available batteries, there are several features which could be improved. A principal goal of the research activities for GaInNAs base devices is to demonstrate the reduction in VBE and Voffset without compromising the high microwave performance of the transistors (including high current gain, low base resistance, low base transit time, high breakdown voltage, high current gain cutoff frequency and high reliability). Research results suggest that the desired material characteristics can be obtained [2]. It is additionally found that with GaInNAs base regions there can be a reduction in the offset voltage, Voffset ; which is the minimum value of VCE when the device is on. This reduction in Voffset can be achieved by designing a device with a higher degree of symmetry between the base – emitter and base – collector junctions [3,4]. This added symmetry is a natural result of DHBTs. This reduction in Voffset ; and the ensuing decrease in knee voltage ðVk Þ; improves the efficiency of the resulting amplifier circuits. An example is included to illustrate the increase in power-added efficiency (PAE) for a reduction in Vk ; where the PAE is defined by the following equation, and is in terms of the rf input ðPrf;in Þ and output power ðPrf;out Þ as well as the dc power ðPdc Þ from the supply: PAE ¼

Prf;out 2 Prf;in : Pdc

For class B operation the PAE is expressed by the following equation:

 p Vk 1 PAE ¼ 12 12 ; G 4 Vbias

ð18:1Þ

ð18:2Þ

where Vbias is the battery supply voltage and G is the gain of the transistor and is taken to be 12 dB. Figure 18.2 shows the bias condition for this example with the input and output waveforms. The input bias is centered at Vbias and swings to a minimum of Vk and a maximum of 2Vbias 2 Vk : The PAE can directly be increased by decreasing the Vk of the transistor. A GaInNAs HBT power device with increased PAE over GaAs HBTs is discussed in Section 18.5. The primary figure of merit to be improved is the turn-on voltage, VBE ; needed to produce a given current flow. The goal is to reduce the turn-on voltage by using lower energy-gap GaInNAs alloys in the base region of an HBT. Power amplifier circuits are customarily operated using a battery as the voltage source, and Li ion cells are widely used at present. The voltage provided by these cells is in the neighborhood of 3.4 –3.6 V, but can drop down to 3.0 V near the end of the battery discharge cycle (and rise up to 4.2 V when fully charged). The core of a reference circuit is shown in Figure 18.3. For present

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Dilute Nitride Semiconductors

Figure 18.2. Biasing condition for Class B power amplifier, with input and output swing also shown.

GaAs-based HBTs the value of VBE is of the order of 1.4 V (near the band gap of the base). Therefore, the reference voltage must be greater than 2.8 V (two stacked transistors in the cascode configuration). For proper current control over a range of temperatures, it is desirable to maximize the voltage across RSET : The present value of VBE for HBTs is marginal for these requirements. As a result, there is substantial benefit that can be obtained by a relatively small decrease in VBE : The turn-on voltage for bipolar transistors is typically uniform across the wafer, which is advantageous for circuit design. This is in contrast to MOS devices which generally suffer from VTh varying considerably across the wafer due to the fluctuation of doping and oxide thickness across the wafer. The VBE value for HBTs is typically hard to change because it involves changing the material of the base layer.

Figure 18.3. Representative bipolar reference voltage circuit.

Application of Dilute Nitride Materials to Heterojunction Bipolar Transistors 583 The collector current JC is represented by Eqs. (18.3) and (18.4) for a base-transport limited device [5]: q expðqVBE =nkTÞ JC ¼ Ð ; ½pdx=Dn n2i ðxÞ ! Ð kT JC p=n2i dx ln ; VBE ¼ q qDn

ð18:3Þ ð18:4Þ

where p; Dn ; n; and ni are the free carrier concentration in the base, minority carrier diffusion constant, ideality factor and intrinsic carrier concentration, respectively. The remaining constants and the variable are the electron charge q; Boltzmann constant k and temperature T: The integral is taken across the quasi-neutral base region (of thickness w). The principal determinant of VBE ; however, is the intrinsic carrier concentration in the base, ni ;
 2Eg 2 ni ¼ NC NV exp ; ð18:5Þ kT where NC and NV are the density of states of the conduction and valence band, respectively. VBE has a weak dependence on Dn ; the diffusion coefficient for electrons in the base, on the hole concentration p in the base, and on the width of the base [6]. The value of ni is largely controlled by the band gap energy Eg of the material used in the base. However, the turn-on voltage can be further increased by a barrier at the base – emitter junction. This is due to the dependence of JC on the ideality factor, n; as shown in Eq. (18.3). The ideality factor for an HBT with a smooth base –emitter heterojunction will have a value of 1.0. The collector current of the device with the large conduction band barrier (Figure 18.4(a)) will no longer be base-transport limited; instead, the barrier will increase the turn-on voltage of the device. The transistor will now require an additional applied voltage to overcome the barrier (generally by thermionic or thermionic field emission current flow). If the collector current has a component of thermionic emission

Figure 18.4. Emitter–base heterojunction for typical HBTs with (a) finite conduction band discontinuity and (b) zero conduction band discontinuity.

584

Dilute Nitride Semiconductors

due to a larger barrier, typically on the order of 100 meV, the ideality factor will be increased to a value greater than 1.0, in the range of 1.1– 1.2. Therefore, for reduced turnon voltage designs it is important that energy band gap engineering is used to smooth out the base – emitter conduction band discontinuity (Figure 18.4(b)). For various circuit applications, as mentioned, it is desirable to decrease the value of VBE by a small amount. Figure 18.5 illustrates the dependence of JC on VBE found for a variety of HBTs fabricated with different material systems. The turn-on voltage for InP-based HBTs is inherently lower than GaAs-based HBTs because the base region material lattice-matched to the InP substrate has a lower band gap energy than GaAs. Ga0.47In0.53As used as the base material, lattice matched to the InP substrate, has a band gap energy of 0.75 eV [7]. Materials containing antimony have also been used recently in high-performance HBTs. GaAs0.5Sb0.5 ðEg , 0:72 eVÞ as the base material grown on InP also provides a corresponding reduction in turn-on voltage [8]. A major advantage of this material system is the fact that InP/GaAs0.5Sb0.5 has a staggered heterojunction (for a review of energy band gap lineups see Ref. [9]). This lineup eliminates the complicated grading schemes necessary at both the base – emitter (for low turn-on voltage) and base – collector (for low output conductance) junctions. In the past, efforts to reduce the turn-on voltage for GaAs technologies have been marginal. InGaAs as the base material in a GaAs technology has had limited success for reducing the turn-on voltage because the materials are not lattice matched. The thickness and indium

Figure 18.5. Representative variation of collector current density, JC ; vs. VBE for HBTs fabricated with various technologically important material systems. The shaded region shows the operating range obtainable with HBTs using GaInNAs base regions.

Application of Dilute Nitride Materials to Heterojunction Bipolar Transistors 585 Table 18.1. Base region material for various bipolar technologies Base material Si GaAsSb, Sb ¼ 0.5% InGaAs, In ¼ 53% GaAs InGaAs, In ¼ 8%

Band gap (eV)

Substrate

1.12 0.72 0.75 1.42 1.3

Si InP InP GaAs GaAs

composition of the InGaAs layer must be kept within the critical thickness such that the strain due to lattice mismatch can be absorbed elastically. If the InGaAs is thicker than the critical thickness, misfit dislocations will occur, which will cause excessive recombination. Ga0.92In0.08As base HBTs grown on GaAs have been successfully fabricated [10]. This indium composition translates into , 0.1 V reduction in turn-on voltage, relative to a GaAs base. This small reduction is a practical limit for GaInAs base HBTs with conventional base widths before reaching the critical layer thickness. To further reduce the turn-on voltage for GaAs-based HBTs, alternative base materials must be investigated. Table 18.1 summarizes values for band gap energy for various base materials and their respective substrate, of which the device is typically grown on. In the next section, it will be shown that incorporating nitrogen into GaInAs drastically decreases the band gap energy of the material. The use of GaInNAs materials in the base can provide a technologically important small shift in band gap, leading to IC vs. VBE dependence in the shaded region of Figure 18.5.

18.2. DESIGN CONSIDERATIONS FOR GaInNAs BASE HBTs

The principal objective of GaInNAs base HBT design is to replace the p-type GaAs base layer of Figure 18.1 with a corresponding layer of GaInNAs that has a lower value of band gap energy. The choice of alloy composition for the base is constrained by a number of factors. Lattice match to the GaAs substrate must be relatively good, in order to avoid exceeding the critical thickness for misfit dislocation formation (which leads to excess recombination in the base). Representative thicknesses of the layers used in the HBT base ˚ . These are substantially greater than the layer thicknesses used are in the range 400– 800 A for quantum wells in laser applications [11 – 13] and, correspondingly, the requirements for lattice match are more stringent for HBTs than for lasers. Using values for material parameters taken for GaAs, the estimated in-plane lattice strain vs. Ga12xInxNyAs12y alloy composition is shown in Figure 18.6. The tensile strain obtained by the addition of nitrogen compensates for the compressive strain obtained by indium additions, in an amount approximately given by 1 mol% nitrogen to compensate 3 mol% indium [13]. ˚ is estimated to be 0.37%, The amount of strain allowed for a critical thickness of 600 A

586

Dilute Nitride Semiconductors

Figure 18.6. Representative values of epitaxial layer strain ð1Þ and band gap energy ðEg Þ; as a function of alloy composition (indium and nitrogen) for GaInNAs on GaAs substrates. From Ref. [2].

˚ (typical of quantum well applications) it is estimated to be while for a thickness of 100 A 1.4%. The associated lines on Figure 18.6 illustrate representative bounds for alloys of interest for the two applications. Figure 18.6 also shows contours for the estimated band gap energy of the alloys, calculated from the approximate relation: GaInx Ny As Eg ðx; yÞ ¼ 1:43 2 1:15x 2 10:0y:

ð18:6Þ

This is based on linear interpolation of the band gap reduction as a result of adding nitrogen [14] or indium [15] under conditions of constant in-plane lattice constant equal to that of the GaAs substrate. The band gap is highly dependent on the growth and subsequent material processing (annealing). Further work is needed to provide a model for the band gap energy of GaInNAs, including the effect of rapid thermal annealing (RTA). In order to provide a useful amount of VBE reduction in HBTs, the band gap of the GaInNAs in the base should be in the range 1.0 – 1.3 eV. By contrast, for lasers it is desirable to reduce the band gap to 0.9 eV or below (to achieve 1.3 or 1.55 mm emission after quantum well confinement energy is accounted for). This constraint allows a further definition of the regions of interest for the different applications, which are shown as shaded areas in Figure 18.6. This figure shows that the target compositions are substantially different for the two different devices; HBTs require a tighter control in lattice match, but have applications with modest reductions in band gap, compared to GaInNAs QW lasers. A wide range of material compositions have been explored in initial laboratory experiments, by a number of investigators. In general, it is found that by using the lowest possible amount of nitrogen the device characteristics are improved.

Application of Dilute Nitride Materials to Heterojunction Bipolar Transistors 587 It has been established that the majority of the change in band gap energy of GaInNAs relative to GaAs occurs in the conduction band, rather than the valence band. This arrangement is relatively unfavorable for npn HBT applications (although as detailed below, favorable for pnp devices [16,17]) since the offset of conduction band energy can produce an energy barrier for electrons at the GaAs/GaInNAs interface. Figure 18.7(a) shows a band diagram for an npn HBT that would result if special care is not given to mitigate the energy barriers. At the base –emitter junction, the presence of

Figure 18.7. Calculator band diagram of an HBT with a GaInNAs base where no provisions are made to reduce base–emitter and base– collector conduction-band barriers. Also shown is the calculated band diagram for the design specified in Table 18.2, which incorporates provisions to overcome conduction band barriers at the base– emitter and base–collector heterojunctions. Calculations are done with a one-dimensional Schro¨dinger/Poisson Solver. From Ref. [18].

588

Dilute Nitride Semiconductors

a barrier dictates that higher applied voltage must be used to inject electrons into the base, and so leads to an increase in VBE (negating the benefit of the GaInNAs base). At the base – collector junction, the effect of a conduction band barrier is even more significant, since it impedes collection of the minority carriers by the high field collector region. This leads generally to a dramatic decrease in current gain and increase in charge storage in the base as well as to a reduction in collector current (which then frequently becomes dependent on the base – collector reverse bias voltage). Research in other material systems (for example, InP/InGaAs/InP HBTs) has shown that a variety of techniques can be used to minimize the effects of the conduction band offset at the junctions. Grading the material composition near the interface decreases the height of the barrier. Adding doping pulses (typically, a sheet of Si donors) can also lead to a charge dipole (from the ionized Si dopants and compensating ionized acceptor dopants in the base) which can produce an electrostatic field to cancel the band offset contributions. A “setback” layer of n-doped low band gap material is also often introduced. A representative overall design, which has been used at University of California at San Diego (UCSD), to produce GaInNAs base HBTs with base band gap down to 1.0 eV, is shown in Table 18.2 [18]. The design uses compositional grading as well as pulse doping to eliminate the effects of conduction band barriers. The growth of this structure was undertaken with gas-source MBE. In order to decrease the difficulty of calibrating the growths of the graded materials at the interfaces, a chirped superlattice was employed, in which the material alternates between the end point compositions (GaAs and GaInNAs) in a superlattice where the thickness of the two materials is progressively changed. In this example, the superlattice consisted of 15 ˚ ; this structure is shown in Figure 18.8. As periods, with a thickness per period of 11 A detailed below, no effects of barriers were detected. In this example, the band gap Table 18.2. Epitaxial layer design for a GaInNAs HBT with 2% nitrogen incorporation Layer Cap Emitter Delta doping Graded Spacer Base Spacer Graded “Delta doping” Collector Sub-collector S.I. GaAs substrate

Material

˚) Thickness (A

Doping (cm23)

GaAs GaAs GaAs GaAs ! Ga0.89In0.11N0.02As0.98 Ga0.89In0.11N0.02As0.98 Ga0.89In0.11N0.02As0.98 Ga0.89In0.11N0.02As0.98 Ga0.89In0.11N0.02As0.98 ! GaAs GaAs GaAs GaAs

2000 2000 5 300 50 400 50 300 50 4000 7000

n, 5 £ 1018 n, 5 £ 1017 n, 3 £ 1019 n, 3 £ 1017 Undoped p, 8 £ 1018 Undoped n, 3 £ 1016 n, 1.5 £ 1018 n, 3 £ 1016 n, 5 £ 1018

Chirped superlattice and delta doping are used at both the base–emitter and base– collector heterojunctions to eliminate conduction band barriers. From Ref. [18].

Application of Dilute Nitride Materials to Heterojunction Bipolar Transistors 589

Figure 18.8. Diagram of chirped superlattice showing electron can tunnel through the conduction band edge of each barrier.

reduction in the base was sufficient that an emitter of GaAs could be used (rather than AlGaAs or GaInP) while still maintaining a large enough difference in band gap between the emitter and base to insure high electron injection efficiency; about 200 –250 meV difference is needed to account for doping differences between the base and emitter. The resulting band diagram is shown in Figure 18.7(b). With MOCVD growth, the grading of composition is easier than in MBE, and a continuous grading is used. In most works a conventional AlGaAs or GaInP emitter layer is maintained, which allows the same processing to be used as for conventional HBTs, and facilitates passivation ledges, etch stop layers, etc. In addition to the band gap energy, other material characteristics are critical for highperformance HBTs. The current gain of the device is influenced by the recombination lifetime of electrons in the base, as well as by the diffusion coefficient of electrons across the base. The component of base current associated with the base recombination, Ibr ; can be expressed as Ibr ¼ IC tbtr =trec ;

ð18:7Þ

where IC is the collector current, trec is the recombination lifetime of electrons in the base, and tbtr is the base transit time. For purely diffusive transport across the base (as obtained with uniform base doping and composition in relatively thick layers), tbtr is given approximately by

tbtr ¼ w2 =2Dn þ w=vex ;

ð18:8Þ

where w is the base thickness, Dn is the electron diffusion constant, and vex is the average velocity at which electrons exit the base. The combination of the two above expressions shows that Ibr ¼ IC ½ðw=Ldiff Þ2 =2 þ w=vex trec ;

ð18:9Þ

where Ldiff is the minority carrier diffusion length in the base. The contributions associated with vex become small for thick base layers or small diffusion lengths. Eq. (18.9) illustrates that it is important to maintain a large value of diffusion length in the base (Ldiff , 0:5 mm ˚ GaAs base). It is noteworthy that the electrons which flow across the base have for a 500 A relatively low density (, 1016 cm23 typically) and thus occupy states at the very bottom of

590

Dilute Nitride Semiconductors

the conduction band, where they are particularly sensitive to band tailing effects, localization of states, etc. Other contributions to base current (including emitter–base recombination, emitter edge recombination and hole injection into the emitter) must also be minimized. To maintain high-frequency operation, the current gain cutoff frequency fT must be high; fT . 30 GHz is desired in most applications. The value of fT can be estimated through the relation:

tec ¼

1 V ¼ tbtr þ tCSCL þ T ðCBE þ CBC Þ þ CBC ðRE þ RC Þ; 2p f T IC

ð18:10Þ

where tbtr is the base transit time, tCSCL is the collector space-charge transit time, and the remaining terms are RC charging times associated with base –emitter and base –collector depletion capacitances (CBE and CBC ; respectively). The base layer influences fT through the base transit time tbtr ; the same parameter that enters the current gain expression above. In conventional HBTs, tbtr is about 1.2 ps, while the entire right-hand side of Eq. (18.7) is 4 ps. Thus, by introducing a GaInNAs base it is necessary to avoid increasing tbtr by more than about 0.4 ps. The microwave power gain of HBTs is specified by the figure of merit fmax ; the maximum frequency of oscillation, which can be calculated by the following equation: fmax

sffiffiffiffiffiffiffiffiffiffiffiffiffiffi fT : ¼ 8pRB CBC

ð18:11Þ

To achieve high fmax ; it is necessary to have high fT ; as well as to maintain low base resistance, RB : The value of RB is directly influenced by the sheet resistance in the base, rB ; given by

rB ¼

1 : qpmp w

ð18:12Þ

The base must maintain a high doping level, p; and a high mobility for holes, mp ; the sheet resistance rB of 300 – 600 V/square achieved in conventional devices must not be increased significantly. The relationship between nitrogen incorporation for a reduction in VBE and low base sheet resistance is one of the primary design tradeoffs for GaInNAs HBTs. With the introduction of GaInNAs in the base in place of GaAs, the values of Dn and Ldiff are found to decrease, which degrades the current gain, and the values of fT drop. One strategy to mitigate these effects is to provide compositional grading across the base. By providing a change in band gap of the base from a large value near the emitter ðEgbe Þ to a smaller value near the base –collector junction ðEgbc Þ; a built-in quasi-electric field of value 1b ¼ ðEgbe 2 Egbc Þ=w can be designed into the device, so that electron flow proceeds

Application of Dilute Nitride Materials to Heterojunction Bipolar Transistors 591 by drift as well as by diffusion. Under such circumstances, the base transit time becomes


 kTw 1 kT kT 2q1b w tbtr ¼ þ 2 1 2 exp : ð18:13Þ qD1b vex qD1b q1b kT This expression, evaluated within the drift – diffusion transport formalism, is valid only for small departures from equilibrium—and thus small values of qD1b =kT relative to vex . The ˚ base, which can built-in field is typically , 5– 10 kV/cm or higher across a 500– 1000 A reduce the transit time by a significant factor, and mitigate the difficulties generated by using GaInNAs.

18.3. MATERIAL GROWTH AND DEVICE PROCESSING

GaAs HBT epitaxial structures are currently produced in commercial quantities using both MBE and MOCVD techniques. Both approaches have been used by investigators to produce GaInNAs HBT structures. Work based on MOCVD typically employs dimethylhydrazine [19], or less commonly used nitrogen triflouride [19] and ammonia [20], as the nitrogen-containing species. For the MBE research to date, nitrogen was derived from an RF or ECR plasma source fed with N2, within a solid-source MBE (SS-MBE) or gas-source MBE (GS-MBE) system. The latter provides the arsenic in the form of AsH3 fed into a suitable cracker. The acceptor dopant of choice for MOCVD growth is carbon (because of its low diffusivity); the acceptor of choice for MBE is beryllium (although carbon can also be used). The addition of indium and nitrogen can lead to significant changes in growth rate and in dopant incorporation, so that extensive calibration is generally required. The material requirements of GaInNAs base HBTs become increasingly difficult to satisfy with increased nitrogen incorporation, such as large free carrier concentration, mobility and diffusion length. To further complicate the material properties, they are significantly altered by thermal annealing [21 –23]. For optical devices this is seen as an increase in luminescence efficiency. For electrical devices the improvement is associated with an increase in free carrier concentration and mobility, this is particularly noticeable in the HBTs with 2% nitrogen. It has been shown that the addition of nitrogen during growth changes the incorporation of hydrogen, which can be prevalent in the MOCVD or GS-MBE growth ambient. The hydrogen has a significant role in compensating the acceptor dopants—so that the hole concentration is generally well below the acceptor impurity concentration. The hydrogen grown into the structure can be partially eliminated by annealing, which can be carried out during growth or subsequent to growth. The material changes that occur during annealing are complex. It has been argued that a portion of the hydrogen exists (or migrates) as a positively charged entity, so that the evolution of hydrogen from the p-type base is impeded by the grown overlayer of n-type

592

Dilute Nitride Semiconductors

material (since the resulting p– n junction provides a built-in electric field which retards the motion). This suggests in situ annealing might be more worthwhile. However, it is possible that even after annealing, hydrogen could become incorporated during the subsequent growth of emitter and cap layers. The status of material growth by MBE (gas source and solid source) and MOCVD is compared below. The use of MBE for GaInNAs HBTs is particularly well suited due to the ability to ˚ level. This is particularly important due to precisely control the material growth at the A the large DEC that exists between the base and emitter for these structures. This was discussed in detail in Section 18.2. In the experimental work done, to date, on Be-doped, gas-source MBE-grown materials, annealing of the material subsequent to growth has been a key step. A principal effect is acceptor activation through hydrogen evolution; reduction of point defect concentrations can also take place. The anneal parameters must be carefully chosen, however, in order to avoid diffusion of the beryllium dopant incorporated in the base. RTA is the preferred process. Figure 18.9 shows the free carrier concentrations as a function of RTA temperature for as-grown and annealed GaInNAs samples [21]. With the nitrogen concentration increasing from 0 to 0.024 and constant flux of the beryllium acceptors (holes), the carrier concentration of the as-grown samples decreases by one order of magnitude. This can be attributed primarily to hydrogen passivation. Another possible effect is the introduction of deep level traps associated with

Figure 18.9. Carrier concentration as a function of RTA temperature for as-grown and annealed GalnNAs samples. The free carrier concentration is reduced with an increase in nitrogen incorporation. From Ref. [21].

Application of Dilute Nitride Materials to Heterojunction Bipolar Transistors 593 nitrogen incorporation. The Hall mobility decreases from 60 to 30– 45 cm2 V21 s21. After RTA at 7008C, the carrier concentration of nitrogen-containing samples is increased to half of that of GaInAs due to the reduced hydrogen passivation effect of beryllium dopants, and the Hall mobility also increases to , 50 cm2 V21 s21. Even after the anneal, the product of carrier concentration and hole mobility is only half that of the GaInAs sample; furthermore, a concern for HBTs is that under anneal cycles out-diffusion of the base dopant will take place which can increase the turn-on voltage of the transistor and cause reliability problems. Secondary ion mass spectroscopy (SIMS) experiments were done to determine if out-diffusion occurs. Figure 18.10 shows the SIMS profiles of as-grown, 700 and 8508C annealed Ga0.892In0.108N0.017As0.983 samples [21]. By annealing, hydrogen atoms dissociate from the Ga0.892In0.108N0.017As0.983 layer, so the hydrogen concentration is reduced. With increasing RTA temperature, the hydrogen concentration is further decreased, and the free carrier concentration increases. There is no detectable beryllium diffusion at 7008C RTA, suggesting that 7008C RTA is suitable for HBTs. At 8508C, some diffusion could be detected, and the free carrier concentration is also decreased to 7.2 £ 1018 cm23, compared to 1.1 £ 1019 cm23 for 7008C annealed sample. Degradation in the acceptor free carrier concentration will increase RB which will in turn reduce fmax :

Figure 18.10. SIMS profile of as-grown Ga0.892In0.108N0.017As0.983, and 700 and 8508C annealed samples. Graph shows the relationship between hydrogen and beryllium. The free carrier concentration increases with the decrease of hydrogen evolution, which occurs with annealing. From Ref. [21].

594

Dilute Nitride Semiconductors

GaInNAs has also been grown by SS-MBE [24 – 27], which may be a promising technique. By using SS-MBE, the hydrogen from the AsH3 used in GS-MBE is avoided, while one is still able to have atomic layer accuracy. There have been basic material studies, which indicate that the material properties seem to be very similar to those grown by GS-MBE. For instance, there is still an increase in photoluminescence after annealing, due to the increase in crystallinity and decrease in nitrogen-ion-induced damage. Initial results [27] show that GaInNAs grown by SS-MBE has a peak photoluminescence at a higher anneal temperature than the samples grown by GS-MBE. However, to date, GaInNAs base HBTs have not been demonstrated with this growth technique. Further work investigating the acceptor free carrier concentration on GaInNAs grown by SS-MBE should be carried out to determine the feasibility of this approach. GaInNAs HBTs grown via MOCVD also exhibit complex behavior. The minority carrier properties of carbon-doped HBTs before and after current stressing have been evaluated via measurements of the dc current gain in the limit of neutral base recombination [28]. GaInNAs HBTs exhibit the same type of transit behavior typically observed in GaAs HBTs, which can be partially correlated to hydrogen incorporation [29]. The highest minority carrier lifetimes have been achieved in material optimized for post-current-stress dc current gain. The base region doping, mobility, and band gap have also been evaluated in an as-grown HBT structure, and then annealed both in situ and ex situ [30]. It was found that the in situ anneal process under nitrogen leads to a better activation of carbon acceptors which gives rise to a lower base resistance and an increase in the current gain compared to the as-grown sample. Alternately, the samples with ex situ annealing resulted in a significant reduction in current gain compared to the as-grown sample. Much of the GaInNAs material work to date has been on undoped MQW structures for lasers. For HBTs the characterizations must be done with pþ layers. The mechanisms affecting transport processes in GaInNAs materials must be further evaluated for various growth techniques and anneal cycles to understand the necessary condition to achieve high base doping, mobility and carrier lifetime. Processing of HBTs employing GaInNAs bases is similar to that employed for conventional GaAs base layers. However, formation of ohmic contacts to the base is more difficult if the base doping is low. If an emitter of GaAs is used in place of GaInP or AlGaAs, then it is difficult to use selective etching that stops accurately at the base layer since it appears that the GaInNAs etches at least as rapidly as GaAs in wet chemical etches. A process simplification when etching down to the base layer is to use plasma etching with a chlorinated gas such as CCl2F2 which has been reported to stop on indiumcontaining materials [31,32]. This technique is possible using low-density etching, i.e. reactive ion etching (RIE). This is due to the large difference in vapor pressure for AlCl3 and GaCl3 compared to InCl3, which has a vapor pressure that is approximately 50 times lower [33]. The vapor pressures correlate with relative etch rates of various III– V alloys [34]. However, using high-density plasma (ECR, ICP) this technique may not work;

Application of Dilute Nitride Materials to Heterojunction Bipolar Transistors 595 with this configuration, indium-containing materials can be etched, depending on the ion density, energy and wafer temperature [33].

18.4. GaInNAs HBT RESULTS

Npn HBTs with GaInNAs base regions have been demonstrated by numerous investigators, with varying amounts of N and In [2,6,18,35 – 42]. Several different devices are described to provide a representative picture of the results obtained. A summary of some of these results is shown in Table 18.3. These results are grouped into three nitrogen level ranges: high, medium and low. For dilute-nitride HBTs the highest reported level of N is 2% [18]. The medium range corresponds to about 1% N and the low range is less than 0.5% N. Figure 18.11 shows the curves of JC vs. VBE measured for the GaInNAs HBTs from Table 18.3. GaInNAs HBT A was grown at UCSD via GS-MBE using 2% N and 11% In, to produce a large change in VBE ; an observed VBE reduction of 0.44 eV was demonstrated [18]. GaInNAs HBT B shows a 0.23 eV reduction in VBE and was grown at Emcore by MOCVD in collaboration with the team at Sandia [37]. GaInNAs HBTs C, D, and E were grown by Kopin using MOCVD; HBT E has a reduction in VBE of 50 meV [2] while D has a 90 meV reduction [2] and C has a reduction of 0.2 eV [28]. Even for the lowest range of nitrogen incorporation, the increase in JC for GaInNAs base HBTs is very large. Figure 18.12 shows a comparison of collector current for GaInNAs HBT E and the conventional GaAs base HBT. The small decrease in turn-on voltage of 50 meV results in a 7.7 £ increase in collector current for 6 decades of collector current. The increase is 6 £ 103 £ for a 0.2 eV VBE reduction and 107 £ for a 0.44 eV reduction. The exponential relationship between collector current and base – emitter voltage VBE leads to a large increase in collector current for a small change in VBE : Representative Gummel plots corresponding to devices A and C are shown in Figure 18.13 (log IC and log IB vs. VBE ; for VBC ¼ 0). The characteristics of device A show relatively large curvature at high currents due to base series resistance effects. The curves indicate that the base current increases with increasing nitrogen and indium content. For device A the base ideality factor is 1.6 suggesting that there is a considerable n ¼ 2 base recombination component (likely from the chirped superlattice). On the other hand, device C has a base ideality factor of 1.01 illustrating very low base recombination with the primary component being in the quasi-neutral base region. For both the devices A and C the collector ideality factor is 1.0 indicating proper elimination of the conduction band barrier was achieved, yielding a device which is base transport limited. The current gain is also evaluated from the Gummel plots. Both beta ðb ¼ IC =IB Þ and the incremental current gain ðhFE ¼ ›IC =›IB Þ are compared for the devices listed in Table 18.3. The incremental current gain is important to consider when excessive leakage

596

Table 18.3. Comparison of figure of merits for GaInNAs base HBTs Sandia—B [37]

Kopin—C [28]

Kopin—D [2]

Kopin—E [2]

GS-MBE High 2 11 d doping and chirped superlattice d doping and chirped superlattice Constant 7000 400 3 £ 3 (2 fingers) 1.03, 1.6 0.44 0.5, 0.08 5, 8 0.08 23, 10

MOCVD Medium 1 3 d doping d doping and step grading Constant 900 700 3 £ 14 1.12, 1.2 0.23 0.35, 0.12 16, 18 0.21 40, 72

MOCVD Medium 0.9 7 Graded Graded Constant 900 500 75 £ 75 1.0, 1.1 0.2 NA 104, 111 0.37 NA

MOCVD Low 0.4 5 None None Constant 700 500 20 £ 20 1.0, 1.1 0.09 0.7, 0.06 49, 51 0.25 NA

MOCVD Low 0.2 3 None None Constant 900 500 2 £ 20 1.0, 1.0 0.05 NA 39, 131 0.4 73, 85

Devices are grouped into high, medium and low levels of nitrogen.

Dilute Nitride Semiconductors

Growth technique N level %N % In BE BC Base profile RSH base (V/square) ˚) Base thickness (A Emitter size (mm2) Ideality factor, base, collector VBE reduction (V) Vk ; Voffset (V) Current gain, b; hfe Ldiff (mm) fT ; fmax (GHz)

UCSD—A [18]

Application of Dilute Nitride Materials to Heterojunction Bipolar Transistors 597

Figure 18.11. Collector current density vs. VBE for GaInNAs base HBTs (which are listed in Table 18.3), showing reduction in VBE :

current is present. Figure 18.14 shows the incremental current gain for the range of turn-on voltage reductions being investigated. We have included a few other results from the literature over what is covered in Table 18.3. The general trend (as seen in Figure 18.14) is the degradation of current gain with increased nitrogen incorporation. The work published

Figure 18.12. Comparison of turn-on characteristics for GaInNAs base HBT type E compared to GaAs base, showing a reduction of 50 meV.

598

Dilute Nitride Semiconductors

Figure 18.13. Gummel plots measured for GaInNAs HBTs of device A (from Ref. [2]) and device C.

by Kopin has the widest range in nitrogen composition. Their first work in 2002 [6] mostly dealt with adding a very small amount of nitrogen into the base layer and aimed at reducing the turn-on voltage while keeping low base resistance and high current gain. It was found that current gains comparable to GaAs base HBTs could be achieved by compositionally grading the base layer [28,40,42]. This is further discussed below. Kopin continues to work on incorporating a larger amount of nitrogen into the base layer. The most up-to-date results show a current gain . 100 for a reduction in turn-on voltage of 0.2 eV [28]. The first npn GaInNAs HBT was published in 2000 by the Sandia/Emcore

Application of Dilute Nitride Materials to Heterojunction Bipolar Transistors 599

Figure 18.14. Comparison of incremental current gain vs. reduction in turn-on voltage (compared to GaAs base HBTs) for GaInNAs base HBTs.

team [36]. This device has a low current gain of 5 and was improved upon by band gap engineering at the junctions to achieve an hFE ¼ 18 [37]. The highest nitrogen incorporation of N ¼ 2% results in a low hFE ¼ 8 [18]. Even though it is clear that increased nitrogen incorporation decreases the current gain, it is also clear that by improving the device design (graded base regions, removing barriers at heterojunctions) and improved growth techniques, the gain can be substantially recovered. The sheet resistance achieved in the base differs significantly among growths. For device D, the base sheet resistance is 700 V/square, while for device A it is 7000 V/square (as evaluated by transmission line method measurements on test patterns incorporated on the same wafer as the HBTs). The strong increase in base resistance in device A is presumed to be the result of hydrogen passivation of the beryllium acceptors, that is only incompletely removed by the RTA process (as well as by a lower acceptor incorporation, [Be] ¼ 8 £ 1018 cm23 vs. [C] ¼ 3 £ 1019 cm23 in device D). The decrease in current gain allows a simple estimate of the diffusion length in the GaInNAs base. Following Eq. (18.9), Ldiff is estimated to be of the order of 0.4 mm for ˚ base) and 0.08 mm in device A (400 A ˚ base). The diffusion length is a device E (500 A material parameter that typically depends strongly on the material preparation technique, as well as on the acceptor doping, and in GaInNAs, on the N concentration. The value of Ldiff for device E shows that even for a small amount of N concentration the transport of ˚ , pþ GaAs, is electrons through the base is degraded. The diffusion length for a 500 A 18 23 0.5 mm. The value of Ldiff for device A, which has p , 8 £ 10 cm ; is significantly lower than would be obtained in GaAs of comparable doping, and is presumably limited

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by reduced electron mobility in GaInNAs, as well as by enhanced recombination. Devices B, C, and D have intermediate values of Ldiff corresponding to nitrogen values in-between the levels in devices A and E. GaInNAs HBTs have a lower offset voltage, Voffset ; than SHBTs due to the heterojunction at the base – collector junction. This can lead to an increase in PAE as discussed in Section 18.1. The offset voltage of SHBTs is relatively large because the base –emitter and base – collector heterojunctions are not electrically symmetrical. On the other hand, DHBTs have added symmetry which decreases the offset voltage. This is shown schematically in Figure 18.15. In SHBTs the base –collector is a homojunction; therefore, the diode current will be composed of both electrons and holes, as shown in Figure 18.15. On the other hand, the base – emitter junction in an HBT is a heterojunction with the only significant current contribution from the electrons in the emitter diffusing into the base. The holes are blocked by the valence-band discontinuity. It is the decrease in base –collector current of the DHBT which decreases the offset voltage. Expressions for the offset voltage have been developed taking into account the specific device structure [3,43,44]. The expression for offset voltage can be determined from Ebers – Moll equations [44]:

 kT A kT JCS Voffset ¼ RE IB þ ln C þ ln : ð18:14Þ q q AE aF JES The first term is due to the emitter resistance. The second term is due to the difference in collector and emitter geometries. The third term is from the electrical differences between each junction. For SHBTs the difference in electrical junctions is the dominant term. Figure 18.16 illustrates that Voffset is lower for the transistor with GaInNAs base material. In the GaInNAs device, the band gap of the base is smaller than that of the collector (GaAs); therefore, the hole current is substantially blocked by the valence band barrier between the two materials (which occurs in the same way as hole current blocking by a wide band gap

Figure 18.15. Representative energy band diagram showing current contributions for a (a) homojunction and (b) heterojunction.

Application of Dilute Nitride Materials to Heterojunction Bipolar Transistors 601

Figure 18.16. Measured values of IC vs. VCE for a GaInNAs HBT device D and a reference HBT with a GaAs base. The offset voltage (value of VCE at IC ¼ 0Þ is reduced by almost 100 meV for the GaInNAs HBT. From Asbeck et al., 2002 [2].

emitter). As a result, the turn-on voltage for the base –collector junction is very similar to that of the base – emitter junction, and the offset voltage is minimized. Microwave measurements have been made on a number of GaInNAs devices. These measurements require fabrication of devices with relatively small dimensions (emitter width below 5 mm), to avoid current crowding at the edges of the emitter which results in the device not having uniform excitation at high frequencies. Figure 18.17 shows the measured variation of fT and fmax with current density for device A (2% N, UCSD [18]), device B (1% N, Sandia [37]) and device E (0.2% N, Kopin [2]). The results indicate a corresponding decrease of high-frequency performance with increased nitrogen incorporation. For device D (low nitrogen level) there is a small decrease in fT ; from 78 to 73 GHz, as a result of the GaInNAs base (GaAs base HBT processed at the same time) [2]. If the reduction in fT is attributed entirely to a larger value of base transit time, then the transit time increase is calculated to be 0.14 ps. This modest increase can be expected for a change in minority carrier mobility of the order of 10%. For the case of the moderate nitrogen incorporation, device B [37], good high-frequency performance is still maintained, with fT of 70 GHz and fmax of 38 GHz (data from Figure 18.17). By analyzing the total delay against the inverse collector current, the base transport time can be extracted. From the base transit time the diffusion constant, Dn ; can be found from Eq. ˚ base width. An (18.8) (neglecting vex ). For device B the delay time is 2.7 ps for a 700 A increase of this magnitude would require an electron diffusion constant of Dn ¼ 9 cm2/s. Similar measurements have been done for device A (highest nitrogen incorporation). In this case the peak fT drops to a value of 23 GHz, at lower than usual JC of 2.6 £ 104 A/cm2,

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Figure 18.17. Experimental values of fT and fmax as a function of current density obtained for GaInNAs HBTs with various nitrogen levels. HBT A (UCSD [18]), 2% N, VCE ¼ 1:5 V; AE ¼ 2 £ 3 mm £ 3 mm; HBT B (Sandia [37]), 1% N, AE ¼ 3 £ 14 mm2 ; VCE ¼ 2:2 V; HBT E (Kopin [2]), N ¼ 0:02; VCE ¼ l:5 V; AE ¼ 2 £ 5 mm2 :

due to large emitter parasitic resistance in this particular device [18]. The results ˚ base width, yielding Dn ¼ 6 cm2/s correspond to a base transit time of 2 ps for a 400 A (lower than that of GaAs by a factor of 3– 5). The diffusion constant for GaAs is dependent on the growth parameters and the base dopant level. An interesting feature that has been determined for GaInNAs base HBTs is the temperature dependence of the current gain. For conventional HBTs the current gain typically decreases with increasing temperature T; as a result of higher injection of holes to the emitter, higher space charge layer recombination current, and possible shorter diffusion length in the base. In the GaInNAs device A, a significant increase in current gain is found with increasing T (0.3% increase for each 18C temperature rise, which corresponds with an “activation energy” in an Arrhenius plot of 40 meV) [18]. This result is interpreted as an increase in diffusion length with increasing temperature. Such an effect would be expected if electrons at the bottom of the band are confined in states that are at least partially localized, and with increasing temperature they are thermally excited out of those states to others in which the electrons can diffuse more readily. Compositional grading within the base layer is a design approach intended to minimize the unfavorable effects of GaInNAs bases such as a reduction in current gain and an increase in base transit time, as described in Section 18.2. Initial demonstrations of such devices have already been demonstrated [28,40,42]. Using MOCVD, HBTs were grown

Application of Dilute Nitride Materials to Heterojunction Bipolar Transistors 603

Figure 18.18. Schematic energy band diagram of base region for (a) constant and (b) graded composition.

˚ and 3 £ 1019 cm23 carbon doping level (together with base regions of thickness 500 A with appropriate spacers to remove conduction band barriers). This device design is a modification of device D. The GaInNAs composition was graded to provide built-in quasi-electric fields of the order of 9 kV/cm (shown schematically in Figure 18.18). The devices showed the expected reduction of VBE of 80 meV, while the current gain of the transistor was improved from that of a device with a GaAs base fabricated at the same time. The corresponding current gain measurements are shown in Figure 18.19. RF measurements were subsequently carried out on the devices, which showed that the GaInNAs transistor with a graded base had performance equivalent to that of the GaAs control HBT (with peak fT of 63 GHz at JC ¼ 105 A/cm2). These results suggest that the effects of reduced electron mobility in GaInNAs can be completely overcome with compositionally graded bases.

Figure 18.19. Experimental results of incremental current gain vs. collector current density for a conventional GaAs base HBT, and GaInNAs base HBTs with constant (type D) and graded alloy composition. From Asbeck et al. (2002) [2].

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18.5. CIRCUIT APPLICATIONS FOR GaInNAs HBTs

As discussed in the previous sections, the incorporation of GaInNAs alloys into the base layer of GaAs-based HBTs both lowers the turn-on voltage and enables the implementation of more sophisticated device structures employing built-in drift fields. At a device level, GaInNAs HBTs are characterized by a reduction in turn-on, offset, and knee voltages, higher speed performance, and improved temperature and bias stability [42, 45]. These improvements in device level characteristics can be leveraged in a variety of circuit applications. As GaInNAs HBTs are a drop-in replacement of conventional GaAs HBTs, we highlight in this section several areas in which GaInNAs HBTs can enhance the performance of circuits already utilizing GaAs HBTs. The most obvious application of GaInNAs HBTs is in circuits sensitive to turn-on voltage. Indeed, one of the difficulties designers encounter applying GaAs HBT technology to increasingly complex circuits is the limited number of transistors that can be stacked within a given power supply rail, as discussed in detail in Section 18.1. For wireless applications, the power supply voltage is restricted by the battery technology and overall phone design. The reference current output from circuits such as the one illustrated in Figure 18.3 is sensitive to the device turn-on voltage over temperature. As the temperature drops, the turn-on voltage of any bipolar technology will increase ðdVBE =dT , 21 mV/8C), and for Vref ¼ 2:7 V the InGaP/GaAs HBT will be nonfunctional well before 2 258C (a typical wireless lower temperature specification). Even aside from functionality, the variation in reference current with temperature can be quite large as 2VBE approaches Vref : Figure 18.20 shows the calculated variation in reference current over a wireless temperature specification range as a function of device turn-on voltage [46]. At a standard Vref ¼ 3 V; any incremental reduction in the turn-on VBE of GaAs-based HBTs reduces the variation in reference current. Moreover, a relatively modest turn-on voltage reduction of 100 mV can make the difference of functionality at lower voltage references for GaAs-based HBTs. For hand-held wireless devices, GaAs-based HBTs have emerged as the technology of choice for building power amplifiers. However, to extend battery life, wireless PAs require increasingly efficient, often linear, power amplification at a relatively low bias voltage ðVbias Þ: GaInNAs HBTs offer several desirable characteristics which can enhance PA efficiency and linearity. PAE, a key parameter characterizing the performance of power amplifiers, is related to the knee voltage ðVk Þ and power gain ðGÞ of the RF device, as discussed in detail in Section 18.1. The lower knee voltage characteristics observed in GaInNAs HBTs can be critical for maximizing PAE in wireless PAs, particularly as the voltage drops toward the end of the battery life and Vk consumes an increasingly larger portion of the available voltage swing. The graded base structure enabled by GaInNAs provides an additional means to enhance power gain via increases in the maximum frequency of operation ðfmax Þ: Improved beta stability with temperature and bias, as

Application of Dilute Nitride Materials to Heterojunction Bipolar Transistors 605

Figure 18.20. Calculated variation in reference current over temperature (225 to 1258C) as a function of turnon voltage for four different reference voltages. The room-temperature turn-on voltage of conventional GaAs and demonstrated GaInNAs HBTs are highlighted. Calculations courtesy of P.J. Zampardi [46].

Figure 18.21. Power-added efficiency performance across a wide range of adjacent channel powers of the GaAs and GaInNAs base material structures at 3 V operation under CDMA IS-95 (reverse link) 1.9 GHz modulation. From Yarborough et al. (2002) [45].

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observed in GaInNAs HBTs, has also been associated with improved linearity characteristics [47]. Recently, enhanced CDMA performance from GaInNAs HBTs has been demonstrated by researches at TriQuint [45]. Figure 18.21 summarizes the PAE and linearity characteristics, as measured by adjacent channel power rejection (ACPR), in GaInNAs and conventional GaAs HBTs. The GaInNAs HBTs have demonstrated 1.9 GHz CDMA IS-95 performance of 21 dBm output power (0.31 mW/mm2 – 933 mW/mm), with 18.5 dB associated gain and greater than 53% PAE at 45 dBc ACPR and 3 V operation. This represents an 83 mW/mm increase in output power and 3.8 percentage points improvement in PAE performance relative to InGaP/GaAs HBTs. GaAs-based HBTs have also been employed in high-speed digital circuits, particularly for fiber-optic telecommunication systems [48]. In these applications, GaAs faces stiff competition for SiGe- and InP-based technologies. For high-speed circuits, maximum cutoff frequency ðfT Þ is the RF device figure of merit correlated to many circuit characteristics (e.g. fall, rise, and jitter times). While the total transit time, and hence fT ; is a function of many parameters, including both epilayer design and device layout, base transit time plays a significant role in limiting the performance of GaAs HBTs. As discussed previously, a compositionally graded GaInNAs structure enhances electron transport through the base, leading to faster transit times and higher peak fT : However, the potential benefits of this structure for extending the life of high-speed GaAs HBT technology are only just beginning to be explored [40].

18.6. FUTURE OUTLOOK

The incorporation of GaInNAs in the base of HBTs is a scientifically interesting and commercially important addition to the material and band gap engineering capabilities for III– V compound devices. GaInNAs enables designs with a narrower band gap in the base, which in turn leads to lower VBE ; lower offset voltage and lower knee voltage. The use of an alloy semiconductor in the base allows the introduction of band gap grading, which can be exploited to achieve higher fT and fmax values. This combination of characteristics in the GaInP/GaInNAs/GaAs HBT is very favorable for high-efficiency microwave power amplifiers which operate with relatively small power supply voltages, as expected in battery-operated applications. All of these benefits can be further enhanced by developing still better materials for the base region. There is an opportunity for further efficiency improvement of the order of several percent by additional reduction of the offset voltage. The dc and ac current gain can be improved, and the device capacitance at maximum power (corresponding to charge storage when the transistor saturates) can be reduced further. The turn-on voltage can also be further reduced, to accommodate even lower battery voltages. Such enhancements can be expected by technological improvements, chiefly associated with the base material characteristics. Higher activated dopant

Application of Dilute Nitride Materials to Heterojunction Bipolar Transistors 607 concentrations and higher electron and hole mobilities, for example, are key directions for the future. Fundamental limits (associated with strain in the base and the transport characteristics of GaInNAs) have yet to be reached. It is as yet uncertain how low the VBE voltage may be shifted with GaInNAs materials. Additional reduction of VBE in the order of several hundreds of millivolts can be anticipated. The long-term application requirements for HBTs in portable systems are dependent, to a considerable degree, on developments in battery technology. For modest changes in battery voltage, the GaInNAs approach is very powerful. One of its highly favorable characteristics is the fact that the manufacturing processes are identical to those for conventional GaAs HBTs, thereby minimizing the barrier to adopting the new material technology. However, if there is a future change to batteries with vastly lower voltage (such as 1.5 –2.5 V) it is unlikely that modifications to the basic GaAs HBT structure can be used to reach the needed VBE (, 0.6– 1.2 V) and entirely different material systems (such as InP HBTs) might be the best choice. HBTs on GaAs substrates with base regions of GaAsSb have been suggested as an alternative to GaInNAs base HBTs to provide a lower turn-on voltage than conventional GaAs HBTs [49]. The GaInNAs material system for the base is potentially more flexible than GaAsSb, because it provides the ability to maintain lattice match to the substrate even with substantial change in band gap. It is important to confirm the reliability of the GaInNAs HBTs; the work on which is still in progress. Reliability of HBTs is a central concern, particularly for the demanding application of power amplifiers, where the current density, the junction voltages and the operating temperature all can reach extremes. It is known that to maintain high reliability, GaAs HBTs need to be operated within strict limits on current density, and the limits from long-term reliability considerations are lower than those determined by short-term performance considerations. Degradation in GaAs HBTs at high current density is a complex process, not fully understood, but believed to involve the motion of defects driven by the energy released in electron – hole recombination [50]. Just as was found in the case of semiconductor lasers, it is reasonable to expect that with lower band gap energy of the GaInNAs base, the energy available for defect motion will be smaller, and as a result, lower recombination rates may be found. In conventional GaAs HBTs, recombination at surfaces and at edges of the base –emitter junctions are also known to accelerate degradation. The GaInNAs devices described here provide built-in quasielectric fields as a result of band gap grading that tend to push minority carriers away from surfaces and junction edges. This effect could produce additional benefits in terms of increased reliability. Any improvement in intrinsic reliability could lead to further changes in the design of GaInNAs base HBTs, enabling tradeoffs between design for reliability and design for performance. Thus, the prospects of further improvements in GaInNAs HBTs continue to be exciting.

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ACKNOWLEDGEMENTS

The authors are grateful to Huoping Xin, Kazuhiro Mochizuki, Peter Zampardi, Richard Pierson, James Li, Hong Hou, Nelson Li, Tatsuo Itoh and Frank Chang for many helpful discussions, and for the efforts of the entire Wafer Engineering Group at Kopin Corporation. We also thank Cedric Monier for generously sharing his GaInNAs HBT data. Funding support from the ARO under the MURI Low Power and Low Noise Electronics for Wireless Communications, and from Rockwell Scientific, and from the Air Force Research Laboratory, Sensors Directorate (STTR funding contract #F33615-99-C-1510) is gratefully acknowledged.

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Dilute Nitride Semiconductors performance of NpN InGaP/InGaAsN heterojunction bipolar transistors. Appl. Phys. Lett., 81 (11), 2002. Cooper, C.B., III, Salimian, S. & MacMillan, H.F. (1987) Use of thin AlGaAs and InGaAs stop-etch layers for reactive ion etch processing of III – V compound semiconductor devices. Appl. Phys. Lett., 51 (26), 2225. Seaward, K.L., Moll, N.J., Coulman, D.J. & Stickle, W.F. (1987) An analytical study of etch and etch-stop reactions for GaAs on AlGaAs in CCl2F2 plasma. J. Appl. Phys., 61 (6), 2358. Pang, S.W. & Ko, K.K. (1992) Comparison between etching in Cl2 and BCl3 for compound semiconductors using a multipolar electron cyclotron resonance source. J. Vac. Sci. Technol. B, 10 (6), 2703. Kubaschevski, O. & Alcook, C.B. (1979) Metallurgical Thermochemistry, 5th Edition Pergamon, Oxford. Welty, R.J., Xin, H.P., Mochizuki, K., Tu, C.W. & Asbeck, P.M. (2002) GaAs/Ga0.89In0.11N0.02As0.98/GaAs NpN double heterojunction bipolar transistors with low turn-on voltage. Solid State Electron., 46, 1. Li, N.Y., Chang, P.C., Baca, A.G., Xie, X.M., Sharps, P.R. & Hou, H.Q. (2000) DC characteristics of MOVPE-grown npn InGaP/InGaAsN DHBTs. Electron. Lett., 36 (1), 81. Monier, C., Baca, A.G., Chang, P.-C., Newman, F.D., Li, N.Y., Sun, S.Z., Armour, E. & Hou, H.Q. (2002) Significant operating voltage reduction on high-speed GaAs-based heterojunction bipolar transistors using a low band gap InGaAsN base layer. IEEE Trans. Electron Devices, 49 (8), 1329. Chang, P.C., Monier, C., Baca, A.G., Li, N.Y., Newman, F., Armour, E. & Hou, H.Q. (2002) High-speed InGaP/InGaAsN/GaAs NpN double heterojunction bipolar transistors with low turn-on voltage. Solid State Electron., 46, 581. Welty, R.J. (2002) GaAs-based epitaxial structures for heterojunction bipolar transistors with increased efficiency. Ph.D. Dissertation, Department of Electrical and Computer Engineering, University of California at San Diego, San Diego, CA. Stevens, K.S., Welty, R.J., Welser, R.E., Landini, B.E., Asbeck, P.M., Hung, S.-C., Lu, W-P. & Feng, S.-C. (2004) Impact of compositionally graded base regions on the DC and RF properties of reduced turn-on voltage InGaP/GaInAsN DHBTs. IEEE Trans. Electron Devices, 51 (10). Welser, R.E., DeLuca, P.M., Landini, B.E., Chaplin, M., Stevens, K.S., Brenner, T.L., Welty, R.J., Asbeck, P.M. & Ikhlassi, A. (2001) Pathway for HBT turn-on voltage reduction on a GaAs platform, International Conference on Gallium-Arsenide Manufacturing, Las Vegas, NV, p. 30. DeLuca, P.M., Lutz, C.R., Welser, R.E., Chi, T.Y., Huang, E.K., Welty, R.J. & Asbeck, P.M. (2002) Implementation of reduced turn-on voltage InGaP HBTs using graded GaInAsN base regions. IEEE Electron Device Lett., 23 (10), 582. McAlister, S.P., McKinnon, W.R. & Driad, R. (2001) Interpretation of the common-emitter offset voltage in heterojunction bipolar transistors. IEEE Trans. Electron Devices, 48 (8), 1745. Won, T., Iyer, S., Agarwala, S. & Morkoc, H. (1989) Collector offset voltage of heterojunction bipolar transistors grown by molecular beam epitaxy. IEEE Electron Device Lett., 10 (6), 274. Yarborough, R., Landini, B., Welser, R., Yang, J. & Henderson, T. (2002) Enhanced CDMA performance from an InGaP/GaInAsN/GaAs N – p – N double heterojunction bipolar transistor, IEEE GaAs IC Symposium Technical Digest, p. 273. Zampardi, P.J. (2002) Designers practical view of device technology, IEEE Bipolar Circuit and Technology Meeting, Short Course, Monterey, CA, p. 19.

Application of Dilute Nitride Materials to Heterojunction Bipolar Transistors 611 [47] RF Micro Devices, (2002) A high gain power amplifier with variable bias for multi-mode WCDMA applications. Microwave J., 45 (2), 154. [48] Surridge, R. & Lester, T. (1998) GaInP/GaAs HBT manufacture for 10 Gb/s telecommunications applications, International Conference on Gallium-Arsenide Manufacturing, Seattle, WA, p. 97. [49] Oka, T., Mishima, T. & Kudo, M. (2001) Low turn-on voltage GaAs heterojunction bipolar transistors with a pseudomorphic GaAsSb base. Appl. Phys. Lett., 78 (4), 483– 485. [50] Welser, R.E. & DeLuca, P.M. (2001) Exploring physical mechanisms for sudden beta degradation in GaAs-based HBTs, Proceedings of the GaAs Reliability Workshop, Baltimore, MD, p. 135.

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Index surfactants 13– 16 APDs see anti-phase domains arsenic sources 123– 6 arsenides 1 – 2, 181– 2 atomic characteristics band structure 395– 7 configurations 416, 421– 2, 424– 5, 437– 8 displacements 421– 2, 424– 5, 437– 8 distances 421– 2, 424– 5, 437– 8 geometries 395 nitrogen 4 – 5 pseudopotenials 396– 7 relaxation 71 – 2, 395– 6 scale disorder 183– 4 supercells 394– 409 Auger recombination 26, 521– 3, 526– 31, 544–5

1.2 mm-wavelength range lasers 106– 7 1.3 mm InGaAsN VCSELs 495–503 1.3 mm-wavelength range lasers 107– 12 1.5mm-wavelength range lasers 112– 13 absorption coefficient 559– 60 edge measurements 144– 5 electronic structure 394 isoelectronic dopants 193– 5 spectrometry 193– 4 accelerated degradation 565– 7 accelerated failure (AF) rate 567 AlAs oxide 543 alkyl sources 121– 6 alloy fluctuations 393– 409 alloy scattering 385–7 aluminum free laser epiwafers 110– 11 amplitudes 77, 263– 4 annealing III – V alloy synthesis 332– 4 chemical beam epitaxy 126– 7 GaInNAs 68 – 80, 168– 9, 592– 4 GaInNAsSb 29– 30, 68 – 80 GaNAsSb 478– 83 HBTs 592– 4 long-wavelength lasers 514–17 quantum dots 168– 9 annihilation effects 458 anti-phase domains (APDs) 451, 458 antibonding 433 anticrossing see band anticrossing antimony GaAsBi 214– 15 GaInNAs 29 – 38, 173 GaInNAs VCSELs 502 HRXRD 20 – 8 long-wavelength lasers 507–68 metastable growth 13 – 16 quantum dots 173 RHEED 16 – 18 SIMS 38 – 44

BA see broad-area lasers BAC see band anticrossing band anticrossing (BAC) 325– 54 III – V nitrogen alloys 326– 54 alloy scattering 385– 7 confined state energy 368– 74 effective masses 378– 85 electron concentration 343– 7 experimental evidence 332– 43 GaAsN energy gaps 142– 5 Ga(In)NAs alloys 361– 88 hole concentration enhancement 343– 7 isoelectronic dopants 186– 7, 202–4 localized nitrogen states 326– 54 mobility 385– 7 nitrogen resonant states 374– 85 tight-binding analysis 368– 74 band discontinuities 471– 2, 475– 8 band edge energy deviation 182–5 band offsets X-ray photoelectron spectroscopy 64 – 6 electroreflectance spectroscopy 59 – 61 GaInNAsSb edge-emitting lasers 527– 8, 531

613

614 GaNAsSb alloy 471– 2, 477– 8 InAs quantum dot burial in GaAsN 152 long wavelength alloys 68 photoreflectance spectroscopy 59 – 61 quantum wells 301– 2 band splitting 332– 43 band structure 122– 3, 253– 75, 285– 93, 395– 7 band-to-band transitions 316– 19 bandgap alignment 293– 309 bandgap bowing coefficients 182 –5, 191– 2, 214– 15, 471– 2, 475 GaAs 182– 5 GaAsN 141– 3, 191– 2 Ga(In)NAs 364– 8 GaNAsSb alloy 471– 2, 475 isoelectronic dopants 182– 5, 191– 2, 214– 15 nitrogen concentration 404 bandgap energy band splitting/anticrossing 332– 43 bulk layers 285– 93 electron effective mass 240– 1 GaAsBi 213– 15 GaInNAs alloy 586– 8, 600– 1, 603 GaNAsSb alloy 475– 6, 488 HBTs 488, 586– 8, 600– 1, 603 isoelectronic dopants 182– 5, 190– 9 quantum wells 271– 5, 293– 309 temperature dependence 339– 40 see also energy levels bandgap reduction 405, 416– 17, 586– 9 bandgap shifts 214– 15 bandgaps GaAsBi 212– 15 GaInNAs alloys 112– 13, 579– 81, 586– 8 GaNAsSb alloy 475– 8 HBTs 579–81, 586–8 lattice constants 1 – 2 long-wavelength lasers 509 silicon substrates 454 see also energy levels barrier designs 530– 1 base collector junctions 581, 587– 8, 601 base emitter junctions 581, 583– 4, 587–8, 601

Index base layers 489– 91 base recombination 589 base transit times 589– 91, 601– 2 beam flux gauges 9– 11 beryllium 593 bias asymmetry 12 – 13 bias plates 10 –13, 52– 7, 516– 17 biasing conditions 582 bimodal distribution 183–4 binding energy 245, 316– 19 bipolar reference voltage circuits 582 bismuth 212– 15 blue shift annealing 69, 311 electronic structure 393 GaNAsSb alloy 478– 81 nitrogen concentration 405 nitrogen incorporation 77 – 9 photoluminescence 35 – 6 post-grown annealing 311 bond lengths 183– 4 bonding 183– 4, 417, 422– 3, 431– 3 Born approximation 385– 6 bottom mirrors 545 bound state probing 256–7 bowing coefficients see bandgap bowing Braggs law 19 Brillouin zones 269– 70 broad-area lasers (BA) 106– 8 broadening band anticrossing 328– 9 electroreflectance resonances 283, 307– 9 GaAsN 241, 253– 4 isoelectronic dopants 195– 6, 199, 201– 3, 216 photoreflectance resonances 283, 307– 9 bulk layers 285– 93, 309– 11 burial, quantum dots 150– 4 capacitance-voltage spectroscopy 264– 6 carbon incorporation 514 carriers concentration 591– 4 GaAsN quantum wells 266– 7

Index leakage 521–3, 525– 31, 536– 9 lifetime 67 localization 223–30, 319–21 mobility 362 transport 66 – 8 catastrophic optical damage (COD) 548– 50 cathodoluminescence (CL) 33, 55 – 9 cavity correction 542– 3 cavity length 523– 5, 542–3 CBE see chemical beam epitaxy; conduction band edge CBM see conduction band minimum CER see contactless electroreflectance characterization GaAsN 138– 45 GaAsNSe 148 –9 long wavelength III – V alloys 16 – 66 see also structural characterization/ properties charge 228, 424– 6, 438 chemical beam epitaxy (CBE) 119– 33 contacts 127– 8 GaInNA VCSELs 131– 2 GaInNAs 120, 124– 32 GaInNAs lasers 128– 32 GaNAs band structure 122– 3 LEDs 128 nitrogen alkyl sources 121–2, 123–6 production potentials 132– 3 quantum dots 131 VCSELs 131– 2 chemical bonding 417, 422– 3 chemical disparity 183– 4 chirped superlattices 588– 9 circuit applications 604– 6 CL see cathodoluminescence cluster states (CS) 378– 85, 394– 409 COD see catastrophic optical damage collector current density 583– 4, 589– 90, 595–7 communication systems 471– 2, 485– 8, 495–503, 606 complex structures 79 – 80, 173, 415– 47 compositional grading 602–3

615 composition-pinning levels 403 conduction 269 –75 conduction band edge (CBE) 334– 6, 361– 88 conduction band minimum (CBM) 230, 340–3, 431– 6 conduction bands barriers 588– 9 density of states singularities 187 disordered Ga(In)NAs 378– 85 dispersion 361 GaAsN quantum wells 255– 6, 259– 64 InGaAsN 230 offsets 65 – 6, 301– 2 perturbation 206 quantum wells 255–6, 259–64, 361 states 207– 11, 326– 54 symmetry-induced splitting GaAs 188 see also L-conduction bands confined states 293– 309, 368– 74 confinement factors 554–6 contactless electroreflectance (CER) 280 contacts 127– 8, 499, 594– 5 covalent radius difference 184– 5 critical point energy 193– 4 critical thickness 141, 162– 3, 585– 6 cross-sectional transmission electron microscopy 47– 57, 453 crystal quality/composition 43 – 4 CS see cluster states current base layers 489– 91 collector density 583– 4, 589– 90, 595– 7 edge-emitting lasers 520– 1 gain 589, 595– 600, 602– 3 injected balance 536 lifetime testing 564– 6 resonant enhancement 258– 9 see also threshold current density CW high power lasers 550– 2 damping coefficient 556– 778 damping factors 553, 556 dangling bonds (DB) 431– 2 dark line effects 563– 4 dark spot effects 563– 4

616 dark-field transmission electron microscopy (DFTEM) 47, 49– 57 DB see dangling bonds DBRs see distributed Bragg reflectors deep level transient spectroscopy (DLTS) 61 – 4 defects 61 – 4, 79 – 80 deflection plate bias 10 – 13, 52 – 7, 516– 17 degradation 6, 99 – 100, 565– 7 delocalization 122– 3, 403– 4 density 163– 4, 183– 4, 365– 6 of states (DOS) 157– 8, 187, 226– 7, 330– 1 see also threshold current density Density Functional Theory –Local Density Approximation (DFT – LDA) 417– 18 design issues 530– 1, 547– 8, 579, 585– 91 devices application 461– 7 design 530– 1, 547– 8, 579, 585– 91 processing 591– 5 structures 519– 20 DFTEM see dark-field transmission electron microscopy DFT – LDA see Density Functional Theory – Local Density Approximation di-hydrogen nitrogen – hydrogen complexes 420– 1, 424– 7 diagonal Green’s function 328 diamagnetic shift 228– 9, 242, 245– 6 dielectric function perturbation 281 differential gain 554–7 diffusion constant 601– 2 interdiffusion 78, 478– 81 lengths 67, 591, 599–600 digital alloying 543– 4 digital circuits 606 dimethylhydrazine (DMHy) 95, 98 – 9, 102– 3, 123– 4 diodes laser diodes 129– 31, 170– 2 light emitting diodes 128, 393, 451, 463– 4 resonant tunnelling diodes 254– 9, 264– 9 dipole moments 419

Index dislocation generation 452– 4 dislocation-free III – V alloys 451– 68 device application 461–7 growth 456– 61 disorder GaNAs structures 378– 85 isoelectronic dopants 183– 4 nitrogen resonant states 374–8 dispersion 329, 368– 74, 383– 5 distributed Bragg reflectors (DBRs) 495– 9, 510, 541– 7 ditertiarybutylselenide (DtBSe) 127–8 DLTS see deep level transient spectroscopy DMHy see dimethylhydrazine doping GaInNAs HBTs 588–9 germanium doped GaNAs 353 long wavelength alloys 66 selenium-doped GaInNAs 344– 6, 349– 50 silicon doped GaInNAs 347– 50 silicon doped GaNAs 62 see also isoelectronic dopants DOS see density of states dot size 164, 166–7 see also quantum dots double heterostructure light emitting diodes 451, 463– 4 DtBSe see ditertiarybutylselenide edge conduction bands 334– 6, 361– 88 edge emitting lasers 120, 517– 31 edge energy deviation 182– 5 edge measurements 144– 5 effective mass band anticrossing 362– 3, 372– 4, 378– 85 confined state energy 372–4 disordered GaNAs 378– 85 long wavelength alloys 67 – 8 pressure dependence 338– 9 see also electron... efficiency GaInAsN lasers 110 power-added 581, 605– 6 quantum 518, 523– 31, 544– 5 quantum dots 153 –4

Index EFTEM see energy-filtered transmission electron microscopy elastic deformation epitaxy 139 electra-modulated reflectance GaAs 188– 206 electrical resistance 544 electroabsorption modulators 558– 62 electroflectance, GaAsBi 212–13 electromodulation 279– 321 electron... concentration 343– 7, 349– 50 conduction 271– 5 confined state energy 361 damage 515– 17 density fluctuations 183–4 hole pair recombination 223–4, 227– 30 lifetime recombination 589– 90 penetration depth 56 plasma source induced ion damage 9 –13 relative effective mass 362– 3 spectroscopy for chemical analysis (ESCA) 64 – 6 traps 62, 228 wave function 241– 2 electron effective mass 404– 5 band anticrossing 330– 1, 362– 3, 372– 4, 378–85 confined state energy 372– 4 disordered Ga(In)NAs 378– 85 InGaAsN 223– 4, 230– 2, 344– 7 magneto-photoluminescence 223– 4, 230–47 quantum wells 293–309, 372– 4 tight-binding analysis 362– 3, 372– 4, 378–85 electron mobility alloy scattering 385– 7 band anticrossing 329– 30, 347– 8 GaAsN quantum wells 271– 5 GaInNAs HBTs 579, 591, 603 long wavelength alloys 66 – 7 electronegativity differences 184– 5, 326 electronic charge 424, 438 electronic structure/properties III – V nitride alloys 393– 409 empirical pseudopotential method 394–7

617 GaAsN quantum wells 253– 75 InGaAsN 223– 48 magneto-tunneling spectroscopy 253– 75 nitrogen effects 326– 54 nitrogen – hydrogen complexes 417 nitrogen-induced perturbations 291 novel 343– 53 resonant tunnelling diodes 254– 9 electroreflectance (ER) III – V nitrogen compounds 279– 321 bulk layer band structure 285– 93 electromodulation principles 280– 5 isoelectronic dopants 188– 206 long wavelength alloys 59 – 61 nitrogen incorporation 75 – 6 post-grown annealing 309–16 quantum wells 293–309 resonances 307– 9 step-like quantum wells 302– 5 emission decay time 405 empirical pseudopotential method (EPM) 394–7 energy band edge deviation 182– 5 binding 245, 316– 19 confined state energy 368– 74 critical point 193– 4 dispersion 368– 74 Fermi 330, 344– 5, 418–19, 428–31, 446–7 formation 417–18, 423, 427– 31, 435– 6, 439–41, 446–7 levels Ga-centered nitrogen clusters 399 GaAs 296– 9, 302– 6 GaAsN 141–5, 271– 5 GaAsNSb 305– 6 GaAsSb 305– 6 GaInNAs HBTs 600– 1, 603 GaInNAs MOMBE 147 GaInNAs quantum wells 294– 9, 302–6 GaInNAsSb 305– 6 long wavelength alloys 66 –8 nitrogen chains in GaP 399 quantum wells 271– 5, 293– 309 step-like quantum wells 302– 5

618 localization phenomena 33 – 4 nitrogen –hydrogen complexes 421– 7 shifts 195, 240, 242– 3 subband inflection points 269– 70 wavevector dispersion 259– 64 see also bandgap.energy; transition.energy energy-filtered transmission electron microscopy (EFTEM) 47 – 8, 51, 53 epilayers 223– 4, 233– 5, 237 epiwafer production 132– 3 EPM see empirical pseudopotential method ER see electroreflectance ESCA see electron spectroscopy for chemical analysis EXAFS see extended X-ray absorption fine structure excitons binding energy 245, 316– 19 bound states 181– 2 diamagnetic shift 242, 245– 6 energy shift 242– 3 radius 223– 4, 230– 47, 344– 7 size 223– 4, 230– 47, 344– 7 transitions 316– 19 wave function size 223– 4, 230– 2, 344– 7 experimental progress in quantum dots 161– 72 exponential density of states 226– 7 extended X-ray absorption fine structure (EXAFS) 70 – 4 extended conduction band states 326– 54 fabrication see growth Fabry –Perot reflection modulators 560– 1 Fermi.energy 330, 344– 5, 418– 19, 428– 31, 446– 7 Fermilevel pinning 525, 535– 6 Fermi wavevectors 330 fiber-optical communications 495– 503, 606 figure of merit 581– 5, 596 fitting parameters 142– 3 forbidden energy gaps 393 formation energy 417– 18, 423, 427– 31, 435– 6, 439– 41, 446– 7

Index Fourier transform infrared (FTIR) absorption spectroscopy 69 –70 Frank –Van der Merwe conditions 17 Free carrier concentration 591– 4 Freeexciton recombinations 232–43 Free hole recombination 223– 4, 227– 30 free electron concentration GaInNAs 349– 50 free electron mobility 329– 30 free electron to carbon acceptor recombinations 232– 43 frequency oscillation 590–1 resonance 554 vibrational 441– 4 see also radio... FTIR see Fourier transform infrared Ga-centered nitrogen clusters 399 GaAs active regions 495, 498– 9 electron effective masses 372– 4 energy levels 296– 9, 302– 6 HBTs 580–1 hydrogen impurities 444– 6 intrinsic nitrogen impurities 444–6 isoelectronic dopants 179– 218 laser performance 105– 13 long-wavelength lasers 486– 8 MOVPE 105– 13 nitrogen incorporation 6 – 8, 13 – 14 nitrogen –hydrogen complexes 444– 6 quantum wells 25, 27 – 8, 296– 9, 302– 6, 372– 4 GaAsBi 212– 15, 217 GaAsN band anticrossing 361– 88 band structure 122– 3, 259– 64 bulk layer band structure 285– 93 carrier localization 319– 21 chemical beam epitaxy 122– 33 defects 61 – 4 disorder influence 374– 8 electron concentration 346– 7 electron effective mass 232– 43 electronic structure 400–3

Index energy gaps 141–5 epilayers 223– 4, 233– 5, 237 exciton size 232– 43 heterogeneous behaviour 393– 409 InAs quantum dot burial 150– 4 isoelectronic dopants 179– 218 molecular beam epitaxy 472– 5 MOMBE 137– 54 n-type scattering cross-sections 361– 2 nitrogen resonant states 364– 8 nitrogen – hydrogen complexes 416– 47 NRA-RBS 44 – 7 quantum wells 230–6, 253 –75, 293– 309, 372–4 conduction bands 259– 64 electron effective mass 230– 1, 372– 4 electroreflectance 293–309 magneto-photoluminescence 233– 4, 236 magneto-tunneling spectroscopy 253– 75 photoreflectance 293– 309 resonant tunnelling diodes 254– 9 tight-binding analysis 361– 88 GaAsNGe layers 351– 3 GaAsNSb annealing 478– 83 band discontinuities 471– 2, 475– 8 band offsets 471–2, 477– 8 bandgaps 475–8 blue shift 478– 81 electronic structure 408– 9 energy levels 305– 6 growth 471– 5 growth parameters 23 – 5 HBTs 471– 2, 482– 3, 488– 91 lasers 471– 2, 485– 8 long-wavelength lasers 485–8 molecular beam epitaxy 472– 5 photoluminescence 35 – 8 quantum wells 305–6 quinary alloy 483– 5 reciprocal space maps 24 – 8 SIMS 38 – 44 telecommunication lasers 471– 2, 485– 8 transition energy 476– 7 GaAsNSe 127– 8, 137– 8, 148– 9 GaAsPN 407–8

619 GaAsSb energy levels 305– 6 long-wavelength lasers 507–68 annealing 514–17 growth 511– 14 ion damage 515– 17 spontaneous emission 532– 9 quantum wells 305–6 gain coefficients 527 GaInAs 57 – 9, 106– 7, 160 GaInNAs alloy scattering 385– 7 annealing behaviour 68 – 80 band anticrossing 361– 88 bandgap reduction 416– 17, 446 bulk layer structures 285– 93, 309– 11 carrier localization 319– 21 cathodoluminescence 57 – 9 chemical beam epitaxy 120, 124– 32 deep level transient spectroscopy 63 – 4 electronic structure 394– 5 electroreflectance 59 – 61, 293– 309, 311–16 energy levels 294– 9, 302– 6 HBTs 579– 608 circuit applications 604– 6 device design 579, 585– 91 device processing 591– 5 growth 591– 5 heterogeneous behaviour 393– 409 heterostructures carrier localization degree 223– 30 electron effective mass 223– 4, 230– 2, 344–7 electronic properties 223– 48 exciton size 223– 4, 230– 2, 344– 7 HRTEM 47 – 57 HRXRD 20 – 8 lasers chemical beam epitaxy 128–32 laser diodes 129– 31 laser performance 105– 13 MOVPE 107–13 quantum dots 131, 160 VCSELs 131 –2, 495– 503 long wavelength lasers 107– 13, 160

620 molecular beam epitaxy 4 – 6, 472– 5 MOMBE 137– 8, 145–8 MOVPE 94 – 105 n-type scattering cross-sections 361– 2 nearest neighbor effects 68 – 80 nitrogen incorporation 68 – 80 nitrogen resonant states 364 –8 nitrogen –hydrogen complexes 446 NRA-RBS 46 – 7 photoluminescence 29 – 38 photoreflectance 59 –61, 293–309, 311– 16 plasma source induced ion damage 8 – 13 post-grown annealing 311– 16 quantum dots 131, 160– 72 quantum wells 129– 31, 293– 309, 311–16, 361 RHEED 17 – 18 short-range ordering 406– 7 SIMS 38 – 44 square quantum wells 361 tight-binding analysis 361– 88 VCSELs 131– 2, 495– 503 GaInNAsSb annealing behaviour 68 – 80 bulk layer band structure 285– 93 cathodoluminescence 57– 9 edge-emitting lasers 517– 31 barrier designs 530– 1 cavity length 523– 5 device structures 519– 20 quantum wells 530– 1 temperature sensitivity 520– 3, 525–8 threshold parameters 528– 30 electroabsorption modulators 558– 62 electroreflectance 59 – 61, 293– 309 energy levels 305– 6 high power lasers 547– 52 HRTEM 47 – 57 HRXRD 20 – 8 lasers 507– 68 long-wavelength lasers 507– 68 annealing 514– 17 edge-emitting 517– 31 electroabsorption modulators 558– 62 growth 511–14

Index high power lasers 539– 47 ion damage 515– 17 reliability 558– 62 saturable absorbers 558– 62 spontaneous emission 532– 9 VCSELs 539– 47 nearest neighbor effects 68 – 80 nitrogen incorporation 68 – 80 NRA-RBS 46 – 7 photoluminescence 29 – 38 photoreflectance 59 –61, 293–309 quantum wells 293– 309 saturable absorbers 558– 62 SIMS 38 – 44 VCSELs 539– 47 GaInNAsSe films 344–6, 349–50 GaInNAsSi 347–8 GaInP laser performance 105– 13 gallium vacancies 64 GaNAs see GaAsN GaNAsSb see GaAsNSb GaP 181– 2, 444– 6 GaPN 393– 409, 444– 7 gas phase composition 98 – 100, 102– 3 gas-source molecular beam epitaxy (GSMBE) 161– 4 Gaussian line shapes 282– 4 germanium doped GaNAs layers 351– 3 Green’s function 327– 8, 331– 2 growth conditions 140– 1 dislocation-free III – V nitrogen alloys 456– 61 GaAsN 138– 45 GaAsNSe 148– 9 GaInNAs 96 – 105, 579, 591– 5 GaInNAs HBTs 579, 591– 5 GaNAsSb alloy 471– 5 gas-source MBE 138– 45 kinetics 165 precursors 94 – 6, 101 rates 100– 1 solid-source MBE 161– 4, 170–2 strained quantum dots 157– 9 temperature 37 – 8, 168

Index see also chemical beam epitaxy; metalorganic molecular beam epitaxy; metal-organic vapour phase epitaxy; molecular beam epitaxy GSMBE see gas-source molecular beam epitaxy Hall bars 271 Hall mobility 593 Hamiltonians 245, 327, 361, 375, 397 hand-held wireless devices 604– 5 HBT see heterojunction bipolar transistors heat removal 549 heat sinking 520– 3, 550 height 158– 9, 163– 4 heterogeneous localization centers 393– 409 heterojunction band offsets 59 – 61, 64 – 6 heterojunction bandgap alignment 294 heterojunction bipolar transistors (HBT) circuit applications 604–6 device design 579, 585– 91 device processing 591– 5 GaInNAs alloys 579– 608 GaNAsSb alloys 471– 2, 482– 3, 488– 91 growth 591– 5 turn-on voltages 471– 2, 488– 91 heterostructure ridge-waveguides 519– 20 high energy electron beams 55– 9 high power lasers 547– 52 high resolution X-ray diffraction (HRXRD) 18– 28, 472– 4 high resolution transmission electron microscopy (HRTEM) 47 – 57 high speed digital circuits 606 higher conduction band minima effects 340– 3 holes concentration enhancement 343– 7 effective mass 229– 30 leakage 531 mobility 66 – 7, 579, 591 traps 61 –2 host states 394, 400– 3 HRTEM see high resolution transmission electron microscopy

621 HRXRD see high resolution X-ray diffraction hybridization 327, 329– 32, 361– 2 hydrogen assisted GaInNAs quantum dots 173 bandgap tuning 224 concentration 124, 239–40 impurities 444– 6 incorporation 513–14, 591–4 passivation 416– 47 III – V alloys band anticrossing 326– 54 mutual passivation 348– 53 novel electronic properties 343– 53 transport properties 343– 53 dislocation-free 451– 68 electronic structure 393– 409 lattice constants 1 – 2, 451, 454– 7, 459 long wavelength characterization 16 – 66 nitrogen – hydrogen complexes 415– 47 ratio 103– 5 silicon substrates 451– 68 device application 461– 7 lasers 451, 464– 5 lattice-mismatched heteroepitaxy 452– 6 light emitting diodes 451, 463– 4 OEICs 451, 466– 7 solar cells 451, 465– 6 III – V compounds electroreflectance 279– 321 lattice-mismatched heteroepitaxy 454–6 MOMBE 137– 54 photoreflectance 279– 321 impurity clusters 397– 409 impurity pair energy levels 403 in-plane hole effective mass 229–30 in-plane strain 20 InAs quantum dots 149– 54, 498 indium cathodoluminescence 57 – 9 electronic properties 223– 48, 300 GaInNAs MOMBE 145– 8 heterostructures 223– 48 InP 495, 497– 8, 512 InSbN 408

622 long wavelength lasers 160 magneto photoluminescence 223– 48 SIMS 38 – 44 VCSELs 495– 503 inflection points 269– 70 information processing 451 infrared (IR) spectroscopy 441– 2 injected current balance 536 InP 495, 497– 8, 512 InSbN 408 integrated intensity 28 – 9 intensity ratio 197– 8, 215– 16 intensity resonance 207– 10 interband coupling 184, 216 interdiffusion 78, 478– 81 intermediate layers 169– 70 intermediate nitrogen concentration 397, 400– 4 intra-cavity contacts 499 intraband coupling 184, 216 intrinsic carrier concentration 583– 4 intrinsic nitrogen impurities 444– 6 ion channelling 46– 7 ion damage 8 – 13, 515– 17 ion implantation 332– 4 ionized net donor concentration 345– 6 IR see infrared isoelectronic dopants in GaAs L-conduction band splitting 188 band anticrossing 186– 7 bandgap dependence 190– 9 bismuth 212– 15 complementary alloys 212– 15 conduction band states 187, 207– 11 density of states 187, 207– 11 electroreflectance 188– 206 nitrogen impurities 180– 2 physics 179– 218 resonant Raman scattering 207– 11 virtual crystal approximation failure 182– 5 zone-center optic phonons 207– 11 isoelectronic dopants in GaAsN 179– 218 isoelectronic electron traps 228 isolated impurities 385– 7

Index isomorphous models 394 isovalent impurity energy levels 326 K factor 556– 7 k-space integration 419 kinetics 145, 165 KKA see Kramers – Kronig analysis knee voltages 579, 604– 5, 607 Kramers – Kronig analysis (KKA) 283– 4, 314– 15, 319– 21 L-conduction bands isoelectronic dopants 188, 206, 210– 11, 216 magneto-tunneling spectroscopy 253– 4 nitrogen induced effects 341–2 perturbation 206 symmetry-induced splitting 188 LAN see local area networks Landau electron levels 235– 6 Langmuir probes 9 – 11 large-scale atomistic supercell calculations 394 lasers III – V alloys on silicon substrates 451, 464– 5 chemical beam epitaxy 128– 31 GaNAsSb alloy 471– 2, 485– 8 heterogeneous localization centers 393 laser action losses 521– 3 laser diodes 129– 31, 170– 2 quantum dots 131, 159– 60 see also long wavelength lasers; vertical cavity surface emitting lasers lattices constants 1 – 2, 139– 40, 451, 454– 9, 509 heteroepitaxy 452– 6 HRTEM 48 – 55 matching 119– 20, 184, 216– 17, 452– 4, 585– 6 parameters 19 – 20, 112– 13, 139– 41 relaxation 20, 138– 41, 433– 5, 452– 4 spacing 19 layer thicknesses 542– 3, 585– 6 LCINS see linear combination of isolated nitrogen resonant states

Index LEDs see light emitting diodes leverage factors 257, 262– 4 lifetime testing 564– 6 light emitting diodes (LEDs) 128, 393, 451, 463–4 light excitation energy 267– 9 light– voltage – current curves 520– 1, 548 line shapes 28 – 9, 31 – 2, 34 – 5, 282– 4 linear combination of isolated nitrogen resonant states (LCINS) 361– 88 linewidth 28 – 9, 31 – 2 local area networks (LAN) 507, 509 localization phenomena degree of carriers 223– 30 impurity levels 398 isoelectronic states 337– 40 nitrogen states 326– 54 photoluminescence 32 – 6 long wavelength alloys characterization 16 – 66 X-ray photoelectron spectroscopy 64– 6 carrier transport 66 –8 cathodoluminescence 33, 55 – 9 cross-section TEM 47 – 57 dark-field TEM 47, 49 – 57 deep level transient spectroscopy 61 – 4 electroreflectance 59– 61 energy band properties 66 – 8 energy-filtered TEM 47 –8, 51, 53 HRTEM 47 – 57 HRXRD 18 –28 NRA-RBS 44 – 7 N – H complex defects 79 – 80 photoluminescence 26, 28 – 38 photoreflectance spectroscopy 59 – 61 Rutherford backscattering 44 – 7 SIMS 38 – 44 molecular beam epitaxy 1 – 16 long wavelength lasers dilute nitride-antimonide 507– 68 annealing 514 –17 Auger recombination 521– 3, 526– 31, 544–5 carrier leakage 521– 3, 525– 31, 536– 9

623 electroabsorption modulators 558– 62 electron damage 515– 17 Fermi-level pinning 525, 535– 6 GaInNAsSb edge-emitting lasers 517– 31 high power lasers 547– 52 ion damage 515– 17 MBE 511– 14 MOVPE 511–14 quantum efficiency 518, 523– 31, 544– 5 recombination/carrier leakage 521– 3, 525–31, 536–9 relative intensity noise 552– 7 reliability 562– 7 saturable absorbers 558– 62 spontaneous emission 522– 3, 532– 9 threshold parameters 520– 31 VCSELs 539 –47 fiber-optical communications 495– 503 GaAs-based lasers 105– 13, 485– 8 MOVPE 105– 13 quantum dots 159– 60 longitudinal resistivity 270– 4 Lorentz force 259 Lorentzian line shapes 282– 4 low dimensional structures 279– 321 lowest occupied molecular orbitals (LUMO) 433–4 luminescence cathodoluminescence 33, 55 – 9 efficiency 153– 4 isoelectronic dopants 193– 4 see also photoluminescence LUMO see lowest occupied molecular orbitals magnetic dependence 261 –4, 273– 4 magneto-photoluminescence 223–48 magneto-tunneling spectroscopy (MTS) 253–75 MAN see metro area networks matching conditions 561– 2 material quality degradation 99 – 100 maximum electron concentration enhancement 343– 7

624 MBE see molecular beam epitaxy metal-organic chemical vapor deposition (MOCVD) 63– 4, 591– 2, 594 metal-organic molecular beam epitaxy (MOMBE) III – V compounds 137– 54 GaAsN 137– 54 GaAsNSe 148– 9 InAs quantum dots 149– 54 indium incorporation 145– 8 nitrogen incorporation 138– 41, 145– 8 see also chemical beam epitaxy metal-organic vapour phase epitaxy (MOVPE) GaInAsN 94 – 105 long wavelength alloys 2 long wavelength lasers 105– 13, 511– 14 molecular beam epitaxy 93 – 114 MOMBE 137 metastable growth 13 – 16 metro area networks (MAN) 507, 509 microwave measurements 601– 2 microwave power gain 590– 1 minority carriers 594 Mio cumulated equivalent device hours 501 miscibility gaps 121 MMHy see monomethylhydrazine mobility band anticrossing 385– 7 carrier 362 Ga(In)NAs 385– 7 Hall mobility 593 holes 66 – 7, 579, 591 long wavelength alloys 66 – 7 tight-binding analysis 385– 7 see also electron mobility MOCVD see metal-organic chemical vapor deposition modulation spectroscopy 279– 321 molecular beam epitaxy (MBE) GaInNAs 499, 591– 3 GaNAs defects 61 – 4 GaNAsSb alloy 472– 5 HBTs 591–3 long wavelength alloys 1 – 16 long-wavelength lasers 511– 14

Index MOVPE 93 – 114 VCSELs 499 molecular nitrogen 4 – 5 MOMBE see metal-organic molecular beam epitaxy monatomic hydrogen in GaAsN 420– 4, 435– 6 monomethylhydrazine (MMHy) 124– 5, 138, 145– 7 MOVPE see metal-organic vapour phase epitaxy MTS see magneto-tunneling spectroscopy mutual passivation 348– 52, 353 n doping effects 430 n-type scattering cross-sections 361– 2 narrow bandgap alloys 160 narrow-stripe ridge lasers 110– 11 nearest neighbor effects 68 – 80 NF3 growth precursors 95 – 6 nGaNAs 62, 63 nitride-antimonide lasers 507– 68 see also long wavelength lasers nitrogen L-conduction band energy 341– 2 alkyl sources 121– 2, 123– 6 chains in GaP 399 concentration bandgap dependence 190– 9 electron effective mass 237– 9, 245– 6, 300 electronic structure 397, 400– 5 GaAsN energy gaps 141– 3 InGaAsN heterostructures 223 MOMBE 137– 41 NRA-RBS 45 – 7 SIMS 38 electronic band structure 291, 326– 54, 397, 400– 5, 431– 6 growth precursors 94 – 6 incorporation CBE 121–2, 123–6 GaInNAs 94 – 105, 145– 8, 164 MBE 6 – 8 MOMBE 138– 41, 145– 8

Index nearest neighbor effects 68 – 80 quantum dots 164 isoelectronic impurities 180– 2 out-diffusion 78 perturbations 291 photoluminescence 167– 8 plasma sources 3 – 6, 8 – 13, 126 resonant states 364–8, 374 –8 structural effects 436– 9 wavelength (effect on) 165–6 nitrogen –hydrogen complexes 415– 47 defects 79 – 80 GaAs 444– 6 GaAsN 416– 47 GaInNAs 446 GaPN 446– 7 non-lithograph fabrication 173 non-radiative recombination 525, 550 novel electronic properties 343–52, 353 novel optical transitions 185–218 npn GaInNAs HBTs 595– 606 nuclear reaction analysis-Rutherford backscattering (NRA-RBS) 44 – 7 OEICs see optoelectronic devices and integrated circuits offset voltages 579, 600– 1, 607 ohmic contacts 594– 5 operating temperatures 111– 12 optical characteristics data transmission 495– 503 excitation 258– 9 losses 499 properties 165– 8 transitions 185– 218, 334– 40 see also bandgap bowing optoelectronic devices and integrated circuits (OEICs) 451, 466– 7 oscillation frequency 590– 1 out-diffusion 78 out-of-plane strain 20 overpressures 23 – 4, 42 – 3 p doping effects 61 – 3, 430 PAE see power-added efficiency

625 PC see photocurrent peak intensity 28 –9, 32 – 5 peak intensity wavelength 28 – 9 penetration depth 56 perturbed host states (PHS) 394, 400–3 pGaNAs 61 – 2, 63 phosphides 181– 2 photo-emitting devices 393 photocurrent (PC) spectroscopy 264, 267– 9 photoluminescence excitation (PLE) 394 photoluminescence (PL) chemical beam epitaxy 122– 3, 126– 7, 128–30 electronic properties 223– 48, 264, 266– 7 electronic structure 393– 4 GaAsN 122– 3, 264, 266– 7 GaInNAs 167– 8, 223– 48 GaNAsSb alloy 478– 9, 483 heterogeneous localization centers 393– 4 isoelectronic dopants 205 long wavelength alloys 26, 28– 38 magneto-photoluminescence 223– 48 nitrogen incorporation 75 – 7 plasma source induced ion damage 8 –9, 13 quinary GaNAsSb alloys 483 photoreflectance (PR) III – V nitrogen compounds 279– 321 apparatus 284– 5 bulk layer band structure 285– 93 carrier localization 319– 21 electromodulation principles 280– 5 exciton binding energy 316– 19 Ga(In)NAs 309–16, 376–7 GaNAsSb alloy 478– 9 long wavelength alloys 59 – 61 nitrogen incorporation 70 post-grown annealing 309–16 quantum wells 293–309 resonances 307– 9 step-like quantum wells 302– 5 PHS see perturbed host states physics of isoelectronic dopants 179–218 pinning 403, 525, 535– 6 PL see photoluminescence plasma sources 3 – 6, 8 – 13, 126

626 PLE see photoluminescence excitation polarization 532–3 polymorphous models 394– 409 positron annihilation 64 post-growth annealing 31, 126– 7, 309– 16 hydrogen irradiation 223 linewidths 31 potential profiles 266– 7 power lifetime testing 564–6 power-added efficiency (PAE) 581, 605– 6 PR see photoreflectance pressure band splitting/anticrossing 336– 40 electronic structure 398–400, 403–4 energy gaps 144 intermediate nitrogen concentration 403– 4 MOVPE 102– 3 probability density 365– 6 production potentials 132– 3 pseudopotenials 395– 7 pulsing doping GaInNAs HBTs 588– 9 GaInNAsSb lasers 545– 7, 551– 2 laser annealing 332– 4 quantum confined Stark effect (QCSE) 558– 9 quantum dots burial 150– 4 experimental progress 161– 72 future challenges 173– 4 GaInNAs-based VCSELs 498 InAs 149– 54 lasers 131, 159– 60 prospects 160– 1 recent progress 157– 74 self-organised 157– 9, 161– 3 strained fabrication 157– 9 quantum efficiency 518, 523– 31, 544– 5 quantum wells bandgap energy 271– 5, 293– 309 barriers 486– 8 bound states 254, 255– 9 broadening 253– 4 conduction bands 255– 6, 259– 64, 361

Index confined state energy 368–74 edge-emitting lasers 530– 1 electron effective mass 230– 1, 372– 4 electronic properties 223–4 electroreflectance 293– 309 energy levels 271– 5, 293– 309 GaAsN 230– 6, 253– 75, 293– 309, 372– 4 laser diodes 129– 31 long wavelength characterization 48 –55 magneto-photoluminescence 233– 4, 236 magneto-tunneling spectroscopy 253– 75 NRA-RBS 46 – 7 photoreflectance 293– 309 resonant tunnelling diodes 254– 9 step-like 302– 5 subband states 259– 64 quaternary alloys 394– 5, 406– 8 quinary GaNAsSb alloys 483– 5 radial distribution functions (RDF) 73 – 4 radiative recombination 223– 4, 227– 30, 525, 550 radio frequency (RF) measurements 603 radio frequency (RF) plasma cells 3 –6, 472 Raman scattering 207– 11, 216 rapid thermal annealing (RTA) 29 – 30 RBS see Rutherford backscattering RDF see radial distribution functions reactive surfactants 15 reciprocal space 235– 6 reciprocal space maps (RSMs) 20, 24 – 8 recombination Auger 26, 521– 3, 526– 31, 544– 5 carrier leakage 521– 3, 525– 31, 536– 9 electron lifetime 589– 90 electron-hole pair 223– 4, 227– 30 free electron to carbon acceptor 232– 43 free exciton 232– 43 free hole 223– 4, 227– 30 GaInNAs HBTs 579, 589 radiative recombination 223– 4, 227– 30, 525, 550 red shift 32, 146, 151– 3, 403 reduced temperature dependence 143– 5

Index reflection high energy electron diffraction (RHEED) 16 – 18, 460– 1 reflectivity 281– 2, 560– 1 relative intensity 198 relative intensity noise (RIN) 552– 7 relaxation atomic 71 – 2, 395– 6 empirical pseudopotential method 395–6 lattices 20, 138– 41, 433– 5, 452– 4 reliability 558– 67, 607– 8 research directions 159 resistance contacts 127– 8 electrical 544 sheet 590– 1, 599 thermal 567 resistivity 270– 4 resonance frequency 554 resonant energy 364– 8 resonant Raman scattering 207– 11, 216 resonant tunnelling diodes (RTDs) 254, 255–9, 264– 9 resonant wave functions 367– 8 retarded Green’s function 327– 8 RF see radio frequency RHEED see reflection high energy electron diffraction ridge-waveguides 519– 20 RIN see relative intensity noise room temperature photoluminescence (RT-PL) 28 – 9 RSMs see reciprocal space maps RTA see rapid thermal annealing RTDs see resonant tunnelling diodes RT-PL see room temperature photoluminescence Rutherford backscattering (RBS) 44– 7 S-matrix theory 385 S-shaped behavior 32 – 5 SAN see storage area networks saturable absorbers 558– 62 scale of energy controls 262– 4 scanning electron microscopes (SEM) 57 –9

627 scattering cross-section 385–7 Schro¨dinger’s equation 368– 9 secondary-ion mass spectroscopy (SIMS) 38– 44, 474, 593 segregation 43 selenium-doped GaInNAs 344– 6, 349– 50 self-annihilation 458 self-organised quantum dots 157– 9, 161– 3 SEM see scanning electron microscopes semiconductor matrices 326–54 sheet resistance 590– 1, 599 short wavelength VCSELs 495– 6 short-range ordering 394– 5, 406– 8 Shubnikov-de Hass oscillations 270– 2 silicon doped GaInNAs 347– 50 doped GaNAs 62 substrates 451– 68 device application 461– 7 growth 456– 61 SIMS see secondary-ion mass spectroscopy single carrier localization 223– 30 single-mode fiber coupling 500– 2 SK see Stranski – Krastanov solar cells 451, 465– 6 solid-source molecular beam epitaxy (SSMBE) 161– 4, 170– 2 spin-orbit splitting GaAs 196– 7, 215 split conduction band edges 334– 6 spontaneous emission 522– 3, 532– 9, 557 sputtering 78 –9 SSMBE see solid-source molecular beam epitaxy stability 5 – 6, 417, 427– 31 stacking faults 451 state energy 378– 85 step grading 543–4 step-like quantum wells 302– 5 Stokes’ shifts 393 storage area networks (SAN) 507, 509 strain compensation 150– 3 GaAsNSb 475

628 GaAsNSe 149 GaInNAs HBTs 585–6 in-plane/out-of-plane 20 InAs quantum dot burial 150– 3 isoelectronic dopants 196– 7 lattice parameters 20 – 5 long wavelength alloys 49 – 55 quantum wells 294– 5 reduction 244 tensile 196– 7, 460– 2 strained quantum dots 157– 9 Stranski– Krastanov (SK) mode 14 – 17, 157– 9, 452– 3 stressor-induced GaInNAs quantum dots 173 structural characterization/properties band 122– 3, 253– 75, 285– 93, 395– 7 complex structures 79 – 80, 173, 415– 47 empirical pseudopotential method 395– 6 GaAsN 138– 45 GaInNAs quantum dots 163– 4 nitrogen –hydrogen complexes 417, 421– 7 see also electronic structure/properties subband energy 142 substrate temperature 23 – 5, 37 – 8, 42 – 4 supercell Hamiltonians 397 superlattices 588– 9 surface... electric fields 297– 8 kinetics 145 morphology 161–3 passivation 549 surfactants 13 – 17, 38 symmetry-induced splitting 188 synthesizing III– V alloys 332– 4 TB see tight-binding TBA see tertiarybutylarsine TDMAAs see triisodimethylaminoarsenic TEIn see triethylindium telecommunications 471– 2, 485– 8, 606 TEM see transmission electron microscopy temperature dependence band splitting/anticrossing 336– 40 carrier localization 319– 21

Index dislocation-free alloys 458 edge-emitting lasers 520– 3, 525–8 electron mobility wells 272– 3 GaAsN energy gaps 143– 5 GaInNAs HBTs 602 GaInNAs lasers 111– 12 isoelectronic dopants 192–4, 201 –2 magneto photoluminescence 225 MOVPE 96 – 8 nitrogen concentration 405 photoluminescence 32 – 3 spontaneous emission 537– 9 GaInNAs quantum dots 168 induced shifts 205– 6, 215– 16 localization 34 sensitivity 520– 3, 525– 8 ten-band k·p model 370– 2, 382– 3 tensile strain 196– 7, 460– 2 tertiarybutylarsine (TBA) 101 thermal features activation energies 153– 4 annealing 168– 9 conductivity 456– 8 expansion coefficients 456– 8, 460– 2 impedance 544 resistance 567 rollover 548, 550– 1 thicknesses critical 141, 162– 3, 585–6 GaInNAs HBTs 585–6 GaInNAsSb VCSELs 542– 3 three-dimensional quantum-confined structures 158 threshold current density GaInAs lasers 106 GaInNAs lasers 107– 9, 130 GaInNAsSb lasers 520– 7, 528– 31 GaNAsSb lasers 485 threshold damping coefficient 556– 7 threshold parameters 520– 31 tight-binding (TB) analysis alloy scattering 385– 7 band anticrossing 361– 88 confined state energy 368–74 effective masses 378– 85

Index Ga(In)NAs 361–88 isoelectronic dopants 190 mobility 385– 7 nitrogen incorporation 70 tilted cross-sectional transmission electron microscopy (X-TEM) 453 transition energy GaAsBi 213– 14 GaNAsSb alloy 476– 7, 479 nitrogen – hydrogen complexes 431– 6 photoluminescence 34 – 8 transition probability 198– 9, 202– 4 transmission distances 507– 8 transmission electron microscopy (TEM) 47– 57, 453, 480– 1, 485 transport properties 66 – 8, 343– 53 transverse resistivity 270– 4 triethylindium (TEIn) 125, 145– 6 triisodimethylaminoarsenic (TDMAAs) 123–4, 138, 149 true-spontaneous emission (TSE) 532– 6 tunnelling distance 262– 4 magneto-tunneling spectroscopy 253– 75 resonant tunnelling diodes 254– 9, 264– 9 turn-on voltages GaInNAs HBTs 581– 5, 595– 600, 604, 607 HBTs 471– 2, 488– 91 two-band model 370– 4 u-DMHy see unsymmetrical dimethylhydrazine UHV nature 121 unreactive surfactants 15 unsymmetrical dimethylhydrazine (u-DMHy) 95 V/III ratio 103– 5 valence band offsets 65, 531 band transitions 196– 7 electrons 457– 8 Varshni behavior 32, 201– 2 VCA see virtual crystal approximation

629 vertical cavity surface emitting lasers (VCSELs) chemical beam epitaxy 120, 131– 2 fiber-optical communications 495– 503 GaInNAs 495– 503 long wavelengths 495– 503, 507– 11, 539–47 nitride-antimonide 507– 11, 539– 47 quantum dots 160 vibrational properties 417– 19, 441– 4 virtual crystal approximation (VCA) failure 182– 5 virtual effective potentials 182 voltage bipolar reference circuits 582 capacitance spectroscopy 264– 6 current curves 520– 1, 548 curves 256– 9, 520– 1, 548 knee voltages 579, 604– 5, 607 modulation 559– 60 offset voltages 579, 600–1, 607 position magnetic dependence 261– 4 turn-on voltages 471– 2, 488– 91, 581– 5, 595–600, 604, 607 volume epiwafer production 132– 3 Wannier functions 327 wave function isosurfaces 399 wavelength effects 165– 7 wavevectors 259– 64, 330 wearout mechanisms 563–4 well width dependence 370– 1 width resonance 208– 11 wireless devices 604– 5 X-ray absorption near edge fine structure (XANES) 70 – 4 X-ray absorption spectroscopy (XAS) 71 – 2, 74 X-ray diffraction (XRD) high resolution 18 – 28, 472– 4 rocking curves 472– 4, 480, 484– 5 X-ray photoelectron spectroscopy (XPS) 64 –6

630 X-TEM see tilted cross-sectional transmission electron microscopy XANES see X-ray absorption near edge fine structure XAS see X-ray absorption spectroscopy

Index XPS see X-ray photoelectron spectroscopy XRD see X-ray diffraction z-parameter 522–3, 536–9, 557 zone-center optic phonons 207–11, 216