Advances in Infrared Photodetectors, Volume 84 (Semiconductors and Semimetals)

SEMICONDUCTORS AND SEMIMETALS VOLUME 84 Advances in Infrared Photodetectors SERIES EDITORS EICKE R. WEBER Director F...

Author: Chennupati Jagadish | Sarath Gunapala | David Rhiger

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SEMICONDUCTORS AND SEMIMETALS VOLUME

84 Advances in Infrared Photodetectors

SERIES EDITORS EICKE R. WEBER Director Fraunhofer-Institut f¨ur Solare Energiesysteme ISE Sprecher, Allianz Energie der Fraunhofergesellschaft Heidenhofstr. 2, 79110 Freiburg, Germany

CHENNUPATI JAGADISH Australian Laureate Fellow and Distinguished Professor Department of Electronic Materials Engineering Research School of Physics and Engineering Australian National University, Canberra, ACT 0200, Australia

SEMICONDUCTORS AND SEMIMETALS VOLUME

84 Advances in Infrared Photodetectors Edited by

SARATH D. GUNAPALA NASA-Jet Propulsion Laboratory, Pasadena, California

DAVID R. RHIGER Raytheon Vision Systems, Goleta, California

CHENNUPATI JAGADISH Australian National University, Canberra, Australia

AMSTERDAM • BOSTON • HEIDELBERG • LONDON NEW YORK • OXFORD • PARIS • SAN DIEGO SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO Academic Press is an imprint of Elsevier

Academic Press is an imprint of Elsevier 525 B Street, Suite 1900, San Diego, CA 92101-4495, USA 225 Wyman Street, Waltham, MA 02451, USA 32 Jamestown Road, London NW1 7BY, UK First edition 2011 c 2011 Elsevier Inc. All rights reserved. Copyright No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means electronic, mechanical, photocopying, recording or otherwise without the prior written permission of the publisher. Permissions may be sought directly from Elsevier’s Science & Technology Rights Department in Oxford, UK: phone (+44) (0) 1865 843830; fax (+44) (0) 1865 853333; email: [email protected]. Alternatively you can submit your request online by visiting the Elsevier web site at http://elsevier.com/locate/ permissions, and selecting Obtaining permission to use Elsevier material. Notice No responsibility is assumed by the publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. Because of rapid advances in the medical sciences, in particular, independent verification of diagnoses and drug dosages should be made. ISBN: 978-0-12-381337-4 ISSN: 0080-8784

For information on all Academic Press publications visit our web site at www.elsevierdirect.com

Printed and bounded in USA 11 12 13 14 10 9 8 7 6 5 4 3 2 1

CONTENTS

Preface

vii

List of Contributors

ix

1. Type-II Superlattice Infrared Detectors

1

David Z.-Y. Ting, Alexander Soibel, Linda H¨oglund, Jean Nguyen, Cory J. Hill, Arezou Khoshakhlagh, and Sarath D. Gunapala 1. Introduction 2. Historical Perspective 3. Basic Properties of Type-II Superlattices 4. Superlattice Infrared Detectors 5. Detector Fabrication and Characterization 6. Conclusions and Outlook Acknowledgments References

2. Quantum Well Infrared Photodetectors

2 3 13 25 37 49 50 50

59

S. D. Gunapala, S. V. Bandara, S. B. Rafol, and D. Z. Ting 1. Introduction 2. Comparison of Various Types of QWIPs 3. Figures of Merit 4. Light Coupling 5. Imaging Focal Plane Arrays 6. Concluding Remarks and Outlook Acknowledgments References

3. Quantum Dot Infrared Photodetectors

60 62 74 91 104 143 145 147

153

Ajit V. Barve and Sanjay Krishna 1. 2. 3. 4.

Introduction Epitaxial Self Assembled Quantum Dots Design of Quantum Dot Infrared Detectors Review of Recent Progress in QDIP Technology

153 158 166 178

v

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Contents

5. Future Directions 6. Summary References

4. Terahertz Semiconductor Quantum Well Photodetectors

183 187 188

195

J. C. Cao and H. C. Liu 1. Introduction 2. Principle of THz QWP 3. Theory and Simulation of THz QWP 4. Design and Characterization of THz QWP 5. Application: THz Free Space Communication 6. Summary Acknowledgments References

5. Homo- and Heterojunction Interfacial Workfunction Internal Photo-Emission Detectors from UV to IR

195 196 201 223 234 239 239 239

243

A. G. U. Perera 1. Introduction 2. Free Carrier–Based Infrared Detectors 3. Inter-Valence Band Detectors 4. Conclusion 5. Nomenclature Acknowledgments References

244 247 277 295 297 298 298

6. HgCdTe Long-Wave Infrared Detectors

303

David R. Rhiger 1. Introduction 2. Material Properties 3. Single Wavelength Ellipsometry for Surface Monitoring 4. Current–Voltage Curve Analysis 5. Published Resources of Broad Interest References Index Contents of Volumes in this Series

303 304 308 315 328 330 333 343

PREFACE

Although the invisible portion of the electromagnetic spectrum includes gamma rays, X-rays, and ultraviolet rays beyond the blue end of the visible spectrum and infrared rays (spanning a wide wavelength swath from ∼0.7 µm to ∼1 mm) and microwaves beyond the red end, light detectors operating in the mid- and long-wavelength infrared ranges hold a special significance. Potential applications at these wavelengths range from the mundane to the sublime. Room temperature objects glow brightest in this wavelength range. Detectors with the sharpest eyes for light at these wavelengths are ideal for a variety of ground- and space-based applications such as night vision, navigation, weather monitoring, security and surveillance, etc. In addition, they can be used to monitor and measure pollution, relative humidity profiles, and the distribution of different gases in the atmosphere. This is due to the fact that most of the absorption lines of gas molecules lie in these infrared spectral regions. The earth’s atmosphere is opaque to most of the infrared rays; of its few transparent windows, the 3–5.5 µm and 8–12 µm are the most useful. Cameras operating in this wavelength range and used in ground-based telescopes will be used to see through the earth’s atmosphere, image distant stars and galaxies (including those invisible to telescopes equipped with normal visible eyes), and help in the search for cold objects such as planets orbiting nearby stars. Thus, infrared detectors operating in the mid- and long-wavelength range have myriad applications. Research in infrared photon detectors led to many new infrared detection devices, materials, and large-format infrared focal plane arrays for imaging applications. Research activities in the areas of HgCdTe, strainedlayer superlattices, quantum-well infrared detectors, homo- and heterojunction devices, quantum-dot infrared detectors, blocked impurity band (BIB) detectors, and quantum wells for far-infrared detection have been very intense over last two decades. Therefore, we collected a comprehensive review of the various topics related to the infrared photon detectors based on II–VI and III–V compound semiconductor materials. We hope this volume will provide a valuable reference for the researchers in the

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Preface

field of infrared detectors, related fields, and for those individuals like graduate students, scientists, and engineers who are interested in learning about these subjects. The six chapters in volume 84 of the Elsevier’s Semiconductors and Semimetals cover the following topics: Chapter 1 describes the development of strained layer superlattice for infrared detection from inception to focal planes; Chapter 2 discusses the progress of quantum-well infrared photodetectors (QWIPs) in the last two decades, which culminated low-cost focal planes for commercial use; Chapter 3 discuss the quantum dots for infrared detection; Chapter 4 describes the quantum-well THz detectors; Chapter 5 describes the homo- and heterojunction interfacial workfunction internal photoemission detectors from ultraviolet to infrared detection; and Chapter 6 describes the advances made in long-wavelength infrared HgCdTe detectors. We thank all the contributors who have devoted their valuable time and effort in putting together a comprehensive volume in timely manner. We also sincerely thank Ben Davie and Paul Chandramohan of Elsevier for providing assistance and accommodating our schedule. SARATH D. GUNAPALA, DAVID R. RHIGER, and CHENNUPATI JAGADISH Editors

LIST OF CONTRIBUTORS

A. G. Unil Perera, Department of Physics and Astronomy, Georgia State University, 29 Peachtree Center Avenue, Science Annex, Suite 400, Atlanta, GA 30303-4106, USA, e-mail: [email protected]. (Ch5) Ajit V. Barve, Center for High Technology Materials, University of New Mexico, 1313, Goddard Street SE, Albuquerque, NM 87106, USA, e-mail: [email protected]. (Ch3) Alexander Soibel, Center for Infrared Sensors, NASA — Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA, e-mail: [email protected]. (Ch1) Arezou Khoshakhlagh, Center for Infrared Sensors, NASA — Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, e-mail: [email protected]. (Ch1) Cory J. Hill, Center for Infrared Sensors, NASA — Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA, e-mail: [email protected]. (Chs 1 and 2) David R. Rhiger, Raytheon Vision Systems, 75 Coromar Drive, Goleta, California 93117, USA, e-mail: [email protected]. (Ch6) David Z.-Y. Ting, Center for Infrared Sensors, NASA — Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA, e-mail: [email protected]. (Chs 1 and 2) H. C. Liu, Key Laboratory of Artificial Structures and Quantum Control, Department of Physics, Shanghai Jiao Tong University, Shanghai 200240, China, e-mail: [email protected], National Research Council, Canada (Ch4)

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List of Contributors

J. C. Cao, Key Laboratory of Terahertz Solid-State Technology, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, 865 Changning Road, Shanghai 200050, China, e-mail: [email protected]. (Ch4) Jean Nguyen, Center for Infrared Sensors, NASA — Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA, e-mail: [email protected]. (Ch1) Linda Hoglund, ¨ Center for Infrared Sensors, NASA — Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA, e-mail: [email protected]. (Ch1) Sanjay Krishna, Center for High Technology Materials, University of New Mexico, 1313, Goddard Street SE, Albuquerque, NM 87106, USA, e-mail: [email protected]. (Ch3) Sarath D. Gunapala, Center for Infrared Sensors, Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA, e-mail: [email protected]. (Chs 1 and 2) Sir B. Rafol, Center for Infrared Sensors, NASA — Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA, e-mail: [email protected]. (Ch2) S. V. Bandara, Night Vision & Electronic Sensors Directorate, FortBelvoir, VA 22060, USA, e-mail: [email protected]. (Ch2)

CHAPTER

1 Type-II Superlattice Infrared Detectors David Z.-Y. Ting, Alexander Soibel, Linda H¨ oglund, Jean Nguyen, Cory J. Hill, Arezou Khoshakhlagh, and Sarath D. Gunapala

Contents

1. Introduction 2. Historical Perspective 2.1. Type-II superlattice and the broken-gap band alignment 2.2. Superlattices for infrared detection 2.3. Superlattice infrared detectors and focal plane arrays 2.4. Recent development 3. Basic Properties of Type-II Superlattices 3.1. The 6.1 A˚ material system 3.2. Tunneling suppression 3.3. Auger reduction 3.4. Effective masses and transport 4. Superlattice Infrared Detectors 4.1. Unipolar barriers 4.2. Dark current reduction using unipolar barriers 4.3. Building unipolar barriers 4.4. Barrier infrared detector 5. Detector Fabrication and Characterization 5.1. Detector fabrication 5.2. Optical characterization of superlattices 5.3. Noise measurement 5.4. Lifetime measurement 5.5. Lifetime and dark current 6. Conclusions and Outlook Acknowledgments References

Semiconductors and Semimetals, Volume 84 ISSN 0080-8784, DOI: 10.1016/B978-0-12-381337-4.00001-2

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c 2011 Elsevier Inc.

All rights reserved.

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1. INTRODUCTION The type-II InAs/GaSb superlattices (Sai-Halasz et al., 1977) have several fundamental properties that make them suitable for infrared detection: their band gaps can be made arbitrarily small by design (Sai-Halasz et al., 1978a), they are more immune to band-to-band tunneling compared with bulk material (Smith and Mailhiot, 1987; Smith et al., 1983), the judicious use of strain in type-II InAs/GaInSb strained layer superlattice (SLS) can enhance its absorption strength over that of the type-II InAs/GaSb superlattice to a level comparable with HgVdTe (MCT) (Smith and Mailhiot, 1987), and furthermore, type-II InAs/Ga(In)Sb superlattices have been shown theoretically (Grein et al., 1992) and experimentally (Youngsdale et al., 1994) to have reduced Auger recombination. These properties generated strong interests and led to the demonstration of the first highperformance photodiodes (Fuchs et al., 1997a; Johnson et al., 1996) and focal plane array (FPA) (Walther et al., 2005b). In the mid-wavelength infrared (MWIR), sophisticated production-ready simultaneous dual-band FPAs already exist (Rehm et al., 2010; Walther et al., 2007). In the long-wavelength infrared (LWIR), heterostructure superlattice detectors (Aifer et al., 2010a; Gautam et al., 2010; Nguyen et al., 2007b; Ting et al., 2009a) that effectively use unipolar barriers (Ting et al., 2009a) have shown strong reduction of generation-recombination (G-R) dark current due to Shockley-Read-Hall (SRH) processes. Higher absorber doping levels afforded by immunity to tunneling has led to reduced diffusion dark current (Ting et al., 2010), despite relatively short lifetimes found in existing superlattice material (Connelly et al., 2010; Donetsky et al., 2010; Pellegrino and DeWames, 2009). The dark current characteristics of type-II superlattice-based single element LWIR detectors are now approaching that of the state-of-the-art MCT detector. Noise measurements highlight the need for surface leakage suppression (Soibel et al., 2010), which can be tackled by improved etching (Nguyen et al., 2010b), passivation (Fuchs et al., 1998a; Mohseni et al., 1999), and device design (Aifer et al., 2007; Wicks et al., 2010). Large-format LWIR FPAs have been demonstrated in research laboratories (Gunapala et al., 2010; Manurkar et al., 2010). The continuous improvement in substrate, material quality, device design, and processing technique, coupled with better understanding of the fundamental properties, could lead to high-performance large-format LWIR focal plane arrays in the near future. The reminder of this chapter is organized as follows: Section 2 reviews the development of the type-II superlattice infrared detectors from a historical perspective. Section 3 discusses basic properties of the type-II superlattice, largely from simple theoretical considerations. Section 4 describes the principles behind advanced superlattice infrared detectors based on heterostructure designs. Section 5 explores some aspects of device fabrication

3

Type-II Superlattice Infrared Detectors

and characterization of contemporary interest. A short summary and outlook is given in Section 5. As this chapter covers only a limited set of ¨ topics, the interested readers are also referred to review articles by Burkle and Fuchs (2002); Fuchs et al. (1997b), and Razeghi and Mohseni (2002), as well as the book by Rogalski (2011) for additional information.

2. HISTORICAL PERSPECTIVE In this section, we review the development of type-II antimonide superlattice infrared detector through a historical perspective. We begin with the discovery of the broken-gap band alignment and the invention of the type-II superlattice from 1976 to 1978. We next examine the period between 1979 and mid-1990s when the concept of using type-II superlattices for infrared detection took shape, supported by theoretical and experimental works. The following period, between 1996 and 2005, saw the first high-performance detectors and the demonstration of the first focal plane array. Finally, rapid growth of the field occurred between 2005 and the present time (2010), with the emergence of detectors based on advanced heterostructure designs, and significant progress in focal plane array technology development.

2.1. Type-II superlattice and the broken-gap band alignment The year 1977 marked the birth of the type-II superlattice with the publication of a seminal paper by Sai-Halasz et al. (1977) from the IBM T. J. Watson Research Center. In the paper, the authors proposed and analyzed theoretically a new type of bilayer semiconductor superlattice in which the lower conduction band (CB) edge is located in one material, whereas the higher valence band (VB) edge is in the other. In this kind of superlattice (Fig. 1.1), the wave functions of the lowest conduction subband and the highest valence subband are localized in the two different Ga(In)Sb

Conduction miniband Heavy-hole miniband

InAs

EC

EV

FIGURE 1.1 Schematic illustration of an InAs/Ga(In)Sb type-II broken-gap superlattice showing the spatial separation of the conduction band and the heavy-hole band wave functions. The infrared transition is indicated by an arrow.

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David Z.-Y. Ting et al.

host semiconductors (spatially delocalized), and therefore, the positions of the CB edge and the VB edge can be, to first order, tuned independently. It was suggested that this type of superlattice could be realized by using the closely lattice-matched semiconductor pairs of InAs/GaSb or InGaAs/GaSbAs. It was also pointed out in particular that based on the known electron affinity values, the CB edge of InAs was expected to be 0.14 eV lower than the VB edge of GaSb (now called the broken-gap band alignment), and this would lead to an interesting behavior since the superlattice CB and VB states are close in energy and could therefore interact. This new type of superlattice, in which the band gaps of the two host semiconductors are in either a staggered or a broken-gap alignment, was later referred to as “type II” (Sai-Halasz et al., 1978b) to distinguish it from the “type I” superlattice originally proposed by Esaki and Tsu (1970), in which the host band gaps are in a nested alignment. The key feature that enabled the concept of the type-II superlattice was the broken-gap band alignment between InAs and GaSb. W. Frensley first noticed the very unusual band alignment between InAs and GaSb in the course of his PhD thesis research under the direction of H. Kroemer at the University of Colorado (Frensley and Kroemer, 1977). The IBM Group came to the realization around the same time. Noting the unusually large electron affinity of InAs, Sai-Halasz et al. (1977) predicted the broken-gap band lineup between InAs and GaSb based on the electron-affinity rule (Anderson, 1962), which, though later found to be inadequate (Niles and Margaritondo, 1986), happened to hold up well in this case. The InAsGaSb broken-gap band lineup was also predicted through the means of more sophisticated theoretical methods, as reported by Harrison (1977) using linear combination of atomic orbital (LCAO) theory and by Frensley and Kroemer (1977) using pseudopotential theory. Although Harrison did not attach any special significance to the broken gap alignment (it was one of many values tabulated in a comprehensive study of heterojunction band offsets), Frensley and Kroemer (1977) pointed out that among all the predicted band offsets, perhaps the most interesting is that for the InAsGaSb system, in which the InAs conduction band edge was predicted to be below that of the GaSb valence band edge. They speculated that this band lineup could lead to very interesting transport properties such as interband tunneling. Indeed, interband tunneling was observed experimentally by Sakaki et al. (1977) from IBM in a study of InGaAs-GaSbAs heterojunction diode current–voltage (I−V) characteristics. In the original study of type-II superlattices, Sai-Halasz et al. (1977) used Kane’s two-band model (Kane, 1957) to treat the interaction between the InAs conduction band and the GaSb light-hole band while ignoring the heavy-hole band. In the following year, Sai-Halasz and Esaki, in

Type-II Superlattice Infrared Detectors

5

collaboration with Harrison, reexamined the band structure of InAs-GaSb superlattices using LCAO theory (Sai-Halasz et al., 1978a). They found that while superlattices with thin InAs and GaSb layers have well-defined energy band gaps and act as semiconductors, those with thick layers behave as semimetals. This means that the band gap of the InAs/GaSb superlattice can be made arbitrarily small — smaller than that of either InAs or GaSb. The IBM Group then proceeded to demonstrate this trend of decreasing band gap with increasing layer thickness experimentally (Sai-Halasz et al., 1978b) using a set of molecular beam epitaxy (MBE) grown samples that showed measured band gaps ranging from 265 to 360 meV at 10 K. Correlation with theoretical calculations also established the InAs CB edge to be at approximately 150 meV below the GaSb VB edge, a value that is still used today. In the literature, “type-II broken gap” is sometimes referred to as “type III” to distinguish it from “type-II staggered” (Davies, 1998; Dragoman and Dragoman, 2002; Sze and Ng, 2007). However, the term “type III” is often used in the infrared detector literature to refer to superlattices consisting of alternating layers of an inverted band structure zero-gap semiconductor and a normal wider gap semiconductor, such as the HgTe/CdTe superlattice (Kinch, 2007). Kroemer advocates using only the descriptive names of nested (or straddling), staggered, and broken gap (or misaligned) and doing away with numerical designation of types I, II, and III altogether. We use “type-II broken gap” or simply “type II” in this work.

2.2. Superlattices for infrared detection The concept of using superlattices for infrared detection started in the HgCdTe (MCT) material system. Although a practical MCT superlattice infrared detector has not been realized, the idea had a major influence on the development of antimonide superlattice infrared detectors. Schulman and McGill (1979a,b) first proposed the use of the CdTe/HgTe superlattice as an infrared material, with possible uniformity advantages over the MCT alloy. In one of their papers, Schulman and McGill (1979a) pointed out that the InAs/GaSb superlattice should have similar band gap properties as the CdTe/HgTe system, but they also expressed the concern that the size of the optical matrix element may be inadequate because electron and hole wave functions of the states involved in the infrared transitions are spatially separated in a type-II superlattice. Later, Smith et al. (1983) revisited the theory of CdTe/HgTe superlattices and identified some key advantages of superlattices over bulk materials for infrared detection: (1) the cutoff wavelengths of MCT superlattices have weaker dependence on composition than the MCT alloy and are, therefore, less susceptible to

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variations due to compositional fluctuation, (2) superlattices have reduced p-side diffusion current due to the larger electron mass, and (3) superlattice tunneling lengths are shorter than for MCT alloys with the same band gap and therefore have reduced band-to-band tunneling. These properties are found in the InAs/GaSb superlattice as well. Regarding the concern for possible weak oscillator strength in type-II superlattices (Schulman and McGill, 1979a), Chang and Schulman (1985) calculated optical properties of InAs/GaSb superlattices. They found that in a (M,N)-InAs/GaSb superlattice (each period consisting of M monolayers of InAs and N monolayers of GaSb), for sufficiently large M and N (>10 or more), the oscillator strength of optical transitions is approximately proportional to 1/MN, decreasing rapidly with layer thickness. In a review article, Kroemer (2004) described this in a simple intuitive manner. Since electron and hole wave functions are separately localized in InAs and GaSb layers, respectively, they overlap each other mostly near the heterointerfaces. Hence, to first order, the optical absorption is proportional to the number of interfaces rather than to the superlattice thickness. This means that much of the volume is optically inactive in InAs/GaSb superlattices with long periods (which are needed to achieve small band gaps for long wavelength infrared detection). So, how can we reduce the superlattice period to enhance oscillator strength without increasing the energy band gap? To address this issue, Smith and Mailhiot (1987) proposed the type II InAs/GaInSb strained layer superlattice (SLS) infrared detector. Smith and Mailhiot considered a freestanding InAs/Ga0.6 In0.4 Sb SLS in which the InAs and GaInSb layers are under tensile and compressive strain, respectively. As illustrated in Fig.1.2, the effect of strain is to lower the InAs CB edge and raise the GaInSb heavy-hole (HH) band edge, which makes both the InAs CB quantum well and the GaInSb HH band quantum well deeper. Consequently, one could employ narrower quantum wells without increasing the superlattice band gap. The SLS has larger optical matrix elements than the InAs/GaSb superlattice. Although the optical matrix element of the type-II SLS is still smaller than that in bulk MCT, its absorption coefficient is comparable to that of MCT because of the higher joint density of states. The electron effective mass for a 10-µm cutoff SLS is ∼0.04 m0 (0.0088 m0 for MCT of comparable cutoff wavelength), which is large enough to reduce band-toband tunneling and still small enough to provide good electron mobility. It was suggested that since electron mobility is much higher than hole mobility, n on p diodes should be used for infrared detection. Smith and Mailhiot also noted that GaSb would be a good substrate on which to grow the InAs/GaInSb superlattice. Miles et al. (1990) experimentally demonstrated LWIR absorption in InAs/GaInSb strained layer superlattices.

Type-II Superlattice Infrared Detectors

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C C

HH C

HH, LH

LH

C LH HH, LH GaSb

Unstrained (A)

Energy

InAs

HH InAs (Tension)

Ga0.6In0.4Sb (Compression) Strained (B)

FIGURE 1.2 Band edge energy positions for (A) unstrained InAs and GaSb and (B) strained InAs and Ga0.6 In0.4 Sb in a free-standing InAs/GaInSb superlattice, after Smith and Mailhiot (1987).

As pointed out by Chow et al. (1991), D. L. Smith also postulated that Auger recombination rates in some superlattices should be lower than those in bulk semiconductors due to the splitting of the heavy-hole (HH) and light-hole (LH) bands and the larger electron effective mass. Smith communicated the idea to McGill, who in turn stimulated H. Ehrenreich’s group at Harvard to perform detailed calculations to put this concept on a firm theoretical basis. Grein et al. (1992) presented a theoretical analysis that showed that p-type Auger lifetimes in a 11-µm cutoff InAs/InGaSb SLS at 77 K could be three to five orders of magnitude longer than those of bulk MCT with the same gap (Grein et al., 1992). Experimental measurements of Auger lifetime enhancement in InAs/GaInSb superlattices were reported by Youngsdale et al. (1994). As the material quality of antimonide superlattices improves and defect-related dark currents decrease, the long Auger lifetimes could yield real advantages in LWIR antimonide superlattice detectors. Some of the other fundamental studies that are important for the development of the type-II superlattice as an infrared material include the theoretical calculation of InAs/GaSb electronic and optical properties using a realistic band structure model that included band mixing effects (Chang and Schulman, 1985; Schulman and Chang, 1985),

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the influence of interface types (Miles et al., 1993), and cross-sectional scanning electron microscopy studies of antimonide superlattices (Feenstra et al., 1994a,b; Lew et al., 1998; Steinshnider et al., 2000b,a). We note that the term strained layer superlattice (SLS) is sometimes used in the literature to refer to both the InAs/GaSb and the InAs/GaInSb superlattices. SLS was originally intended for the InAs/GaInSb superlattices, in which the GaInSb layers are intentionally strained for the purpose of increasing oscillator strength (Smith and Mailhiot, 1987). The slight lattice mismatch (0.6%) between InAs and GaSb was not considered significant in the InAs/GaSb superlattice as the effects on electronic and optical properties are minimal. In this work, we reserve the term SLS for the InAs/GaInSb superlattices. However, we note that the small lattice mismatch between InAs and GaSb can cause sufficient strain build up to affect the material quality in thick InAs/GaSb superlattices. When InAs/GaSb superlattices are grown on GaSb substrates, InSb-like interfaces are often used to provide strain relief. The same interface engineering techniques can also be applied to minimize the average strain in the InAs/GaInSb SLS as has been demonstrated by the work from the Fraunhofer IAF (Fuchs et al., 1997a). It is interesting to note that while the oscillator strength of the InAs/GaSb superlattice is not as strong as that of the InAs/GaInSb SLS, both types of antimonide superlattices are being actively investigated today. In particular, Professor Razeghi’s group at the Northwestern University has been reporting results on the InAs/GaSb superlattice since 1998 (Mohseni et al., 1998b,a). Although the oscillator strength of the InAs/GaSb SL is weaker, like its InAs/GaInSb SLS counterpart it also has a higher joint density of states than bulk semiconductors and therefore has an adequately large absorption coefficient. The InAs/GaSb superlattice, which uses unstrained and minimally strained binary semiconductor layers, may also have material quality advantages over the SLS, which uses a strained ternary semiconductor (GaInSb).

2.3. Superlattice infrared detectors and focal plane arrays During the next development period, roughly from 1996 to 2005, there was important progress in the SL detector technology that made the realization of the first generation of high-performance antimonide-based SL detectors and focal plane arrays (FPAs) possible. During this time, the development of superlattice-based photodetectors has been performed mainly in universities and government laboratories. This period began with the demonstration of high-performance InAs/GaInSb SLS LWIR photodiodes (Fuchs et al., 1997a; Johnson et al., 1996) that generated strong interests in the antimonide superlattices and culminated in the demonstration of the first 256 × 256 FPA (Walther et al., 2005b). Significant advances

Type-II Superlattice Infrared Detectors

9

in growth, characterization, design and fabrication were achieved during this time. Even though we will discuss progress in these technological areas individually, the overall progress in each and all of these areas was crucial for improving detector performances. In particular, the importance of material quality and of proper fabrication techniques for achieving highperformance devices was recognized early on (see, e.g., Fuchs et al., 1999). It is important to note that attention to superlattice material has been driven not only by photodetectors but also by infrared lasers. The improved understanding of the proper growth conditions for superlattices was one of the major achievements during this time period. One aspect that makes the growth of the Sb-based superlattices challenging is the absence of common atoms across the InAs/GaSb heterointerface. Two types of interface layers, InSb-like and GaAs-like, can be formed. A detailed study of the structural properties of InAs/GaSb superlattices with different interface types was performed and showed the advantages of InSb-like interfaces for achieving superior SL structural properties (Herres et al., 1996). Detailed investigations of As/Sb exchange across heterointerfaces, which affects interface roughness and material composition, helped to identify the growth conditions for achieving smooth interfaces (Xie et al., 1999). Interface properties were further investigated using cross-sectional scanning tunneling microscopy to reconstruct antimony segregation that affects compositional grading and interface roughness (Steinshnider et al., 2000b,a). Cross-sectional STM was also used to investigate the atomic scale interface morphology of InAs/(GaIn)Sb superlattices grown by MBE showing a semiquantitative correlation between atomic scale interface structure and transport properties in these structures (Lew et al., 1998). Several studies of SL growth conditions including dependence of interface quality on growth temperatures, effects of group V to group III beam equivalent pressure ratio on surface morphology, and variation of residual doping type and concentration with growth temperature were ¨ performed (Bennett et al., 1999; Burkle et al., 2000; Fuchs et al., 1999). Moreover, growth studies of different antimonide materials, such as AlSb and InAlSb, which are of interest for SL heterostructure development, were conducted (Bracker et al., 2001; Plis et al., 2003). High-quality, lattice-matched substrates are required for epitaxial growth of SL detectors. GaSb substrates are the most closely lattice matched to InAs/GaSb superlattice and thus were commonly used; however, the GaSb substrates commercially available at this time often suffered from high defect density, poor surface morphology, limited size, and high cost. Due to this fact, GaAs substrates, which have better quality and commercially available in large sizes, were evaluated for the growth of SL detectors (Bennett, 1998), demonstrating very promising results when complaint GaAs substrates were used (Brown et al., 2000).

10

David Z.-Y. Ting et al.

In parallel with growth optimization, studies of SL material properties were performed and new characterization methods were evaluated. SL detectors were predicted to have Auger recombination rates lower than in MCT detectors (Grein et al., 1992, 1995). Auger rates were measured in InAs/InGaSb SLS using pump-probe experiment involving free electrons and were found to be indeed much lower than in MCT at room temperature (Ciesla et al., 1996). In another work, the Auger recombination coefficients in InAs/GaSb SL’s were deduced from the optical and electrical measurements that revealed a temperature behavior different from the bulk-like Auger process (Mohseni et al., 1998b). Several important studies were performed to evaluate basic SL properties. From spectrally resolved measurements of the infrared photodiode responsivity in applied magnetic fields, reduced effective masses and anisotropy of magnetic field–induced widening of the band gap were observed (Fuchs et al., 1998b). Magnetotransport and photoluminescence measurements of superlattices grown at different substrate temperatures showed a transition from residual n-type to residual p-type doping with increasing growth temperature. It was found that a decrease in the electron concentration led to a strong increase in the PL intensity for n-type samples when the PL intensity of p-type samples was only weakly dependent on the hole concentration. These dissimilarities in PL characteristics were attributed to the difference in electron and hole transport and scattering ¨ mechanisms (Burkle et al., 2000). The minority electron diffusion lengths in n+ − p InAs/GaSb superlattice photodiode with cutoff wavelength at 7.7 µm were measured from 5.3 to 100 K using temperature-dependent EBIC technique, and the electron lifetime was obtained (Li et al., 2004). In addition, new characterization methods, such as spectral ellipsometry, were successfully used for spectroscopic assessment of composition and structural quality of InAs/GaInSb SL (Wagner et al., 1998). In 1996, Johnson et al. (1996) demonstrated a double heterojunction InAs/GaInSb SLS photodiode operating at 77 K with dark current density of Id = 0.08 A/cm2 and responsivity of 0.8 A/W at 9 µm. At the same time, Fuchs and colleagues at Fraunhofer IAF in Freiburg started on a series of work that significantly advanced the performance of MWIR and LWIR SL detectors (Fuchs et al., 1998a, 1997a; Walther et al., 2005a; Yang et al., 2002) and led to the demonstration of the first 256 × 256 focal plane array (FPA). At T = 77K, the FPA showed a cutoff wavelength of 5 µm, quantum efficiencies of 30%, detectivity values exceeding 1013 Jones, and a noise equivalent temperature difference (NETD) of 11.1 mK for an integration time of 5 ms and f/2 optics (Walther et al., 2005b). Other significant works from the Fraunhofer Group included the analysis of dark current mechanisms in SL detectors (Yang et al., 2002), the study of surface leakage, and passivation development (Fuchs et al., 1998a; Rehm et al., 2005).

Type-II Superlattice Infrared Detectors

11

Another major contribution to LWIR SL detector development during this time frame came from Professor Razeghi’s group at the Northwestern University. Their work resulted in the demonstration of InAs/GaSb superlattice photodiodes with a cutoff wavelength around 7 µm at 77 K and the dark current density of about 10−5 A/cm2 in devices with sulfide-based passivation (Mohseni and Razeghi, 2001; Mohseni et al., 2001, 1999, 2000; Wei et al., 2005). Researchers at Northwestern University, the U.S. Naval Research Laboratory, and U.S. Air Force Research Laboratory also made important progress in the development of very long-wavelength infrared (VLWIR) SL detectors operating in the spectral range 15–32 µm (Aifer et al., 2003; Hood et al., 2005b; Mohseni et al., 2001; Wei et al., 2002a,b).

2.4. Recent development Research and development effort from 2006 to 2010 centered on two key areas. In device development, the emphasis has been on detectors based on heterostructure designs to reduce dark current and increase quantum efficiency (QE). There has also been a large investment in FPA development, with emphasis on improving fabrication processes to attain high uniformity and repeatability. The interest in the technology grew significantly during this period, involving more research teams including those from industry. Heterojunction-based detector designs were shown to be highly effective in improving detector characteristics. Broadly speaking, they are either based on the nBn (Maimon and Wicks, 2006), pBp (Maimon, 2010), or XBn (Klipstein, 2008) design or variations of the double heterojunction (DH) design. The first category includes the single-band superlattice nBn detector (Rodriguez et al., 2007), the dual-band superlattice nBn detector (Khoshakhlagh et al., 2007), the superlattice pMp detector (Nguyen et al., 2009a), and the superlattice pBn detector (Hood et al., 2010a). The second category includes the superlattice DH structure (Delaunay et al., 2007a; Vurgaftman et al., 2006), the p-π -M-n detector (Nguyen et al., 2007b), the PbIbN structure (Gautam et al., 2010), and the complementary barrier infrared detector (CBIRD; Ting et al., 2009a). Superlattices with complex supercells were also incorporated in heterojunction designs, either as barriers or as absorbers. These include the “W” (Aifer et al., 2010b, 2006, 2005, 2010a; Canedy et al., 2007; Kim et al., 2007; Vurgaftman et al., 2006) and the “M” (Nguyen et al., 2009a, 2008b, 2007b, 2008a; Nguyen and Razeghi, 2007a) superlattices. A more detailed description of these designs is given in Section 4. There has been continuous effort to improve material quality by optimizing growth parameters. Studies of doping levels, growth temperature, interfacial layer thicknesses, and material strain demonstrated the effect

12

David Z.-Y. Ting et al.

of these parameters on device performance (Canedy et al., 2010; Haugan et al., 2010; Hoffman et al., 2007, 2008; Khoshakhlagh et al., 2009). Although there has been constant improvement in the quality, size, and availability of commercially available GaSb substrates, the requirements have become even more stringent for FPA fabrications. As an alternative to SL growth on GaSb substrates, very promising results of SL growth on GaAs substrates have been demonstrated (Abdollahi Pour et al., 2009; Das et al., 2008; Nguyen et al., 2009c). With the general improvement in device dark current density, the side wall surface leakage currents have become more noticeable. Surface leakage current reduction in fully pixelated devices has become a topic of interest. The surface leakage current depends on the etching process parameters, postetch cleaning, and surface passivation. The need for highquality sidewalls led to the development of effective pixel isolation technique using dry etching with inductively coupled plasma (ICP) systems as reported by groups from the Northwestern Univeristy (NWU; Huang et al., 2009), the Jet Propulsion Laboratory (JPL; Nguyen et al., 2010a), and the University of New Mexico (UNM; Tan et al., 2010). Many passivation methods have been explored. These include side wall treatment with ammonium sulfide (Hood et al., 2005a), AlGaAsSb regrowth (Rehm et al., 2005), deposition of SiO2 (Herrera et al., 2008; Hood et al., 2005b), polyimide (Hood et al., 2007), and SU-8 (Kim et al., 2009). A shallow-etch mesa isolation (SEMI) technique (Aifer et al., 2007) has also been developed for leakage current reduction. Following the first 256 × 256 SL FPA demonstration in 2005, Fraunhofer IAF and NWU demonstrated 288 × 384 (Walther et al., 2007) and 320 × 256 (Delaunay et al., 2007b) FPAs in 2007. Fraunhofer’s array showed good NETD values of 27.9 mK at the cutoff wavelength of 4.9 µm, whereas NWU’s array showed a longer cutoff of 12 µm with NEDT of 340 mK. In the same year, JPL and Raytheon Vision Systems (RVS) demonstrated their first 256 × 256 p-i-n detector-based FPA with 10.5 µm cutoff wavelength (Rhiger et al., 2007). In 2008, UNM demonstrated a 256 × 256 MWIR FPA based on a type-II InAs/GaSb superlattice detector with an nBn design (Kim et al., 2008). Also in 2008, NWU fabricated a 320 × 256 FPA with 10 µm cutoff wavelength using a double heterostructure (DH) design to minimize the surface leakage (Delaunay et al., 2008); this resulted in an improvement in the NETD value to 33 mK. In 2009 NWU developed an 320 × 256 FPA from their recently introduced M-structure (Delaunay et al., 2009). This array demonstrated similar QE as previous FPAs, but a dark current level that was seven times lower. In the same year, JPL and RVS demonstrated the capabilities for larger format FPA fabrication with a 1k × 1 k FPA with 4 µm cutoff. A 640 × 512 LWIR FPA based on heterostructure designs was demonstrated (Hill et al., 2009b) by JPL. RVS and

Type-II Superlattice Infrared Detectors

13

JPL have also demonstrated CBIRD-based 256 × 256 LWIR FPA (Rhiger et al., 2010). In 2010, Teledyne and HRL joined in FPA development. Teledyne utilized the graded gap “W” hybrid SL design in a 256 × 256 FPA with a 9.4 µm cutoff (Hood et al., 2010b), while HRL used the barrier heterostructure design for a 320 × 256 FPA with a 9.0-µm cutoff (Terterian et al., 2010). During this same year, the largest LWIR SL FPA was fabricated by both NWU and JPL with 1k × 1 k format (Gunapala et al., 2010; Manurkar et al., 2010), and these achievements can be contributed to the improvement in FPA manufacturing processes (Delaunay et al., 2007c; Nguyen et al., 2010b). In efforts to find a solution to the cost and limitation issues with GaSb substrates, NWU demonstrated a 320 × 256 MWIR FPA based on the p-i-n detector design and a 320 × 256 LWIR FPA based on the p-π -M-n design (Razeghi et al., 2010), both grown on GaAs substrates. The successful demonstration of type-II superlattice FPAs on alternative substrates makes the technology promising for third-generation imaging.

3. BASIC PROPERTIES OF TYPE-II SUPERLATTICES In this section, we explore the basic properties of the type-II InAs/ Ga(In)Sb superlattices that distinguish them from bulk infrared material and describe how these properties lead to tunneling suppression and Auger reduction, and how they affect carrier transport. We begin with a brief overview of the antimonide material system from which the type-II superlattices are constructed.

˚ material system 3.1. The 6.1 A Table 1.1 lists some basic properties of common families of semiconductors used for making infrared photodetectors. All have diamond or zincblende crystal structures. In general, as we move from the covalent group IV semiconductors on the left side of the table to the more ionic II–VI semiconductors on the right, the lattice constant becomes larger, the chemical bond becomes weaker, and the material becomes softer as reflected in the values of the bulk modulus. The materials toward the left of the table are more mechanically robust, which leads to better manufacturability, as is evident in the dominance of silicon and GaAs among electronic/optoelectronic semiconductor materials. On the other hand, the semiconductors on the right side of the table tend to have smaller direct band gaps, which enable strong, bulk band-to-band absorption, leading to high quantum efficiency mid-wave infrared (MWIR) and long-wave infrared (LWIR) detectors such as those based on InSb and HgCdTe (MCT).

14 David Z.-Y. Ting et al.

TABLE 1.1

Selected properties of common families of semiconductors used in mid-wave and long-wave infrared photodetectors Si IV 5.431

Ge IV 5.658

GaAs III-V 5.653

AlAs III-V 5.661

Bulk Modulus [GPa]

98

75

75

74

71

69

66

Direct Gap [eV]

-

-

1.426

-

1.350

0.735

-

Group Lattice ˚ Constant [A]

MWIR/LWIR Detection Method

Heterojunction Internal photoemission (HIP)

Quantum well/dot Intersubband (QWIP/QDIP)

InP InGaAs III-V III-V 5.870 5.870

AlInAs III-V 5.870

Quantum well Intersubband (QWIP)

InAs GaSb III-V III-V 6.058 6.096 58

56

0.354 0.730

AlSb III-V 6.136

InSb III-V 6.479

HgTe II-VI 6.453

CdTe II-VI 6.476

55

47

43

42

-

0.175

−0.141

Bulk B-B

Bulk Band-to-Band

Bulk (MW)/ Superlattice (MW/LW) Band-to-Band

1.475

Type-II Superlattice Infrared Detectors

2

15

AISb

AIAs

T = 80 K

1.5

Energy (eV)

1 GaSb

GaAs 0.5

InSb

0 InAs −0.5 EC

−1

EV

−1.5 5.6

5.7

5.8

5.9 6 6.1 6.2 Lattice constant (A)

6.3

6.4

6.5

FIGURE 1.3 Zone center (0-point) conduction and valence band edge positions plotted against lattice parameter for antimonide, arsenide, and arsenide-antimonide III–V semiconductors.

Figure 1.3 shows the (0-point) conduction and valence band edge positions for antimonide, arsenide, and arsenide-antimonide group III–V semiconductors plotted against their lattice constants. The nearly lattice-matched semiconductors of InAs, GaSb, and AlSb are referred to ˚ material system (Kroemer, 2004) since InAs, GaSb, and AlSb as the 6.1 A ˚ They are also commonly all have lattice constants of approximately 6.1 A. referred to as the antimonides (InAs is included by virtue of being closely lattice-matched to GaSb and AlSb). As illustrated in Fig. 1.4, with the availability of type-I nested or straddling, type-II staggered, and type-II broken-gap (misaligned, or type III) band offsets among the GaSb/AlSb, InAs/AlSb, and InAs/GaSb material pairs, respectively; there is considerable flexibility in forming a rich variety of alloys and superlattices. ˚ semiTogether with their alloys with InSb, GaAs, and AlAs, the 6.1 A conductors provide a great degree of versatility. In particular, the overlap between the InAs conduction band and the GaSb valence band in the typeII broken gap alignment is unique among common semiconductor families and the so-called interband devices exploit this property specifically. ˚ material system occupies an interesting position among The 6.1 A the infrared semiconductor families listed in Table 1.1. Although it has

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David Z.-Y. Ting et al.

AlSb

InAs

Type II staggered

GaSb Type I (nested)

AlSb

Ec

Band gap

EV Type II broken-gap

FIGURE 1.4 Schematic illustration of the energy band alignment in the nearly lattice-matched InAs/GaSb/AlSb material system. The shaded solid rectangles indicate the relative positions of the InAs, GaSb, and AlSb energy band gaps. Three types of band alignment are available in this material system: (1) type-I (nested) band alignment between GaSb and AlSb, (2) type-II staggered alignment between InAs and AlSb, and (3) type-II broken-gap alignment between InAs and GaSb.

intermediate material robustness, it is capable of strong, normal-incidence band-to-band absorption for high quantum efficiency, with bulk GaSb having a direct band gap in the short-wave infrared (SWIR), InAs in the MWIR, and InAs/Ga(In)Sb superlattices in the SWIR, MWIR, and LWIR. The valence-to-conduction band infrared absorption mechanism also avoids the operating-temperature-limiting phonon scattering problem encountered in detectors based on the intersubband absorption mechanism. The antimonides can be epitaxially grown on GaSb or InAs substrates with very close lattice matching. In particular, 4-inch diameter GaSb substrates became commercially available in 2009. As their quality continue to improve, large diameter substrates offer economy of scale for focal plane array (FPA) fabrication, as well as the prospect for very large format arrays. The antimonides are used in a wide variety of semiconductor devices. The InAs/GaAs/AlSb resonant interband tunneling diodes (RITD) exhibit ¨ ¨ et al., very large peak-to-valley ratios at room temperature (Soderstr om 1989; Ting et al., 1990). An InAs/AlSb resonant tunneling diode had demonstrated record-breaking oscillation frequency for a room temperature solid-state electronic oscillator in 1991 (Brown et al., 1991). Antimonide-based high-electron mobility transistor (HEMT) and heterojunction bipolar transistor (HBT) showed high-frequency operation with much lower power consumption than GaAs- and InP-based devices (Bennett et al., 2005). Antimonide-based devices are highly effective in

Type-II Superlattice Infrared Detectors

17

thermophotovoltaics (TPV) applications (Hitchcock et al., 1999; Wang et al., 1999). The antimonides are used for making state-of-the-art high-power solid-state infrared lasers in 2–3 µm range (Shterengas et al., 2007). An antimonide-based mid-infrared interband cascade laser (Yang et al., 2007) is employed in a tunable laser spectrometer for methane detection on the Mars Science Laboratory. The type-II interband heterostructure backward diode (“Schulman diode”) is a highly sensitive detector essential for passive millimeter-wave imaging cameras (Moyer et al., 2008; Schulman et al., 2002). Asymmetric InAs/GaSb/AlSb resonant interband tunneling diodes have been proposed for use as nonmagnetic spin filters (Ting and Cartoix`a, 2002, 2003), whereas asymmetric InAs/GaSb/AlSb quantum wells have been predicted to exhibit quantum spin Hall effect (Liu et al., 2008). The application of the antimonides in MWIR/LWIR photodetectors is the focus of this work.

3.2. Tunneling suppression In constructing superlattice-based infrared detector structures, special considerations should be given to the absorber superlattice intrinsic properties, many of which are revealed by band structure. We begin by examining the complex band structure of bulk InAs and GaSb in Fig. 1.5, calculated using an enhanced effective bond orbital model (Cartoix`a et al., 2003) that includes bulk inversion asymmetry effects. The material parameters 1

1

InAs GaSb substrate

GaSb

C

0.5 E(eV)

E(eV)

0.5 C

0

HH

0

LH −0.5

HH SO

−1 0.25

Im kz

−0.5 SO

LH

0 Re kz 0.15

−1 0.25

Im kz

0 Re kz 0.15

k(2π/a)

k(2π/a)

(A)

(B)

FIGURE 1.5 Complex band structure in the [001] direction for (A) InAs and (B) GaSb. In each graph, real wave vector is plotted in the right portion and imaginary wave vector in the left portion.

18

David Z.-Y. Ting et al.

are taken from Vurgaftman et al. (2001). The complex band structure shows the conduction and valence bands, as well as the evanescent states. The evanescent states may be believed as “propagating” according to exp(−|kz |z) or exp(ikz z), where kz is an imaginary quantity. Therefore, they are associated with imaginary wave vectors as shown in the left panels of Fig. 1.5A and B. The tunneling leakage property of an infrared photodiode is controlled by the characteristics of the evanescent waves in the band gap. At a given energy, if allowed by symmetry, the most favorable tunneling leakage path is provided by the evanescent state with the smallest imaginary wave vector. This is given by the branch of imaginary band connecting the conduction band edge to the light-hole band edge. This is seen clearly in Fig. 1.5A, where the InAs heavy-hole and light-hole bands are split slightly due to a small strain (we intentionally strained InAs to the GaSb substrate lattice constant). In general, the magnitude of the imaginary wave vector is larger in semiconductor with larger band gaps (specifically, the energy gap between the conduction band edge and the light-hole band edge) as can been seen by comparing the complex band structures of InAs and GaSb in Fig. 1.5. Alternatively, it can be said that larger conduction band effective mass also results in reduced tunneling since semiconductors with larger band gaps also have larger conduction band effective masses. The fact that small imaginary wave vector is associated with small band gap is the fundamental reason for the tunneling leakage problem encountered in LWIR homojunction pn diode based on narrow-gap bulk semiconductors. We next examine a superlattice band structure to see how tunneling leakage is reduced in LWIR type-II superlattices. Figure 1.6 shows the band structure of a (22,6)-InAs/GaSb LWIR superlattice, calculated using an enhanced effective bond orbital model (Cartoix`a et al., 2003). The calculation does not include space charge effects (charge transfer from GaSb to InAs due to the broken-gap alignment), interface type, or interfacial diffusion, and it is subject to the limitations of the band structure model and uncertainties in the accuracy of material parameters. Therefore, as with other band structure calculations presented in this work, it should be treated only as semiquantitative when comparing with experimental results. A prominent feature of the superlattice band structure that distinguishes it from that of the typical bulk semiconductor is the splitting of the highest heavy-hole band (HH1) and the highest light-hole band (LH1) at the zone center. Although the infrared absorption edge is determined by the gap between the lowest conduction band (C1) and the HH1 band, the electron effective mass is determined by the C1-LH1 gap. In unstrained bulk semiconductors, the two gaps are the same. In the superlattice, the larger C1-LH1 gap leads to a substantially larger electron effective mass relative to that of a bulk semiconductor with the same fundamental band gap. The larger electron effective mass

Type-II Superlattice Infrared Detectors

E (eV)

0

19

(22,6)-InAs/GaSb

−0.1

c1

−0.2

hh1

−0.3

lh1 −0.4

0.04

←[100]

0

[001]→

0.036

k (2π/a)

FIGURE 1.6 Band structure of a (22,6)-InAs/GaSb superlattice along the growth direction (right portion) and the in-plane direction (left portion).

is beneficial for reducing band-to-band tunneling, as well as trap-assisted tunneling.

3.3. Auger reduction The splitting of the HH1 and LH1 bands can also result in the suppression of the Auger-7 recombination process, in which a minority electron recombines with a majority hole across the band gap while exciting another majority hole deeper into the valence bands. In the case of the (22,6)InAs/GaSb superlattice shown in Fig. 1.6, because the HH1-LH1 separation is actually larger than the C1-HH1 separation, energy and momentum conservation considerations render it difficult to find matching HH1-LH1 transitions for C1-HH1 transitions, thereby suppressing Auger-7 events. Note that the degree to which a given type-II superlattice can benefit from Auger suppression depends on the details of the band structure and doping levels; the subject has been studied extensively by Grein and coworkers (Flatte and Grein, 2009; Grein and Ehrenreich, 1997; Grein et al., 2002, 1992, 1995).

20

David Z.-Y. Ting et al.

3.4. Effective masses and transport Another prominent feature of the band structure shown in Fig. 1.6 is that the HH1 band is nearly dispersionless along the growth direction. Both the dispersionless HH1 band structure and the increased electron effective mass contribute to a larger joint density of states (JDOS). This results in a larger absorption coefficient, which, to first order, is directly proportional to the JDOS. This helps to compensate for the small optimal matrix element disadvantage inherent in type-II superlattices. The band structure in Fig. 1.6 reveals important information about carrier transport properties that can affect detector design. We note that the C1 band shows strong dispersion along both the growth (z) and an in-plane direction (x), whereas the HH1 band is highly anisotropic and appears nearly dispersionless along the growth (transport) direction. Therefore, we expect the electron and hole density of states to be 3D and 2D, respectively. The calculated conduction and valence subband zone center effective masses along the x (in-plane) and z (transport) directions are as follows: mxc ∗ = 0.023 m0 and mzc ∗ = 0.022 m0 , and mxhh1 ∗ = 0.04 m0 and mzhh1 ∗ = 1055 m0 . It is interesting to note that the electron effective mass along the growth direction is quite small (even slightly smaller than in-plane electron effective mass), and the superlattice conduction band structure near the zone center is approximately isotropic. This is in stark contrast to the highly anisotropic valence band structure. Recalling that carrier group velocity is given by v = ∇k E(k)/~, where E(k) describes the band structure, we would expect very low hole mobility and diffusivity along the growth direction. Therefore, for this LWIR superlattice absorber, detector designs based on hole transport would be unfavorable. The fact that holes have more difficulty diffusing along the growth direction toward the collecting contact than diffusing laterally can be problematic in a focal plane array (FPA). For an FPA with fully reticulated pixels (physically isolated pixels, defined by etching), lateral diffusion transports the minority carriers to the pixel sidewalls, where surface recombination could take place readily in the absence of good surface passivation. In a planar-processed FPA with nonreticulated pixels, strong lateral diffusion means that minority carriers can spread easily to neighboring pixels, resulting in image blurring. To understand the physical origin for the near isotropy in the conduction band and the extreme anisotropy of the valence band, we compare the band structure of the (22,6)-InAs/GaSb superlattice (Fig. 1.6) with that of the (6,34)-InAs/GaSb superlattice shown in Fig. 1.7. The calculated effective masses for the (6,34)-InAs/GaSb superlattice are as follows: mxc ∗ = 0.173 m0 and mzc ∗ = 0.179 m0 , and mxhh1 ∗ = 0.062 m0 and mzhh1 ∗ = 6.8 m0 . Figure 1.8 shows the schematic energy band diagrams for both superlattices, along with the positions of the C1, HH1, and LH1 states relative to

Type-II Superlattice Infrared Detectors

21

0.4

c1

0.3 (6,34)-InAs/GaSb

E (eV)

0.2

0.1

0 hh1 lh1 −0.1 0.04

←[100]

0

hh2

[001]→

0.025

k (2π/a)

FIGURE 1.7 Band structure of a (6,34)-InAs/GaSb superlattice along the growth direction (right portion) and the in-plane direction (left portion).

the InAs and GaSb band gaps. Figure 1.8A shows that the C1 level of the (22,6)-InAs/GaSb superlattice is in the broken gap region. Therefore, an electron in the C1 level can travel along the growth direction without having to tunnel through any forbidden band gap regions. This explains the low electron effective mass in the growth direction. If we decrease the InAs quantum well width and push the C1 level into the GaSb band gap, as in the case of the (6,34) superlattice shown in Fig. 1.8B, the growth direction electron effective mass then becomes considerably larger. It is interesting that the in-plane electron effective mass in the (6,34) superlattice has also become nearly as large; this is mainly due to nonparabolicity in the bulk InAs conduction band. Returning to the (22,6)-InAs/GaSb superlattice, we note in Fig. 1.8A that the HH1 level is also in the broken gap region. Then why is the HH1 effective mass so large along the growth direction? The reason is that the

22

David Z.-Y. Ting et al.

(A)

c1 hh1 lh1 InAs

GaSb

(B)

c1 hh1 lh1

FIGURE 1.8 Schematic energy band diagrams of (A) (22,6)-InAs/GaSb superlattice and (B) (6,34)-InAs/GaSb superlattice, along with the c1, hh1, and lh1 energy levels. The energy band gaps of InAs and GaSb are indicated by shaded solid rectangles.

symmetry of the heavy-hole states. In the C1 level, the quantized level in the InAs conduction band quantum well can couple with the propagating light-hole states in the GaSb layers. For the HH1 level, by symmetry, the quantized heavy-hole states in the GaSb quantum well cannot couple to the propagating conduction band states in InAs despite having the same energy and instead has to couple with evanescent states with large wave vectors in InAs. As a result, the quantized heavy-hole states in neighboring GaSb quantum wells are essentially isolated from one another, leading to the dispersionless HH1 band. Hole mobility along the growth direction may be quite acceptable in some superlattice structures. Figure 1.9 shows the detailed HH1 band structure for a (14,7)-InAs/GaSb superlattice and a (8,6)-InAs/GaSb superlattice, which are used in LWIR and MWIR detector structures, respectively. We note that the dispersion of the MWIR superlattice is much stronger than the LWIR superlattice; the MWIR HH1 effective mass is ∼20 times smaller than that for the LWIR superlattice. Even for the LWIR superlattice, a closer look at the HH1 band structure reveals that the hole velocity may not be as low as first appeared. Figure 1.9A shows that in

Type-II Superlattice Infrared Detectors

0.06

0.03

(14,7)-InAs/Gasb

(8,6)-InAs/Gasb

ky = 0.0

ky = 0

0.005

0.005

0.055

0.015

0.045

0.010

E (eV)

0.05

KBT (T = 80 K)

0.025

0.010

E (eV)

23

0.02

0.015

0.020

0.015

0.020 0.04 0.02 ← kx 0

kz

1/Lz kx→

k (2π/a) (A)

0.03

0.01 0.02 ← kx 0

kz

1/Lz kx→

0.03

k (2π/a) (B)

FIGURE 1.9 The heavy-hole 1 subband band structure of the (14,7)-InAs/GaSb superlattice in Graph (A) and the (8,6)-InAs/GaSb superlattice in Graph (B). In each graph, the central panel shows band structure along the growth direction (kz ) from the reduce zone center to the zone boundary. The side panels show the continuation of the band structure plotted along the in-plane direction kx . The HH1 bands for several ky values are plotted. In each graph, Lz is the number of monolayers in each period of the superlattice. A vertical bar inserted between the two graphs indicates the size of kB T (6.9 meV for T = 80 K) on the energy scale; the top of the bar coincides with the HH1 valence band edges of the two superlattices.

the LWIR superlattice, for ky = 0, the HH1 band has very little dispersion along kz (z being the growth direction), with maximum occurring at the center of the reduced Brillouin zone. But as the result of interaction with other subbands, the HH1 band dispersion along the growth direction becomes appreciably larger as the in-plane momentum (ky ) increases; the band maximum along the kz direction quickly switches from the reduced zone center to the zone boundary. At lower temperatures, we expect holes to occupy the less dispersion portions of the HH1 band, for which the hole density of states (DOS) is more like 2D and hole velocities along the growth direction are low. At higher temperatures, we expect the more dispersive parts of the HH1 to be occupied also. The thermalized holes would occupy the part of the DOS that is more 3D-like, and would attain higher velocities. Figure 1.9B shows the corresponding HH1 band structure plot for the (8,6)-InAs/GaSb MWIR superlattice. Note that in this case, the HH1 band shows a reasonable amount of dispersion even at ky = 0 and its hole

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0.0004

Density of states

Density of states

0.0004 (14,7)-InAs/GaSb 0.0003 0.0002 0.0001 0 0.17

C1

0.18

0.19

0.2

C1

0.0001

0.28

0.29

0.3

0.31

0.02

0.03

0.015

Density of states

Density of states

0.0002

0 0.27

0.21

0.015

0.01

0.005

0 0.02

(8,6)-InAs/GaSb 0.0003

HH1

0.03

0.04

Energy (eV) (A)

0.05

0.06

0.01 HH1 0.005

0 −0.01

0

0.01

Energy (eV) (B)

FIGURE 1.10 Conduction and valence band edge density of states (DOS) for the (14,7)-InAs/GaSb superlattice in Graph (A) and the (8,6)-InAs/GaSb superlattice in Graph (B). The portions of conduction and valence band DOS shown originate from the C1 and HH1 subbands, respectively.

transport properties should be much better than that of the LWIR superlattice. Nevertheless, even for the MWIR superlattice, the dispersion along the in-plane directions are much larger (see the side panels of Fig. 1.9B), thus favoring lateral hole diffusion. This is an issue that should be considered when choosing an n-doped type-II superlattice as an infrared absorber. Figure 1.10 shows the actual calculated density of states for the (14,7)InAs/GaSb LWIR superlattice and the (8,6)-InAs/GaSb MWIR superlattice. √ The conduction band DOS resembles the standard 3D DOS ∝ E − Ec though with distinct differences due to band nonparabolicity. The HH1 DOS differs qualitatively from both the standard 3D and the 2D (step-like) DOS. The form of the DOS can affect our understanding of device performance. A standard tool used to study detector characteristics is dark current analysis, in which we fit experimentally measured dark current to analytical forms for various dark current sources (diffusion, generation-recombination, tunneling). This allows us to extract information on the dark current–generating mechanisms and carrier lifetimes (Pellegrino and DeWames, 2009; Rhiger et al., 2009). In the typical dark current analysis, the carrier densities are modeled using the standard 3D DOS appropriate for bulk semiconductors. But as shown in Fig. 1.10,

Type-II Superlattice Infrared Detectors

25

superlattice DOS (specifically VB DOS) can be quite different from bulk DOS. This can affect the accuracy of dark current analysis. We note that there is tentative indirect evidence from LWIR superlattice infrared detector dark current analysis that the hole density switches from 2D to 3D with increasing temperature (Nguyen et al., 2009b).

4. SUPERLATTICE INFRARED DETECTORS The key to achieving high-performance infrared detection is in attaining high quantum efficiency and low dark current. With the ability to grow thick layers of high-quality superlattices with low defect density, resulting in sufficiently high absorption coefficient and large diffusion length, high quantum efficiency is now readily achievable. The typical dark current mechanisms include tunneling leakage, Auger processes, Shockley-ReadHall (SRH) processes, and surface leakage. In the previous section we discussed how the band structure of appropriately designed superlattices leads to tunneling reduction and Auger suppression. In this section, we discuss how unipolar barriers are used to reduce dark currents associated with SRH processes and surface leakage.

4.1. Unipolar barriers The use of heterostructures to improve HgCdTe (MCT) infrared detector performance is a well-established practice (Arias et al., 1991; Pultz et al., 1991; Tung et al., 1992). Detector structures such as the double-layer heterojunction (DLHJ) have demonstrated significant advantages over their homojunction counterparts. The use of heterostructures is also prevalent in group III–V semiconductor-based infrared detectors. A particularly useful heterostructure construct is the unipolar barrier. The term “unipolar barrier” was introduced recently to describe a barrier that can block one carrier type (electron or hole) and allows the unimpeded flow of the other (Ting et al., 2009b,a) as illustrated in Fig. 1.11. The concept of the unipolar barriers existed long before they were called as such. The double-heterostructure (DH) laser, which makes use of a pair of complementary unipolar barriers, was first described in 1963 (Alferov and Kazarinov, 1963; Kroemer, 1963), soon after the concept of heterostructure devices. Unipolar barriers have also been used extensively to enhance infrared detector performance. White (1987) used unipolar barriers to block the flow of majority carrier dark current in photoconductors without impeding minority carriers. A DH detector design can be used to reduce diffusion dark current emanating from the diffusion wings surrounding the absorber layer (Carras et al., 2005). The nBn (Maimon and Wicks, 2003, 2006; Pedrazzani et al., 2008) or XBn (Klin et al., 2009; Klipstein, 2005, 2008;

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Electron-blocking unipolar barrier

Hole-blocking unipolar barrier

EC

EC

O

O

EV

EV

FIGURE 1.11 Schematic illustration of the energy and diagrams of an electron- and a hole-blocking unipolar barriers.

Klipstein et al., 2010) detector structure uses a unipolar barrier to suppress dark current associated with Shockley-Read-Hall processes without impeding photocurrent flow, as well as to suppress surface leakage current (Pedrazzani et al., 2008). In general, unipolar barriers can be used to implement the barrier infrared detector architecture for increasing the collection efficiency of photogenerated carriers (by deflecting them towards the collector, in the same way a back-surface field layer functions in a solar cell structure) and reducing dark current generation without inhibiting photocurrent flow.

4.2. Dark current reduction using unipolar barriers We illustrate the use of unipolar barriers for dark current reduction by comparing diodes based on homojunction and heterojunction designs. One of the key uses for the unipolar barrier is in the suppression of generation-recombination (G-R) dark current due to SRH processes. As discussed by Klipstein (2008), in a conventional photodiode, there exists a threshold temperature T0 , above which the dark current is diffusion limited and below which G-R limited. In a homojunction pn diode, the G-R current is proportional to exp(−Eg /2kT) (assuming mid-gap defect level) and is predominantly generated in the depletion region. If the depletion region of the pn diode is replaced by a larger gap semiconductor (a barrier), in which the exp(−Eg /2kT) factor is greatly reduced (particularly at lower temperatures), the SRH dark current generation can be virtually eliminated. The suppression of the G-R dark current allows the detector to operate at higher temperature or with higher sensitivity. It is important that the G-R reducing barrier does not block the photocurrent. In a p on n structure, this can be accomplished by inserting an electron-blocking unipolar barrier at the junction of the pn diode to form the pBn diode (Klipstein, 2008). Figure 1.12 shows the reverse bias energy

Type-II Superlattice Infrared Detectors

27

band diagrams of a pn diode and a pBn diode, calculated using heterojunction drift-diffusion simulation (Daniel et al., 2000). Both structures use an n-type MWIR InAs/GaSb superlattice as the absorber. The doping levels in the p and n regions are taken to be p = 1 × 1016 cm−3 and n = 1 × 1016 cm−3 , respectively. The pBn structure contains an undoped ˚ wide electron-blocking unipolar barrier made from a GaSb/AlSb 2000 A superlattice. The bottom panel of Fig. 1.12 shows the calculated magnitudes of the SRH recombination rates given by the expression rSRH = (np − n2i )/[τp (n + ni ) + τn (p + pi )]. A value of τp = τn = 100 ns (Donetsky et al., 2010) is used in the simulation. For the pn junction, the calculated peak SRH recombination rate in the middle of the depletion region is approximately five orders of magnitude larger than the baseline rate outside the depletion region. In the pBn structure, the calculated SRH recombination rate is greatly reduced. We next examine the suppression of G-R dark current in a p-type LWIR detector using a hole-blocking unipolar barrier. We consider a homojunction np diode and a heterojunction NIp diode, both with p-type 10-µm LWIR InAs/GaSb superlattice as the absorber. The reverse bias energy band diagrams for the two devices are shown in Fig. 1.13, along with the calculated magnitudes of the SRH recombination rates. The doping densities in the p and n regions of the homojunction diode are taken to be p = 1 × 1016 cm−3 and n = 1 × 1016 cm−3 , respectively. The NIp structure uses an InAs/AlSb superlattice as the wide-gap “N” and “I” region, which acts as a hole-blocking unipolar barrier to the LWSL superlattice absorber. ˚ segment of the barrier adjacent to the p-type In the NIp structure, the 3000 A absorber (doped to p = 1 × 1016 cm−3 ) is undoped, whereas the remaining portion of the wide-gap region is doped to n = 1 × 1016 cm−3 . A value of τp = τn = 35 ns (Connelly et al., 2010; Donetsky et al., 2010; Pellegrino and DeWames, 2009) is used in the simulation. For the superlattice homojunction np diode, the calculated peak SRH recombination rate in the middle of the depletion region is approximately three orders of magnitude larger than the baseline rate outside the depletion region. In the NIp structure, the calculated SRH recombination rate is again greatly reduced. Note that in the NIp structure, as well as in the pBn structure discussed above, photogenerated minority carriers in the absorber region can flow towards the collector without being impeded. The use of the unipolar barrier can suppress SRH-related dark current without reducing photoresponse. The pBn and the NIp structures described above are actually quite similar. If we took an nBp structure (the complement of the pBn structure, with a hole-blocking unipolar barrier) and replaced the “n” contact layer with a wider gap “N” layer (which would not affect device performance, so long as we could make ohmic contact to the “N” layer), then we end up with the NIp structure (the “B” barrier layer is now called

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Energy (eV)

0.4 pn n = 1016cm−3

0 p = 1016cm−3 −0.4 1.6 pBn

Energy (eV)

1.2

0.8

Ec

T = 120 K

Ev

VL = −0.1V

EF,n

0.4

EF,p

0

−0.4

|rSRH| (cm−3S−1)

1018 1016

pn pBn

1014 1012 1010

0

0.5

1

1.5

2

2.5

Position (µm)

FIGURE 1.12 The top and middle panels show the calculated 80 K reverse-bias energy diagrams along with quasi Fermi levels for a mid-wavelength infrared superlattice pn junction diode and a pBn diode, respectively. The bottom panel shows the calculated magnitude of the Shockley-Read-Hall recombination rates for the two structures as functions of position.

3

29

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0.2 Energy (eV)

np 0

n = 1016 cm−3

p = 1016 cm−3

−0.2

0.2 NIp

Energy (eV)

0

T = 80 K

Ec

−0.2

Ev VL = 0.1 V

EF,n

−0.4

EF,p −0.6

|rSRH| (cm−3S−1)

1020 np NIp 1018

1016 0

0.5

1

1.5

2

2.5

3

Position (µm)

FIGURE 1.13 The top and middle panels show the calculated 80 K reverse-bias energy diagrams along with quasi Fermi levels for a long-wavelength infrared superlattice np junction diode and a NIp diode, respectively. The bottom panel shows the calculated magnitude of the Shockley-Read-Hall recombination rates for the two structures as functions of position.

the “I” layer). Calculations on the nBn structure also show similar SRH recombination rate suppression (Ting et al., 2010). In all cases, a majority carrier blocking unipolar barrier is used for G-R dark current suppression, without blocking minority carrier photocurrent.

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Unipolar barriers can also be used to suppress surface leakage current. Wicks and coworkers demonstrated experimentally that by introducing a judiciously placed unipolar barrier into an n-type InAs photoconductor or an InAs pn photodiode, forming an nBn detector or a unipolar barrier photodiode, the surface leakage current can be substantially reduced (Savich et al., 2010; Wicks et al., 2010). Although these demonstrations were done using InAs photodetectors, which are known to suffer from surface leakage, the operating principles should apply equally well to superlattice-based photodetectors.

4.3. Building unipolar barriers In general, unipolar barriers are not always readily attainable for the desired infrared absorber material as both the absorber and barrier materials require (near) lattice matching to available substrates, and the proper band offsets must exist between the absorber and the barrier. The practical realization of the MWIR nBn detectors (Maimon and Wicks, 2006) is enabled only by the fortuitous existence of the approximate valence band alignment between the InAs0.91 Sb0.09 absorber and AlSbAs electronblocking barriers, both can be epitaxially grown on GaSb substrate. (Alternatively, InAs absorber and AlSbAs barrier can be grown on an InAs substrate.) As described by Carras et al. (2005), finding a hole-blocking unipolar barrier for InAs0.91 Sb0.09 is challenging and considerable effort was required to circumvent such difficulties. Building unipolar barriers for InAs/GaSb superlattices is relatively straightforward because of the flex˚ materials afforded by the three different types of band ibility of the 6.1 A alignments among InAs, GaSb, and AlSb. For electron-blocking unipolar barriers to InAs/GaSb superlattices, we note that for superlattices with the same GaSb layer widths, their valence band edges tend to line up fairly closely. This is because the large heavy-hole mass makes the HH1 energy level relatively insensitive to the well width. Therefore, an electron-blocking unipolar barrier for a given InAs/GaSb superlattice can be formed by using either another InAs/GaSb with thinner InAs layers (Nguyen et al., 2008a; Ting et al., 2009a) or a GaSb/ AlSb superlattice (all with approximately the same GaSb layer widths to ensure valence band alignment). For hole-blocking unipolar barriers to InAs/GaSb superlattices, there are many options as illustrated in Fig. 1.14. Superlattices with complex supercells, such as the four-layer InAs/GaInSb/InAs/AlGaInSb “W” structure (Aifer et al., 2006, 2010a; Canedy et al., 2007; Kim et al., 2007; Vurgaftman et al., 2006) or the four-layer GaSb/InAs/GaSb/AlSb “M” structure (Nguyen et al., 2009a, 2008b, 2007b, 2008a; Nguyen and Razeghi, 2007a), have been used as hole-blocking unipolar barriers. Alternatively,

Type-II Superlattice Infrared Detectors

InAs

GaSb

31

AIGalnSb

GaInSb

InAs

(A)

(B) AISb AISb

GaSb

InAs

InAs

(C)

(D)

FIGURE 1.14 Schematic energy band diagrams of (A) an InAs/GaSb superlattice, (B) an InAs/GaSb/InAs/AlSb “W” superlattice, (C) an InAs/GaSb/AlSb/GaSb “M” superlattice, and (D) an InAs/AlSb superlattice.

the two-layer InAs/AlSb superlattice (Fig. 1.14D) has also served well (Ting et al., 2009a). Incidentally, both the conduction band edge and the valence band edge of the “W” superlattice (WSL) can be adjusted. As a result of this flexibility, the WSL has been used as a hole-blocking unipolar barrier, an absorber, as well as an electron-blocking unipolar barrier. Figure 1.15 illustrates another aspect of the usefulness of the unipolar barrier. Figure 1.15A shows the calculated energy band diagram of a LWIR superlattice detector based on an earlier double heterostructure design similar to the one described by Johnson et al. (1996). In this structure, p-GaSb and n-GaSb are used as electron and hole barriers to the LWIR absorber superlattice. Because the band edges of GaSb does not line up with those of the absorber, there are energy spikes that can block photocurrent. Figure 1.15B shows a more recent double heterostructure design that incorporates unipolar barriers. The LWIR InAs/GaSb absorber SL is surrounded by an electron-blocking unipolar barrier made from an MWIR InAs/GaSb superlattice and a hole-blocking unipolar barrier made from an InAs/AlSb superlattice. The spikes are no longer present, and photocurrent can flow unimpeded.

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0.8

T = 80 K

0.6

Energy (eV)

0.4 0.2

p-SL

n-GaSb

0 −0.2

p-GaSb

Ec

−0.4

Ev

−0.6

EF

−0.8 0

1

2

3

4

5

6

0.4

Energy (eV)

0.2

Absorber SL

hB SL

0 eB SL

−0.2 −0.4 0

1

2

3

4

5

6

Distance (µm)

FIGURE 1.15 The top panel shows the energy band diagram of double heterostructure (DH) consisting of a InAs/GaSb superlattice absorber surrounded by p-GaSb and n-GaSb barriers. The bottom panel shows the energy band diagram of DH with the superlattice absorber surrounded by a pair of electron- and hole-blocking unipolar barriers.

4.4. Barrier infrared detector The type-II broken-gap InAs/Ga(In)Sb superlattice can be used as mid- or long-wavelength infrared absorber. As discussed earlier, superlattices or alloys built from the InAs/GaSb/AlSb material system can also be customdesigned to build matching unipolar barriers to the infrared absorber

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EC EC EV

EV (A)

(B) EC EC EV

(C)

EV

(D)

FIGURE 1.16 Schematic flat-band energy band diagrams of (A) a double heterostructure (DH), (B) a dual-band nBn structure, (C) a DH with a graded-gap junction, and (D) a complementary barrier structure.

superlattice. In particular, the ability to tune the positions of the conduction and valence band edges independently in a type-II superlattice is especially helpful in the design of unipolar barriers. Figure 1.16 illustrates the energy band diagrams of some idealized examples of the type-II superlattice-based infrared detectors that make use of unipolar barriers. Broadly speaking, they are based on either the nBn/pBp/XBn architecture (Klipstein, 2008; Maimon, 2010; Maimon and Wicks, 2003, 2006) or the variations of the double heterostructure design. Figure 1.16A illustrates a dual-band superlattice nBn detector (Khoshakhlagh et al., 2007) in which an LWIR superlattice and an MWIR superlattice are separated by an AlGaSb unipolar barrier. This follows an earlier single-band superlattice nBn detector with an MWIR absorber and an AlGaSb barrier (Rodriguez et al., 2007). The advantage of this type of architecture is simplicity (which often leads to better manufacturability) and the ability to suppress G-R and (electron) surface leakage dark current (Maimon and Wicks, 2006; Pedrazzani et al., 2008; Wicks et al., 2010). The concerns for the nBn architecture, when used with an n-doped type-II superlattice absorbers, are possible low hole mobility (particularly in LWIR structures) and strong lateral diffusion (Plis et al., 2008). A variation of the superlattice nBn detector, in which the n-type contact layer is replaced by a p-type contact and thus forming the pBn structure, has also been reported (Hood et al., 2010a).

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Figure 1.16B illustrates a double heterostructure (DH) detector structure. The DH design is commonly used in laser structures and has been used in MWIR detectors with bulk semiconductor absorbers (Carras et al., 2005; Reverchon et al., 2004). Johnson et al. (1996) used a DH structure similar to the one shown in Fig. 1.15A, in which an LWIR superlattice is surrounded by barriers made from p-GaSb and n-GaSb. A more recent design consists of an LWIR InAs/GaSb absorber superlattice surrounded by an electron-blocking unipolar barrier made from an MWIR InAs/GaSb superlattice and a hole-blocking unipolar barrier made from an InAs/GaSb/AlSb/GaSb (“M”) superlattice (Nguyen et al., 2008b, 2007b, 2008a). Figure 1.16C illustrates a variation of the double heterostructure (DH) detector structure, in which a graded gap region is inserted between the absorber and the hole barrier to reduce tunneling and G-R dark currents (Vurgaftman et al., 2006). The structure is also used to enable the shallowetch mesa isolation (SEMI) structure for surface leakage current reduction (Aifer et al., 2010a). The design is very flexible. The hole-blocking unipolar barrier is typically made from a four-layer InAs/GaInSb/InAs/AlGaInSb “W” superlattice (WSL), although an InAs/AlInSb superlattice has also been used. The graded gap region is typically made from multiple segments of WSLs with progressively changing band gaps. The absorber has been made from a WSL or an InAs/GaInSb superlattice. The electronblocking unipolar barrier has been made from WSL or p-GaSb. Figure 1.16D illustrates another variation of the double heterostructure (DH) detector structure, called a complementary barrier structure (Ting et al., 2009c), or a PbIbN structure (Gautam et al., 2010). This is basically a DH structure surrounded by additional narrow-gap contact layers. The narrow-gap layers can be useful in the case in which it is difficult to make ohmic contact to the wide-gap barrier layers. In the PbIbN structure (Gautam et al., 2010), all the layers are made from InAs/GaSb superlattices with different layer widths. Yet another variation on the DH structure is the complementary barrier infrared detector (CBIRD) structure (Ting et al., 2009a) illustrated in Fig. 1.17. The CBIRD design consists of a lightly p-doped InAs/GaSb absorber SL sandwiched between an n-doped InAs/AlSb hole-barrier (hB) SL, and a wider gap InAs/GaSb electron-barrier (eB) SL. The hB SL and the eB SL are designed to have approximately zero conduction and valence subband offset with respect to the absorber SL, that is, they act as a pair of complementary unipolar barriers with respect to the absorber SL. A heavily doped n-type InAsSb region adjacent to the eB SL acts as the bottom contact layer. The unipolar-barrier-based Np junction between the hB SL and the absorber SL acts to reduce SRH-related dark current. The wider gap hB SL also serves to reduce trap-assisted tunneling. The eB SL serves

35

Type-II Superlattice Infrared Detectors

AlSb

GaSb

InAs

GaSb

InAs

InAs

EC hB SL

Absorber SL

eB SL

InAsSb EV

FIGURE 1.17 Schematic energy band diagram of a complementary barrier infrared detector (CBIRD) structure, in which a long-wave infrared InAs/GaSb superlattice absorber is surrounded by a InAs/AlSb superlattice hole-blocking unipolar barrier and a shorter period InAs/GaSb superlattice electron-blocking unipolar barrier.

to deflect photogenerated electrons toward the Np junction for collection (similar to back surface field in solar cells). Although the InAsSb layer also appears to provide a hole barrier on the left, the broken-gap band alignment between the eB SL and InAsSb facilitates interband tunneling and interface recombination, which reduces hole accumulation in the absorber region. In addition, the eB SL presents a taller barrier against extra electron injection from the bottom contact. Detailed results on this particular CBIRD device have been reported earlier (Ting et al., 2009a, 2010). Figure 1.18 shows the dark current–voltage characteristics of a CBIRD device compared to a homojunction device made with nominally the same absorber superlattice. The two detectors have approximately the same photoresponse, but the CBIRD shows a substantial dark current reduction over the homojunction superlattice detector. In general, the use of heterostructures, particularly unipolar barriers, has been highly effective in dark current reduction in type-II superlattice-based LWIR detectors. Figure 1.19 shows a compilation by D. R. Rhiger of the 78 K dark current densities plotted against detector cutoff wavelengths for homojunction and heterojunction type-II superlattice detectors reported in the literature since late 2010. In general, the devices with the lowest dark current densities are heterojunction devices. Furthermore, the dark current densities of several heterojunction devices reported by different institutions (Canedy et al., 2009; Nguyen et al., 2009a, 2010b) are approaching the levels calculated using the empirical “Rule 07” model (Tennant, 2010; Tennant

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101 T = 77 K

Current density (A/cm2)

100 10−1 10−2

SL Homojunction

10−3 10−4 10−5

SL Heterojunction

10−6 10−7

−0.4

−0.2

0 Bias (V)

0.2

0.4

FIGURE 1.18 Dark current densities for a superlattice homojunction long wavelength infrared (LWIR) detector and a superlattice heterojunction LWIR detector taken at 77 K.

10−2 10−3 10−4 10−5 10−6 10−7 10−8 10−9

T = 78 K 6

8

10 12 Cutoff wavelength (µm)

Rule 07 Non-barrier Barrier

14

Jdark-survey3-78K-1d.qpc

Dark current density (A/cm2)

10−1

16

FIGURE 1.19 The 78 K dark current densities plotted against cutoff wavelength for type-II superlattice detectors reported in the literature since late 2010. The open and solid symbols indicate homojunction and heterojunction devices, respectively. The solid line indicates the dark current density levels calculated using the empirical “Rule 07” model. (Courtesy by D. R. Rhiger.)

Type-II Superlattice Infrared Detectors

37

et al., 2008), which provides a heuristic predictor of the state-of-the-art MCT photodiode performance. Finally, we note that there is another type of antimonide superlattice infrared detector called the interband cascade infrared photodetector (ICIP), which is based on a radically different design (Li et al., 2005; Yang et al., 2010b,a). In its original incarnation (Li et al., 2005), it was simply an interband cascade laser (ICL) diode structure (Yang, 1995) running in “reverse operation” as a photodetector. The operation of the ICIP is similar to that of the quantum cascade detector (Gendron et al., 2004), except that since it is based on interband than intersubband transitions, it is capable of normal incidence infrared absorption. The operating principle of the ICIP is described in detail by Yang et al. (2010b).

5. DETECTOR FABRICATION AND CHARACTERIZATION In order to evaluate the superlattice material and the detector structures described in the earlier sections, different structural, optical, and electrical ¨ characterization tools are used (Burkle and Fuchs, 2002; Fuchs et al., 1997b). In this section, we will focus on a few of these characterization techniques, including optical characterization, lifetime measurements, and noise measurements. We will also describe one of the biggest challenges faced during fabrication of superlattice detectors, namely, the etching and passivation of the detector surfaces and how this affects the dark current and noise properties.

5.1. Detector fabrication Surface leakage is a major challenge in the fabrication of InAs/GaSb superlattice-based detectors and arrays. High surface leakage current prevents full operation of the detector due to the high 1/f noise or can lead to excess charging of the ROIC and cause saturation. This requires the ROIC to have a larger electron capacity or high diode impedances in order to maximize full potential of the camera system. One source of surface leakage comes for the presence of a nonzero surface potential. A nonzero surface potential at the sidewall interface leads to band bending, resulting in a high flat band voltage. If the overall surface potential is positive (negative), then the electron energy is decreased (increased) and the bands must bend downward (upward). The resulting accumulation/inversion of majority carriers can create conductive leakage pathways parallel to the sidewalls (Fuchs et al., 1998a). For LWIR detector structures, especially with cutoff wavelengths longer than 10 µm, the amount of band bending becomes comparable to the band gap of

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the device (Herrera et al., 2008), so achieving near flat band condition is essential for high performance. One source of nonzero surface potential is the improper termination of the crystalline lattice at the semiconductor–air interface. Tetrahedral GaSb, InAs, and AlSb lattice is abruptly terminated at the surface during etching and leaves one or two dangling crystal bonds per surface atom. These dangling bonds can act as reaction sites for chemical reactions or surface states for electronic processes. Dangling bonds that are empty can contribute to the reduction in free energy and the lowering of the surface band profile, or they can be satisfied through adsorption of water, oxygen, etch byproducts, contaminants, or foreign atoms. Surface states are another source of leakage current. The typical surface states are interfacial traps that come from attachment of etch byproducts, contaminants, or foreign atoms to the dangling bonds. These traps can be charged via interaction with the conduction and/or valence band of the semiconductor and capturing or emitting electrons or holes. Acceptor interface traps are negative when filled and neutral when empty, and donor interface traps are neutral when filled and positive when empty. If a large number of surface states are positioned within the band gap of the semiconductor, pinning of the Fermi level will occur. This can lead to a number of different undesirable effects, such as increased trap-assisted tunneling dark current, minority carriers drifting to the surface, and contribute to high surface recombination velocity, loss of quantum efficiency, or the creation of excess leakage current. The problem with high surface leakage can begin with the quality of the etched sidewalls. It is important that unwanted contaminants, etch byproducts, or foreign atoms do not attach to the dangling bonds, leading to a change in the resistance at the surface. For the InAs/GaSb superlattice, the presence of a native oxide can form secondary compounds on the sidewall surface (such as In2 O3 or Ga2 O3 ) that acts as a good conductor and decrease the surface resistance. Good sidewall profile and high fill factor are highly desirable characteristics, especially for large format focal plane arrays with small pixels. Chemical wet etch is advantageous due to the minimal amount of sidewall damage; however, this becomes an unacceptable option due to the large degree of undercut and concave sidewall profiles. High-density plasma etching can alleviate this issue with its anisotropy due to the plasma sheath and ionized gas directionality, but poses challenges of its own. One challenge is plasma-induced damage, which has been found to leave etch residues and ripple patterns in the sidewalls (Kutty et al., 2010; Nguyen et al., 2009c; Rehm et al., 2006). Another challenge with etching group III–V materials is preferential etching, where preferential loss of group V elements can create ripples along the sidewalls. The rough morphologies of the ripples become an additional source for electrical active sites. With a clean surface that is smooth and free

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from unwanted contaminants, the challenge for passivation is alleviated, and any encapsulation that occurs during passivation can preserve the high-quality state of the sidewall surface. Surface passivation is as important as the etching mechanism since it affects the electrical performance by satisfying dangling bonds with atoms that can modify the surface potential and possibly counteract any charges on the surface. It is important that the passivation technique does not etch the surface or roughen the surface. Further, the material needs to be nonconductive and does not contribute to the surface resistance. It can be seen that the resistance-area product has a linear relationship with the surface resistivity as given by the relation 1 P 1 1 + = , RA (RA)bulk rsurface A where (RA)bulk is the resistance-area product of the bulk material, rsurface is the surface resistivity, P is the perimeter of the diode, and A is the area of the diode. In addition to protecting the surface from chemical reactions, passivation can physically protect the surface from degradation and ensure stability of the device. Any passivation that encapsulates the surface can provide physical protection and also acts as a barrier to prevent diffusion of unwanted reactive species. This may be beneficial for subsequent steps in the FPA fabrication process such as epoxy underfill.

5.2. Optical characterization of superlattices During the development of superlattice detectors, several different optical and optoelectronic characterization techniques have been used to study InAs/Ga(In)Sb superlattices. Photoluminescence (PL), absorption, and electroluminescence (EL) spectroscopy are all very useful tools for extracting information about the material quality, energy-level structure, dopant levels, etc. of these superlattices. PL spectroscopy is a nondestructive characterization technique that provides information about the band structure, dopants, and trap energy levels. It is a well-established technique widely used to study material properties of bulk semiconductors, as well as of quantum structures (Lacroix et al., 1996; Pavesi and Guzzi, 1994). This technique has also shown to be a powerful tool when studying the optical performance of superlattices. Information about the material quality is obtained from the ¨ PL intensity (Burkle et al., 2000; Canedy et al., 2003; Haugan et al., 2008; Schmitz et al., 1995) and the width of the PL peak (Canedy et al., 2003; Haugan et al., 2006; Ongstad et al., 2000). By studying the influence of

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temperature and excitation power density on the PL peak amplitude and the peak position, respectively, other physical properties of the superlattice such as the recombination processes in the material and the variation of the band gap with temperature are revealed. In EL charges are generated electrically rather than optically thus device fabrication is needed. This offers some additional degrees of freedom since specific regions of the detector structure can be studied separately. EL has been used as a tool to extract information about the material quality. In addition, it has served to explain some device characteristics in superlattice detectors. Rodriguez et al. (2005) observed a temperature dependence of the photoresponse for MWIR InAs/GaSb superlattices with activation energy of approximately 28 meV, which later was attributed to the activation energy of Be-dopants (Hoffman et al., 2006), extracted with EL measurements. Furthermore, trap centers located in the band gap of a LW InAs/GaSb superlattice, observed by EL, contributed to the understanding of the dark current characteristics of those detectors (Yang et al., 2002). Absorption spectroscopy is a straightforward technique for extracting essential parameters about the detector performance, such as absorption quantum efficiency and spectral response. Very little sample preparation is required, which makes it a convenient way to extract quick feed¨ back in the optimization process of the detector material (Hoglund et al., 2010). As described below, by combining absorption spectroscopy with the information gained from PL and EL, a good indication of the attainable performance of detectors fabricated from the studied material can be obtained. Good IR detector material is characterized by high-absorption quantum efficiency (QEa ) and a long lifetime of the minority carriers (τ ). Those properties are essential since the density of photon-generated carriers (QEa 8τ/t) need to be larger than the thermally generated carrier density for optimal performance of a detector fabricated from that material (Kinch, 2000; t is the thickness of the detector material and 8 is the photon flux). The absorption QE is easily attainable from transmission measure¨ ments (Hoglund, 2010). By comparing the absorption QE with the external QE obtained by responsivity measurements, information about the transport properties in the material can be obtained. In Fig. 1.20, the spectra of the external QE and the absorption QE of a LW InAs/GaSb CBIRD detector are well correlated in terms of spectral distribution; however, the amplitude of the absorption QE is higher than the corresponding external QE. Since the absorption QE serves as an upper limit of the external QE (unless there is a gain in the structure), the difference between these QEs indicates that not all photogenerated carriers reach the contacts.

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0.5 Quantum efficiency (QE)

41

0.4 Absorption QE 0.3

External QE

0.2 0.1 0.0

5

6

7 8 9 Wavelength (µm)

10

FIGURE 1.20 Absorption quantum efficiency versus external quantum efficiency in an InAs/GaSb CBIRD detector at an applied bias of 0.15 V.

To achieve a high collection efficiency of excited carriers the minority carrier lifetime should be long. The minority carrier lifetime is dependent on the radiative lifetime (τ R ), as well as the nonradiative lifetime (τ nR ). The nonradiative lifetime is influenced by several different recombination processes of which the most important ones are the Shockley-Read-Hall (SRH) recombination, Auger processes, and surface recombination. All of these processes add to the minority carrier lifetime according to the follow1 1 + τAuger + τ 1 (Ahrenkiel and Lundstrom, ing equation: τ1 = τ 1 + τSRH Rad surface 1993). This equation illustrates that the recombination process with the shortest lifetime dominates the minority carrier lifetime. Different optical methods are used to extract the minority carrier lifetime in superlattice material (Connelly et al., 2010; Donetsky et al., 2010, 2009; Hoffman et al., 2005), described in more detail in the next subsection. In order to distinguish which recombination process has the major influence on the minority carrier lifetime, PL and EL spectroscopy are used. When performing these studies, it is preferable to sandwich the absorber between two barriers to reduce the effect of surface recombination. (see suggestions by Ahrenkiel and Lundstrom, 1993). To get an understanding of the possible Auger-related processes that might limit the lifetime, the band structure of the material is studied. The band gap of the superlattice can be approximated by the peak energy of the PL (or EL) spectrum or with the cutoff wavelength of the absorption spectrum (Fig. 1.20). Some deviation

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from the exact band gap energy is expected, depending on the temperature and on the excitation power that sets the excess carrier density in PL experiments. Bertru et al. (1999) observed a blueshift of the PL peak with increasing excess carrier density, varying as the third root of the excitation density. The blueshift was caused by filling of triangular wells formed at the InAs/GaSb interfaces. The triangular wells are induced by the Coulomb attraction between the separated holes and electrons located in the GaSb and the InAs layers, respectively. As with all semiconductors, the band gap of InAs/GaSb superlattices changes with temperature. In addition to this bandgap variation, the temperature change affects other processes that shift the PL peak position. For bulk material, a continuous redshift of the PL peak position with increasing temperature is observed. However, in a InAs/GaSb superlattice blueshift of the PLpeak with increasing temperature in the 2–125 K temperature range was observed by Bertru et al. (1999). The explanation given by this group was that the joint density of states of type-II quantum wells (QWs) differs from bulk and also from type-I QW structures. Band-to-band absorption behaves like (ε − ε0 )1.5 , which means that high k-value transitions will be favored. As the temperature is increased, the higher k-value states will be populated, which could cause the observed blueshift. These effects will cause minor errors in the estimation of the band gap, which should be considered when analyzing luminescence data. Whereas the luminescence spectrum mainly probes the interband transitions between the lowest conduction band and the highest valence band (typically the heavy-hole band), absorption spectroscopy or Fourier transform PL excitation (PLE) could be used to study interband transitions between higher energy bands. To our knowledge, no PLE studies have been performed on InAs/GaSb superlattices so far. However, this technique has been successfully utilized to study higher energy transitions in other medium-infrared detector materials such as HgCdTe and InSb (Fuchs et al., 1993); therefore, it could be a possible candidate for future studies of superlattice band structure. Several groups have used absorption spectroscopy to study interband transitions between higher energy levels in the superlattice. For example, excitonic peaks have been observed from interband transitions between the light-hole band and the conduction band and from the second heavy-hole band to the conduction band (Kaspi et al., 2000; Rodriguez et al., 2005). The energy subband separations obtained in these experiments can be used to identify the possible Auger processes in the material. Near mid-gap energy levels are the main contributors to the SRH processes that limit the minority carrier lifetime. There were several attempts to measure these levels using optical techniques but so far they did not produce any conclusive results. However, indirectly the temperature

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Integrated PL intensity (arb. units)

10000 InAs/GaSb CBIRD 1/T 2 dependence

1000

100

10

100 Temperature (K)

FIGURE 1.21 Temperature dependence of the integrated PL intensity of a LW InAs/GaSb CBIRD superlattice compared to the 1/T2 temperature dependence, which is characteristic for a material with SRH-limited minority carrier lifetime.

dependence of the luminescence intensity and the dependence of the luminescence intensity on excess carrier density indicate that such levels are present. The PL intensity is related to the nonradiative lifetime (τnR ) (∞)

τnR according to the following: η = PL ρ0 = τnR +τR , where η is the internal QE, IPL (∞) is the total number of emitted photons, ρ0 is the total number of absorbed photons, and τR is the radiative lifetime (Ahrenkiel and Lundstrom, 1993). If τnR << τR , the PL intensity varies with temperature as τnR /τR . If the nonradiative processes are dominated by either ShockleyRead-Hall processes or Auger processes, τnR /τR varies proportionally to 1/T2 (Canedy et al., 2003) or 1/T1.5 (Fuchs et al., 2006). The experimentally observed PL intensity variation with temperature is plotted in Fig. 1.21 together with the theoretical 1/T2 dependence. This shows a strong correlation between the experimental data of the temperature dependence and the 1/T2 trend at temperatures higher than 77 K, which indicates that SRH processes limit the lifetime in this material. As the temperature is decreased below 77 K, the integrated PL intensity deviates from the 1/T2 temperature dependence and approaches a constant value. This is expected when the SRH lifetime and the radiative lifetime are comparable (Canedy et al., 2003). Further information about processes dominating the nonradiative lifetime can be obtained from the dependence of the EL intensity on the injected carrier density. Hoffman et al. (2005) and Fuchs et al. (2006) showed that for material in which Auger processes dominate the carrier lifetime, I

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the internal QE drops quickly with increasing excess carrier density, whereas the internal QE is almost independent of the excess carrier density when SRH processes dominate the lifetime. By using calibrated measurement setups and comprehensive analysis of the results, quantitative information about the Auger coefficient and the minority carrier lifetime was obtained from studies of the temperature dependence of the EL intensity (Fuchs et al., 2006; Hoffman et al., 2005). The temperature dependence of the internal QE was correlated with the modeled QE for SRH-limited (QE ∝ 1/T2 ) and Auger-limited (QE ∝ 1/T1.5 ) minority carrier lifetime. When fitting the modeled QE to the measured QE, the Auger coefficient for a LWIR superlattice was extracted to be 10−24 cm6 s−1 and the minority carrier lifetime of a MWIR superlattice was deduced as a function of p-type background concentration. For a carrier background of 1015 cm−3 , the lifetime was deduced to be 100 ns, which is in reasonable agreement with the values measured by time-resolved PL spectroscopy for similar material (Donetsky et al., 2009). With the information obtained from absorption measurements and lifetime measurements, a good prediction of the fitness of the superlattice as an IR detector material can be obtained. The recombination processes limiting the lifetime are identified from variation of PL and EL intensities with temperature and excess carrier density. This information combined with the band structure of the superlattice is essential in the optimization process of the detector material and serves to improve the performance of the IR detectors.

5.3. Noise measurement The detector performance is limited by the noise equivalent intensity (NEI) value that defines the minimal optical power the detector (or FPA) is capable of resolving for given optics and integration time. NEI gives the optical intensity that produces the electrical signal equivalent to the noise signal of the detector, so the lower noise of the detector, the lower optical flux it can detect. The noise power spectrum of a photovoltaic detector, Spv , is given by Spv ( f ) = Sph + Si + Se ( f ), where Sph , Si , and Se ( f ) are the photon shot noise, the detector “fundamental” (shot and thermal), and detector excess noise, respectively. The photon shot noise is given by Sph = 2η8A, where η is the detector external quantum efficiency and 8 is the radiation flux density on the detector of area A. The detector “fundamental” noise is given by Si = 2e(I + 2I0 ) = 2eI + 4kB T/R0 , where I and I0 = kB T/R0 are the diode current and the diode saturation current, respectively, T is the temperature, kB is Boltzmann’s constant, and R0 is the differential resistance at zero bias (van der Ziel, 1970). The detector excess noise, which is very

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often 1/f noise, can significantly degrade the detector performance and has to be minimized or preferably eliminated. The 1/f noise plays a significant role in MCT detectors, so significant research efforts were dedicated to understand the origin of the noise in these devices. In the initial works, the noise spectra of the illuminated SL detector were studied and 1/f noise was not observed, yet the detector noise in these experiments was dominated by photon shot noise (Mohseni and Razeghi, 2001; Plis et al., 2006). Recently, direct measurements of the noise spectra of high-performance SL heterodiodes based on a variant CBIRD design (Hill et al., 2009a) were performed at different operational conditions to understand the effects of dark current and of the surface current on detector noise (Soibel et al., 2010). These results demonstrated that intrinsically SL photodetectors do not exhibit 1/f noise. At the same time, these measurements clearly showed that sidewall leakage current not only increases the shot noise by contributing to higher dark current but more importantly it also introduces additional frequency dependent noise, resulting in much higher noise in the detector. Since strongly frequency-dependent noise can be generated by sidewall leakage current, it is important to fabricate high-performance SL detectors and focal plane arrays (FPAs) using a technology that minimizes the mesa sidewall leakage current. One way to achieve this is by the development of reliable sidewall passivation that can suppress the leakage current and prevent the onset of frequency-dependent noise. These results are described in more detail below and also in the reference (Soibel et al., 2010). The study focused on two representative devices designated as d1 and d2, which were fabricated simultaneously by wet etching from the same CBIRD wafer (Sb1593). These devices have very similar differential resistance-area product of R0 A = 1200 ohm cm2 (d1) and R0 A = 1000 ohm cm2 (d2) at T = 77 K, but the dark current in device d2 is higher than in device d1 (Fig. 1.22). Based on measurement of dark current density dependence on device area/perimeter ratio, we attribute the higher dark current to detector mesa sidewall surface leakage current. The bottom panel of Fig. 1.23 shows the current noise, in , of the device d1 at several applied biases ranging from Vb = 0 V to Vb = 0.4 V. The noise spectra are relatively flat from 1 Hz to 5 kHz, showing the absence of 1/f noise in this device. The shot noise in the device increases with an increase of the applied bias/current, as can be seen clearly from the noise spectral density at frequencies higher than 1 kHz; however, the general “flatness” of the noise spectra does not change with bias, and no onset of 1/f noise is observed. In contrast, the noise characteristics are profoundly different in the device d2 (Fig. 1.23, top). The noise amplitude is much larger than in device d1 and noise increases rapidly with the applied bias Vb ; thus,

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T = 77 K

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d1 d2

Current density (A/cm2)

1 0.1 0.01 1E-3 1E-4 1E-5 1E-6 1E-7 −0.6 −0.4 −0.2

0.0

0.2 0.4 Vb(V)

0.6

0.8

1.0

1.2

FIGURE 1.22 Current–voltage (I–V) characteristics of two CBIRD devices, d1 and d2, measured at T = 77 K. 1

10

100

1000

1E-11

0V 0.10 V 0.17 V

Noise (A/Hz0.5)

1E-12 1E-13 Sb1593 d2

1E-11

Sb1593 d1

0V 0.20 V 0.40 V

1E-12 1E-13 1

10

100 f (Hz)

1000

FIGURE 1.23 The current noise, in , versus frequency of the devices d1 and d2 at several applied bias voltages as indicated on the graph. The dark current in the device d2 is higher than in the device d1, and the higher dark current, which is attributed to detector mesa sidewall surface leakage current, results in large frequency-dependent noise. A small hump seen in the noise spectra near 100 Hz is attributed to the instrument noise since the hump size and shape is independent of detector bias.

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the noise in this device is much higher than can be expected from a simple theoretical estimation of the shot noise. Moreover, the noise spectra are frequency dependent even at zero bias. At Vb = 0.1 V and Vb = 0.17 V, the noise spectra have a 1/f 0.9 frequency dependence in the f = 100 Hz–4 kHz frequency range but become almost frequency independent at lower frequencies. The observed noise has frequency dependence similar to that of 1/f noise in the limited frequency interval of f = 100 Hz–4 kHz, and it becomes frequency independent at lower frequency. Such behavior is characteristic of flicker noise that is attributed to the surface states (van der Ziel, 1970). Indeed, the appearance of additional frequency noise associated with the surface states is consistent with the observation of surface leakage current that is also attributed to an electrical activity of the surface states. In particular, these noise measurements show that while intrinsic 1/f noise is absent in superlattice heterodiode, sidewall leakage current can become a source of strong frequency-dependent noise. This result underscores the importance of the development of reliable etching and sidewall passivation that can suppress the surface leakage current and prevent the onset of frequency-dependent noise. There are additional sources of temporal noise in SL FPA such as the read-out noise, as well as the spatial noise, resulting from variations of the pixel characteristics across FPA. Recently, noise of the LWIR InAs/GaSb superlattices FPA with 9.6 µm cutoff wavelength was characterized at 80 K (Delaunay and Razeghi, 2009). This 320 × 256 array of 25 × 25 µm2 detectors with a 30-µm pitch array was passivated with SiO2 and hybridized to an ISC 9705 ROIC from Indigo Systems. The noise equivalent temperature difference in the array was found to be 23-mK for an integration time of 0.129 ms. The observed noise was described in terms of thermal, shot, read-out integrated circuit and photon noise. It was found that the FPA noise was dominated by the dark current shot noise or by the noise of the testing system at lower illuminations, whereas photon shot noise was the major noise source at photon fluxes higher than 1.8 ×1015 ph s−1 cm−2 . The 1/f noise was not observed in this FPA for frequencies above 4 mHz.

5.4. Lifetime measurement The lifetime of minority carriers is a key parameter that defines both the dark current and quantum efficiency of photodetectors. Achievement of a long lifetime material is an important task for superlattice detector development that will advance the current state-of-the-art technology and will enable high-performance detectors and FPAs. The minority carrier lifetime in superlattices is set by both radiative and nonradiative (Auger and SRH) recombination processes, so it is essential for future material development to understand the contribution from each of these processes,

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as well as the material and device design parameters affecting them. Several measurements of the minority carrier lifetime in superlattices were performed utilizing different techniques including photoconductivity measurements (Yang et al., 2003), an electron beam–induced current technique (Li et al., 2004), and time-resolved photoluminescence (Connelly et al., 2010; Donetsky et al., 2010, 2009), and by analyzing detector dark current (Pellegrino and DeWames, 2009). In photoconductivity measurements, lifetime was determined from the change in the photoconductivity response with increase of the carrier density proportional to the laser excitation power (Yang et al., 2003). Several LWIR detector samples with various doping densities were measured, and a lifetime decrease with temperature was observed, which was attributed to SRH recombination processes. The analysis of current versus voltage data of p-n + LWIR SL detector showed that generation-recombination currents dominate the dark current at modest reverse bias at 80 K, and by taking the energy of the dominant recombination centers to be located at the intrinsic Fermi level, the lowest minority carrier lifetime was determined to be 35 ns (Pellegrino and DeWames, 2009). This lifetime provides an excellent fit to the current–voltage characteristics of the detectors in the temperature range T = 40−130 K and explains the observed quantum efficiency. The minority carrier lifetimes in the absorbers of mid- and longinfrared SL detectors were measured by time-resolved photoluminescence using an optical modulation technique (Donetsky et al., 2010, 2009). The measured lifetimes for mid- and long-infrared superlattices were 100 ns and 31 ns, respectively, which is much shorter than the lifetime of 1 µs in the MCT detector material that was studied in the same experiment. It was proposed that the short minority carrier lifetime in Sb-based material is a consequence of higher phonon energy, resulting in exponential increase of the electron capture cross-sections of nonradiative traps (Donetsky et al., 2010). In another work, the lifetime was extracted from the exponential decay of the photoluminescence signal to be 30 ns at 77 K, dominated by SRH recombination processes (Connelly et al., 2010). In addition, a radiative recombination constant of 1.8 × 10−10 cm3 /s, an upper limit of the Auger recombination coefficient of 10−28 cm6 /s at 60 K, and an acceptor level of ∼20 meV above the valence band were determined. These tests provide important information about lifetime and recombination mechanisms, and more work is currently underway to further understand factors affecting lifetime and the correlation between the lifetimes observed in the time-resolved PL experiments and dark current measurements. It is not clear at this point what sets the short lifetime in Sb-based SL and how to increase it to desirable values of several hundred nanoseconds (Pellegrino and DeWames, 2009). The influence of the shallow defect levels on the lifetime is another open question. The nonradiative

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recombination process identified in PL measurements was attributed to the defects with energy located near valence band edge; however, these defects are not expected to provide a large contribution to generationrecombination current, which is typically associated with defects near middle of the band gap. Recently, a theory postulating existence of two trap levels in the band gap was proposed to explain these results, yet additional experimental and theoretical work is required to fully understand this phenomenon.

5.5. Lifetime and dark current MWIR and LWIR superlattices (Connelly et al., 2010; Donetsky et al., 2010, 2009; Pellegrino and DeWames, 2009) studied so far found to have substantially short lifetimes compared with MCT (Edwall et al., 1998; Kinch et al., 2005). As described in the previous section, direct time-resolved photoluminescence measurements at 77 K yielded a lifetime of 100 ns for MWIR SL and ∼30 ns (Donetsky et al., 2010, 2009) for LWIR SL (Connelly et al., 2010; Donetsky et al., 2010), whereas indirect inference through dark current analysis of an LWSL SL yielded a lifetime of 35 ns (Pellegrino and DeWames, 2009). The question then arises as to why the observed dark current densities (as reflected in the RAeff value) are not correspondingly worse for the superlattices. This turns out to be related to tunneling suppression in superlattices. Recall that the diffusion dark current density from the p-side of a pn diode is given by Jdiff = qn2i LN /(NA τn ), where ni is the intrinsic carrier density, LN is the diffusion length (or absorber width), NA is the acceptor dopant density, and τn is the minority carrier (electron) lifetime. In a typical LWIR superlattice, the doping density is on the order of p = 1 − 2 × 1016 cm−3 , which is considerably higher than the doping level found in the LWIR MCT (typically low, 1015 cm−3 ). This is possible because of tunneling current suppression in superlattices. The higher doping compensates for the shorter lifetime, resulting in relatively low diffusion dark current. However, to achieve the true promise of superlattices with performance exceeding that of MCT requires the understanding of the origin of the relatively short carrier lifetimes found in the present generation of InAs/GaSb superlattices (Donetsky et al., 2010, 2009; Pellegrino and DeWames, 2009) and developing methods for increasing carrier lifetime.

6. CONCLUSIONS AND OUTLOOK Remarkable progress has been achieved in the antimonide superlattices since the analysis by Smith and Mailhiot (1987) first pointed out their advantages for infrared detection. In the LWIR, type-II InAs/Ga(In)Sb

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superlattices have been shown theoretically to have reduced Auger recombination and suppressed band-to-band tunneling. Suppressed tunneling in turn allows for higher doping in the absorber, which has led to reduced diffusion dark current. The versatility of the antimonide material system, with the availability of three different types of band offsets, provides great flexibility in device design. Heterostructure designs that make effective use of unipolar barriers have demonstrated strong reduction of G-R dark current. As a result, the dark current performance of antimonide superlattice-based single element LWIR detectors is now approaching that of the state-of-the-art MCT detector. To date, the antimonide superlattices still have relatively short carrier lifetimes; this issue needs to be resolved before type-II superlattice infrared detectors can achieve their true potential. The antimonide material system has relatively good mechanical robustness when compared with II–VI materials; therefore, FPAs based on type-II superlattices have potential advantages in manufacturability. In the MWIR, production-ready simultaneous dual-band FPA has been fabricated (Rehm et al., 2010; Walther et al., 2007). In the LWIR, large-format FPAs have been demonstrated in research laboratories (Gunapala et al., 2010; Manurkar et al., 2010). Improvements in substrate quality and size and reliable surface leakage current suppression methods, such as those based on robust surface passivation or effective use of unipolar barriers, could lead to high-performance large-format LWIR focal plane arrays.

ACKNOWLEDGMENTS The authors thank S. Bandara, E. R. Blazejewski, E. S. Daniel, R. E. DeWames. W. R. Frensley, D. R. Rhiger, J. N. Schulman, and D. L. Smith for helpful discussions; S. A. Keo, J. M. Mumolo, B. Yang, J. K. Liu, A. Liao, M. C. Lee, and R. T. Ting for assistance; and M. Tidrow, R. Liang, M. Herman, E. Kolawa, and P. Dimotakis for encouragement and support. A part of the research described in this publication was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. Government sponsorship acknowledged.

REFERENCES Abdollahi Pour, S., Nguyen, B.-M., Bogdanov, S., Huang, E. K., and Razeghi, M. (2009). Appl. Phys. Lett. 95, 173505. Ahrenkiel, R. K., and Lundstrom, M. S. (1993). Minority carriers in III-V Semiconductors: Physics and Applications. in: “Semiconductors and Semimetals.” edited by Williardson, R. K., Beer, A. C., Weber, E. R. vol. 39, Academic Press, San Diego, pp. 40–74. Aifer, E. H., Jackson, E. M., Boishin, G., Whitman, L. J., Vurgaftman, I., Meyer, J. R., Culbertson, J. C., and Bennett, B. R. (2003). Appl. Phys. Lett. 82(25), 4411–4413. Aifer, E. H., Maximenko, S. I., Yakes, M. K., Yi, C., Canedy, C. L., Vurgaftman, I., Jackson, E. M., Nolde, J. A., Affouda, C. A., Gonzalez, M., Meyer, J. R., Clark, K. P., and Pinsukanjana, P. R. (2010b). Proc. SPIE 7660, 76601Q. Aifer, E. H., Tischler, J. G., Warner, J. H., Vurgaftman, I., Bewley, W. W., Meyer, J. R., Kim, J. C., Whitman, L. J., Canedy, C. L., and Jackson, E. M. (2006). Appl. Phys. Lett. 89, 053519.

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CHAPTER

2 Quantum Well Infrared Photodetectors S. D. Gunapala, S. V. Bandara, S. B. Rafol, and ∗ D. Z. Ting

Contents

1. Introduction 2. Comparison of Various Types of QWIPs 2.1. n-Doped QWIPs 2.2. p-Doped QWIPs 2.3. n-Doped Bound-to-Continuum QWIPs 2.4. n-Doped Bound-to-Quasibound QWIPs 2.5. n-Doped Broadband QWIPs 2.6. n-Doped Bound-to-Bound Miniband QWIPs 2.7. n-Doped Bound-to-Continuum Miniband QWIPs 2.8. n-Doped Bound-to-Miniband QWIPs 2.9. n-doped In0.53 Ga0.47 As/In0.52 Al0.48 As QWIPs 2.10. n-doped In0.53 Ga0.47 As/InP QWIPs 3. Figures of Merit 3.1. Absorption spectra 3.2. Dark current 3.3. Responsivity 3.4. Dark current noise 3.5. Noise gain and Photoconductive gain 3.6. Quantum efficiency 3.7. Detectivity 4. Light Coupling 4.1. One-dimensional periodic gratings 4.2. Two-Dimensional Periodic Gratings 4.3. Gratings for multi-color and broadband detectors 4.4. Effect of finite-size pixels

60 62 62 64 65 66 67 69 70 71 72 73 74 75 77 79 82 83 86 89 91 92 93 95 98

∗ Center for Infrared Sensors, Jet Propulsion Laboratory, California Institute of Technology, Pasadena,

CA 91109, USA Semiconductors and Semimetals, Volume 84 ISSN 0080-8784, DOI: 10.1016/B978-0-12-381337-4.00002-4

c 2011 Elsevier Inc.

All rights reserved.

59

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4.5. Random Reflectors 4.6. Corrugated Structure 5. Imaging Focal Plane Arrays 5.1. Effect of Non-uniformity 5.2. 128 × 128 Pixels VLWIR Focal Planes 5.3. 256 × 256 Pixels LWIR Focal Planes 5.4. VGA Format LWIR Focal Planes 5.5. 1024 × 1024 Pixels MWIR & LWIR Focal Planes 5.6. Dualband (MWIR & LWIR) Focal Planes 6. Concluding Remarks and Outlook Acknowledgments References

100 102 104 105 106 108 110 121 136 143 145 147

1. INTRODUCTION Intrinsic infrared detectors in the mid-wavelength and long-wavelength ranges are based on interband transition, which promotes an electron across the band gap (Eg ) from the valence band to the conduction band as shown in Fig. 2.1. These photoexcited-electrons can be collected efficiently, thereby producing a photocurrent in the external circuit. Because the incoming photon has to excite an electron from the valence band to the conduction band, the energy of the photon (hν) must be higher than the band gap of the photosensitive material. One possible way of detecting the infrared radiation is using narrow band-gap semiconductors such as HgCdTe and InSb, which is described in the previous chapter of this volume. The other possibility is to create artificial, narrow band gaps by high band-gap materials such as GaAs. The second method involves multi-quantum-wells (MQWs) and superlattices structures. This chapter e − Conduction band

Valence band h +

FIGURE 2.1 Band diagram of conventional intrinsic infrared photodetector. (Gunapala and Bandara, 1995)

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Conduction band E2 hυ1 E1 Eg(AlxGa1−xAs)

Intersubband Absorption

Eg(GaAs) H1

hυ2

H2 Valence band

FIGURE 2.2 Schematic band diagram of a quantum well. Intersubband absorption can take place between the energy levels of a quantum well associated with the conduction band (n-doped) or the valence band (p-doped). (Levine, 1993)

describes the use of MQW-based intersubband transition for infrared detection (Fig. 2.2). Additionally, the spectral response of the detectors can be tuned by controlling the Eg of the photosensitive material. The idea of using MQW structures to detect infrared radiation can be explained by using the basic principles of quantum mechanics. The quantum well is equivalent to the well-known “particle in a box” problem in quantum mechanics, which can be solved by the time independent Schrodinger equation. The solutions to this problem are the Eigen values that describe energy levels inside the quantum well in which the particle is allowed to exist. The positions of the energy levels are primarily determined by the quantum-well dimensions (height and width). For the infinitely-high barriers and parabolic bands, the energy levels in the quantum well are given by Weisbuch (1987) Ej =

~2 π 2 2m∗ L2w

! j2 ,

(2.1)

where Lw is the width of the quantum well, m∗ is the effective mass of the carrier in the quantum well, and j is an integer. Thus, the intersubband energy between the ground and the first excited state is (E2 − E1 ) = (3~2 π 2 /2m∗ L2w ).

(2.2)

The quantum-well infrared photodetectors (QWIPs) discussed in this article use the photo-excitation of the electron (hole) between the ground

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state and the first excited state in the conduction band (valance band) quantum well (See Fig. 2.2). The quantum-well structure is designed so that these photoexcited carriers can escape from the quantum well and get collected as photocurrent. In addition to the larger intersubband oscillator strength, these detectors afford greater flexibility than the extrinsically doped semiconductor infrared detectors because the wavelength of the peak response and the cutoff can be continuously tailored by varying the layer thickness (quantum-well width) and the barrier composition (barrier height). The lattice-matched GaAs/Alx Ga1−x As material system is a very good candidate to create such a quantum-well structure, because the band gap of Alx Ga1−x As can be changed continuously by varying the x value (and hence the height of the quantum well). Thus, by changing the quantumwell width Lw and the barrier height (Al molar ratio of Alx Ga1−x As alloy), this intersubband transition energy can be varied over a wide range, from short-wavelength infrared (SWIR; 1–3 µm), mid wavelengthinfrared (MWIR; 3–5 µm), through long-wavelength (LWIR; 8–12 µm), and into the VLWIR (>12 µm). It is important to note that unlike intrinsic detectors, which utilize interband transition, quantum wells of these detectors must be doped because the photon energy is not sufficient to create photocarriers (hν < Eg ). The possibility of using GaAs/Alx Ga1−x As MQW structures to detect infrared radiation was first suggested by Esaki and Sakaki (1977), experimentally investigated by Smith et al. (1983), and theoretically analyzed by Coon and Karunasiri (1984). The first experimental observation of the strong intersubband absorption was performed by West and Eglash (1985), and the first QWIP was demonstrated by Levine et al. (1987b) at Bell Laboratories. Levine et al. (1988c) also introduced QWIP involving bound-tocontinuum intersubband transitions with wider Alx Ga1−x As barriers and demonstrated dramatically-improved detectivity. Recent developments in these detectors have already led to the demonstration of large, highsensitivity staring arrays by several groups (Andersson et al., 1997; Breiter et al., 1998; Choi et al., 2009; Goldberg et al., 2005; Gunapala et al., 2005a, 2010, 2003a; Rafol 2008b; Rafol and Cho 2008a; Rafol et al., 2007; Robo et al., 2009; Schneider et al., 2004).

2. COMPARISON OF VARIOUS TYPES OF QWIPS 2.1. n-Doped QWIPs As mentioned previously, the first bound-to-bound state QWIP was demon˚ GaAs strated by Levine et al. (1987b). It consisted of 50 periods of Lw = 65 A

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63

˚ Al0.25 Ga0.75 As barriers sandwiched between the top (0.5 µm and Lb = 95 A ˚ thick) and the bottom (1 µm thick) GaAs contact layers. The center 50 A 18 −3 of the GaAs wells were doped to ND = 1.4 × 10 cm and the contact layers were doped to ND = 4 × 1018 cm−3 . This structure was grown by the molecular beam epitaxy (MBE). These thicknesses and compositions were chosen to produce only two states in the quantum well with energy spacing giving rise to a peak wavelength of 10 µm. The measured (Levine et al., 1987b) absorption spectra peaked at λp = 10.9 µm with a full-width at half-maximum of 1υ = 97 cm−1 . The peak absorbance a = −log(transmission) = 2.2 × 10−2 corresponds to a net absorption of 5% (i.e., a = 600 cm−1 ). After the absorption of infrared photons, the photoexcited carriers can be transported either along the plane of quantum wells (with an electric field along the quantum wells) or perpendicular to the wells (with an electric field perpendicular to the epitaxial layers). As far as the infrared detection is concerned, perpendicular transport is superior to parallel transport (Wheeler and Goldberg, 1975) because the difference between the excited state and the ground state mobilities is much larger in the latter case, and consequently, transport perpendicular to the quantum wells (i.e., growth direction) gives a substantially-high photocurrent. In addition, the heterobarriers block the transport of ground-state carriers in the quantum wells, and thus the lower-dark current. For these reasons, QWIPs are based on the escape and perpendicular transport of photoexcited carriers as shown in Fig. 2.3.

− − −

GaAs

− AlxGa1−xAs

− −

FIGURE 2.3 Conduction-band diagram for a bound-to-bound QWIP, showing the photoexcitation (intersubband transition) and tunneling out of well. (Levine, 1993)

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In the later versions of the bound-to-bound state QWIPs, Choi et al. (1987c) has used slightly thicker and higher barriers to reduce the tunneling-induced dark current. When they increased the barrier ˚ to 140 A ˚ and Alx Ga1−x As barrier height from thickness from Lb = 95 A x = 0.25 to 0.36, the dark current (also the photocurrent) was significantly reduced. The nonlinear behavior of the responsivity and the dark current versus bias voltage observed in the bound-to-bound QWIPs are due to the complex tunneling process associated with the high-field domain formation (Choi et al., 1987c).

2.2. p-Doped QWIPs Levine et al. (1991b) experimentally demonstrated the first QWIP that used the hole-intersubband absorption in the GaAs valence band. The strong mixing (Chang and James, 1989; Chiu et al., 1983; Karunasiri et al., 1990; Pinczuk et al., 1986; Wieck et al., 1984) between the light and the heavy holes (at k = 0) allows the desired normal incidence illumination geometry to be used. The samples were grown on a (100) semi-insulating GaAs substrate ˚ (or using gas source MBE, and they consisted of 50 periods of Lw = 30 A ˚ quantum wells (doped ND = 4 × 1018 cm−3 with Be) separated Lw = 40 A) ˚ barriers of Al0.3 Ga0.7 As, and capped by ND = 4 × 1018 cm−3 by Lb = 300 A contact layers. ˚ QWIP are comThe unpolarized responsivity spectra of the Lw = 40 A ◦ pared for the two geometries (i.e., 45 and normal incidence as discussed in Section 4). The two spectra are essentially identical (peak wavelength λp = 7.2 µm and long wavelength cutoff λc = 7.9 µm) and the normal incidence responsivity is larger than that of 45◦ illumination, which is consistent with both the polarizations contributing to the photoresponse. The ˚ sample at λp = 7.2 µm peak unpolarized responsivities (for the Lw = 40 A and Vb = +4 V) are Rp = 39 mA/W and 35 mA/W for the normal and the 45◦ incidence, respectively, which are approximately an order of magnitude smaller than the responsivities for n-QWIPs. As a further test of polarization behavior, Levine et al. (1991b) found that by using the 45◦ geometry, s-polarized light had twice the photoresponse of p-polarization. This is again in strong contrast with the n-QWIPs for which the s-polarized photoresponse is forbidden by the symmetry. A comparison between the ˚ detectors shows that, as expected, the narrower well Lw = 30 and 40 A QWIP has a broader spectral response (λc = 8.6 µm) because of the excited state being pushed further up into the continuum and thereby broaden˚ well detector also has a ing the absorption (Levine et al., 1989). The 30 A slightly longer peak wavelength (λp = 7.4 µm), consistent with the ground state being pushed up even further than the excited state. Similar lineshape

Quantum Well Infrared Photodetectors

65

effects (Levine et al.,√1989) have been seen in the √ n-QWIPs. Peak detectivities of 1.7 × 1010 cm Hz/W and 3.5 × 109 cm Hz/W were measured at ˚ and 40 A ˚ detectors, respectively. T = 77 K for Lw = 30 A The experimentally-measured photoconductive gains are g = 3.4 × ˚ respectively. This yield hot 10−2 and g = 2.4 × 10−2 for Lw = 30 and 40 A, ˚ hole mean free path L = 510 and 360 A for the two samples (i.e., the photoexcited carrier travels only one or two periods before being recaptured). It should be noted that both g and L are over an order of magnitude smaller than the corresponding values for n-QWIPs (where the photoconductive gains of g = 1 have been obtained [Levine et al., 1990a]). Since [where is the well recapture time (Levine et al., 1992b)], we can see that the lower g is due to a lower velocity associated with the higher hole effective mass, and a shorter lifetime due to increased scattering between the light and heavy hole bands. Having now obtained g, we can relate it to the peak responsivity, and thus using the measured values for Rp and g, we can directly determine the low-temperature quantum efficiency. This yields ˚ QWIPs, double pass values of 17% and 28% for the Lw = 30 and 40 A respectively. Thus, in spite of the larger effective mass of the holes compared to that of the electrons, the different symmetry (normal incidence) of the intersubband absorption, the much smaller photoconductive gain and mean free path, and the quantum efficiency (and hence escape probability) for bound-to-continuum n- and p-QWIPs are similar.

2.3. n-Doped Bound-to-Continuum QWIPs In the previous section, we mentioned the QWIP containing two bound states. By reducing the quantum well width, it is possible to push the strong bound-to-bound intersubband absorption into the continuum, resulting in a strong bound-to-continuum intersubband absorption. The major advantage of the bound-to-continuum QWIP is that the photoexcited electron can escape from the quantum well to the continuum transport states without tunneling through the barrier as shown in Fig. 2.4. As a result, the bias required to efficiently collect the photoelectrons can be reduced dramatically, and hence lower the dark current. Due to the fact that the photoelectrons do not have to tunnel through the barriers, the Alx Ga1−x As barrier-thickness of the bound-to-continuum QWIP can be increased without reducing the photoelectron collection efficiency. ˚ to 500 A ˚ can reduce the Increasing the barrier width from a few hundred A ground-state sequential tunneling by an order of magnitude. By making use of these improvements, Levine et al. (1990a) has successfully demonstrated the first bound-to-continuum QWIP with a dramatic improvement

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S. D. Gunapala, D. Z. Ting, S. B. Rafol, and S. V. Bandara

− − − − GaAs ° 40 A AlxGa1−xAs ° 500 A

FIGURE 2.4 Conduction-band diagram for a bound-to-continuum QWIP, showing the photoexcitation and hot-electron transport process. (Levine, 1993)

√ in the performance (i.e., detectivity 3 × 1010 cm Hz/W at 68 K for a QWIP which had cutoff wavelength at 10 µm).

2.4. n-Doped Bound-to-Quasibound QWIPs Improving the QWIP performance depends largely on minimizing the parasitic current (i.e., dark current) that plagues all the light detectors. The dark current is the current that flows through a biased detector in the dark (i.e., with no photons impinging on it). As Gunapala and Bandara (1995) have discussed elsewhere, at temperatures above 45 K (typical for λ < 14 µm), the dark current of the QWIP is entirely dominated by the classical thermionic emission of the ground-state electrons directly out of the well into the energy continuum. Minimizing the dark current is critical to the commercial success of the QWIP as it allows the highly-desirable high-temperature detector operation. Therefore, Gunapala and Bandara (1995) have designed the bound-toquasibound quantum well by placing the first excited state exactly at the well top as shown in Fig. 2.5. The best previous QWIPs pioneered by Levine et al. (1988c) at AT&T Bell Laboratories were of the bound-tocontinuum variety, so-called because the first excited state was a continuum energy band above the quantum well top (typically 10 meV). Dropping the first excited state to the quantum well-top causes the barrier to thermionic emission (roughly the energy height from the ground state to the well top) to be ∼10 meV more in the bound-to-quasibound

Quantum Well Infrared Photodetectors

67

Conduction band −

Energy

Quasi bound state

−

Continuum −

Bound state

3 AlGaAs

−

2

GaAs

Photocurrent

1 “Dark current” mechanisms Positions

FIGURE 2.5 Schematic diagram of the conduction band in a bound-to-quasibound QWIP in an externally applied electric field. Absorption of infrared photons can photoexcite electrons from the ground state of the quantum well into the continuum, causing a photocurrent. Three dark current mechanisms are also shown: ground state tunneling (1); thermally assisted tunneling (2); and thermionic emission.

QWIP than in the bound-to-continuum one, causing the dark current to drop significantly at the elevated operating temperatures. The advantage of the bound-to-quasibound QWIP over the bound-to-continuum QWIP is that in the case of bound-to-quasibound QWIP, the energy barrier for the thermionic emission is same as it is for the photoionization as shown in Fig. 2.5 (Gunapala and Bandara, 1995). In the case of a boundto-continuum QWIP, the energy barrier for the thermionic emission is 10–15 meV less than the photoionization energy. Thus, the dark current of the bound-to-quasibound QWIPs is reduced by an order of magnitude 1E

(i.e., Id ∝ e− kT ≈ e−2 for T = 55 K) as shown in Fig. 2.5.

2.5. n-Doped Broadband QWIPs A broad-band MQW structure can be designed by repeating a unit of several quantum wells with slightly different parameters such as quantumwell width and barrier height. The first device structure (shown in Fig. 2.6) demonstrated by Bandara et al. (1998a) has 33 repeated layers of GaAs ˚ thick Alx Ga1−x As and three-quantum-well units separated by LB ∼ 575 A barriers (Bandara et al., 1998b). The well thicknesses of the quantum

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GaAs

e

e

e e

e e Lu x Repeat unit

AlxGa1−xAs LB

FIGURE 2.6 Schematic diagram of the conduction band in broadband QWIP in an externally applied electric field. The device structure consists of 33 repeated layers of three-quantum-well units separated by thick Alx Ga1−x As barriers. Also shown are the possible paths of dark current electrons and photocurrent electrons of the device under a bias (Bandara et al., 1998b)

wells of three-quantum-well units are designed to respond at peak wavelengths of around 13, 14, and 15 µm, respectively. These quantum wells ˚ are separated by 75 A-thick Alx Ga1−x As barriers. The Al mole fraction (x) of barriers throughout the structure was chosen such that the λp = 13 µm quantum well operates under the bound-to-quasibound conditions. The excited-state energy-level broadening has further enhanced due to overlap of the wave functions associated with the excited states of quantum wells separated by thin barriers. Energy band calculations based on a twoband model shows excited state energy levels spreading about 28 meV. An experimentally measured responsivity curve at VB = −3 V bias voltage has shown broadening of the spectral response up to 1λ ∼ 5.5 µm, i.e. the full width at half maximum from 10.5–16 µm. This broadening 1λ/λp ∼ 42% is about a 400% increase compared to a typical bound-to-quasibound QWIP. Later, Nedelcu et al. also developed broadband QWIPs for spectrometer applications (Nedelcu et al., 2010). Three QWIP layers have been specifically designed, grown, processed, and characterized for broadband applications. For the active layer, two very-different design approaches have been tested. The first one is based on the implementation of different quantum wells (QW) into the active layer. Each QW has a different peak absorption wavelength. Consequently the total absorption spectrum is given by the sum of the individual absorption peaks. For this study, four different QW types with nominal peak absorption wavelengths at 11.5 µm, 12.5 µm, 13.7 µm, and 14.7 µm have been used. The design has been optimized in order to achieve spectral shapes robust with respect to the temperature and applied bias. The dark current has not been optimized, as the main concern here was the achievement of a broadband

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response. The second design approach was based on the replacement of individual quantum wells by short superlattices. Each superlattice is made of four coupled-quantum wells, separated by AlGaAs barriers that were only 6–7 nm thick. The superlattices are separated from one another by 36 nm-thick barriers. In order to achieve a truly broadband absorption spectrum, a specific optical coupling scheme is required and it’s discussed in the “light coupling” section of this chapter.

2.6. n-Doped Bound-to-Bound Miniband QWIPs The superlattice miniband detector uses the concept of infrared photoexcitation between the minibands (ground state and first excited state) and transport of these photoexcited electrons along the excited-state miniband. When the carrier de Broglie wavelength becomes comparable to the barrier thickness of the superlattice, the wave functions of the individual wells tend to overlap because of tunneling, and the energy minibands are formed. The miniband occurs when the bias voltage across one period of the superlattice becomes smaller than the miniband width (Capasso et al., 1986). Experimental work on infrared detectors involving the miniband concept was initially carried out by Kastalsky et al. (1988). The spectral response of this GaAs/AlGaAs detector was in the range 3.6–6.3 µm and this indicated that low-noise infrared detection was feasible without the use of external bias. O et al. (1990) reported experimental observations and related theoretical analysis for this type of detectors with absorption peak in the LWIR spectral range (8–12 µm). Both these detectors consist of a bound-to-bound miniband transition (i.e., two minibands below the top of the barrier) and a graded barrier between the superlattice and the collector layer as a blocking barrier for ground-state miniband tunneling dark current. In order to further reduce the ground-state miniband tunneling dark current, Bandara et al. (1992) used a square-step barrier at the end of the superlattice. This structure, illustrated in Fig. 2.7A, was grown by MBE and ˚ GaAs quantum wells and 45 A ˚ Al0.21 Ga0.79 As consists of 50 periods of 90 A ˚ barriers. A 600 A-Al Ga As blocking layer was designed in such a way 0.85 0.15 that it has two minibands below the top of the barrier, with the top of the step blocking barrier being lower than the bottom of the first excited state miniband, but higher than the top of the ground state miniband. The spectral photoresponse was measured at 20 K with a 240 mV bias voltage across the detector and at 60 K with a 200 mV bias voltage. The experimental response band of this detector was in the VLWIR range, with peak response at 14.5 µm. The rapid fall-off in the photocurrent at higher bias voltage values was observed and attributed to the progressive decoupling

S. D. Gunapala, D. Z. Ting, S. B. Rafol, and S. V. Bandara

Al

Al

xG

a

1− xA

s

xG G a1 aA − x A s s

70

° 45 A ° 90 A

600 A° (A)

As

−x

a1

s

aA G

G Al x

(B)

FIGURE 2.7 (A) Parameters and band diagram for LWIR GaAs /Alx Ga1−x As superlattice miniband detector with λc ∼ 15 µm. (Bandara et al., 1988); (B) device structure of bound-to-continuum miniband (Gunapala et al., 1991b)

of the miniband as well as the rapid decrease in the impedance of the detector. The peak responsivity of this detector at 20 K and 60 K are 97 and 86 mA/W for unpolarized light. Based on these values and noise measurements,√the estimated detectivity at 20 K and 60 K are 1.5 × 109 and 9 × 108 cm Hz/W, respectively. Although this detector operates under a modest bias and power conditions, the demonstrated detectivity is relatively lower than the responsivity of usual QWIPs. This is mainly due to the lower collection efficiency. Although there is enough absorption between minibands, only the photoexcited electrons in few quantum wells near the collector contact contribute to the photocurrent.

2.7. n-Doped Bound-to-Continuum Miniband QWIPs It is anticipated that placing the excited state miniband in the continuum levels would improve the transportation of the photoexcited electrons, i.e., responsivity of the detector. This is same as in the case of the wide barrier bound-to-continuum detectors discussed previously. A detector based on the photoexcitation from a single miniband below the top of the barriers to one above the top of the barriers is expected to show

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a higher performance. Gunapala et al. (1991b) proposed and demonstrated this type of bound-to-continuum miniband photoconductor based on GaAs/Alx Ga1−x As superlattice operating in the 5–9 µm spectral range. Their structure shows more than an order of magnitude improvement in electron transport and detector performance, compared with the previous bound-to-bound state miniband detectors. Device structures (as shown in Fig. 2.7B) studied by Gunapala et al. ˚ (1991b) consisted of 100 periods of GaAs quantum wells of either Lb = 30 A ˚ barriers of Al0.28 Ga0.72 As, and Lw = 40 A ˚ GaAs wells (doped or Lb = 45 A ND = 1 × 1018 cm−3 ) sandwiched between the doped GaAs contact layers. The absolute values for the peak absorption coefficients are α = 3100 cm−1 ˚ structures, respectively. Strucand α = 1800 cm−1 for the Lb = 30 and 45 A ˚ have a higher peak absorption tures with a narrower barrier (Lb = 30 A) coefficient as well as a broader spectrum, resulting in significantly larger integrated absorption strength. Also, the dark current of this structure ˚ is much larger than that of the other (Lb = 45 A) ˚ structure. (Lb = 30 A) Detectivities at peak wavelength for the above miniband detectors were calculated using the measured responsivities and the dark cur∗ 9 ˚ rents. For √ the Lb = 30 A structure, the result was D = 2.5 × 10 and 5.4 × 11 ˚ 10 cm Hz/W for T = 77 and 4 K at −80 mV bias. For √ Lb = 45 A structure, they obtained D∗ = 2.0 × 109 and 2.0 × 1010 cm Hz/W for T = 77 and 4 K at −300 mV bias. These values are significantly higher than the previous bound-to-bound miniband results. Although the responsivity is improved by placing the excited state in the continuum, it also increases the thermionic dark current because of the lower barrier height. This fact is more critical for LWIR detectors because the photoexcitation energy becomes even smaller, i.e., the detector operating temperature will be lowered.

2.8. n-Doped Bound-to-Miniband QWIPs Yu and Li (1991a) and Yu et al. (1991b) proposed and demonstrated a miniband transport QWIP which contained two bound states with higher energy level being resonance with the ground state miniband in the superlattice barrier. (see Fig. 2.8A). In this approach, infrared radiation is absorbed in the doped quantum wells, exciting an electron into the miniband and transporting it in the miniband until it is collected or recaptured into another quantum well. Thus, the operation of this miniband QWIP is analogous to that of a weakly-coupled MQW boundto-continuum QWIP. In this device structure, the continuum states above the barriers are replaced by the miniband of the superlattice barriers. These miniband QWIPs show lower photoconductive gain than the boundto-continuum QWIPs because the photoexcited electron transport occurs in the miniband where electrons have to transport through many thin

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(A)

(B)

FIGURE 2.8 Band diagrams for (A) bound-to-miniband; (B) step bound-to-miniband QWIP structures. (Levine, 1993)

heterobarriers resulting in lower mobility. Bandwidth of the absorption spectrum is controlled by the position of the miniband, relative to the barrier threshold, as well as the width of the miniband, which is exponentially dependent on the thickness of the superlattice barriers. Faska et al. (1992) adopted this bound-to-miniband approach and demonstrated excellent LWIR images from a 256 × 256 focal plane array (FPA) camera. These bound-to-miniband QWIPs have been demonstrated using a GaAs/Alx Ga1−x As material system. In order to further improve the performance (by decreasing the dark current) of these miniband QWIPs, Yu et al. (1992) proposed a step bound-to-miniband QWIP which is shown in Fig. 2.8B. This structure consists of GaAs/Alx Ga1−x As superlattice barriers and In0.07 Ga0.93 As- strained quantum wells, which are deeper than the superlattice barrier wells, as shown in Fig. 2.8B (Li et al., 1993).

2.9. n-doped In0.53 Ga0.47 As/In0.52 Al0.48 As QWIPs In order to shift the intersubband absorption resonance into the higher energy spectral region (λ = 3–5 µm), Levine et al. (1988a) have investigated lattice-matched quantum well superlattices of In0.53 Ga0.47 As/ In0.52 Al0.48 As grown using MBE on an InP substrate and reported intersubband absorption in this heterosystem. This direct gap heterostructure has a conduction band discontinuity of 550 meV, which is significantly higher than that of the direct gap GaAs/Alx Ga1−x As system, therefore allowing for a shorter-wavelength operation. A 50-period MQW superlattice consisting of In0.53 Ga0.47 As wells ˚ and 150 A ˚ bar(doped ND = 1 × 1018 cm−3 ) and having a width Lw = 50 A, riers of In0.52 Al0.48 As was grown on an InP substrate. The experimental absorption peak is at λ = 4.4 µm, in good agreement with the theoretical estimation of the energy separation of bound states (see reference (Levine et al., 1988a) for details. In order to achieve higher performances

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in the MWIR range, Hasnain et al. (1990a) designed a MQW structure of the same materials system involving bound-to-continuum intersubband ˚ In0.53 Ga0.47 As absorption. This structure consisting of 50 periods of 30 A 18 −3 ˚ wells (doped ND = 2 × 10 cm ) and 300 A In0.52 Al0.48 As barriers, was grown by MBE on an InP substrate. The absorption spectrum is peaked at 279 meV (λ = 4.4 µm) with a full width at half maximum of 93 meV. Although the peak absorption of this bound-to-continuum detector is 4.2 times lower than that of a bound-to-bound detector (Levine et al., 1988a); the line width is five times greater. Thus, it has comparable (20% higher) absorption strength covering the full 3–5 µm MWIR band. The noise measured in these MQW detectors at 500 Hz corresponds to the shot noise of the K of √ dark current resulting peak detectivity at 77 ◦ field D∗ = 1.5 × 1012 cm Hz/W with a background limited (for a 180 √ of view) D∗BL = 2.3 × 1010 cm Hz/W at 120 K and lower temperatures. These values are comparable to those demonstrated with the Pt-Si devices (Shepherd, 1988) presently used in MWIR band.

2.10. n-doped In0.53 Ga0.47 As/InP QWIPs An InGaAs/InP materials system has been used extensively for optical communication devices and therefore has a highly developed growth and processing technology. Since the quality of barriers is extremely important for optimum QWIP performance and InP is binary, whereas Alx Ga1−x As is a ternary alloy, Gunapala et al. (1991a) investigated the hot electron transport and performance of detectors fabricated from these two materials. Two structures were grown by metal organic molecular beam epitaxy (MOMBE) with arsine and phosphine as group V sources, trimethylindium and trimethylgallium as group III sources, and elemental Sn as n-type dopant sources (Gunapala et al., 1991a; Ritter et al., 1991). The first struc˚ In0.53 Ga0.47 As quantum wells ture consisted of 20 periods of Lw = 60 A ˚ lattice matched to 500 A InP barriers. The second structure contained 50 ˚ In0.53 Ga0.47 As wells separated by 500 A-InP ˚ periods of Lw = 50 A barriers. 17 −3 These MQWs were doped ND = 5 × 10 cm , and had top and bottom 0.4 µm contact layers of ND = 1 × 1018 cm−3 doped In0.53 Ga0.47 As. The intersubband absorption was measured on a 45◦ multipass waveguide. The peak (λp = 8.1 µm) room temperature absorption coefficient α = 950 cm−1 is expected to increase by a factor of 1.3 at T = 77 K resulting in a lowtemperature quantum efficiency of η = 12% (Gunapala et al.1991a; 1991c; ˚ well QWIP, the corresponding value is η = 11%. 1992a; 1992b). For the 50 A These values are quite comparable to those of GaAs samples, when the lower doping level of ND = 5 × 1017 cm−3 in the wells is taken into account. The bias dependence of the responsivities (which was essentially independent of temperature T = 10–80 K) was measured. Extremely large values of the responsivity, reaching R = 6.5 A/W at Vb = +3.5 V and

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S. D. Gunapala, D. Z. Ting, S. B. Rafol, and S. V. Bandara

R = 3.5 A/W at Vb = −3.5 V have been observed. This responsivity is five times larger than that of the similar GaAs/Alx Ga1−x As QWIPs, which demonstrates the excellent transport in this materials system. These large responsivity values yield very large values of photoconductive gain of g = 9.0 for Vb = +3.5 V and g = 4.8 for Vb = −3.5 V (Gunapala et al., 1991a). The corresponding value of the hot electron mean free path L = 10 µm at Vb = +3.5 V, which is five times larger than that for the similar GaAs/Alx Ga1−x As QWIPs. This excellent transport may be associated with the high-quality binary InP barriers, and higher mobility of InP compared √ with Alx Ga1−x As. The calculated peak detectivity D∗λ = 9 × 1010 cm Hz/W based on the noise current and the measured ˚ QWIP compare favorresponsivity at Vb = +1.2 V and T = 77 K of 60 A ably with GaAs/Alx Ga1−x As QWIPs operating at this wavelength. Jelen et al. (1998a,b) also investigated lattice-matched InGaAs/InP QWIPs and observed large photoconductive gain indicating the improved transport properties in the binary InP barrier. (Jelen et al., 1998a,b). See Gunapala et al., 1994a,b for QWIPs based on InGaAs/GaAs materials system.

3. FIGURES OF MERIT Now we will discuss and compare the optical and transport properties of bound-to-continuum QWIPs, bound-to-bound QWIPs, and bound-toquasibound QWIPs with one another. The structures of the six samples to be discussed are listed in Table 2.1. These n-doped QWIPs were grown using MBE and the wells and contact layers were doped with ˚ while the barrier Si. The quantum well widths Lw range from 40–70 A, ˚ widths are approximately constant at Lb = 500 A. The Al molar fraction in the Alx Ga1−x As barriers varies from x = 0.10 to 0.31 (corresponding to the cutoff wavelengths of λc = 7.9–19 µm). The photosensitive doped MQW region containing 25 to 50 periods is sandwiched between the similarly-doped top (0.5 µm) and bottom (1 µm) ohmic contact layers. TABLE 2.1 Structure parameters for samples A–F, including quantum well width Lw , barrier width Lb , Alx Ga1−x As composition x, doping density ND , doping type, number of MQW periods, and type of intersubband transition bound-to-continuum (B-C), bound-to-bound (B-B), and bound-to-quasibound (B-QB). (Levine et al., 1992a) ˚ ND (A) Doping Intersubband ˚ ˚ Sample Lw (A) Lb (A) x (1018 cm−3 ) type Periods transition A 40 500 0.26 1.0 n 50 B–C B 40 500 0.25 1.6 n 50 B–C C 60 500 0.15 0.5 n 50 B–C D 70 500 0.10 0.3 n 50 B–C E 50 500 0.26 1.4 n 25 B–B F 45 500 0.30 0.5 n 50 B–QB

Quantum Well Infrared Photodetectors

75

These structural parameters have been chosen to give a wide variation in QWIP absorption and transport properties (Levine et al., 1992b). In particular, samples A through D are n-doped with intersubband infrared transition occurring between a single localized bound state in the well and a delocalized state in the continuum (denoted as B–C in Table 2.1) (Andersson and Lundqvist, 1991b; Andrews and Miller, 1991; Janousek et al., 1990; Kane et al., 1989; Levine, 1991e; Levine et al., 1987d, 1990a; Steele et al., 1991; Wu et al., 1992). Sample E has a high Al concentration x = 0.26 cou˚ yielding two bound states in the well. pled with a wide well Lw = 50 A, Thus, the intersubband transition occurs from the bound ground state to the bound first-excited state, (denoted as B–B in Table 2.1), and therefore requires electric field assisted tunneling for the photoexcited carrier to escape into the continuum as discussed in the previous section (Choi et al., 1987b; Levine et al., 1987b, 1989). Sample F was designed to have a quasibound excited state [denoted B-QB in Table 2.1 (Gunapala and Bandara, 1995; Kiledjian et al., 1991)], which is intermediate between a stronglybound excited state and a weakly-bound continuum state. It consists of ˚ doped quantum well and 500 A ˚ of a Alx Ga1−x As barrier with a Lw = 45 A x = 0.3. These quantum-well parameters result in a first excited-state in resonance with the barriers and are thus expected to have an intermediate behavior.

3.1. Absorption spectra The infrared absorption spectra for samples A–F were measured at room temperature using 45◦ multipass waveguide geometry (except for sample D, which was at such a long-wavelength that the substrate multiphonon absorption obscured the intersubband transition). As can be seen in Fig. 2.9, the spectra of the bound-to-continuum QWIPs (samples A, B, and C) are much broader than the bound-to-bound or bound-to-quasibound QWIPs (samples E and F or the QWIPs discussed in the previous section). Correspondingly, the magnitude of the absorption coefficient α for the continuum QWIPs (left-hand scale) is significantly lower than that for the bound-to-bound QWIPs (right-hand scale), due to the conservation of oscillator strength. That is, αp (1λ/λp )/ND is a constant, as was previously found (Gunapala et al., 1990b). The values of the peak room-temperature absorption αp , peak wavelength λp , cutoff wavelength λc (long wavelength λ for which α drops to half αp ), and spectral width 1λ (full width at half αp ) are given in Table 2.2. The room-temperature absorption quantum efficiency ηa (300 K) is evaluated from αp (300 K) using ηa =

1 1 − e−2αp l 2

(2.3)

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S. D. Gunapala, D. Z. Ting, S. B. Rafol, and S. V. Bandara

700

1500 T = 300K

B

600 500

1200

C A

400

800 300 F

200

400

100 0

6

8

10 12 Wavelength λ (µm)

Absorption coefficient α (cm−1)

Absorption coefficient α (cm−1)

E

0 16

14

FIGURE 2.9 Absorption coefficient spectra versus wavelength measured at T = 300 K for samples A, B, C, E, and F. (Levine et al., 1992a) TABLE 2.2 Optical absorption parameters for samples A, B, C, E, and F, including peak absorption wavelength λp , long wavelength cutoff λc , spectral width 1λ, fractional spectral width 1λ/λp , peak room temperature absorption coefficient dp (300 K), peak room temperature absorption quantum efficiency ηa (300 K), T = 77 K absorption quantum efficiency ηa (77 K), and maximum high bias net quantum efficiency ηmax . (Levine et al., 1992a) Sample

λp (µm)

λc (µm)

1λ(µm)

1λ/λ (%)

αp (300 K) (cm−1 )

ηa (300 K) (%)

ηa (77 K) (%)

ηmax (%)

A B C E F

9.0 9.7 13.5 8.6 8.9

10.3 10.9 14.5 9.0 9.4

3.0 2.9 2.1 0.75 1.0

33 30 16 9 11

410 670 450 1490 451

10 15 11 17 11

13 19 14 20 14

16 25 18 23 20

where ηa is the unpolarized double-pass absorption quantum efficiency, l is the length of the photosensitive region, and the factor of two in the denominator is a result of the quantum mechanical selection rules, which only allows the absorption of radiation polarized in the growth direction. The low-temperature quantum efficiency ηa (77) was obtained by using αp (77 K) ≈1.3 αp (300 K) as previously discussed. The last column containing ηmax will be discussed later. In order to clearly compare the line shapes of the bound, quasibound, and continuum QWIPs, the absorption coefficients for the samples A, E, and F have been normalized to unity and plotted as e α in Fig. 2.10, and the wavelength scale has been normalized by plotting the spectra against 1λ ≡ (λ − λp ), where λp is the wavelength at the absorption peak. The

Quantum Well Infrared Photodetectors

77

∼ Absorption coefficient α

1.0

0.5 A 0.4

Δλ = 33% λ

0.3 Δλ = 11% λ 0.2

0.0

Δλ = 9% λ 0

−2

F E

−1

0

1

2

3

Wavelength difference Δλ (μm)

FIGURE 2.10 Normalized absorption spectra versus wavelength difference 1λ = (λ − λp ). The spectral width 1λ/λ are also given. The insert show the schematic conduction band diagram for sample A (bound-to-continuum), sample E (bound-to-bound), and sample F (bound-to-quasibound). (Levine et al., 1992a)

very large difference in spectral width is apparent with the bound and continuum excited state transitions (1λ/λp = 9%–11%) being three to four times narrower than for the continuum excited state QWIPs (1λ/λp = 33%).

3.2. Dark current In order to measure the dark-current voltage curves, 200-µm-diam mesas were fabricated as described elsewhere (Gunapala and Bandara, 1995) and the results are shown in Fig. 2.11 for T = 77 K. Note that the asymmetry in the dark current (Zussman et al., 1991) with Id is larger for positive bias (i.e., mesa top positive) than for negative bias. This can be attributed to the dopent migration in the growth direction (Liu et al., 1993), which lowers the barrier height of the quantum wells in the growth direction compared to the quantum-well barriers in the other direction (which are unaffected). Note that, as expected, the dark current Id increases as the cutoff wavelength λc increases. At bias Vb = −1 V and 1 V, the curves for the samples E and F cross. This is due to the fact that even though sample E has a shorter cutoff wavelength than sample F, it is easy for the excited electrons to tunnel out at sufficiently high bias. In contrast, sample F has a quasibound ˚ thick barrier top. excited state, which is in resonance with the Lb = 500 A

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S. D. Gunapala, D. Z. Ting, S. B. Rafol, and S. V. Bandara

10−2

D

Dark current Id (A)

C 10−4 B A

10−6

E 10−8 F T = 77K

10−10

−8

−6

−4

−2 0 2 Bias voltage Vb (V)

4

6

8

FIGURE 2.11 Dark current Id as a function of bias voltage Vb at T = 77 K for samples A–F. (Levine et al., 1992a)

Levine et al. (1990a) has analyzed the origin of the dark current in detail and showed that thermionic-assisted tunneling is a major source of dark current (Andrews and Miller, 1991; Gunapala et al., 1990b; Kinch and Yariv, 1989; Pelve et al., 1989; Zussman et al., 1991). In that analysis, they first determined the effective number of electrons n(V), which are thermally excited out of the well into the continuum transport states, as a function of bias voltage V; n(V) =

m∗ π~2 Lp

Z∞

f (E)T(E, V)dE

(2.4)

E0

where the first factor containing the effective mass m∗ is obtained by dividing the two-dimensional density of states by the superlattice period Lp (to convert it into an average three-dimensional density), f(E) is the Fermi factor f(E) = [1 + exp(E − E0 − EF )/kT]−1 , E0 is the energy, EF is the two-dimensional Fermi level, and T(E, V) is the bias-dependent tunneling current transmission factor for a single barrier, which can be calculated using Wentzel-Kramers-Brillouin (WKB) approximation to a biased quantum well. Eq. (2.4) accounts for both thermionic emission above the energy barrier Eb (for E > Eb ) and thermionically assisted tunneling (for E < Eb ). Then they calculated the bias-dependent dark current Id (V) using

Quantum Well Infrared Photodetectors

79

Id (V) = n(V)ev(V)A, where e is the electronic charge, A is the area of the detector, and v is the average transport velocity, which is given by 1

v(V) = µF[1 + (µF/vs )2 ] 2

(2.5)

where µ is the mobility, F is the average electric field, and vs is the saturated drift velocity. The good agreement is achieved as a function of both bias voltage and temperature over a range of eight orders of magnitude in the dark current (Levine et al., 1990a).

3.3. Responsivity The responsivity spectra R(λ) were measured (Zussman et al., 1991) on 200-µm-diam. mesa detectors using a polished 45◦ incident facet on the detector, together with a globar source and a monochromator. A dual lock-in ratio system with a spectrally-flat pyroelectric detector was used to normalize the system spectral response due to wavelength dependence of the blackbody, spectrometer, filters, etc. The absolute magnitude of the responsivity was accurately determined by measuring the photocurrent Ip with a calibrated blackbody source. This photocurrent is given by the following equation. Zλ2 Ip

R(λ)P(λ)dλ

(2.6)

λ1

where λ1 and λ2 are the integration limits that extend over the responsivity spectrum and P(λ) is the blackbody power per unit wavelength incident on the detector, which is given by P(λ) = W(λ) sin2 (θ/2)AF cos φ

(2.7)

where A is the detector area, φ is the angle of incidence, θ is the optical field of view angle. That is, sin2 (θ/2) = (4 f 2 + 1)−1 ; where f is the number of the optical system; in this case, θ is defined by the radius ρ of the blackbody opening at a distance D from the detector so that tan(θ/2) = ρ/ D). F represents all the coupling factors and F = Tf (1 − r)C, where Tf is the transmission of filters and windows, r = 28% is the reflectivity of the GaAs detector surface, C is the optical beam chopper factor (C = 0.5 in an ideal optical beam chopper), and W(λ) is the blackbody spectral density given by the following equation (i.e., the power radiated per unit wavelength

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S. D. Gunapala, D. Z. Ting, S. B. Rafol, and S. V. Bandara

interval at wavelength λ by a unit area of a blackbody at temperature TB ). W(λ) = (2πc2 h/λ5 )(ehc/λkTB − 1)−1

(2.8)

Combining Eqs. (2.6) and (2.7), and using R(λ) = Rpe R(λ), where Rp is the peak responsivity and e R(λ) is normalized (at peak wavelength λp ) experimental spectral responsivity, we can rewrite the photocurrent Ip as follows. Zλ2 Ip = Rp G

e R(λ)W(λ)dλ

(2.9)

λ1

where G represents all the coupling factors and is given by G = sin2 (θ/2)AF cos φ. Thus, by measuring the TB = 1000 K blackbody photocurrent, Rp can be accurately determined. The normalized responsivity spectra e R(λ) are given in Fig. 2.12 for samples A–F, where we again see that the bound and quasibound excited state QWIPs (samples E and F) are much narrower 1λ/λ = 10%–12% than the continuum QWIPs 1λ/λ = 19%–28% (samples A–D). Table 2.3 gives the responsivity peak λp and cutoff wavelengths λc , as well as the responsivity 1.0 E

~ Responsivity (R)

0.8 A

0.6

B

C

F

D T = 20K

0.4

0.2

0.0

4

6

8

10 12 14 Wavelength λ (µm)

16

18

20

FIGURE 2.12 Normalized responsivity spectra versus wavelength measured at T = 20 K for samples A–F. (Levine et al., 1992a)

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TABLE 2.3 Responsivity spectral parameter for samples A–F, including peak responsivity wavelength λp , long wavelength cutoff λc , spectral width 1λ, and fractional spectral width 1λ/λp . (Levine et al., 1992a) Sample

λop (µm)

λc (µm)

1λ (µm)

1λ/λ (%)

A B C D E F

8.95 9.8 13.2 16.6 8.1 8.4

9.8 10.7 14.0 19.0 8.5 8.8

2.25 2.0 2.5 4.6 0.8 1.0

25 20 19 28 10 12

0.4

D

C

Responsivity Ro p (AW)

0.3 T = 20 K λ = λp

0.3

B A

0.3 F

E

0.3 0.2 0.1 0.0

0

−1

−2 Bias voltage Vb (V)

−3

−4

FIGURE 2.13 Bias dependent peak (λ = λp ) responsivity R0p measured at T = 20 K for samples A–F. The inserts show the conduction band diagrams. (Levine et al., 1992a)

spectral width 1λ. These responsivity spectral parameters are given in Table 2.3 and are similar to the corresponding absorption values listed in Table 2.2. The absolute peak responsivity Rp can be written in terms of quantum efficiency η and photoconductive gain g as follows. Rp = (e/hν)ηg.

(2.10)

Responsivity versus bias voltage curves for the bound, quasibound, and continuum, samples are shown in Fig. 2.13. Note that at low bias,

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the responsivity is nearly linearly-dependent on bias and it saturates at high bias. This saturation occurs due to the saturation of drift velocity. For the longest wavelength sample D, where λc = 19 µm, the dark current becomes too large at high bias to observe the saturation in Rp . The quasibound QWIP (sample F) behaves quite similarly to the bound QWIPs. The fully bound sample E has a significantly lower responsivity. The responsivity does not start out linearly with bias but is in fact zero for finite bias. That is, there is a zero-bias offset, due to the necessity of field-assisted tunneling for the photoexcited carrier to escape from the well (Choi et al., 1987b; Levine et al., 1988b, 1987b; Vodjdani et al., 1991).

3.4. Dark current noise The dark current noise in was measured on a spectrum analyzer for all of the samples at T = 77 K as a function of bias voltage (Zussman et al., 1991). The result for sample B is shown in Fig. 2.14. The solid circles were measured for negative bias (mesa top negative), while the open circles are for positive bias. The smooth curves are drawn using the experimental data. Note that the current shot noise for positive bias is much larger than that 40

Current noise ln (PA/√Hz)

Sample B T = 77 K λc = 10.7 μm

30

Positive bias

20

10 Negative bias

0

0

2

4

6

8

Bias voltage Vb (V)

FIGURE 2.14 Dark current noise in (at T = 77 K) versus bias voltage Vb for sample B. Both positive (open circles) and negative (solid circles) bias are shown. The smooth curves are drawn through the measured data. The insert shows the conduction band diagram. (Levine et al., 1992a)

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for negative bias (e.g., at Vb = 3.5 V, it is four times larger). Also that near Vb = 4V, there is a sudden increase in the noise due to a different mechanism (possibly due to the avalanche gain (Levine et al., 1987c) process). This asymmetry in the dark-current noise is because of the previously mentioned asymmetry in Id . The photoconductive gain g can now be obtained using the current shot noise expression (Beck, 1993; Hasnain et al., 1990b; Levine et al., 1990a; Liu, 1992a,b) in =

q 4eId gn 1f,

(2.11)

where 1f is the bandwidth, (taken as 1f = 1 Hz).

3.5. Noise gain and Photoconductive gain For a typical QWIP, where the dark current is dominated by thermionic emission, noise gain gn and photoconductive gain g can be written in terms of well-capture probability pc (capture probability of electrons by the next period of the MQW) and the number of quantum wells N in the MQW region (Beck, 1993; Choi, 1996; Levine et al., 1992a; Liu, 1992a,b), gn =

1 − pc /2 Npc

(2.12)

g=

(1 − pc ) Npc

(2.13)

where pc is capture probability of electrons by the next period of the MQW. Combining in from Fig. 2.14 and Id from Fig. 2.11 allows the experimental determination of g as shown in Fig. 2.15. The solid circles are for negative bias while the open circles are for positive bias, and the smooth curves are drawn through the experimental points. As shown in Fig. 2.15, the photoconductive gain increases approximately linearly with the bias at low voltage and saturates near Vb = 2 V (due to velocity saturation) at g ∼ 0.3. It is worth noting that in spite of the large difference between the noise current in for the positive and the negative bias (as shown in Fig. 2.14), the photoconductive gains are quite similar. This demonstrates that the asymmetry in in is due quantitatively to the asymmetry in Id . It further shows that, although the number of carriers that escape from the well and enter the continuum [transmission factor, γ (Choi, 1996)] is strongly dependent on the bias direction (due to the asymmetrical growth interfaces), the continuum transport (i.e., photoconductive gain), is less sensitive to the direction of the carrier motion. The reason for this difference is that the transmission factor, γ (and hence Id ), depends exponentially on

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Photoconductive gain g

0.4

0.3

Sample B

1.0

T = 77 K λc = 10.7 µm

0.8

Positive bias

0.6

0.2 0.4 Negative bias 0.1 0.2

0

0

1

2 Bias voltage Vb (V)

3

0.0

FIGURE 2.15 Photoconductive gain g (left-hand scale) and hot electron mean free path L (right-hand scale) versus bias voltage Vb for sample B at T = 77 K. Both positive (open circles) and negative (solid circles) bias are shown. The smooth curves are drawn through the measured data. The insert shows the conduction band diagram. (Levine et al., 1992a)

the bias, whereas photoconductive gain is only linearly dependent on bias Vb . The photoconductive gain of QWIPs can be written as (Hasnain et al., 1990b; Kastalsky et al., 1988) g = L/l,

(2.14)

where L is the hot carrier mean free path and l is the superlattice length (l = 2.7 µm for sample B). Therefore, we can evaluate L as shown on the right hand scale of Fig. 2.15. Thus for this device, L saturates at ∼ 1 µm. As mentioned above, the dramatic increase in in near Vb = 4 V in Fig. 2.14 is due to additional noise mechanisms and, therefore, should not be attributed to a striking increase in g. From the strong saturation of Rp for sample A (in Fig. 2.13), we would also expect the photoconductive gain to be completely saturated for |Vb | > 2 V, which is how we have drawn the smooth curve in Fig. 2.16. However, if one obtains g by simply substituting the measured in into eq. (2.11), the result is the dotted line in Fig. 2.16. Interpreting the large excess noise in above 4 V in Fig. 2.14, as Id shot noise would lead to an

Quantum Well Infrared Photodetectors

0.8

0.6 0.2

Sample A T = 77 K λc = 9.8 µm

0.1

0.0

0

−0.2

−0.4 −0.6 Bias voltage Vb (V)

0.4

Mean free path (µm)

Photoconductive gain g

0.3

85

0.2

0.0 −0.8

FIGURE 2.16 Photoconductive gain g (left-hand scale) and hot electron mean free path L (right-hand scale) versus bias voltage Vb for sample A at T = 77 K. The solid curve drawn through the points is the correct interpretation; the dashed line is not. The insert shows the conduction band diagram. (Levine et al., 1992a)

incorrectly large gain. Likewise, interpreting the low in above Vb = −2 V in Fig. 2.16 as a result of a low gain would also be incorrect. Levine et al. (1992b) have explained this by attributing the excess noise at high bias to the ground state sequential tunneling, which is increasing the dark current Id above that because of the thermionic emission and thermionically assisted tunneling through the tip of the barriers. That is Id,m = Id,th + Id,tu

(2.15)

where Id,m is the total measured current, Id,th is the usual thermionic contribution, and Id,tu is the ground-state tunneling current. It should be noted (Levine et al., 1990a) that electrons near the top of the well, which contribute to the dark current Id,tu , are same as those which can transport in the continuum and thus contribute to the photocurrent Ip . In contrast, the electrons that contribute to the ground-state tunneling current Id,tu do not enter the continuum, but sequentially, tunnel from one well to the next (Choi et al., 1987a). The gain associated with this process is gtu = Lp /l (where Lp is the superlattice period) and is very small compared with

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the usual continuum transport gain g = L/l. These two current processes contribute to the shot noise. i2d,m = i2d,th + i2d,tu .

(2.16)

By combining eqs. (2.11), (2.15), and (2.16) and using the fact that gtu g, we can write gm = (1 − f)g

(2.17)

where gm is the measured gain and f = Id,tu /Id,m . Therefore, at high bias when the current contribution from sequential tunneling increases, the measured gain decreases, exactly as found in Fig. 2.16. A more general formula for noise gain was derived by Beck (1993) and Choi (1996), which incorporated the tunneling and thermionic contributions of the dark current. Bandara et al. (1998b) have observed two different gain mechanisms associated with the photocurrent electrons and dark current electrons, which transported in two difference paths in a QWIP structure. More appropriately, gn given in Eq. (2.12) should be used for the noise current calculation (using Eq. (2.11)) because it gives the overall noise of the detector because of the thermionic current and other extraneous sources such as tunneling, surface leakage, contacts, etc. Under normal operating conditions (i.e., moderate operating bias), noise gain gn is equal to the photoconductive gain g, thus, it is customary to use the photoconductive gain g for the transport (i.e., Eq. 2.10) and noise calculations.

3.6. Quantum efficiency By using eq. (2.10), the bias-dependent photoconductive gain (Figs. 2.15 and 2.16), and the responsivity (Fig. 2.13), we can now determine the total measured quantum efficiency η (Levine et al., 1992a). The results of the continuum samples A–D are shown in Fig. 2.17. It is important to note that the total quantum efficiency does not vanish at zero bias but has a substantial value ranging from η0 = 3.2%–13%, corresponding to a finite probability of escaping from the quantum well. As the bias is increased, quantum efficiency increases approximately linearly and then saturates at high bias reaching maximum values of ηmax = 8%–25%. The saturation values of the total quantum efficiencies are listed in Table 2.2, where they appear to be comparable with the values obtained from the zero-bias absorption measurements ηa (77 K). The difference in these values ([i.e., between ηmax and ηa [77 K]) can be attributed to the lower measured gain as described in subsection 3.5.

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25 B

Quantum efficiency η (%)

20

ηmax = 25%

ηmax = 18% C

15 ηo = 13%

A ηmax = 16%

ηo = 6.2% 10

ηmax = 8% D

ηo = 5.6% 5 ηo = 3.2% 0

0

−1

−2 Bias voltage Vb (V)

−3

−4

FIGURE 2.17 Quantum efficiency η versus bias voltage Vb (negative) for samples A-D. The zero bias quantum efficiencies η0 and the maximum quantum efficiencies ηmax are shown. The insert shows the conduction band diagram. (Levine et al., 1992a)

We now consider the bound and quasibound QWIPs (samples E and F). The photoconductive gains are plotted in Fig. 2.18, where they appear to be quite similar to the continuum QWIPs shown in Fig. 2.16, and the quantum efficiencies are shown in Fig. 2.19. For these QWIPs (sample E and F), η is quite similar to that of the continuum QWIPs (Fig. 2.17), having a saturation values at high-bias voltages. However, the required bias voltage to reach the saturation value is higher for the bound and the quasibound QWIPs than that for the continuum QWIPs. Also, zero-bias quantum efficiency of these QWIPs (sample E and F) has much lower values. These differences are due to the necessity of the field-assisted tunneling to aid the bound-state excited photoelectrons to escape from the quantum well. This transmission factor (γ ) can be included in the effective quantum efficiency (η) such that (Choi, 1996; Levine et al., 1992b) η = γ ηa

(2.18)

where ηa is the absorption quantum efficiency of the MQW structure. In this case, responsivity (R) and photoconductive gain (g) are related by

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Photoconductive gain g

0.3

E 0.2

F 0.1 T = 77 K

0.0

−1

0

−2 Bias voltage Vb (V)

−3

−4

FIGURE 2.18 Photoconductive gain g versus bias voltage Vb (negative) for samples E and F at T = 77 K. The inserts show the conduction band diagram. (Levine et al., 1992a)

Quantum efficiency η (%)

20

15

F

10

E

5

T = 77 K 0 0

−1

−2 −3 Bias voltage Vb (V)

−4

FIGURE 2.19 Quantum efficiency η versus bias voltage Vb (negative) for samples E and F. The zero bias quantum efficiencies η0 and the maximum quantum efficiencies ηmax are shown. The inserts show the conduction band diagram. (Levine et al., 1992a)

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R = eηg/hν, where hν is the photoexcitation energy. Also, this transmission factor can be included in the optical gain (go ) which is defined (Choi, 1996) as go = γ g, and as a result, Rp = eηa go /hv. Typically, γ value of the bound-to-continuum detectors is larger than γ of the bound-to-bound detectors, and has a weaker bias-voltage dependence. This is to be expected since the photoexcited carriers in the boundto-continuum QWIPs are above the barriers and, thus, readily escape before being recaptured. However, the bound-to-bound QWIP is quite different because of the necessity of field-assisted tunneling in order for excited photoelectrons to escape from the quantum well (Choi, 1996; Levine et al., 1992b).

3.7. Detectivity We can now determine the peak detectivity D∗λ defined as (Levine et al., 1990a; Zussman 1991) √ D∗λ

=

R0p

A1f in

(2.19)

where A is the detector area and 1f = 1 Hz. This is done as a function of bias for a continuum (A), a bound (E), and a quasibound (F) QWIP in Fig. 2.20. (The dashed lines near the origin are extrapolations.) For all the three samples, D∗ has a maximum value at a bias between Vb = −2 and −3 V. Since these QWIPs all have different cutoff wavelengths, these maximum D∗ values cannot be simply compared. In order to facilitate this comparison, we note that the dark current has been demonstrated to follow an exponential law (Levine et al., 1990a, 1992a; Zussman et al., 1991) Id ∞e−(Ec −Ef )/kT (where Ec is the cutoff energy Ec = hc/λc ) over a wide range of both temperature and cutoff wavelength. Thus using D∗ ∝ (Rp /in ), we have D∗ = Dλ0 eEc /2kT

(2.20)

In order to compare the performance of these different QWIPs Levine et al. (1992b) have plotted D∗ against Ec on a log scale as shown in Fig. 2.21 (Gunapala et al., 1991a; Levine et al., 1990a, 1991b; Zussman et al., 1991). The straight line fits the data very well, which is satisfying considering that the samples have different doping densities, ND , different methods of crystal growth, different spectral widths 1λ, different excited states (bound, quasibound, and continuum) and even, in one case, a different materials system (InGaAs) (Gunapala et al., 1991a). The best fit for T = 77 K

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12 F

Detectivity D* (1010 cm √Hz/W)

10

8

6

E

4

2 A 0

−1

0

−2 Bias voltage Vb (V)

−3

−4

FIGURE 2.20 Detectivity D∗ (at T = 77 K) versus bias voltage Vb for samples A, E and F. The inserts show the conduction band diagram. (Levine et al., 1992a)

1012 InGaAs T = 77K

Detectivity D* (cm √Hz/W)

1011

F

D* = 1.1 ×106 eEc /2kT

A E

1010

B C

109 D 108 0 107 60

80

100 120 Cutoff energy Ec (meV)

140

160

FIGURE 2.21 Detectivity D∗ (at T = 77 K) versus cutoff energy Ec for n-doped QWIPs. The straight line is the best fit to the measured data. (Levine et al., 1992a)

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detectivities of n-doped QWIPs is √ D∗e = 1.1 × 106 eEc /2kT cm Hz/W

(2.21)

Another useful figure of merit is the blackbody responsivity RB and detectivity D∗B , which can be written as p D∗B

= RB

A1f in

(2.22)

with Rλ2 RB =

R(λ)W(λ)dλ

λ1

Rλ2

(2.23) W(λ)dλ

λ1

It is worth noting that for most applications, the blackbody responsivity RB is reduced only a relatively small amount from the peak value Rp . Also note that, since the QWIP dark current is mostly because of the thermionic emission and thermionically-assisted tunneling, unlike other detectors, QWIP detectivity increases nearly exponentially with the decreasing temperature as shown in Fig. 2.22.

4. LIGHT COUPLING QWIPs do not absorb radiation incident normal to the surface since the light polarization must have an electric field component normal to the superlattice (i.e., growth direction) to be absorbed by the confined carriers (Gunapala and Bandara, 1995; Levine, 1993). When the incoming light contains no polarization component along the growth direction, the matrix element of the interaction vanishes [i.e., εE.Epz = 0 where (Eε) is the polarization and (Epz ) is the momentum along growth direction (z)]. As a consequence, these detectors have to be illuminated through a 45◦ polished facet (Gunapala and Bandara, 1995; Levine, 1993). Clearly, this illumination scheme limits the configuration of detectors to linear arrays and single elements. For imaging, it is necessary to be able to couple the light uniformly to two-dimensional arrays of these detectors. Several different monolithic grating structures such as linear gratings (Goosen and Lyon, 1985; Hasnain et al., 1989), two-dimensional (2-D) periodic gratings (Andersson and Lundqvist, 1991b; Andersson et al., 1991a;

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1013

Detectivity D*λ (cm √Hz/W)

λc = 10.7 μm 1012

Vb = 0.5V, 1V 1011 Vb = 3V 1010

109

40

50

60

70

80

Temperature T (K)

FIGURE 2.22 Peak detectivity for a QWIP having cutoff wavelength of λc = 10.7 µm as a function of temperature T for several bias voltages Vb . (Gunapala et al., 1990b) D∗λ

Andersson et al., 1991c; Bandara et al., 1997; Sarusi et al., 1994b), and random-reflectors (Xing and Liu, 1996), have demonstrated efficient light coupling to QWIPs, and have made two-dimensional QWIP imaging arrays feasible (see Fig. 2.23). These gratings deflect the incoming light away from the direction normal to the surface, enabling intersubband absorption. These gratings were made of metal on the top of each detector or crystallographically etched through a cap layer on the top of the MQW structure.

4.1. One-dimensional periodic gratings Goosen and Lyon first suggested the QWIP with a metallic diffraction grating (Goosen and Lyon, 1985) for light coupling with normal incident light. In addition, the grating modes have large, normal electric fields, allowing efficient excitation of intersubband transitions. With the grating, (Goosen and Lyon, 1985). predicted that the quantum efficiency of 90% is possible, assuming a single quantum well with 1012 electrons per square centimeter. There are two main aspects of the problem of analyzing the performance of this grating-coupled QWIP device. First, the electromagnetic fields in the detector are obtained by matching to the incident wave, assuming a form for the dielectric constant of the quantum well. Second, the dielectric function is found by performing a quantum mechanical analysis of the intersubband transition rate. When a plane, light wave strikes a grating, the

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2D Grating grating and cavity

Reflected radiation

Incident radiation

Thin GaAs Substrate

FIGURE 2.23 Schematic diagram of 2-D periodic grating specifications. The grating features are spaced periodically along the x and y directions. (Gunapala et al., 1997b)

light is scattered into orders (indexed by an integer), whose wave vectors have parallel components equal to that of the incident wave, plus integer multiples of the reciprocal lattice vector of the grating. A few years later Hasnain et al. (1989) demonstrated the first uniformly illuminated 2-D array of QWIP pixels (200 µm in diameter) with 1-D gratings fabricated by wet chemical etching. In one method, a diffraction grating was etched on the back surface of detector substrate and the detector array was back illuminated. In the second scheme, the grating was etched on the top contact layer and both front, and illumination at normal incidence was achieved. The responsivities of the QWIP pixels illuminated by the above two methods were equal to that of the identical QWIP pixels that are back-illuminated at 45◦ through a polished facet. The 45◦ back illumination approach is regarded as the standard for comparison because in this configuration, the absolute responsivity or quantum efficiency of these QWIPs can be easily determined. The diffraction grating (4-µm period) was chemically etched through a photoresist mask consisted of 2-µm wide stripes spaced by 2 µm. The etchant (H2 SO4 :H2 O2 :H2 O = 1 : 8 : 10) used was blocked by the {111} Ga planes forming V-shaped grooves and undercuts the photoresist mask; etching was stopped when the mask falls off leaving a triangular grating with {111} Ga sidewalls. To maximize the light coupling efficiency, the grating period was chosen such that the first diffracted order coincided with the refracted beam, that is, the blaze wavelength matched the peak of the detector spectral response.

4.2. Two-Dimensional Periodic Gratings Detailed theoretical analysis has been carried out on both linear and 2-D periodic gratings on QWIPs. In 2-D gratings, the periodicity of the grating repeats in two perpendicular directions on the detector plane, leading

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to the absorption of both polarizations of the incident infrared radiation. Also, experiments have been carried out for 2-D grating coupled QWIP detectors designed for wavelengths λ ∼ 9 µm (Andersson and Lundqvist, 1991b; Andersson et al., 1991a; Andersson et al., 1991c; Bandara et al., 1997) and λ ∼ 16–17 µm (Sarusi et al., 1994b). A factor of 2–3 responsivity enhancement relative to the standard 45◦ polished facet illumination was observed for large area mesas (500 × 500 µm) with a total internal reflection optical cavity which can be created with an additional Al GaAs layer (Andersson and Lundqvist, 1991b; Andersson et al., 1991a; Andersson et al., 1991c) or with a thinned substrate (Sarusi et al., 1994b). This optical cavity is responsible for an extra enhancement factor of about 2 due to the total internal reflection from the AlGaAs layer or from the thinned substrate as shown in Fig. 2.23. Because of the resonance nature, the light coupling efficiency of the 2-D gratings depends strongly on the wavelength and, thus, exhibits narrow-bandwidth spectral responses. The normalized responsivity spectrum for the 2-D periodic grating coupled QWIP samples (with six different grating periods, D and a fixed groove depth) and for the standard 45◦ sample are shown in Fig. 2.24. Note the normalized spectral peak shifts from 7.5 to 8.8 µm as the grating period increases from D = 2.2–3.2 µm. These measurements were repeated for three groove depths. The grating peak wavelength λgp (where the grating enhancement is maximized) and the peak enhancement (enhancement at λgp ) associated with each grating period was obtained by normalizing the absolute spectral responsivity of the grating detectors relative to the 45◦ detector sample. As expected from 1.2 Normalized responsivity

Detector area 200 × 200 µm 1.0 2.2 µm 0.8

2.4 µm

0.6

2.6 µm

3.0 µm

4.5°

3.2 µm 2.8 µm

0.4 0.2 0.0

5

6

7

8 9 Wavelength (mm)

10

11

FIGURE 2.24 Measured normalized responsivity spectra as a function of grating period D vary from 2.2–3.2 µm. The solid curve represent responsivity spectra same QWIP with 45◦ polished edge. (Bandara et al., 1997)

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Grating responsivity/45° responsivity

4.0 3.5 3.0 2.5

(a), (b): h ∼ 1.0 μm (c): h ∼ 0.87 μm (d): h ∼ 0.75 μm

(a)

2.0

(b)

1.5 (c)

1.0

(d) 0.5 0.0 2.0

2.2

2.4

2.6 2.8 3.0 Grating period (μm)

3.2

3.4

FIGURE 2.25 The experimental responsivity enhancement at λgp for each grating period with different groove depths. Curves a and b represent gratings with same groove depth but different in detector area (a: 200 × 200 µm2 and b: 400 × 400 µm2 ). Curve c and d represent 200 × 200 µm2 area detectors with different groove depths. (Bandara et al., 1997)

the theory, measured λgp linearly depends on the grating period and it is independent of the groove depth of the grating (Bandara et al., 1997). Figure 2.25 shows experimental responsivity enhancement because of 2D grating at λgp for each grating period with different groove depths. One sample shows enhancement up to a factor of 3.5 (curves a and b in Fig. 2.25) depending on the grating period, while the other two samples show no enhancement and no dependence on the grating period. This high enhancement factor was measured in a similar (same gratings and groove depth) sample with different detector area. Scanning Electron Microscopic (SEM) of two samples, associated with curve c and d of Fig. 2.25, show apparent distortion in the features of the gratings (Bandara et al., 1997). This can be attributed to the partial contact between the grating mask and the wafer during the photolithography.

4.3. Gratings for multi-color and broadband detectors Light coupling to a pixel co-registered dual-band QWIP device is a challenge since each device has only a single top surface area. We have developed two different optical coupling techniques. The first technique uses a dual period Lamellar grating structure. However, the fabrication

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of dual-period light-coupling grating structure is much more complicated than the single-period light-coupling grating. A detailed description of this grating can be found in literature (Choi et al., 2003; Mao et al., 2002). The second technique uses the multiple diffraction orders. In this light coupling technique, we have used a 2-D grating with a single pitch. The first diffraction orders (1,0), (0,1), (−1,0), and (0,−1) couple infrared radiation into LWIR pixels, and the higher orders diffraction orders (1,1), (−1,1), (1,−1), (−1,−1), etc. couple infrared radiation into MWIR pixels. The grating was optimized for LWIR light coupling. The grating pitch is 2.7 µm with 50% fill factor. The depth of the grating pixels are quarter wavelength of LWIR radiation within GaAs. The top 0.7-µm-thick GaAs cap layer was used to fabricate the light coupling 2-D periodic grating. Light coupling grating parameters were optimized by exploring the parameter space experimentally. Usually the spectrometer application requires either broadband sensors or focal planes with spatially varying sensitivity. In this section, we discuss the light coupling of a 640 × 512-pixel monolithic spatiallyseparated four-band QWIP focal plane (Gunapala et al., 2003a). The unique feature of this spatially separated four-band FPA is that the four infrared bands are independently and simultaneously readable on a single imaging array. The individual pixels of the four-color detector array were defined by the photolithographic processing techniques (masking, dry etching, chemical etching, metal deposition, etc.). Four separate detector bands were defined by a deep-trench etch process and the unwanted spectral bands were eliminated by a detector short-circuiting process. The unwanted top detectors were electrically shorted by gold-coated reflective two-dimensional etched gratings as shown in Fig. 2.26. In addition to shorting, these gratings serve as light couplers for active QWIP stack in each detector pixel. Design and optimization of these two-dimensional gratings to maximize QWIP light coupling are extensively discussed earlier. The unwanted bottom QWIP stacks were electrically shorted at the end of each detector pixel row. Typically, quarter-wavelength deep (h = λp /4nGaAs ) grating grooves are used for efficient light coupling in single-band QWIP FPAs. However, in this case, the height of the quarterwavelength deep grating grooves is not deep enough to short circuit the top three MQW QWIP stacks (for example, three top QWIP stacks on 13–15 µm QWIP in Fig. 2.26). Thus, three-quarter-wavelength groove depth, two-dimensional gratings (h = 3λp /4nGaAs ) were used to short the top unwanted detectors over the 10–12 and 13–15 µm bands. This technique optimized the light coupling to each QWIP stack at corresponding bands while keeping the pixel (or mesa) height at the same level, which is essential for the indium bump-bonding process used for detector array and readout multiplexer hybridization. In order to achieve a truly broadband

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Light coupling gratings/Au metal contacts 640

128

128

Indium bump 128

128

FIGURE 2.26 Layer diagram of the four-band QWIP device structure and the deep groove two-dimensional periodic grating structure. Each pixel represents a 640 × 128 pixel area of the four-band focal plane array.

(A)

(B)

(C)

(D)

(E)

(F)

FIGURE 2.27 Optical coupling structures: (A) regular 2D crossed gratings; (B,C) Optical Coupling Scheme (OCS) based on surface sharing; (D) OCS with a gradient of the grating period; (E,F) OCS with matching of the Fourier Transform components. (Nedelcu et al., 2010)

light coupling, a different light coupling scheme is required. Nedelcu et al. (2010) have demonstrated a few interesting broadband optical coupling structures shown in Fig. 2.27.

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4.4. Effect of finite-size pixels The trend for focal planes is towards smaller pixels; this can either be used to decrease the focal plane size and thus the system cost or to increase the number of pixels, resulting in either better detection range or better situation awareness (same detection range, but bigger field of view). One of the main obstacles for smaller pixels in QWIPs is the light coupling into the pixel, which is crucial for QWIPs because of its polarization sensitivity of absorption. This is normally accomplished with a 2-D grating converting the normally incident light into absorbable state. The grating however, becomes less effective for smaller pixels, simply because fewer grating dots fit on one pixel. Martijn et al. (2009) have reported on the result of a full 3-D finite element simulation; these simulation results are here experimentally verified. Figure 2.28 shows their results. The dark current scaled as expected with the pixel size, confirming the absence of side wall leakage currents. As expected they showed a reduction of the responsivity of 40% for smaller pixels. Grating coupling structures are typically strongly wavelengthdependent and must be tuned to the waveband of interest. A finiteelement electromagnetic simulation can be performed using COMSOL Multiphysics software (version 3.5a with RF Module, COMSOL AB). If the substrate is thinned and the grating periodicity is infinite, total internal reflection (TIR) of the diffracted orders occur at the substrate-air 1.2

Response (A.U.)

1.0

0.8 0.6 0.4 Measured Simulated

0.2 0 10

15

20 Pixel pitch (µm)

25

30

FIGURE 2.28 Response as function of pixel pitch, simulated and measured. (Martijn et al., 2009)

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interface, significantly enhancing the absorption at Fabry-Perot resonances that involve 5-surface reflections (substrate, grating, substrate (TIR), grating, and substrate). Figure 2.29 shows the absorption QE for three substrate thicknesses (Wilson, 2009). The resonant absorption peaks are shifted away from the λ = 8.25 µm θ = 90◦ peak for the infinite substrate and are very sensitive to thickness, but they can absorb nearly 80% of the incident 1.0

Absorption QE

0.8

Subs = 0.2 µm Subs = 0.4 µm Subs = 0.6 µm αqw = 0.1µm−1

0.6

1.0

0.2

0 6.5

7.0

(B)

7.5 Wavelength (µm) (A)

8.0

8.5

(C)

FIGURE 2.29 (A) Absorption QE of infinite periodic grating on QWIP having quantum well stack thickness = 2.2 µm and substrate thicknesses of 0.2, 0.4, and 0.6 µm, with αqw = 0.1 µm−1 . (B) and (C) Image plots of |Ey | at λ = 7.95 µm and λ = 6.6 µm (absorption peaks for substrate = 0.6 µm thick).

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power, including the loss at the air-substrate boundary. If a reduced refractive index QW is included in the model, the QE curves get blue-shifted, but do not change their shape significantly because the QW anti-guiding is dominated by the substrate-air TIR. The situation becomes even more complex when the finite width of the QWIP pixel is included in the simulation. The mesa walls diffract the incoming radiation and reflect the radiation that is diffracted laterally by the grating. In combination of TIR and thinned-substrate-air interface, these reflections cause lateral Fabry-Perot resonances to develop. Figure 2.30A shows the absorption QE versus. wavelength for three different quantum well stack absorption coefficients, αqw . If the absorption is weak, multiple resonances exist because the light is allowed to reflect multiple times inside the mesa cavity. If the absorption is strong, the resonances are damped because the light is quickly absorbed after being diffracted by the grating. Figure 2.30B and C show image plots of |Ey | at the resonant wavelengths of 7.25 µm and 8.15 µm, respectively, for αqw = 0.1 µm−1 . Both resonances are clearly Fabry-Perot modes involving the mesa sidewalls. As the QW absorption increases, the peak near 7.25 µm dominates, indicating that total internal reflection by the substrate-air interface is critically important. This wavelength is also very similar to the anti-guiding peak wavelength of the QW stack (1nqw = 0 in this simulation, but the strong QW absorption causes the same effect). This is probably due to the fact that the substrate is so thin that the TIR-mode and the anti-guide mode dimensions are very similar. There is also an enhanced absorption near 9.4 µm (evanescent regime of grating) but the field (not shown) is concentrated near the upper corners of the QW, so it may not be effective in actual devices (Wilson, 2009).

4.5. Random Reflectors Random reflectors have demonstrated excellent optical coupling for individual QWIPs as well as for large area FPAs (Gunapala et al., 1997a,b; Sarusi et al., 1994a; Xing and Liu, 1996). It has been shown that many more passes of infrared light (Fig. 2.31), and significantly higher absorption can be achieved with a randomly roughened reflecting surface. By careful design of surface texture randomization (with a three-level random reflector), an enhancement factor of eight in responsivity compared to 45◦ illumination was demonstrated experimentally (Sarusi et al., 1994a). The random structure on the top of the detector prevents the light from being diffracted normally backward after the second bounce, as happens in the case of 2-D periodic grating (See Fig. 2.23). Naturally, thinning down the

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0.8 αqw = 0.1 µm−1

0.7

αqw = 0.5 µm−1

Absorption QE

0.6

αqw = 1 µm−1

0.5 0.4 0.3 0.2 0.1 0.0 6.5

7.0

7.5 8.0 8.5 Wavelength (µm) (A)

9.0

9.5

(B)

(C)

FIGURE 2.30 Simulation of a finite width (18 µm) QWIP pixel mesa with quantum well stack thickness = 2.2 µm, substrate thickness = 0.6 µm, grating period = 2.5 µm, grating depth = 0.6 µm. (A) Absorption QE vs. wavelength for αqw = 0.1, 0.5, and 1 µm−1 , (B) image plot of |Ey | at λ = 7.25 µm for αqw = 0.1 µm−1 , (C) image plot of |Ey | at λ = 8.15 µm for αqw = 0.1 µm−1 .

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Random reflector

Individual pixel Incident radiation

θC

FIGURE 2.31 Schematic side view of a thin QWIP pixel with a random grating reflector. Ideally all the radiation is trapped except for a small fraction which escapes through the escape cone.

substrate enables more bounces of light and, therefore, higher responsivity (Gunapala et al., 1997a; Sarusi et al., 1994a). All these gratings were fabricated on the detectors by using standard photolithography and selective dry etching. The advantage of the photolithograpic process is its ability to accurately control the feature size and preserve the pixel-to-pixel uniformity, which is a prerequisite for highsensitivity imaging FPAs. However, the resolution of photolithographs and accuracy of etching processes become key issues in producing smaller grating feature sizes. These feature sizes are proportionally scaled with the peak response wavelength of the QWIP. The minimum feature size of random reflectors implemented in 15-µm and 9-µm cutoff FPAs were 1.25 and 0.6 µm, respectively (Gunapala et al., 1997a,b). Thus, the random reflectors of the 9-µm cutoff FPA were less sharp and had fewer scattering centers compared to the random reflectors of the 15-µm cutoff FPA. These lesssharp features in the random gratings lowered the light coupling efficiency than expected. Therefore, it could be advantageous to use a 2-D periodic grating for light coupling in shorter wavelength QWIPs. However, one can avoid this problem by designing a random reflector which has the features similar to the 2-D periodic gratings (Xing and Liu, 1996).

4.6. Corrugated Structure Recently, Choi et al. (1998a) has demonstrated a new light coupling geometry for QWIPs based on the total internal reflection at the corrugated

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80 60

40

QWIP

50

Contact

60

40

40 20 20 Substrate (A)

90

90 (B)

FIGURE 2.32 (A) The 3-dimensional perspective of a corrugated QWIP detector pixel and (B) the ray diagram at the side view. (Choi et al., 1998b)

surface created within a detector pixel (Choi et al., 1998a,b). In these structures, linear V-grooves are chemically etched through the active detector region down to the bottom contact layer to create a collection of angled facets within single-detector pixels as shown in Fig. 2.32A. These facets deflect the normally incident light into the remaining QWIP active area through total internal reflection. For certain chemical solutions, such as 1H2 SO4 : 8H2 O2 : 10H2 O, the etching rate is different for different crystallographic planes. As a result, triangular wires are created, with sidewalls inclined around 54◦ with (1, 0, 0) surface along the (0, 1, 1) plane. In practice, the angle was found to be at 50◦ (Choi et al., 1998a,b). See Fig. 2.32B. Because the corrugated QWIP structure exposes the active layers of the detector, top metal contact cannot be deposited directly on the detector pixel. Two different approaches have been considered addressing this problem: (i) to leave out an unetched area for the contact as illustrated in Fig. 2.32A; and (ii) to isolate the active layers with a dielectric such as polymide. One of the main advantages of this light coupling technique is the reduction in pixel dark current due the smaller QWIP active area. In addition, the coupling scheme does not show significant wavelength and size dependence, and is therefore suitable for multi-color or broadband QWIPs. Figure 2.33 shows the spectral responsivity of the corrugated QWIP under normal incident illumination from the back of the wafer. For comparison, spectral responsivity of the same QWIP with 45◦ edge coupling is also illustrated in Fig. 2.33. It clearly shows that the corrugated structure does not change the intrinsic absorption line shape, which is represented by the 45◦ edge-coupling response, but increases the magnitude by a factor of 1.5. Also, this structure shows about 2.6 factor lower dark current due to the less active material, resulting in about 2.4 times improved D∗ (Choi et al., 1998a,b).

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0.5 Corrugated coupling

V = −2 V Responsivity (A/W)

0.4 0.3 0.2

45° Coupling × 1.5

0.1 0.0

8

9

10 Wavelength (µm)

11

12

FIGURE 2.33 Spectral responsivity of the corrugated QWIP and the same QWIP using 45◦ edge coupling. (Choi et al., 1998b)

5. IMAGING FOCAL PLANE ARRAYS There are many ground-based and space-borne applications that require long-wavelength, large, uniform, reproducible, low-cost, low-1/f noise, low-power dissipation, and radiation hard infrared FPAs. For example, the absorption lines of many gas molecules such as ozone, water, carbon monoxide, carbon dioxide, and nitrous oxide occur in the wavelength region from 3–18 µm. Thus, the infrared imaging systems that operate in the LWIR and VLWIR regions are required in many space applications such as monitoring the global atmospheric temperature profiles, relative humidity profiles, cloud characteristics, and the distribution of minor constituents in the atmosphere, which are being planned for NASA’s Earth Observing System (Chahine, 1990). In addition, 8–15 µm FPAs would be very useful in detecting cold objects such as ballistic missiles in the midcourse [when a hot rocket engine is not burning, most of the emission peaks are in the 8 to 15-µm infrared region (Duston, 1995)]. The GaAs/Alx Ga1−x As material system allows the quantum well shape to be tweaked over a range wide enough to enable light detection at wavelengths longer than ∼6 µm. Thus, the GaAs-based QWIP is a potential candidate for such space-borne and ground-based applications and many research groups (Andersson et al. 1997; Breiter et al. 1998; Choi et al. 2009; Goldberg et al. 2005; Gunapala et al. 1998b,c, 2003b, 2005a,b, 2010; Rafol 2008b; Rafol and Cho 2008a; Rafol et al. 2007; Schneider et al. 2004) have already demonstrated large uniform FPAs of QWIPs tuned to detect light at wavelengths from 6 to 25 µm in the GaAs/Alx Ga1−x As material system.

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5.1. Effect of Non-uniformity The general figure of merit that describes the performance of a large imaging array is the noise equivalent temperature difference NE1T. NE1T is the minimum temperature difference across the target that would produce a signal-to-noise ratio of unity and it is given by (Kingston, 1978; Zussman et al., 1991) p NE1T =

A1f

, D∗B (dPB /dT)

(2.24)

where D∗B is the blackbody detectivity (defined by Eq. 2.22) and (dPB /dT) is the change in the incident integrated blackbody power in the spectral range of detector with temperature. The integrated blackbody power PB , in the spectral range from λ1 to λ2 , can be written as Zλ2 θ PB = A sin cos ϕ W(λ)dλ, 2 2

(2.25)

λ1

where θ, φ, and W(λ) are the optical field of view, angle of incidence, and blackbody spectral density, respectively, and are defined by Eqs. 2.7 and 2.8 in sub-section 3.3. Before discussing the array results, it is also important to understand the limitations on the FPA imaging performance due to pixel non-uniformities (Levine, 1993). This point has been discussed in detail by Shepherd (1988) for the case of PtSi infrared FPAs (Mooney et al., 1989), which have low response, but very high uniformity. The general figure of merit to describe the performance of a large imaging array is the noise equivalent temperature difference NE1T, including the spatial noise which has been derived by Shepherd (1988). It is given by NE1T =

Nn , dNb /dTb

(2.26)

where Tb is the background temperature, and Nn is the total number of noise electrons per pixel, which is given by Nn2 = Nt2 + Nb2 + u2 Nb2 .

(2.27)

Where the photoresponse-independent temporal noise electrons is Nt , the shot noise electrons from the background radiation is Nb , and residual non-uniformity after correction by the electronics is u. The temperature

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derivative of the background flux can be written to a good approximation as hcNb dNb , = dTb kλ¯ Tb2

(2.28)

where λ¯ = (λ1 + λ2 )/2 is the average wavelength of the spectral band between λ1 and λ2 . When temporal noise dominates, NE1T reduces to Eq. (2.24). In the case where residual nonuniformity dominates, Eqs. 2.26 and (2.28) reduces to NE1T =

¯ 2 uλT b 1.44

.

(2.29)

The unit of the constant is cm K, λ¯ is in cm and Tb is in K. Thus, in this spatial noise limited operation, NE1T ∝ u and higher uniformity means higher imaging performance. Levine (1993) has shown as an example, taking Tb = 300 K, λ¯ = 10 µm, and u = 0.1% results in the NE1T value of 63 mK, while an order of magnitude uniformity improvement (i.e., u = 0.01%) gives NE1T value of 6.3 mK. By using the full expression Eq. (2.27), Levine (1993) has calculated NE1T as a function of√ D∗ as shown ∗ 10 in Fig. 2.34. It is important to note that when D ≥ 10 cm Hz/W, the performance is uniformity limited and thus essentially independent of the detectivity, i.e., D∗ is not the relevant figure of merit (Grave and Yariv, 1992).

5.2. 128 × 128 Pixels VLWIR Focal Planes By carefully designing the quantum well structure, as well as the light coupling (as discussed in Section 4) to the detector, it is possible to optimize the material to an optical response in the desired spectral range, determine the spectral response shape, as well as reduce the parasitic dark current, and therefore increase the detector impedance. Generally, in order to tailor the QWIP spectral response to the VLWIR spectral region, the barrier height should be lowered and the well width should be increased relative to the shorter cutoff wavelength QWIPs. For a detailed analysis of design and performance optimization of VLWIR QWIPs, see Sarusi et al. (1994c). The first VLWIR FPA camera was demonstrated by Gunapala et al. (1997a) which consisted of bound-to-quasibound QWIPs as shown in Fig. 2.5. Samples were grown using MBE and their well widths Lw vary ˚ while barrier widths are approximately constant at from 65 to 75 A,

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100 90 80

NEΔT (mk)

70 60

λ = 10 μm TB = 300 k a = (50 μm)2 f/2; Δf = 60 Hz u = 10−3

50 40 30 20 10 0 109

u = 10−4 1010 1011 Detectivity (cm √Hz/W)

1012

FIGURE 2.34 Noise equivalent temperature difference NE1T as a function of detectivity D∗ . The effects of nonuniformity are included for u = 10−3 and 10−4 . Note that for √ D∗ > 1010 cm Hz/W detectivity is not the relevant figure of merit for FPAs. (Levine, 1993)

˚ These QWIPs consisted of 50 periods of doped (ND = 2 × Lb = 600 A. 1017 cm−3 ) GaAs quantum wells, and undoped Alx Ga1−x As barriers. Very low doping densities were used to minimize the parasitic dark current. The Al molar fraction in the Alx Ga1−x As barriers varies from X = 0.15 to 0.17 (corresponding to cutoff wavelengths of 14.9 to 15.7 µm). These QWIPs had peak wavelengths from 14 to 15.2 µm as shown in Fig. 2.35. The peak quantum efficiency was 3% (lower quantum efficiency is due to the lower well doping density) for a 45◦ double pass. Four device structures were grown on 3-in. GaAs wafers and each wafer processed into 35 128 × 128 FPAs. The pixel pitch of the FPA is 50 µm and the actual pixel size is 38 × 38 µm2 . Two-level random reflectors used to improve the light coupling can be seen on the top of each pixel. These random reflectors, which were etched to a depth of half a peak wavelength in GaAs using reactive-ion etching, had a square profile. These reflectors are covered with Au/Ge and Au (for Ohmic contact and reflection), and In bumps are evaporated on the top for Silicon multiplexer hybridization. A single QWIP FPA was chosen from the sample 7060 (cutoff wavelength of this sample is 14.9 µm) and bonded to a silicon readout multiplexer. FPA

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1.2 7060

T = 55 K

7059

Responsivity (arb. unit)

1.0

7058 7057

0.8

0.6

0.4

0.2

0.0 10

11

12

13 14 15 Wavelength (µm)

16

17

18

FIGURE 2.35 Normalized responsivity spectra of four bound-to-quasibound VLWIR QWIP FPA samples at temperature T = 55 K. (Gunapala et al., 1997a)

was back-illuminated through the flat-thinned substrate. This initial array gave excellent images with 99.9% of the pixels working, demonstrating the high yield of GaAs technology. As mentioned earlier, this high yield is due to the excellent GaAs growth uniformity and the mature GaAs processing technology. The uniformity after two-point correction was u = 0.03% (Gunapala et al., 1997a). Video images were taken at various frame rates varying from 20 to 200 Hz with f/2.6 KRS-5 optics at temperatures as high as T = 45 K, using a multiplexer having a charge capacity of 4 × 107 electrons. However, the total charge capacity was not available during the operation, since the charge storage capacitor was partly filled to provide the high-operating bias voltage required by the detectors (i.e., Vb = −3 V). This FPA has given the NE1T value of 30 mK (Gunapala et al., 1997a) at 300 K background with f/2 apperture. It should be noted that these initial unoptimized FPA results are far from optimum.

5.3. 256 × 256 Pixels LWIR Focal Planes Infrared imaging systems that work in the 8–12-µm (LWIR) band have many applications, including night vision, navigation, flight control, and early warning systems. Several research groups have demonstrated (Asom et al., 1991; Bethea and Levine, 1992; Bethea et al., 1993, 1991; Kozlowski et al., 1991a,b; Levine et al. (1991d)) the excellent performance of QWIP

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arrays. For example, Faska et al. (1992) have obtained very good images using a 256 × 256 bound-to-miniband MQW FPA. The first 256 × 256 LWIR hand-held imaging camera was demonstrated by Gunapala et al. (1997b). The device structure of this FPA consisted of a bound-to-quasibound ˚ well of GaAs (doped n = 4 × QWIP containing 50 periods of a 45 A 17 −3 ˚ 10 cm ) and a 500 A barrier of Al0.3 Ga0.7 As. Ground-state electrons are provided in the detector by doping the GaAs well layers with Si. This photosensitive MQW structure is sandwiched between 0.5-µm GaAs top and bottom contact layers doped n = 5 × 1017 cm−3 and grown on a semiinsulating GaAs substrate by MBE. Then a 0.7-µm thick GaAs cap layer ˚ Al0.3 Ga0.7 As stop-etch layer was grown in situ on the top of a 300 A on the top of the device structure to fabricate the light coupling optical cavity. The detectors were back illuminated through a 45◦ polished facet as described earlier and a responsivity spectrum is shown in Fig. 2.36. The responsivity of the detector peaks at 8.5 µm and the peak responsivity (Rp ) of the detector is 300 mA/W at bias VB = −3 V. The spectral width and the cutoff wavelength are 1λ/λp = 10% and λc = 8.9 µm, respectively. The measured absolute peak responsivity of the detector is small, up to about VB = −0.5 V. Beyond that, it increases nearly linearly with bias reaching Rp = 380 mA/W at VB = −5 V. This type of behavior of the responsivity versus bias is typical for a bound-to-quasibound QWIP. The peak quantum efficiency was 6.9% at bias VB = −1 V for a 45◦ double pass. The lower quantum efficiency is due to the lower well-doping density (5 × 1017 cm−3 ) as it is necessary to suppress the dark current at the highest possible operating temperature.

Responsivity (mA/W)

150 Bias voltage = −2 V Operating temperature = 77 K

100

50

0 4

5

6

7 8 9 Wavelength (µm)

10

11

12

FIGURE 2.36 Responsivity spectrum of a bound-to-quasibound LWIR QWIP test structure at temperature T = 77 K. The spectral response peak is at 8.5 µm and the long wavelength cutoff is at 8.9 µm. (Gunapala et al., 1997a)

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After the random reflector array was defined by the lithography and dry etching, the photoconductive QWIPs of the 256 × 256 FPAs were fabricated by wet chemical etching through the photosensitive GaAs/Alx Ga1−x As MQW layers into the 0.5-µm-thick doped GaAs bottom contact layer. The pitch of the FPA is 38 µm and the actual pixel size is 28 × 28 µm2 . The random reflectors on the top of the detectors were then covered with Au/Ge and Au for Ohmic contact and reflection. A single QWIP FPA was chosen and hybridized (via indium bump-bonding process) to a 256 × 256 CMOS readout multiplexer (Amber AE-166) and biased at VB = −1.0 V. The FPA was back-illuminated through the flat˚ This array gave excellent thinned substrate membrane (thickness ≈1300 A). images with 99.98% of the pixels working (number of dead pixels ≈10), demonstrating the high yield of the GaAs technology (Gunapala et al., 1997b). The measured NE1T (mean value) of the FPA at an operating temperature of T = 70 K, bias VB = −1 V, and 300 K background is 15 mK. This agrees reasonably with our estimated value of 8 mK based on test structure data. The peak quantum efficiency of the FPA was 3.3% (lower FPA quantum efficiency is attributed to the 54% fill factor and 90% charge injection efficiency) and this corresponds to an average of three passes of infrared radiation (equivalent to a single 45◦ pass) through the photosensitive MQW region. A 256 × 256 QWIP FPA hybrid was mounted onto a 250 mW integral Sterling closed-cycle cooler assembly and installed into an Amber RADIANCE 1TM camera-body to demonstrate a hand-held LWIR camera (shown in Fig. 2.37). The camera was equipped with a 32-bit floating-point digital signal processor combined with multi-tasking software, providing the speed and power to execute complex image-processing and analysis functions inside the camera body itself. The other element of the camera is a 100 mm focal length germanium lens, with a 5.5 degree field of view. It is designed to be transparent in the 8–12 µm wavelength range to be compatible with the QWIP’s 8.5-µm operation. The digital acquisition resolution of the camera is 12-bits, which determines the instantaneous dynamic range of the camera (i.e., 4096). However, the dynamic range of QWIP is 85 dB. Its nominal power consumption is less than 50 Watts. Later, Amber Engineering commercialized this camera. It’s worth noting that Jiang et al. demonstrated 256 × 256 pixels LWIR InGaAs/InP-based QWIP FPA with reasonably good performance (Jiang et al., 2003).

5.4. VGA Format LWIR Focal Planes In this section, we will discuss the demonstration of the 640 × 486 LWIR imaging camera by Gunapala et al. (1998a). Although random reflectors have achieved relatively high quantum efficiencies with large area test

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FIGURE 2.37 Picture of the first 256 × 256 hand-held long wavelength QWIP camera (QWIP RADIANCETM ). (Gunapala et al., 1997a)

device structures, it is not possible to achieve similar high quantum efficiencies with random reflectors on the small area FPA pixels due to the reduced width-to-height aspect ratios. In addition, because of the fabrication difficulties of random reflector for shorter wavelength FPAs, as described in subsection 4.1, a 2-D periodic grating reflector was fabricated for light coupling of this 640 × 486 QWIP FPA. After the 2-D grating array was defined by the photolithography and dry etching, the photoconductive QWIPs of the 640 × 486 FPAs were fabricated by wet chemical etching through the photosensitive GaAs/Alx Ga1−x As MQW layers into the 0.5-µm-thick doped GaAs bottom contact layer. The pitch of the FPA is 25 µm and the actual pixel size is 18 × 18 µm2 . The 2-D gratings on the top of the detectors were then covered with Au/Ge and Au for Ohmic contact and reflection. Figure 2.38 shows twelve processed QWIP FPAs on a 3-in. GaAs wafer (Gunapala et al., 1998a). Indium bumps were then evaporated on the top of the detectors for silicon readout circuit (ROC) hybridization. A single QWIP FPA was chosen and hybridized (via indium bump-bonding process) to a 640 × 486 direct injection silicon readout multiplexer (Amber AE-181) and biased at VB = −2.0 V. At temperatures below 70 K, the signal-to-noise-ratio of the system is limited by the multiplexer readout noise and the shot-noise of the photo current. At temperatures above 70 K, temporal noise, caused because of the QWIP’s higher dark current, becomes the limitation. As mentioned earlier, this higher dark current is due to the thermionic emission and thus causes the charge storage capacitors of the readout circuitry

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FIGURE 2.38 Twelve 640 × 486 QWIP FPAs on a 3-in. GaAs wafer. (Gunapala et al., 1997a)

to saturate (Gunapala et al., 1998a). Since QWIP is a high impedance device, it should yield a very high charge injection coupling efficiency into the integration capacitor of the multiplexer. In fact, Bethea et al. (1993) have demonstrated charge injection efficiencies approaching 90%; The charge injection efficiency can be obtained from 

ηinj =

gm RDet  1 + gm RDet 1 +

1 jωCDet RDet 1+gm RDet

 

(2.30)

where gm is the transconductance of the MOSFET and is given by gm = eIDet /kT. The differential resistance RDet of the pixels at −2 V bias is 5.4 × 1010 Ohms at T = 70 K, and detector capacitance CDet is 1.4 × 10−14 F. The detector dark current IDet = 24 pA under the same operating conditions. According to Eq. (2.30), the charge injection efficiency ηinj = 99.5% at a frame rate of 30 Hz. The FPA was back- illuminated through the ˚ This thinned GaAs flat-thinned substrate membrane (thickness ≈1300 A). FPA membrane completely eliminated the thermal mismatch between the silicon CMOS readout multiplexer and the GaAs based QWIP FPA. Basically, the thinned GaAs based QWIP FPA membrane adapts to the thermal expansion and contraction coefficients of the silicon readout multiplexer. Thus, thinning has played an extremely important role in the fabrication of the large area FPA hybrids. In addition, this thinning has completely

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eliminated the pixel-to-pixel optical cross-talk of the FPA. This initial array gave very good images with 99.97% of the pixels working, demonstrating the high yield of GaAs technology. The operability was defined as the percentage of pixels having noise equivalent differential temperature less than 100 mK at 300 K background with f /2 optics and, in this case, operability happened to be equal to the pixel yield. We have used the following equation to calculate NE1T of the FPA √ NE1T =

AB

D∗B (dPB /dT) sin2 (θ/2)

(2.31)

where D∗B is the blackbody detectivity, dPB /dTdPB /dT is the derivative of the integrated blackbody power with respect to temperature, and θ is the field of view angle [i.e., sin2 (θ/2) = (4f 2 + 1)−1 , where f is the f-number of the optical system]. The background temperature TB = 300 K, the area of the pixel A = (18 µm)2 , the f-number of the optical system is 2, and the frame rate is 30 Hz. Fig. 2.39 shows the experimentally measured NE1T histogram of the FPA at an operating temperature of T = 70 K, bias VB = −2 V, and 300 K background with f /2 optics. The mean value of the NE1T histogram is 36 mK (Gunapala et al., 1998a). This agrees reasonably well with our estimated value of 25 mK based on the test structure data.

Number of pixels

16,095

0

28 31 34 37 40 43 46 Noise equivalent temperature difference (NEΔT) mK

FIGURE 2.39 Noise equivalent temperature difference (NE1T) histogram of the 311,040 pixels of the 640 × 486 array showing a high uniformity of the FPA. The uncorrected non-uniformity (is equal to standard deviation/mean) of this unoptimized FPA is only 5.6% including 1% non-uniformity of ROC and 1.4% non-uniformity due to the cold-stop not being able to give the same field of view to all the pixels in the FPA. (Gunapala et al., 1998a)

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The read noise of the multiplexer is 500 electrons. The 44% shortfall of NE1T is mostly attributed to unoptimized detector bias (i.e., VB = −2 V was used, instead of optimum VB = −3 V based on the detectivity data, as a function of bias voltage), decrease in the bias voltage across the detectors during charge accumulation (common in many direct injection type readout multiplexers), and the read noise of the readout multiplexer. The experimentally measured peak quantum efficiency of the FPA was 2.3% (lower FPA quantum efficiency is attributed to 51% fill factor and 30% reflection loss from the GaAs back surface). Therefore, the corrected quantum efficiency of the focal plane detectors is 6.5% and this corresponds to an average of two passes of infrared radiation through the photosensitive MQW region. A 640 × 486 QWIP FPA hybrid was mounted onto a 84-pin lead-less chip carrier and installed into a laboratory dewar, which was cooled by liquid nitrogen, to demonstrate a LWIR imaging camera. The FPA was cooled to 70 K by pumping on the liquid nitrogen, and the temperature was stabilized by regulating the pressure of gaseous nitrogen. The other element of the camera is a 100-mm-focal length AR coated germanium lens, which gives a 9.2◦ × 6.9◦ field of view. It is designed to be transparent in the 8–12 µm wavelength range for compatibility with the QWIP’s 8–9-µm operation. An Amber ProViewTM image processing station was used to obtain clock signals for the readout multiplexer and to perform digital data acquisition and non-uniformity corrections. The digital data acquisition resolution of the camera is 12-bits, which determines the instantaneous dynamic range of the camera (i.e., 4096). The measured mean NE1T of the QWIP camera is 36 mK at an operating temperature of T = 70 K, bias VB = −2 V, and 300 K background with f/2 optics. This is in good agreement with the expected FPA sensitivity due to the practical limitations on charge handling capacity of the multiplexer, read noise, bias voltage, and operating temperature. The uncorrected NE1T non-uniformity (which includes a 1% non-uniformity of the ROC and a 1.4% non-uniformity due to the cold-stop in front of the FPA not yielding the same field of view to all the pixels) of the 311,040 pixels of the 640 × 486 FPA is about 5.6% (equal to sigma/mean). The non-uniformity of the FPA after two-point (17◦ and 27◦ C) correction improves to an impressive 0.04%. As mentioned earlier, this high yield is due to the excellent GaAs growth uniformity and the mature GaAs processing technology. After the two point correction, measurements of the residual non-uniformity were made at temperatures ranging from 10◦ C (the cold temperature limit of the blackbody source) up to 40◦ C. The non-uniformity at each temperature was found by averaging the 16 frames, calculating the standard deviation of the pixel-to-pixel variation of the 16 frame average, and then dividing by the mean output, producing non-uniformity that may be reported as a percentage. For camera systems

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% nonuniformity

that have NE1T of about 30 mK, the corrected image must have less than 0.1% non-uniformity in order to be a standard television (TV) quality. Only at a temperature of 38◦ C did the camera’s non-uniformity exceed the 0.1% non-uniformity threshold. Figure 2.40 shows residual non-uniformity versus scene temperature plot. The 33◦ C window where the correction is below 0.1% is based on the measured data and one extrapolated data point at 5◦ C (Gunapala et al., 1998a). Later Gunapala et al. developed a 640 × 512 pixel VGA format LWIR QWIP FPA (Gunapala et al., 2003a). VGA format QWIP FPAs fabrication is described elsewhere (Gunapala et al., 2003a). These initial arrays gave excellent images with 99.92% of the pixels working (number of dead pixels ≈250), demonstrating the high yield of GaAs technology. Fig. 2.41 shows the NE1T of the FPA estimated from test structure data as a function of temperature for bias voltage VB = −1.1 V. The background temperature TB = 300 K, the area of the pixel A = (23 µm)2 , the f number of the optical system is 2, and the frame rate is 30 Hz. Figure 2.42 shows the measured NE1T histogram of the FPA at an operating temperature of T = 65 K, 16 msec integration time, bias VB = −1.1 V for 300 K background with f/2 optics, and the mean value is 20 mK. The absorption quantum efficiency of the FPA was 10%, which also agrees closely with the single element test detector results. A 640 × 512 QWIP FPA hybrid was integrated with a 330-mW integral Stirling closed-cycle cooler assembly (see Fig. 2.43) and installed into an Indigo PhoenixTM camera-body to demonstrate a hand-held LWIR camera (see Fig. 2.44). The camera head consists of a 640 × 512 format LWIR QWIP array hybridized with Indigo’s ISC 9803 ROIC, a cold-stop, a Stirling cooler, pre-amplifiers, and analog-to-digital converters. The optical element of the camera is a 100-mm-focal length germanium lens assembly, with a 9.2 degree field-of-view. It is designed to be transparent in the 0.20 0.18 0.16 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0

Less than 0.1% nonuniformity over 32°C Scene dynamic range

6

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13

17

19 22 25 27 30 Scene dynamic range

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36

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FIGURE 2.40 Residual non-uniformity after two point correction as a function of scene temperature. This corrected uniformity range is comparable to 3–5 µm IR cameras. (Gunapala et al., 1998a)

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NETD (mK)

1.E + 03

1.E + 02

Background Optics Bias tint

300 K f/2 -1.1 V 25 ms

1.E + 01

1.E + 00 60

70 80 Temperature (K)

90

FIGURE 2.41 Noise equivalent differential temperature NE1T estimated from test structure data as a function of temperature for bias voltage VB = −1.1 V. The background temperature TB = 300 K and the area of the pixel A = (23 µm)2 . (Gunapala et al., 2003a) 1000 900 800

Number of pixels

700 600 500 400 300 200 100 0

0.02 0.03 Noise equivalent temperature difference (K)

0.04

FIGURE 2.42 NETD histogram of the 327,680 pixels of the 640 × 512 array, showing a high uniformity of the FPA. The uncorrected non-uniformity (=standard deviation/mean) of the FPA is only 5% including 1% non-uniformity of ROC and 1.4% non-uniformity due to the cold-stop not being able to give the same field-of-view to all the pixels in the FPA. The non-uniformity was reduced to an impressive 0.02% after two-point correction. No 1/f noise was observed down to 10 mHz. (Gunapala et al., 2003a)

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FIGURE 2.43 1 K × 1 K Integrated Dewar Cooler Assembly (IDCA). (Rafol et al., 2007)

FIGURE 2.44 Simultaneously measured responsivity spectrum of vertically integrated LWIR and VLWIR dualband QWIP detector. (Gunapala et al., 1998a)

7–14-µm wavelength range, to be compatible with the QWIP’s 8.5–µm operation. The digital acquisition resolution of the camera is 14 bits, which determines the instantaneous dynamic range of the camera (i.e., 16,384). However, the dynamic range of QWIP is 85 dB. The measured mean NE1T of the QWIP camera system is 20 mK at an operating temperature of T = 65 K and bias VB = −1.1 V for a 300 K background with germanium f/2 optics. The uncorrected photocurrent non-uniformity (which includes a 1% non-uniformity of the ROIC and a 1.4% non-uniformity due to the cold-stop in front of the FPA not yielding the same field-of-view to all the pixels) of the 327,680 pixels of the 640 × 512 FPA is about 5% (equal to sigma/mean). The non-uniformity after a two-point (17◦ and 27◦ C) correction improves to an impressive 0.02%.

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The FPA performance data reported in this section was taken with the first LWIR PhoenixTM camera (see Fig. 2.44). Estimates based on the single pixel data show that these FPAs should be able to provide 7-mK NE1T with a 30-msec integration time, which can be achieved at VB = 1.1 V bias. The measured NE1T of the LWIR QWIP PhoenixTM camera is 20 mK with a 16 msec integration time. The noise of the camera system can be written 2 as, NSYS = n2Detector + n2ADC + n2MUX ; where nDetector is the noise of the FPA, nADC is the noise of the analog-to-digital converter, and nMUX is the noise of the silicon ROIC. The experimentally measured NSYS is 2 units, and the nADC and nMUX are 0.8 and 1 unit, respectively. This yields 1.5 noise units for nDetector . Thus, the NE1T of the FPA is 15 mK at 300 K background with f /2 optics and 16-msec integration time. This agrees reasonably well with our estimated value of 10 mK based on the test detector data. Therefore, these FPAs should be able to achieve 10.6 mK NE1T at the same operating conditions with 32 msec integration time. Figure 2.45 shows four frames of

FIGURE 2.45 Four frames of video images taken with the 9 µm cutoff 640 × 512 pixel QWIP PhoenixTM camera. These four images were taken at six-hour time intervals during a single day. Top left (6 AM), top right (noon), lower left (6 PM), and lower right (mid-night). (Gunapala et al., 2003a)

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video images taken with this large-format LWIR camera at six-hour time intervals within a day. As described in Sections 2.9 and 2.10, InGaAs/InP based QWIPs are excellent candidates for MWIR and LWIR FPAs. Higher responsivity in InGaS/InP QWIPs, as a result of larger gain offered by this material system, arises from the higher drift distance of the photoexcited electrons, which can be attributed either to better transport properties of the binary InP barriers or the larger photoexcited carrier lifetime (Gunapala et al., 1991a). Larger 0-L energy spacing in the barrier of InP/InGaAs QWIPs and higher valley occupancy of the continuum electrons with relatively high kinetic energy improve the drift distance of the photoexcited carriers, mainly due to the increase in the excited electron lifetime (Cellek et al., 2004; Gunapala et al., 1991a). Cellek et al. demonstrated molecular beam epitaxy grown InP/InGaAs 640 × 512 format QWIP FPA (Cellek et al., 2005). Figure 2.46 shows the spectral responses of the InP/InGaAs and AlGaAs/GaAs QWIP test detectors at 80 K. The responsivity of the InP/ In0.53 Ga0.47 As QWIP peaks at 7.85 µm with 1λ/λp of 11%, and Al0.27 Ga0.73 As/GaAs QWIP responsivity peaks at 7.74 µm with 1λ/λp of 15%. Figure 2.47 shows the uncorrected NE1T histogram of the FPA. The NE1T non-uniformity (σ /mean) is 17%, which is comparable to that of the LWIR AlGaAs/GaAs QWIP FPAs with the same format. Eker et al. demonstrated the first strained InP/ In0.48 Ga0.52 As QWIP with 9.7-µm cutoff (Eker et al., 2010). The epilayer structure of the InP/InGaAs QWIP was grown on a 3-in. semi-insulating InP substrate

Normalized response (a.u.)

10 InP/InGaAs QWIP AlGaAs QWIP

0.8

0.6

0.4

0.2

0.0 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 Wavelength ( µm)

FIGURE 2.46 Spectral response of 21 µm × 21 µm InP/InGaAs and AlGaAs/GaAs QWIPs under −1.5 V bias at 80 K. (Cellek et al., 2005)

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3.0 × 104 2.5 × 104

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Pixel count

2.0 × 104 1.5 × 104 1.0 × 104 5.0 × 103 0

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30

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NETD (mK)

FIGURE 2.47 Uncorrected NE1T histogram of the 640 × 512 pixels InP/InGaAs QWIP FPA at 70 K with 0.5 V bias. (Cellek et al., 2005)

˚ thick, ND = 5.5 × by solid source MBE. Forty In0.48 Ga0.52 As QWs (55-A 17 −3 ˚ 10 cm ) were sandwiched between 400-A thick undoped InP barriers. The top and bottom In0.53 Ga0.47 As contact layers were doped at ND = 1 × 1018 cm−3 . A cross type optical grating structure was defined by optical lithography and dry etching. Mesas with 25-µm pitch were formed by reactive ion etching with SiCl4 :Ar mixture using an inductively coupled plasma system. Following the formation of ohmic contacts, reflectors and underbump metallization, In bumps were grown on the mesas through electro-plating. The FPA was hybridized to Indigo ISC9803 ROIC using a high precision flip-chip aligner/bonder. After underfill injection, the substrate of the FPA was thinned to 10 µm followed by polishing with a high resolution lapping/polishing system. The VGA format strained InP/InGaAs FPA was characterized in a dewar with f /1.5 aperture connected to Pulse Instruments-System 7700. Without field of view correction and any calibration, the DC signal and NE1T non-uniformities of the FPA are as low as 4.5% and 11%, respectively. Figure 2.48 shows the NE1T of the FPA calculated using the spectral response and detectivity measurements on the test detectors which are identical to the FPA pixels. The integration times shown at each bias voltage correspond to half-filled ROIC capacitors (1.1 × 107 electron capacity). The number of g − r noise electrons generated by the FPA pixels during this duration is also given for comparison with the ROIC noise level. NE1T measurements made directly on the FPA are in reasonable agreement with those calculated with

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80 70

NETD (mK)

60

ms 65 K, 300 K background, f/1.5 τ = 0.25 g − r e− = 4368 50% filled ROIC capacitors 61% BLIP τ = 0.7 ms τ = 1 ms g − r e− = 2432 − g − r e = 1972 72% BLIP τ = 0.43 ms 76% BLIP g − r e− = 2876 67% BLIP τ = 1.8 ms g − r e− = 1530 78% BLIP

50 40 30 20 10 0

121

1.5

2.0

2.5 Bias voltage (V)

3.0

3.5

FIGURE 2.48 NE1T of the FPA calculated using the measurements on the test detectors (identical to the FPA pixels). The integration times (corresponding to half-filled ROIC capacitors with 1.1 × 107 electron capacity) and the number of g-r noise electrons generated by the FPA pixels are given for each bias voltage. (Eker et al., 2010)

test detector data (25 mK under 1.5 V bias, tint = 1.8 ms). The operability of the FPA is 99.5%.

5.5. 1024 × 1024 Pixels MWIR & LWIR Focal Planes In the MWIR device described here, each period of the MQW struc˚ containing 10-A ˚ GaAs, ture consists of coupled quantum wells of 40 A 18 ˚ ˚ 20 A In0.3 Ga0.7 As, and 10 A GaAs layers (doped n = 1 × 10 cm−3 ), a ˚ undoped barrier of Al0.3 Ga0.7 As between coupled quantum wells, 40-A ˚ and a 400-A-thick undoped barrier of Al0.3 Ga0.7 As. Stacking many identical periods (typically 50) together increases photon absorption. Ground state electrons are provided in the detector by doping the GaAs well layers with Si (Gunapala et al., 2005a). This photosensitive MQW structure is sandwiched between the 0.5-µm GaAs top and bottom contact layers doped n = 5 × 1017 cm−3 , grown on a semi-insulating GaAs substrate by molecular beam epitaxy (MBE). Then a 0.7-µm thick GaAs cap layer on ˚ Al0.3 Ga0.7 As stop-etch layer was grown in situ on top of the top of a 300 A device structure to fabricate the light coupling optical cavity. The experimentally measured peak absorption (or internal) quantum efficiency (ηa ) of this material at room temperature was 19%. Due to the fact that the n-i-n QWIP device is a photoconductive device, the net (or external) quantum efficiency η can be determined using η = ηa · g, where g is the photoconductive gain of the detector. The epitaxially grown material

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was processed into 200 µm diameter mesa test structures (area = 3.14 × 10−4 cm2 ) using wet chemical etching, and Au/Ge ohmic contacts were evaporated onto the top and bottom contact layers. The detectors were back-illuminated through a 45◦ polished facet and a responsivity spectrum is shown in Fig. 2.49. The responsivity of the detector peaks at 4.6 µm and the peak responsivity (Rp ) of the detector is 170 mA/W at bias VB = −1 V. The spectral width and the cutoff wavelength are 1λ/λp = 15% and λc = 5.1 µm, respectively. The photoconductive gain, g, was experimentally determined using g = i2n /4eID B + 1/2N, where B is the measurement bandwidth, N is the number of quantum wells, and in is the current noise, which was measured using a spectrum analyzer. The photoconductive gain of the detector was 0.23 at VB = −1 V and reached 0.98 at VB = −5 V. Since the gain of a QWIP is inversely proportional to the number of quantum wells N, the better comparison would be the well-capture probability pc , which is directly related to the gain by g = 1/Npc . The calculated well capture probabilities are 25% at low bias (i.e., VB = −1 V) and 2% at high bias (i.e., VB = −5 V), which together indicate the excellent hot-electron transport in this device structure. The peak net quantum efficiency was determined using η = ηa · g. Thus, the net peak quantum efficiency at bias VB = −1 V is 4.6%. The lower quantum efficiency is due to the lower photoconductive gain at lower operating bias. A lower operating bias is used to suppress the detector dark current. Due to a low readout multiplexer well 0.20

R (Amp/W)

0.15

0.10

0.05

0 3.5

4.0

4.5

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Wavelength (µm)

FIGURE 2.49 Responsivity spectrum of a bound-to-quasibound MWIR QWIP test structure at temperature T = 77 K. The spectral response peak is at 4.6 µm and the long wavelength cutoff is at 5.1 µm. (Gunapala et al., 2005a)

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depth (i.e., 8 × 106 electrons) a lower dark current is mandatory to achieve a higher operating temperature and longer integration times. In BLIP conditions the NE1T improves with increasing integration time. However, the absorption quantum efficiency can be increased further up to 60%– 70% with higher quantum well doping densities. As a result, the operating temperature of the devices will decrease. Figure 2.50 shows the peak detectivity as a function of detector operating temperature at bias VB = −1 V. These detectors show BLIP at a bias VB = −1 V and temperature T = 90 K for 300 K background with f /2.5 optics. After the two-dimensional grating array was defined by lithography and dry etching, the photoconductive QWIPs of the 1024 × 1024 FPAs were fabricated by dry chemical etching through the photosensitive GaAs/Alx Ga1−x As MQW layers into the 0.5-µm thick doped GaAs bottom contact layer. The pitch of the FPA is 19.5 µm and the actual pixel size is 17.5 × 17.5 µm2 . The two-dimensional gratings on top of the detectors were then covered with Au/Ge and Au for Ohmic contacts and high reflectivity. Figure 2.51 shows the nine processed 1024 × 1024 QWIP FPAs on a 100-mm GaAs wafer. Indium bumps were then evaporated on top of the detectors for a silicon CMOS readout integrated circuit (ROIC) hybridization process. A few QWIP FPAs were chosen and hybridized (via an indium bump-bonding process) to a 1024 × 1024 silicon CMOS ROICs and biased at VB = −1 V. At temperatures below 90 K, the signal to noise ratio of the system is limited by array non-uniformity, ROIC readout noise, and photo 1013

D*(cm Hz1/2/W)

1012

1011

1010

109 60

TBackground = 300 K Optics = f /2.5 Bia = −1 V 80

100 Temparature (K)

120

FIGURE 2.50 Detectivity as a function of detector operating temperature at bias of VB = −1 V. (Gunapala et al., 2005a)

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FIGURE 2.51 Nine 1024 × 1024 QWIP focal plane arrays on a 4 in. GaAs wafer. (Gunapala et al., 2005a)

current (photon flux) noise. At temperatures above 90 K, temporal noise due to the QWIP’s higher dark current becomes the limitation. As mentioned earlier, this higher dark current is due to thermionic emission and thus causes the charge storage capacitors of the readout circuitry to saturate. Because the QWIP is a high-impedance device, it should yield a very high charge-injection coupling efficiency into the integration capacitor of the multiplexer. In fact, Gunapala et al. have demonstrated that charge injection efficiencies in excess of 90% can be achieved in QWIPs. Charge injection efficiency data can be obtained from Eq. 2.30, the differential resistance RDet of the pixels at –1 V bias is 6.3 × 1012 Ohms at T = 85 K and detector capacitance CDet is 2.0 × 10−14 F. The detector dark current IDet = 0.1 pA under the same operating conditions. According to equation 2.30 the charge injection efficiency is ηinj = 98.8% at a frame rate of 10 Hz. The FPA was back-illuminated through the flat-thinned substrate ˚ This initial array gave excellent images with membrane (thickness ≈800 A). 99.95% of the pixels working (number of dead pixels ≈500), demonstrating the high yield of GaAs technology. The operability was defined as the percentage of pixels having noise equivalent differential temperature less than 100 mK at 300 K background and in this case, the operability happens to be equal to the pixel yield. We have used Eq. 2.31 to calculate the NE1T (used Eq. 2.31) of the FPA and Fig. 2.52 shows the NE1T of the FPA estimated from test structure data as a function of temperature for bias voltages VB = −1 V. The background temperature TB = 300 K, the area of the pixel A = (17.5 × 17.5 µm2 ), the f number of the optical system is 2.5, and the frame rate is 10 Hz. Figure 2.53

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100 Detector

NEΔT (mK)

System

TBackground = 300 k Optics = f/2.5 10 60

80

100 Temperature (K)

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FIGURE 2.52 Noise equivalent differential temperature NE1T estimated from test structure data as a function of temperature for bias voltage VB = −2 V. The background temperature TB = 300 K and the area of the pixel A = (17.5 µm)2 . (Gunapala et al., 2005a)

shows the measured NE1T of the imaging system at an operating temperature of T = 90 K, 60 msec integration time, bias VB = −1 V for 300 K background with f /2.5 optics and the mean value is 23 mK. As shown in this figure 2.53, the measured NE1T of the MWIR 1K × 1K QWIP cam2 era is 23 mK. The noise of the camera system can be written as, NSYS = 2 2 2 nDetector + nADC + nMUX , where nDetector is the noise of the FPA, nADC is the noise of the analog-to-digital converter, and nMUX is the noise of the silicon ROIC. The experimentally measured NSYS is 2 units, and the nADC and nMUX are 0.8 and 1 unit, respectively. This yields 1.5 noise units for nDetector . Thus, the NE1T of the FPA is 17 mK at 300 K background with f/2.5 optics and 60 msec integration time. This agrees reasonably well with our estimated value of 20 mK based on test detector data (see Fig. 2.52). (Gunapala et al., 2005a) This agrees well with our estimated value of 15 mK based on test structure data (see Fig. 2.52). It is worth noting that the NE1I of the detector array is reduced to 17 mK after removing the noise factors associate with ROIC, electronics, etc. The net peak quantum efficiency of the FPA was 3.8% (lower focal plane array quantum efficiency is attributed to lower photoconductive gain at lower operating bias and lower well doping densities used in this device structure) and this corresponds to an average of three passes of infrared radiation (equivalent to a single 45◦ pass) through the photosensitive MQW region. It is worth noting that under BLIP conditions, the performance of the detectors is independent of

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8000 7000

Number of pixels

6000 5000 4000 3000 2000 1000 10

0

0.02

0.04 0.06 NEΔT (K)

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FIGURE 2.53 NE1T histogram of the 1,048,576 pixels of the 1024 × 1024 array showing a high uniformity of the FPA. The uncorrected non-uniformity of the FPA is only 5.5% including 1% non-uniformity of ROC and 1.4% non-uniformity due to the cold-stop not being able to give the same field of view to all the pixels in the FPA.

the photoconductive gain, and it depends only on the absorption quantum efficiency. A 1024 × 1024 QWIP FPA hybrid (see Fig. 2.54) was mounted onto a 5 W integral Sterling closed-cycle cooler assembly to demonstrate a portable MWIR camera. The digital acquisition resolution of the camera is 14 bits, which determines the instantaneous dynamic range of the camera (i.e., 16,384). However, the dynamic range of QWIP is 85 dB. The preliminary data taken from a test set up has shown mean system NE1T of 22 mK (the higher NE1T is due to the 65% transmission through the lens assembly, and system noise of the measurement setup) at an operating temperature of T = 90 K and bias VB = −1 V, for a 300 K background. It is worth noting that these data were taken from the first 1024 × 1024 QWIP FPA that we have produced. Thus, we believe that there is a plenty of room for further improvement of these FPAs. Video images were taken at a frame rate of 10 Hz at temperatures as high as T = 90 K, using a ROIC capacitor having a charge capacity of 8 × 106 electrons (the maximum number of photoelectrons and dark electrons that can be counted in the time taken to read each detector pixel). Figure 2.55 shows a frame of a video image taken with a 5.1-µm-cutoff, 1024 × 1024-pixel QWIP camera (Gunapala et al., 2005a). Modulation transfer function (MTF) is the ability of an imaging system to faithfully image a given object. The MTF of an imaging system

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FIGURE 2.54 Picture a 1024 × 1024 pixel QWIP focal plane array mounted on a 84-pin lead less chip carrier.

FIGURE 2.55 One frame of video image taken with the 5.1 µm cutoff 1024 × 1024 pixel QWIP camera.

quantifies the ability of the system to resolve or transfer spatial frequencies. Consider a bar pattern with a cross-section of each bar being a sine wave. Since the image of a sine wave-light distribution is always a sine wave, the image is always a sine wave independent of the other effects in the imaging system such as aberration. Usually, the imaging systems have no difficulty in reproducing the bar pattern when the bar pattern is closely spaced. However, an imaging system reaches its limit when the features of

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the bar pattern get closer and closer together. When the imaging system reaches this limit, the contrast or the modulation (M) is defined as M=

Emax − Emin , Emax + Emin

(2.32)

where E is the irradiance. Once the modulation of an image is measured experimentally, the MTF of the imaging system can be calculated for that spatial frequency, using, MTF =

Mimage . Mobject

(2.33)

Generally, MTF is measured over a range of spatial frequencies using a series of bar pattern targets. It is also customary to work in the frequency domain rather than the spatial domain. This is done using a fast Fourier transform (FFT) of the digitally recorded image. The absolute value of the FFT of the point spread function is then squared to yield the power spectral density of the image, Simage . The MTF can be calculated using the formula s MTF =

Simage . Sobject

(2.34)

We have used a well collimated 20-µm diameter spot to estimate the MTF of the MWIR breadboard imaging system we have built using the 1024 × 1024 pixel QWIP FPA discussed in this section. Figure 2.56A shows a three-dimensional plot of the signal observed from this imaging system, and Fig. 2.56B shows the horizontal and vertical point spread functions (PSF) of the image in Fig. 2.56A. Figure 2.57 shows the MTF of the imaging system as a function of spatial frequency. This was evaluated by taking the FFT of the point spread functions shown in Fig. 2.56B and using Eq. 2.34. It is important to remember that the MTF of a system is a property of the entire system, therefore, all of the system components such as the FPA, lens assembly, cabling, framegraber, etc. contribute to the final MTF performance of the system as shown in Eq. 2.35. Thus, the system MTFsystem is given by, MTFSystem = MOptics × MTFFocalPlane × MTFElectronics × MTFCables (2.35) The MTF of the spot scanner optics at Nyquist frequency is 0.2, thus the MTF of the FPA should be 30% and 45% at the Nyquist frequency Ny = 25.6 Cy/mm (Ny = 1/2 pixel pitch) along horizontal and vertical

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Signal strength

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20 Column position

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FIGURE 2.56 (A) Signal strength of individual pixels of MWIR megapixel FPA in response to the illumination of 20 µm diameter spot. (B) Horizontal and vertical point spread functions of megapixel MWIR FPA.

axes, respectively. This difference in the measured PSF becomes visible also on the MTF since the frequency contents of differently shaped PSFs are different. The narrower the PSF the more it contains higher frequency components. The lens MTF measurement does not show a large difference between horizontal and vertical. We believe that the difference is probably due to the ROIC and electronics (Gunapala et al., 2005a; Rafol, 2008b; Rafol and Cho, 2008a; Rafol et al., 2007). Higher MTF at Nyquist indicates that QWIP FPA has the ability to detect smaller targets at large distances since optical and electronic energy

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FIGURE 2.57 Horizontal and vertical MTF of the MWIR imaging system based on a 1024 × 1024 pixel QWIP MWIR camera.

are not spread among adjacent pixels. It is already shown elsewhere the MTF of a perfect FPA (i.e., no pixel-to-pixel cross-talk) is 0.64 at the Nyquist frequency. In other words, this data shows that the pixel-to-pixel crosstalk (optical and electrical) of MWIR megapixel FPA is almost negligible at Nyquist. This was to be expected, because this FPA was back-illuminated ˚ This subthrough the flat thinned substrate membrane (thickness ≈800 A). strate thinning (or removal) should completely eliminate the pixel-to-pixel optical cross-talk of the FPA. In addition, this thinned GaAs FPA membrane has completely eliminated the thermal mismatch between the silicon CMOS ROIC and the GaAs based QWIP FPA. Basically, the thinned GaAs based QWIP FPA membrane adapts to the thermal expansion and contraction coefficients of the silicon ROIC. For these reasons, thinning has played an extremely important role in the fabrication of large area FPA hybrids. Each period of this LWIR MQW structure consists of quantum wells of ˚ and a 600 A ˚ barrier of Al0.27 Ga0.73 As. As mentioned earlier, stacking 40 A many identical periods (the device in this study has 50 periods) together increases photon absorption. Ground state electrons are provided in the detector by doping the GaAs well layers with silicon impurities up to n = 5 × 1017 cm−3 . This photosensitive MQW structure is sandwiched between 0.5 µm GaAs top and bottom contact layers doped n = 5 × 1017 cm−3 , grown on a semi-insulating GaAs substrate by MBE. Then a 0.7-µm˚ Al0.27 Ga0.73 As stop-etch layer thick GaAs cap layer on top of a 300 A was grown in situ on top of the device structure to fabricate the light

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coupling optical cavity. The MBE grown material was tested for absorption efficiency using a FTIR spectrometer. Test detectors with a 200 µm diameter were fabricated and back-illuminated through a 45◦ polished facet for optical characterization and an experimentally measured responsivity spectrum is shown in Fig. 2.58. The responsivity of the detector peaks at 8.4 µm and the peak responsivity (RP ) of the detector is 130 mA/W at bias VB = −1 V. The spectral width and the cutoff wavelength are 1λ/λp = 10% and λc = 8.8 µm, respectively. The photoconductive gain g was experimentally determined as described in the previous section. The peak detectivity of the LWIR detector was calculated using experimentally measured noise current in . The calculated peak √ detectivity at bias VB = −1 V and temper11 ature T = 70 K is 1 × 10 cm Hz/W (see Fig. 2.59). These detectors show BLIP at bias VB = −1 V and temperature T = 72 K for a 300 K background with f /2.5 optics. A light-coupling two-dimensional grating structure was fabricated on the detectors by using standard photolithography and CCl2 F2 selective dry etching. After the two-dimensional grating array was defined by lithography and dry etching, the photoconductive QWIPs of the 1024 × 1024 FPAs were fabricated by dry chemical etching through the photosensitive GaAs/Alx Ga1−x As MQW layers into the 0.5-µm-thick doped GaAs bottom contact layer as described earlier. The pitch of the FPA is 19.5 µm and the actual pixel size is 17.5 × 17.5 µm2 . The two-dimensional gratings on top of

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the detectors were then covered with Au/Ge and Au for Ohmic contacts and high reflectivity. Nine 1024 × 1024 pixel QWIP FPAs were processed on a 4-in. GaAs wafer. Indium bumps were then evaporated on the top of the detectors for hybridization with silicon CMOS ROICs. A single QWIP FPA was chosen and hybridized (via indium bump-bonding process) to a 1024 × 1024 CMOS multiplexer and biased at VB = −1 V. At temperatures less than 72 K, the signal-to-noise ratio of the system is limited by array non-uniformity, ROIC readout noise, and photocurrent (photon flux) noise. At temperatures more than 72 K, the temporal noise due to the dark current becomes the limitation. The differential resistance RDet of the pixels at −1 V bias is 7.4 × 1010 Ohms at T = 70 K and detector capacitance CDet is 1.7 × 10−14 F. The detector dark current IDet = 1.6 pA under the same operating conditions. The charge injection efficiency into the ROIC was calculated as described in earlier section. An average charge injection efficiency of ηinj = 95% has been achieved at a frame rate of 30 Hz. It is worth noting that, the charge injection efficiency gets closer to one, especially when photocurrent is present. Since we are using direct injection ROIC, the injection efficiency gets better at higher drain current or when there is more photocurrent. Charge injection efficiency becomes worst at very low background flux, but limited by the dark current for QWIP detector, i.e., the dark current keeps the pixel on. This initial array gave excellent images with 99.98% of the pixels working (number of dead pixels ≈ 200), again demonstrating the high yield of GaAs technology.

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FIGURE 2.60 Noise equivalent temperature difference NE1T estimated from test structure data as a function of temperature for bias voltage VB = −2 V. The background temperature TB = 300 K, optics f# = 2.5, and the area of the pixel A = (17.5 µm)2 .

NE1T of the FPA was calculated using Eq. 2.32. Figure 2.60 shows the NE1T of the FPA estimated from the test structure data as a function of temperature for a bias voltage VB = −1 V. The background temperature TB = 300 K, the area of the pixel A = (17.5 × 17.5 µm2 ), the f number of the optical system is 2.5, and the frame rate is 30 Hz. Figure 2.61 shows the measured NE1T of the system at an operating temperature of T = 72 K, 29 sec integration time, bias VB = −1 V for 300 K background with f /2.5 optics and the mean value is 16 mK. The noise of the camera system can be 2 written as NSYS = n2Detector + n2ADC + n2MUX ; where nDetector is the noise of the FPA, nADC is the noise of the analog-to-digital converter, and nMUX is the noise of the silicon ROIC. The experimentally measured NSYS is 2.4 units; the nADC and the nMUX are 0.8 and 1 unit, respectively. This yields 2.0 noise units for nDetector . Thus, the NE1T of the detector array is 13 mK at 300 K background with f /2.5 optics and 29-msec integration time. This agrees reasonably well with our estimated value of 15 mK based on the test detector data (see Fig. 2.60). As described in the previous section, we have used a well-collimated 20-µm-diameter LWIR spot to estimate the MTF of the LWIR breadboard imaging system we have built using the 1024 × 1024-pixel QWIP FPA. Figure 2.62 shows the MTF of the imaging system as a function of spatial frequency. The MTF of the spot scanner optics at Nyquist frequency is 0.2, thus the MTF of the FPA should be >0.5 at the Nyquist frequency

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FIGURE 2.62 Horizontal and vertical MTF of the MWIR imaging system based on a 1024 × 1024 pixel QWIP MWIR camera.

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Ny = 25.6 Cy/mm. As mentioned earlier, the MTF of an ideal FPA (i.e., no pixel to pixel cross-talk) is 64% at Nyquist frequency. Thus, the pixel to pixel optical and electrical cross-talk of this LWIR megapixel FPA is negligibly small. We have observed oscillations in many of our MTF measurements, and this may be due to the unfiltered high frequency noise on the PSF due to pattern noise. This becomes more pronounced at higher frequency when it approaches the noise floor. The source of this is most likely the ROIC and electronics. We do not think this is temporal in origin since we have averaged 64 frames or more for the PSF measurement. At 15 Cy/mm, the lens MTF is approximately 0.38, so the detector MTF at 15 Cy/mm is approximately 26.3%. This is much less than the ideal MTF of the FPA. A 1024 × 1024 QWIP FPA, hybrid was mounted onto a 5-W integral Sterling closed-cycle cooler assembly to demonstrate a portable LWIR camera. The digital data acquisition resolution of the camera is 14 bits, which determines the instantaneous dynamic range of the camera (i.e., 16,384). The preliminary data taken from a test set up has shown mean system NE1T of 16 mK at an operating temperature of T = 72 K and bias VB = −1 V, for a 300 K background. Video images were taken at a frame rate of 30 Hz at temperatures as high as T = 72 K, using a ROIC capacitor having a charge capacity of 8 × 106 electrons. Figure 2.63 shows one frame of a video image taken with a 9-µm cutoff 1024 × 1024 pixel QWIP camera (Goldberg et al., 2005; Gunapala et al., 2005a; Rafol, 2008b; Rafol and Cho, 2008a; Rafol et al.,

FIGURE 2.63 A frame of the video image taken with the 9 µm cutoff 1024 × 1024 pixel QWIP camera.

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2007). In addition, the minimum resolvable temperature difference was measured by a single observer using seven bar targets ranging in spatial frequency from 0.1 cycles/milli radian up to 1.33 cy/mr, which was the first target where no contrast could be measured (unclear). While the collection of the data does not adhere to the generally accepted requirements of having multiple observers, the data is consistent with the NE1T measurement and worth reporting. At the lowest spatial frequency, the minimum resolvable differential temperature (MRDT) was 16 mK.

5.6. Dualband (MWIR & LWIR) Focal Planes There are many applications that require MWIR and LWIR dual-band FPAs. For example, a dual-band FPA camera would provide the accurate temperature (Dereniak and Boreman, 1996) of a target with unknown emissivity which is extremely important to the process of identifying objects based on their surface temperature. Dual-band infrared FPAs can also play many important roles in the Earth and planetary remote sensing, astronomy, etc. Furthermore, the monolithically integrated, pixel co-located, simultaneously readable dual-band FPAs eliminate the beam splitters, filters, moving filter wheels, and rigorous optical alignment requirements imposed on dual-band systems based on two separate single-band FPAs or a broad-band FPA system with filters. Dual-band FPAs also reduce the mass, volume, and power requirements of dual-band systems. Because of the inherent properties such as narrow-band response, wavelength tailorability, and stability (i.e., low 1/f noise) associated with GaAs based QWIPs (Cho et al., 2003a,b; Gunapala et al., 2007, 2009, 2010, 2000; Goldberg et al., 2000, 2003; McQuiston et al., 2004; Schneider et al., 2004), it is an appropriate detector choice for large format dual-band infrared FPAs. As shown in Fig. 2.64, our dual-band FPA is based on two different types of QWIP devices (i.e., MWIR and LWIR) separated by a 0.5micron-thick, heavily doped, n-type GaAs layer. One can stack the MWIR and LWIR multi-quantum-well (MQW) structures in different ways. The MWIR MQW structure is placed on the top of the LWIR MQW structure because the MWIR MQW region consists of the lattice mismatch InGaAs layers. This has an advantage from the epitaxial materials growth perspective. However, this is a disadvantage from the material processing standpoint since it is hard to etch InGaAs material compared to other III–V materials such as GaAs and AlGaAs. The device structure shown in Fig. 2.64A is commonly used and described in reference (Goldberg et al., 2000, 2003). Figure 2.64B and C are novel and these structures have two heavily doped GaAs contact layers between MWIR and LWIR MQW regions and an undoped AlGaAs layer embedded between these two GaAs

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FIGURE 2.64 3-D view of four possible dual-band QWIP device structures showing via connects for independent access of MWIR and LWIR devices. The speckled areas are heavily doped GaAs layers for making Ohmic contacts. Pixel shown in (a) is completely isolated from neighboring pixels. In contrast, devices (b), (c), and (d) have common ground connections with neighboring pixels. The cross-hatched layers (i.e., undoped AlGaAs layers) split center contact layers of devices (b), (c), and (d) in to two Ohmic contact layers. A, B, and G are indium bumps. It is worth noting that device structure (d) uses only two bumps per pixel.

contact layers. Device structure in Fig. 2.64B uses two separate detectorcommon (or ground) contacts, which are connected via the ROIC. Also, it is worth noting in this structure that MWIR and LWIR detectors operate with opposite polarities. Figure 2.64C shows a similar device structure to Fig. 2.64B, the only difference is both the MWIR and LWIR device will operate on the same polarity. Figure 2.64D shows an interesting dual-band device structure that uses only two indium bumps per pixel compared to three indium bumps per pixel with all pixel co-located dual-band devices (Goldberg et al., 2000; Gunapala et al., 2007). In this device structure the detector-common is shorted to the bottom detector-common plane via a metal bridge. Thus, this device structure reduces the number of indium bumps by 30% and has a unique advantage in large format FPAs, since

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more indium bumps require additional force during the FPA hybridization process. A coupled-quantum well structure was used in this device to broaden the responsivity spectrum. In the MWIR device, each period of the MQW ˚ thick un-doped barrier of Al0.25 Ga0.75 As, and structure contains a 300 A a double quantum well region. The double QW region contains two ˚ of Al0.25 Ga0.75 As un-doped identical quantum wells separated by a 45 A ˚ AlAs, 5 A ˚ GaAs, barrier. Each of the two quantum wells consists of 3 A ˚ In0.3 Ga0.7 As, 5 A ˚ GaAs, and 3 A ˚ AlAs; the quantum well is doped 32 A n = 4 × 1018 cm−3 . This period was repeated 13 times. In the LWIR device, ˚ thick un-doped of each period of the MQW structure contains a 580 A Al0.25 Ga0.75 As barrier, and a triple quantum well region. The triple QW ˚ GaAs quantum wells (doped to n = region contains three identical 50 A ˚ of Al0.25 Ga0.75 As un-doped barriers. This 5 × 1017 cm−3) separated by 50 A period was repeated 16 times. These two photosensitive MQW structures are sandwiched between GaAs top and bottom contact layers doped n = 1 × 1018 cm−3 , grown on a semi-insulating GaAs substrate by molecular beam epitaxy (MBE). Top contact was a 0.7-µm-thick GaAs cap layer on ˚ Al0.25 Ga0.75 As stop-etch layer grown in situ on top of the top of a 350 A dual-band device structure to fabricate the light coupling optical cavity. The bottom contact layer was a 2-µm-thick GaAs layer. A 0.4-µm-thick undoped AlGaAs layer was embedded between the top contact of the LWIR and bottom contact of the MWIR MQW regions. As shown in Fig. 2.65, the MWIR device uses a bound-to-continuum design to help further broaden the spectrum; a single monolayer of AlAs on each side of quantum well is used to help increase the oscillator strength. The LWIR device uses a standard bound-to-quasibound design, where the upper levels involved in the infrared optical transition is in approximate resonance with the conduction band edge of the barrier. Note that the same AlGaAs barrier composition

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FIGURE 2.65 Energy band diagram of the dual-band QWIP structure.

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is used throughout the structures. For the LWIR structure, the calculated energy levels of the ground states in the unbiased triple-well are found to be at 147 meV, 151 meV, and 155 meV below the AlGaAs barrier, while the upper states are in approximate resonance with the top of the barrier. For the MWIR structure, the energy levels of the ground states in the unbiased double-well are found to be at 276 and 277 meV below the AlGaAs barrier, while the upper states are slight above the top of the barrier. It is worth noting that the photo-sensitive MQW region of each QWIP device is transparent at other wavelengths, which is an important advantage over conventional interband detectors. This spectral transparency makes QWIP an attractive detector material for pixel co-located dual-band FPAs with minimal spectral cross-talk. As shown in Fig. 2.64D, the carriers emitted from each MQW region are collected separately using two indium bumps. The bottom of the MWIR device is shorted to the detectorcommon (i.e., LWIR bottom contact) layer by a metal bridge fabricated through a via-hole. Top contact of the LWIR detector is accessed by another metal bridge fabricated through a via-hole. The MBE grown material was tested for absorption efficiency using a Fourier Transform Infrared (FTIR) spectrometer. The experimentally measured peak absorption (or internal) quantum efficiency (ηa ) of this material at room temperature was 19%. The infrared absorption of QWIPs is due to the intersubband transition between quasi-two-dimensional electronic states in semiconductor subbands, which are formed due to the confinement of electrons wave functions in one dimension (i.e., growth direction). A full account of intersubband absorption of QWIP is given by Helm (2000). The n-i-n QWIP device is a photoconductor, where not every photo-generated carrier is collected like in a photo-diode due to re-capturing by quantum wells. The detectors were back illuminated through a 45◦ polished facet and a responsivity spectrum is shown in Fig. 2.49. The responsivity of the detector peaks at 4.6 µm and the peak responsivity (Rp ) of the detector is 170 mA/W at bias VB = −1 V. The spectral width and the cutoff wavelength are 1λ/λp = 15% and λc = 5.1 µm, respectively. The photoconductive gain of the detector was 0.23 at VB = −1 V and reached 0.98 at VB = −5 V. The peak net quantum efficiency was determined using η = ηa · g. Thus, the net peak quantum efficiency at bias VB = −1 V is 4.6%. The lower quantum efficiency is due to the lower photoconductive gain at lower operating bias. The measured peak √ detectivity at bias VB = −1 V and temperature T = 11 90 K is 4 × 10 cm Hz/W. These detectors show BLIP at a bias VB = −1 V and temperature T = 90 K for 300 K background with f /2.5 optics. The experimentally measured LWIR responsivity spectrum is shown in Fig. 2.58. The responsivity of the detector peaks at 8.4 µm and the peak responsivity (RP ) of the detector is 130 mA/W at bias VB = −1 V. The spectral width and the cutoff wavelength are 1λ/λp = 10% and λc = 8.8 µm, respectively. The photoconductive gain g was experimentally

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determined as described in the previous section. The peak detectivity of the LWIR detector was calculated using experimentally measured noise current in . The calculated peak √ detectivity at bias VB = −1 V and temperature T = 70 K is 1 × 1011 cm Hz/W. These detectors show BLIP at bias VB = −1 V and temperature T = 72 K for a 300 K background with f /2.5 optics. Most infrared FPAs consist of non-silicon detector arrays and silicon ROICs. ROICs are usually fabricated on large area (i.e., 8–12-in. dia.) silicon wafers. In the process of large format IR FPA development, it is necessary to select an IR detector technology based on large area wafers. QWIP FPA technology is entirely based on the highly stable GaAs material system (i.e., 6–8-in. diameter wafers) that can be easily processed with the more mature fabrication technologies. The state-of-the-art array fabrication processes are based on reticle-based steppers. A typical reticle field is 22 × 22 mm2 . The pixel pitch of the largest 1K × 1K array fits in to a reticle field that is 18 µm. The pixel pitch of the 1K × 1K pixel dual-band QWIP FPA is 30 µm. Thus, a 30-µm pixel pitch 1K × 1K array cannot be fabricated using conventional reticle stepping or mask aligning methods. A large detector array can be fabricated using “Stitching”. Stitching is a new photolithographic technique that can be used to fabricate detector arrays larger than the reticle field of photolithographic steppers. We have used the stitching technique to fabricate 1K × 1K arrays that can be easily extended into the fabrication of 2K × 2K and 4K × 4K detector arrays. In this case, the detector array layout is divided into smaller portion “tiles”, which together fit in the reticle field. Array characteristics or repeated sections of the detector array are exploited to minimize the required reticle area by using multiple exposures of smaller blocks to create a large array. Each detector array is then photocomposed on the wafer by multiple exposures of detector array sections at appropriate locations on the wafer. Single sections of the detector array are exposed at one time, as the optical system allows shuttering, or selectively exposing only a desired section of the reticle. It should be noted that stitching creates a truly seamless detector array, as opposed to an assembly of closely butted pieces. After the 2-D grating array was defined by stepper based photolithography and dry etching, the MWIR detector pixels of the 1024 × 1024 pixel detector arrays, and the via-holes to access the detectorcommon, were fabricated by dry etching through the photosensitive GaAs/Iny Ga1−y As/Alx Ga1−x As MQW layers into the 0.5 µm thick doped GaAs intermediate contact layer. Then LWIR pixels and via-holes for MWIR pixels to access the array detector-common were fabricated. A thick insulation layer was deposited and contact windows were opened at the bottom of each via-hole and on the top surface. Ohmic contact metal was

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evaporated and unwanted metal was removed using a metal lift-off process. The pitch of the detector array is 30 µm and the actual MWIR and LWIR pixel sizes are 28 × 28 µm2 . Five detector arrays were processed on a four-in. GaAs wafer. Indium bumps were then evaporated on top of the detectors for hybridization with ROICs. Several dual-band detector arrays were chosen and hybridized (via an indium bump-bonding process) to grade A 1024 × 1024 pixel dual-band silicon ROICs. Array thinning or the substrate removal process is critical to the success and durability of large format cryogenic FPAs. Thus, after the detector array and ROIC hybridization process via indium bumps, the gaps between FPA detectors and the ROIC are backfilled with epoxy. This epoxy backfilling provides the necessary mechanical strength to the detector array and ROIC hybrid prior to the thinning process. During the first step of the thinning process, an approximately 630-µm-thick GaAs layer was removed using diamond point turning. Then Bromine-Methanol chemical polishing was used to remove another approximately 100-µm-thick GaAs layer. This step is very important because it removes all scratch marks left on the substrate due to abrasive polishing. Otherwise these scratch marks will be enhanced and propagated into the final step via preferential etching. Then, wet chemical etchant was used to reduce the substrate thickness to several microns and a SF6 :BCl3 selective dry etchant was used as the final etch. This final etching completely removed the remaining GaAs substrate. At this point the remaining GaAs/AlGaAs material contains ˚ The thermal only the QWIP pixels and a very thin membrane (∼500 A). mass of this membrane is insignificant compared to the rest of the hybrid. This allows it to adapt to the thermal expansion and contraction coefficients of the silicon ROIC and completely eliminates the thermal mismatch problem between the silicon based readout and the GaAs based detector array. This basically allows QWIP FPAs to go through an unlimited number of temperature cycles without any indium bump breakage and array de-lamination. Furthermore, this substrate removal process provides two additional advantages for QWIP FPAs: those are the complete elimination of pixel-to-pixel optical cross-talk and a significant (a factor of two with 2-D periodic gratings) enhancement in optical coupling of infrared radiation into QWIP pixels. Figure 2.66 shows a megapixel dual-band QWIP FPA mounted on a 124 pin LCC. A direct injection dual-band ROIC was developed for this dual-band QWIP detector array. A direct injection read out circuit is suitable for low impedance detector interface using a single MOSFET. The source of MOSFET keeps the detector bias constant and photon-induced charge carriers from the detector pixel integrate onto the capacitor at the drain of the MOSFET. A MWIR:LWIR pixel co-registered simultaneously readable

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FIGURE 2.66 Picture a 1024 × 1024 pixel dual-band QWIP FPA mounted on a 124-pin lead less chip carrier.

dual-band QWIP FPA has been mounted onto the cold finger of a pour fill dewar, cooled by liquid nitrogen, and the two bands (i.e., MWIR and LWIR) were independently biased. Some imagery was performed at a temperature of 68 K. An image taken with the first megapixel simultaneous pixel co-registered MWIR:LWIR dual-band QWIP camera is shown in Fig.2.67. The flame in the MWIR image (left) looks broader due to the detection of heated CO2 (from a cigarette lighter) re-emission in a 4.1–4.3micron band, whereas the heated CO2 gas does not have any emission line in the LWIR (8–9 microns) band. Thus, the LWIR image shows only thermal signatures of the flame. This initial array gave good images with 99% of the MWIR and 97.5% of the LWIR pixels working in the center 512 × 512 pixels region, which is excellent compared to the difficultness in the fabrication process of this pixel co-registered simultaneously readable dual-band QWIP FPA. The digital acquisition resolution of the imaging system was 14-bits, which determines the instantaneous dynamic range of the camera (i.e., 16,384). However, the dynamic range of QWIP is 85 dB. Video images were taken at a frame rate of 30 Hz at temperatures as high as T = 68 K. The total ROIC well depth is 17 × 106 electrons with LWIR to MWIR well depth ratio of 4:1. The estimated NE1T based on single pixel data of MWIR and LWIR detectors at 68 K are 22 and 24 mK, respectively. Sequence of consecutive frames is collected for equivalent noise determination as well as other optical properties of FPA. The photo response matrices of FPA is derived at the low and high blackbody temperatures (i.e., 295 K and 305 K), and temporal

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FIGURE 2.67 An image taken with the first megapixel simultaneous pixel co-registered MWIR:LWIR dual-band QWIP camera. The flame in the MWIR image (left) looks broader due to the detection of heated CO2 (from cigarette lighter) re-emission in 4.1–4.3-micron band, whereas the heated CO2 gas does not have any emission line in the LWIR (8–9 microns) band. Thus, the LWIR image shows only thermal signatures of the flame.

noise matrix of FPA is estimated at the mid-point temperature by taking 64 frames of data. The temporal NE1T of pixels are numerically evaluated from the relations, NE1T = σTemporal 1T/[Mean(TH ) − Mean(TL )]. The mean signal Mean (TL ) and Mean (TH ) are evaluated at blackbody temperatures of TL = 295 K and TH = 305 K. The temporal noise is measured at 300 K using 64 frames, and 1T ∼ 10 K. The measured mean NE1T was estimated at 27 and 40 mK for MWIR and LWIR bands, respectively at a flat plate blackbody temperature of 300 K with f /2 cold stop. The experimentally measured NE1T histograms distributions at blackbody temperature of 300 K with f /2 cold stop are shown in Figure 2.68A and B. The experimentally measured MWIR NE1T value closely agrees with the estimated NE1T value based on the results of a single element test detector data.

6. CONCLUDING REMARKS AND OUTLOOK We have attempted to give an introductory overview of the QWIP devices physics, operating mechanisms, noise, signal-to-noise-ratios, focal plane array development, and its current status. At present, much development effort is being devoted to the development of multi-band and large area focal planes. As a result, in recent years, many groups working in QWIPs managed to demonstrate high performance highly uniform IR FPAs using

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various different device and materials technologies (Asplund et al., 2006; Cellek et al., 2005; Cho et al., 2003a,b; Choi et al., 2009; Eker et al., 2009; Goldberg et al., 2005, 2000, 2003; Gunapala et al., 2005a, 2007, 2010, 2003a, 2000; Martijn et al., 2009; McQuiston et al., 2004; Ozer et al., 2007; Rafol, 2008b; Rafol and Cho, 2008a; Rafol et al., 2007; Robo et al., 2009; Schneider et al., 2004). Figure 2.69 shows the natural abundance of elements in the solar system in terms of mass. Solar system abundances are quite similar to those found in most stars and interstellar material in our neighborhood and in corresponding parts of other galaxies, where minor variations may occur in the relative amounts of hydrogen and helium, on the one hand, and carbon and heavier elements on the other. Relative abundances of the elements in the solar system span some 12 orders of magnitude (see Fig. 2.69). The two lightest elements, hydrogen and helium, together constitute more than 99 per cent of the atoms and the mass of the solar system. Silicon is the most important electronic material and it is the eighth most abundant material in the solar system with strong covalent bonds. However, silicon is the second most abundant material on Earth’s upper crust. Germanium is the second in the electronics materials list in terms of mass. The rest of the important electronic and photonics materials are compound

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85

90

95

Z (Atomic number)

FIGURE 2.69 Natural abundance (in mass) of elements in our solar system. Abundance of silicon is normalized to 106 .

semiconductors such as GaAs, InSb, CdTe, etc. The stability and hardness of compound semiconductors depends on many factors, but, the most important data point is their covalent radius. The covalent radius, is a measure of the size of an atom that forms part of one covalent bond. Strong covalent bonds occur with atoms having smaller and similar covalent radii (see Table 2.4). Table 2.4 makes it clear that GaAs is much stronger and available than other photonics materials. Thus, GaAs based QWIPs are much easier to grow and process into large format FPAs at lower cost. The only issue with QWIPs is the lower quantum efficiency due to intersubband transition. The high stability (Choi et al., 2009; Goldberg et al., 2005; Gunapala et al., 2001; Martijn et al., 2009; Rafol, 2008b; Rafol and Cho, 2008a; Rafol et al., 2007; Robo et al., 2009; Schneider et al., 2004) GaAs based QWIP IR FPAs are attractive for many terrestrial high background imaging applications and due to the availability in large format for low cost.

ACKNOWLEDGMENTS We are grateful to M. T. Chahine, R. S. Cox, P. E. Dimotakis, M. I. Herman, E. A. Kolawa, A. S. Larson, R. H. Liang, T. S. Luchik, and C. F. Ruoff of Jet Propulsion Laboratory, A. F. Milton and M. Z. Tidrow of Army Night Vision Electronic Sensor Directorate for encouragement and support. Also, authors would like to give their special thanks to C. J. Hill, J. K. Liu, E. M. Luong, J. M. Mumolo, and S. B. Rafol of Jet Propulsion Laboratory for materials growth, device & FPA fabrication, detector & FPA characterization, data analysis, and stimulating discussions. The QWIP research and applications described in this chapter was performed partly by the Center for Infrared Sensor Technology, Jet Propulsion Laboratory, California Institute of Technology, and were jointly sponsored by the JPL’s Research Technology and Development Funds, the Missile Defense Agency, the National Aeronautics and Space Administration, and Air Force Research Laboratory.

146

Element

Si

Ge

Ga

As

In

Sb

Cd

Te

Hg

3.8 × 10−3

3.8 × 10−6

1.1 × 10−8

2.6 × 10−8

4.3 × 10−10

3.0 × 10−9

7.1 × 10−9

1.5 × 10−8

2.3 × 10−9

Covalent Radius ˚ (A)

1.11

1.22

1.26

1.2

1.44

1.41

1.48

1.36

1.49

Bulk Modulus [Gpa]

98

75

Solar Abundance (%)

GaAs - 75 InAs - 58 InSb - 47 GaSb - 56

CdTe - 42 HgTe - 43

S. D. Gunapala, D. Z. Ting, S. B. Rafol, and S. V. Bandara

TABLE 2.4 Solar abundance, covalent radii, and hardness of groups II, III, IV, V, and VI elements and compound materials relevant for IR detectors.

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CHAPTER

3 Quantum Dot Infrared Photodetectors Ajit V. Barve and Sanjay Krishna

Contents

1. Introduction 2. Epitaxial Self Assembled Quantum Dots 2.1. Growth of InAs quantum dots 2.2. Growth trade-offs for detector optimization 2.3. Modeling the electronic structure of the quantum dot 3. Design of Quantum Dot Infrared Detectors 3.1. Different figures of merit 3.2. Design considerations 3.3. Design examples 4. Review of Recent Progress in QDIP Technology 4.1. Single pixel 4.2. Focal plane arrays 5. Future Directions 5.1. Growth optimization for higher normal incidence absorption 5.2. Submonolayer quantum dots 5.3. Device modeling 5.4. Barrier engineering 6. Summary References

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1. INTRODUCTION Depending on their applications, infrared (IR) photodetectors have diverse design requirements placed on their performance parameters such as the required sensitivity, spectral selectivity, operating temperature, peak wavelength, and cost. Typical characteristics of the third-generation imaging Semiconductors and Semimetals, Volume 84 ISSN 0080-8784, DOI: 10.1016/B978-0-12-381337-4.00003-6

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systems are high-operating temperature, multispectral operation, and large format arrays. The quantum dot infrared photodetectors (QDIPs) technology, owing to the three-dimensional confinement of carriers, the richness of electronic spectra in the quantum dots, and the mature III-V based fabrication technology, satisfy these requirements. In QDIP devices, the infrared absorption is a result of intersubband transitions from the quantum dot ground state to various excited states in the conduction band. The QDIP technology has seen a rapid progress over the last decade, making it a competitive technology for the third-generation imaging system. Quantum dot infrared detectors have already demonstrated high operating temperature imaging (Tsao et al., 2007), room temperature operation at midwave infrared (MWIR; Lim et al., 2007a) and longwave infrared (LWIR) and very longwave infrared (VLWIR; Bhattacharya et al., 2005) regimes, excellent characteristics in far-infrared (FIR) and terahertz (THz) (Su et al., 2006) detection and excellent imaging with large format arrays (Ting et al., 2009) in LWIR regime. However, QD-based detectors currently suffer from lower absorption quantum efficiency as compared with the band-to-band photodetectors. Nevertheless, for the photon-rich terrestial applications, the focal plane array performance is usually limited by the charge capacity of the readout circuit. In this regime, QDIP detectors can achieve similar performance as compared with band-to-band photodetectors because of ultralow dark current levels in QDIPs. Quantum well infrared photodetectors (QWIP; Gunapala et al., 2002; Levine, 1993; Liu et al., 2000; Rogalski, 2003), using intersubband absorption in quantum wells, are well-established as a technology and are commercially available in large format focal plane arrays (FPA; Gunapala et al., 2004), due to a mature and relatively inexpensive III-V epitaxial growth and fabrication technology. QWIPs are technologically important for LWIR photon-rich systems such as medical imaging, gas sensors, and surveillance applications. However, they suffer from low quantum efficiency, higher dark current, lack of normal incidence absorption, and require cryogenic operation temperatures. Quantum dot infrared photodetectors (QDIP) are generically similar to QWIPs but promise to solve these problems by the virtue of zero-dimensional quantum confinement. Some of the potential advantages of QDIPs over QWIPs include the following: 1. Ability to absorb normally incident light because of three-dimensional confinement, thereby eliminating the need of special light coupling techniques such as gratings. 2. Reduced dependence of the carrier distribution on the temperature. 3. Carrier lifetimes 10–100 times longer than QWIPs, giving rise to a lower dark current. The latter two advantages can be explained qualitatively in Fig. 3.1. In a perfect zero-dimensional system, the density of states is represented

Bulk

Quantum well

g(E)

g(E) E-EC − − − −

Eg

E-EC

g(E) E-EC

Ec

+ + + + Ev

e−E/kT 1.8 kT E-EC (A)

g(E)

Quantum dot

E-EC

− − Ec

E2 E1

n(E)

E2 E1

Ec

n(E) E-EC (B)

− −

E-EC (C)

E1

Ec

n(E)

0.7 kT

E2

Independent of temperature E-EC (D)

155

FIGURE 3.1 Schematics, density of states, and the carrier distribution for (A) bulk, (B) quantum wells, (C) quantum wires, and (D) quantum dots. Note that the quantum dot density of states is independent of temperature. Because the carrier distribution in quantum dots is discrete in energy, thermal transitions between the states require absorption of one or multiple phonons of the energy equal to the energy spacing, unlike the continuous distribution in the case of quantum well. This leads to lower dark current in QDIPs.

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n(E)

Quantum wire

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by a series of delta-functions in energy. This eliminates the dependence of the density of states on the temperature, leading to a greatly reduced dependence of carrier distribution on the temperature. Because the carriers are confined in all the three dimensions, if the energy separation between the two states is higher than the longitudinal optical (LO) phonon energies, carriers need to absorb multiple phonons in order to get to the excited state. This reduces the efficiency of the scattering mechanisms and hence reduces the dark current significantly, as compared with the QWIP devices, by increasing the carrier lifetimes in the excited state of the quantum dot. Theory and experiments confirmed that quantum dots have much higher carrier lifetimes, upto of 100 ps (Urayama et al., 2001), as compared to bulk or quantum wells that are limited to about 1–5 ps. Although the advantages of an ideal zero-dimensional system in optoelectronic devices were predicted much earlier (Arakawa and Sakaki, 1982; Asada et al., 1986), it was only after the repeatable and controllable epitaxial growth of self-organized quantum dots in Stranski-Krastanov (SK) mode that researchers began to probe into quantum dot physics by growth optimization (Leonard et al., 1994; Madhukar et al., 1995; Solomon et al., 1995), spectroscopy (Drexler et al., 1994; Heitz et al., 1997), band structure modeling (Franceschetti and Zunger, 1996; Jiang and Singh, 1997) and device-related studies. Because of the interesting physical properties and the relative ease of fabrication, researchers were attracted toward QDIPs. Berryman et al. (1997) were among the first groups to demonstrate MWIR photoresponse. QDIPs in the LWIR (Maimon et al., 1998; Pan et al., 1998) and VLWIR (Phillips et al., 1998) wavelengths were also demonstrated. It has been predicted (Martyniuk et al., 2008; Phillips, 2002; Ryzhii, 1996) that QDIPs will significantly outperform QWIPs to emerge as an important technology for infrared detection. Currently various research groups from around the world are working toward realizing the theoretically predicted advantages of QDIPs. After about a decade of research, QDIPs are beginning to outperform QWIPs by demonstrating lower dark current and higher operating temperature (Chakrabarti et al., 2005a; Kim et al., 2004; Zhang et al., 2005). Various groups have been working on methods to improve the structural and optical properties of quantum dots (Chen et al., 2001; Fu et al., 2006; Kim et al., 2001; Le Ru et al., 2003; Mi and Bhattacharya, 2005; Shao et al., 2008; Stewart et al., 2002; Stintz et al., 2000; Zhang et al., 2005) to increase the carrier lifetime, as well as to increase the quantum dot density. Dark current levels have been significantly reduced by using various barriers, such as AlGaAs current blocking layers (Chakrabarti et al., 2004a; Ling et al., 2008; Ye et al., 2002a) on GaAs-based QDIPs. Quantum dots-in-a-well (DWELL) designs (Amtout et al., 2004; Krishna, 2005b; Raghavan et al., 2002) have attracted a lot of researchers as they allow superior control of peak wavelength of operation, improve

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optical properties of quantum dots, and reduce dark currents (Aivaliotis ¨ et al., 2007a,b; Ariyawansa et al., 2005; Han et al., 2005; Hoglund et al., 2006; Jolley et al., 2008; Kim et al., 2001; Naser et al., 2007). The infrared absorption is from the quantum dot ground state to one of the eigenstates of the quantum well. Multiple peaks arise from transitions to different final states and can be efficiently selected by changing the bias voltage. Recently, band-structure engineering approaches to reduce dark current levels and improve transport properties have been demonstrated. Some of the approaches include resonant tunneling QDIPs (Barve et al., 2008; Bhattacharya et al., 2005, 2007; Su et al., 2004) and superlatticebased QDIPs (Chakrabarti et al., 2004b). Theoretical modeling of quantum dots (Boucaud and Sauvage, 2003; Jiang and Singh, 1997; Stanko et al., 2006; Stier et al., 1999) has been carried out to analyze and predict the quantum dot characteristics measured from photoluminescence (PL), ¨ photoluminescence excitation (PLE; Hoglund et al., 2006), spectral response, and absorption studies. Most popular methods include atomistic pseudopotential approach (Williamson and Zunger, 1999), eight-band k.p analysis (Jiang and Singh, 1997; Stanko et al., 2006; Stier et al., 1999; Stoleru and Towe, 2003) based on valence force field method for strain calculations and numerical simulations based on finite volume methods (Hwang et al., 2004; Wu et al., 2006). Various groups around the world have successfully demonstrated good-quality infrared imaging (Gunapala et al., 2007a; Krishna et al., 2005; Ting et al., 2009; Tsao et al., 2007; Vandervelde et al., 2008) with QDIP-based focal plane arrays. There are excellent articles that review the physics of QDIPs (Bhattacharya et al., 2006; Boucaud and Sauvage, 2003; Towe and Pan, 2000) and also discuss the fundamental advantages and device characteristics, as well as the state-of-the-art reviews (Campbell and Madhukar, 2007; Krishna, 2005b; Martyniuk et al., 2008; Stiff-Roberts, 2000; Vandervelde et al., 2008), which are very useful. In this chapter, we will review the growth, modeling, and device designs for the QDIPs. Various trade-offs associated with the growth parameters and their effects on device performance will be discussed. Popular algorithms used for modeling the strain and energy levels in the quantum dots will be discussed in some details. Roles of different elements such as quantum dot shape and size, doping, barrier layer composition and structure on the physical and device properties will be discussed with some specific examples. Recent progress made by QDIP technology for both single-pixel detectors and focal plane arrays will be reviewed and compared with QWIPs. In the final section, key areas of research in QDIPs will be identified and discussed. The focus of this chapter is to take a broad overview of different aspects of QDIP technology and the review of the literature. Epitaxial, self-assembled quantum dots will be discussed with the focus on popular In(Ga)As-based quantum dots.

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2. EPITAXIAL SELF ASSEMBLED QUANTUM DOTS For the growth of strained epilayer on the substrate, the three wellknown growth modes (Bimberg et al., 1999) are Frank-van der Merwe, Stranski–Krastanov, and Volmer-Weber, depending on the interface and surface energies. Formation of the exitaxial, self-assembled quantum dots, Stranski–Krastanov (SK) growth mode is by far the most popular and widely studied growth mechanism for the growth of coherently strained, dense, self-assembled arrays of quantum dots. In the Stranski–Krastanov growth mode, the strained layer undergoes a transition from the planar growth mode to 3D island formation after the critical thickness (2c ) has been grown. This reduces the total free energy of the system, which is a sum of interface, bulk, and surface energies. The abrupt 2D–3D transition occurs within 0.2 monolayers (ML) after the critical thickness, showing rapid rise of the density of the quantum dots. This strain mediated formation of quantum dots on a planar, strained “wetting layer” is observed across different strained material systems such as InAs/GaAs, InGaAs/GaAs, InAs/InP, Ge/Si, and so on. Although observed across wide variety of materials and conditions, the driving kinetic mechanisms for these processes are highly dependent on the material conditions, such as orientation, flatness, and growth conditions such as growth temperature, growth interruptions, growth rate, III-V flux ratios, and so on. Comprehensive studies of these transitions have been published (Bimberg et al., 1999; Kobayashi et al., 1996; Kratzer et al., 2006; Leonard et al., 1994; Placidi et al., 2007; Stangl et al., 2004) in the literature.

2.1. Growth of InAs quantum dots 2.1.1. 2D–3D transition The structural evolution of InAs quantum dots with increasing InAs deposition can be studied by varying the InAs thickness across the sample linearly in the absence of sample rotation (Placidi et al., 2007). This allows the study of all the stages of evolution, such as 2D growth, island nucleation, and achieving the equilibrium distribution on the same sample. Various processes can then be studied by in situ methods such as reflection high energy electron diffraction (RHEED) and ex-situ methods such as atomic force microscopy (AFM), transmission electron microscopy (TEM), and photoluminescence (PL) measurements. Various phases in the evolution of InAs quantum dots, such as the wetting layer formation, nucleation of quantum dots, and ripening of quantum dots are shown in Fig. 3.2 (Placidi et al., 2007). For the 2D growth of the so-called wetting layer, the critical thickness is dependent on the segregation of In adatoms during the deposition. Interestingly, the value of the critical thickness is similar in various growth

GaAs(001) c4 × 4

RHEED intensity (arb.units)

Quantum Dot Infrared Photodetectors

50 × 50 nm2

1 × 1 µm2

159

3 ML 1.6 ML In shutter closed 3 ML In shutter open

0

20 40 60 80 100 120 Growth time (s)

1.4 ML

400 × 400 nm2

350 × 350 nm2

1.6 ML

FIGURE 3.2 Evolution of the InAs quantum dots monitored by the RHEED intensity, the surface reconstruction patterns, and AFM analysis showing the 2D wetting layer growth, and surface morphology just before the nucleation, nucleation of large quantum dots, and the equilibrium distribution of the quantum dots, from Placidi et al. (2007).

modes such as continuous growth mode (CG), growth interrupt (GI) mode (Placidi et al., 2007), in which the In shutter is closed for few seconds, periodically, during the InAs deposition, even though the underlying kinematics is vastly different. For InAs-GaAs(001) system, the critical thickness is approximately 1.45 ML, indicated by the onset of spotty RHEED pattern. The steep rise in the RHEED intensity indicates a rapid increase in the diffraction volume because of the quantum dot island formation. The quantum dot nucleation location and subsequent ripening is dependent on the surface morphology, such as presence of steps, defects, crystal orientation, growth temperature, flux ratios, and growth rate. These parameters need to be separately optimized with a systematic AFM and photoluminescence study in order to achieve high quantum dot density with excellent structural and optical qualities. Such elaborate studies (Chia et al., 2007; Liu et al., 2003b; Mi and Bhattacharya, 2005; Mukhametzhanov et al., 1999; Stintz et al., 2000) for different material systems have been published before. 2.1.2. Growth modes for QD detectors Various approaches have been taken by different groups for optimizing the performance of QDIPs through the growth optimization of the

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quantum dots. For MBE growth of quantum dots, the popular growth mode is the continuous growth mode (Stintz et al., 2000), in which the quantum dot material is deposited without any growth interruption. Other popular approach is the punctuated island growth (PIG) method (Mukhametzhanov et al., 1999), in which the InAs deposition during the formation of quantum dot is divided into two to three stages; where the first stage is interrupted after the critical thickness required for formation of 3D islands is reached. The quantum dot size variation is reduced as the larger quantum dots grow at a slower growth rate due to the inherent strain buildup. However, this technique is useful only for large dots (3 ML InAs deposition) and suffers from slightly reduced dot density. More recently, researchers at Jet Propulsion Laboratory (JPL) have realized detectors using sub-monolayer quantum dot in a DWELL heterostructure (Ting et al., 2009). This follows the approach of Germann et al. (Germann et al., 2008) who have investigated the effect of using the submonolayer growth on the shape and size of the QD. In SML growth mode, wetting layer is avoided by the formation of InAs islands in GaAs by partial monolayer deposition. This is proposed to allow for higher number of stacks because of the reduced strain while retaining the key properties of quantum dots such as normal incidence absorption and reduced LO phonon scattering. 2.1.3. Effect of growth temperature and growth rate Two of the most important parameters in the growth optimization of quantum dots are the growth temperature and growth rate of the quantum dots and surrounding matrix material. For higher growth temperatures, the adatom mobility increases, thereby increasing the size of the dot. This, in turn, leads to a red shift in the PL wavelength. At lower growth temperatures, the dot sizes are smaller because of the reduced surface mobility. However, the PL intensity decreases as a result of higher size variation. Typical growth temperatures for the MBE growth of InAs QD are from 450 to 510◦ C . The growth optimization involves finding the optimum temperature with high dot density with reduced size variation. For higher rate of QD deposition, the effect is similar to the reduction in growth temperature with increase in the dot density and reduction in dot size. However, it is difficult to precisely control the deposition at very-high rate. Typically, deposition rates of 0.05–0.2 ML/s are used for InAs QD growth. 2.1.4. Effect of annealing on QDIP performance The postgrowth annealing of the quantum dots results in a blueshift in the PL wavelength, with corresponding redshift in the intersubband spectral response wavelength. Rapid thermal annealing is sometimes performed for thermally induced strain relaxation of the quantum dots. It has been

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observed that the detector response degrades (Fu et al., 2006; Krishna et al., 2002) as a result of high-temperature annealing of the sample, because of enhanced interdiffusion. 2.1.5. Different material systems for QDIPs Although InAs/GaAs system is a popular choice of material system in QDIPs, several variations especially in the choice of strain bed and capping material surrounding quantum dots exist. The quantum dots-in-a-well heterostructure (Krishna, 2005b; Raghavan et al., 2002), where InAs quantum dots are embedded in an InGaAs quantum well, has been investigated by many research groups. Infrared transitions are from the quantum dot ground state to either a bound level in quantum well or to the continuum. This allows precise control over wavelength by changing the well composition and width (Krishna, 2005a), at the expense of adding more compressive strain per stack, thereby reducing the number of stacks that can be grown with minimal defects. The quantum well also allows efficient capture of carriers into the DWELL heterostructure. Moreover, this structure allows growth of an InGaAs capping layer, which leads to a better optical quality. Capping quantum dots with GaAs or AlGaAs has disadvantage that they have to be grown typically 60–100◦ C less than their optimum growth temperature (Stintz et al., 2000). This can be avoided by using migration-enhanced epitaxy (MEE), in which the capping layers are grown at much lower temperatures. This approach claims to reduce chemical intermixing during the capping as opposed to typical MBE-grown capping layers of the same materials. Capping quantum dots with several materials such as GaAs, AlGaAs, InGaAs, and InGaAlAs has been experimented and compared (Campbell and Madhukar, 2007). Capping the quantum dot is currently a very important topic of research (Litvinov et al., 2008; Liu et al., 2004; Shao et al., 2008) because a good capping material reduces the intermixing of species between the quantum dot and capping layer, thereby preserving the shape and enhancing the quantum confinement. Capping the quantum dots with InAlAs results in higher dot density and smaller quantum dots; however, it offers large barrier to the carriers in the quantum dot. This barrier can be reduced by optimizing InGaAlAs matrix material (Shao et al., 2008) for quantum dots. It has been observed that during the capping of InAs QDs with GaAs (Costantini et al., 2006), for the first 4–5 ML of GaAs growth, the material is deposited only around the quantum dot, reducing the height of the island faster than the growth rate. After 4–5 ML, the true overgrowth of capping is achieved. Active research has been going on InAs quantum dots on InP substrates using MBE and MOCVD (Lim et al., 2007a; Tsao et al., 2007), with excellent device results. Since the strain in these systems is lower than InAs/GaAs system, the dimensions of quantum dots are much larger. For MBE-grown InAs quantum dots on InP substrates, the higher index substrates such as

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InP (311B) are more popular choice (Akahane et al., 2002) as a result of symmetric quantum dot formation and ultrahigh quantum dot densities (1012 /cm2 ) on these substrates. MBE-grown InAs quantum dots on InP ¯ direction, forming quan(001) substrates are elongated and aligned in [110] tum dashes (Ukhanov et al., 2002). For the MOCVD-grown InAs QDs on InP substrates, growth on (001) substrates results in symmetric quantum dot formation.

2.2. Growth trade-offs for detector optimization For designing the quantum dot detector, various tradeoffs exist during the growth, such as the choice of material system, doping density in the quantum dots, size of quantum dots. For example, we have a choice in the quantum dot material. In InAs quantum dots, the carriers inside the quantum dots are better confined because of a stronger potential well and hence have higher activation energies that makes them harder to extract in QDIP device. In InGaAs quantum dots, carriers are easier to extract from the quantum dots, so it is easier to fabricate very long wavelength (VLWIR) devices, while dark currents are higher because of smaller activation energy for ground state of quantum dot. Another important trade-off comes in the selection of doping level inside the quantum dots. Some groups prefer to keep the wetting layer undoped and only dope above the critical thickness to reduce the dark current originating from the wetting layer. Higher doping levels inside the quantum dots give rise to higher absorption quantum efficiency but also increases the dark current (Attaluri et al., 2006; Drozdowicz-Tomsia et al., 2006), as the excited states of quantum dots are also filled, even at lower temperatures. Hence, adjusting the quantum dot doping such that there are only one (Attaluri et al., 2006) or two (Chakrabarti et al., 2004a) electrons per dot is a common choice, so that only the quantum dot ground state is filled at a lower temperature. Use of unintentionally doped quantum dots in an n-i-n structure, where the carriers within the quantum dots are injected from the contacts has also been demonstrated (Campbell and Madhukar, 2007) with excellent results. Quantum dot size is another important choice. Large quantum dots result in smaller quantum dot density and many electronic levels in the conduction band. These are the preferred choice for far infrared (FIR) and terahertz (THz) regime (Su et al., 2006) because of smaller separation between the energy levels. Smaller quantum dots result in higher dot density and smaller number of energy levels in the conduction band, which is favorable for higher absorption strength. However, higher dot density with smaller quantum dots typically results in higher inhomogenous broadening because of greater size variation, which results in lowering the absorption coefficient.

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2.3. Modeling the electronic structure of the quantum dot For understanding the physics of quantum dots and designing better devices, the electronic structure modeling of quantum dot is an important problem. However, there are several challenges for an accurate modeling of self-assembled quantum dots, such as the following: 1. Size and shape of the quantum dots is variable, depending on the growth conditions, because of the presence of intermixing. Even for the same growth conditions, the size and shape of quantum dots vary significantly in the ensemble. For a physical model, the size of the quantum dots has to be guessed from the TEM data, which may not give correct representation of the average size in the ensemble. Large area techniques, such as AFM cannot be used for predicting the size, as the size and shape distribution are significantly altered, during capping of quantum dots. In practice, the quantum dots have to be approximated to ideal shapes, such as pyramids, hemispheres, and so on. 2. As a result of segregation and intermixing of group III elements, the composition inside the quantum dots is not uniform. 3. Physical size of self-assembled quantum dots is large, which makes atomistic simulations demanding. 4. Large-scale effects such as vertical and lateral coupling between the quantum dots are extremely difficult to model because of the random distribution of quantum dots. 5. Effect of doping is extremely difficult to model because of random placement of doping, band bending, Coulombic interactions between the dopents, and so on. 6. Values of several important variables such as the band offsets and deformation potentials are either unknown or highly uncertain, which prevents models from being accurate. Despite these difficulties, there have been several reports of quantum dot modeling. The general approach involves approximating the quantum dot with some ideal shape, such as a pyramid, calculating the strain in the system as a function of position and solving for the eigenvalues and eigenfunctions of the Hamiltonian to give energies and wavefunction of various states. Various corrections such as piezoelectric effects, coulombic interactions are applied to modify the Hamiltonian. After solving for the wavefunctions, values for band-to-band as well as intersubband absorption coefficient, polarization dependence, and so on can be easily calculated (Cusack et al., 1997) using the selection rules. Most popular method for solving the Schroedinger equation is the eight band k.p approach (Cusack et al., 1996; Jiang and Singh, 1997; Pryor, 1998; Stier et al., 1999). Other approaches include atomistic pseudopotential method

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(Bester et al., 2003), one-band nonparabolic effective mass model (Betcke and Voss, 2008), multiband k.p in the plane wave basis (Stanko et al., 2006). Here, we review the basic approach used for modeling the strain in the quantum dot system with valence force field (VFF) method and using the strain tensor to calculate the band structure of the quantum dot using k.p method. 2.3.1. Strain calculations Valence force field approach is a popular method to accurately model the strain in the quantum dot heterostructures. This method, originally proposed by Keating (1966), uses atomistic calculations to minimize the strain energy of each atom in the entire structure. Only the nearest neighbors are considered to be important for contributing to the strain interactions, which are bond-stretching and bond-bending interactions. The total strain energy in the system (Jiang and Singh, 1997), V is given by, V=

2 1 X X 3 βijk 1X3 2 αij dij + d20ij /d20ij + (dij ·dik + d0ij d0ik /3)2 4 4 2 4 d0ij d0ik ij

i

j6=k

(3.1) Here, i runs over all the atoms inside the computational grid, while j and k run over the nearest neighbors of atom i· d0ij is the unstrained bond length between the atom i and j, while dij is the distance between the two atoms during the computation. The first term of the equation refers to the bond-stretching interactions between the atom i and its nearest neighbor j, while the second term considers the bond-bending interactions for the nearest neighbors j and k. The bond stretching (α) and bond bending (β) parameters (Martin, 1970) are defined for each bond. p At the boundaries between InAs and GaAs regions, βijk is taken as βij ·βik . The following procedure is used to calculate the strain tensor. • At the start of simulations, all the atoms are placed on the GaAs lattice grid. This choice of initialization is arbitrary but results in faster convergence. Material parameters are assigned and the nearest neighbors are identified. • Each atom in the grid is allowed to displace one at a time, and the position which minimizes the strain energy is calculated. Conjugate gradient minimization is popularly used for this minimization. All the atoms are sequentially displaced, and then the entire sequence is repeated till convergence is reached, which is indicated by a negligible change in total strain energy in the system. Typically, periodic boundary conditions are used in xy plane, while Dirichlet boundary conditions are used in the z direction. This process is approximate but fairly accurate and gives much faster convergence as compared with solving

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a minimization problem over 3N dimensions simultaneously, where N is total number of atoms. For a system with large number of atoms typically encountered in self-assembled quantum dot simulations, a large number of iterations (typically, ≈ 2000) are required for convergence. • Once the relaxed state of the system is obtained, the strain tensor is calculated at each atom by definition of the strain. Such calculations are illustrated in the study of Pryor (1998). Hydrostatic and biaxial strains are calculated by definition (Cusack et al., 1996), h = xx + yy + zz and b = 2zz − xx − yy . Note that several different definitions of biaxial strains are used in literature (e.g., Cusack et al. (1996); Jiang and Singh (1997); Stier et al. (1999)). A typical strain profile in pyramidal self-assembled quantum dots is shown in Fig. 3.3. The values of both hydrostatic and biaxial components of strain have quite large and highly nonuniform values in the quantum °) z (A −100

−50

0

50

100

30

z (nm)

Strain (%)

−4

−10 −12

10

−0.04

25

0 −2 −6 −8

15

0.06 0.04 0.02 0 −0.02

zz

4 2

20

−0.06 −0.08

5

xx zz

2

7

12 17 22 2730 y (nm)

10 8 6 4 2 0 −2 −4 −6 −8 −10 −12 −14

(C) 30

0.15

xx

25 z (nm)

Strain (%)

(A)

0.1

20

0.05

15

0

10 Hydrostatic Biaxial

−0.05

5

−0.1 10

(B)

−0.1

20 x (nm)

50

(D)

FIGURE 3.3 (A) Strain tensor components xx and zz . (B) Hydrostatic and biaxial components of strain along z directions through the center of the quantum dot calculated for pyramidal InAs QD with base = 12.4 nm and height = 6.2 nm (Cusack et al., 1996). Reprinted with permission from 1996 American Physical Society. (C) and (D) are yz and xz cross-sections for zz and xx , respectively, calculated by Barve et al. (unpublished).

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dot. The effect of strain on the potential profile is calculated by scaling it with the appropriate deformation potential values. The numerical values of parameters used in these calculations are tabulated in the study of Stier et al. (1999). The confinements for heavy holes and light holes are quite different, with light holes confined near the top of the quantum dot while heavy holes confined near the bottom of the quantum. 2.3.2. Electronic structure calculations It is now known that the simple effective mass approach to calculate the band structure of decoupled conduction band and k.p for valence bands leads to some serious errors, especially for self-assembled quantum dot simulations. This is because (1) the band gap of bulk InAs is 0.4 eV, while the effective gap of the dot is close to 1.0 eV; (2) the nature of the strain tensor is such that there is a strong spatial variation in strain; and (3) the strain components are very large, and the resultant splitting in the bands are comparable with the interband separations in the bulk material (Jiang and Singh, 1997). A popular approach to model the quantum dot energy spectrum is eight-band k.p, which includes the influence of remote bands on conduction band and valence band. In the eight-band k.p analysis, 8× 8 Hamiltonian acts on eight envelope functions corresponding to conduction band and the three valence bands (heavy holes, light holes, and split off bands) and their time-reversed conjugates. These envelope functions are linear combinations of band edge Bloch functions. The exact form of 8 × 8 k.p Hamiltonian is given in the study of Jiang and Singh (1997), and the formalism is explained in more detail in the study of Bimberg et al. (1999); Enders et al. (1995); Gershoni et al. (1993). Implementation details for k.p formulation are given in the study of Stier et al. (1999). Calculated energy levels and wavefunctions for 13.6 nm base InAs/GaAs pyramidal quantum dots with {101} facets are shown in Fig. 3.4 (Bimberg et al., 1999).

3. DESIGN OF QUANTUM DOT INFRARED DETECTORS In this section, we discuss the important figures of merit of a QDIP device and popular approaches toward designing high-performance QDIP devices.

3.1. Different figures of merit 3.1.1. Dark current From a system-design perspective, dark current of the detector is one of the key figures of merit. Dark current determines the maximum operating

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GaAs EC

167

1.518 eV 1.429 eV 1.372 eV 1.360 eV

1.283 eV

1.222 eV

1.206 eV

1.098 eV

1.274 eV 000

100

010

000

010

020

0.1762 eV 0.1662 eV 0.1461 eV 0.1385 eV EVGaAs

0 (A)

(B)

FIGURE 3.4 (A) Energy level structure of b = 13.6 nm InAs/GaAs pyramid with {101} facets calculated with eight-band k.p theory and VFF model (Bimberg et al., 1999). (B) Wavefunctions of the first conduction band and valence band states (Stier et al., 1999).

temperature for the detector for a given signal-to-noise ratio (SNR). In QDIPs, the prime source of dark current is thermionic emission of carriers from the quantum dots, while field-assisted tunneling, interdot tunneling (Duboz et al., 2003), sequential resonant tunneling through defects (Drozdowicz-Tomsia et al., 2006), and thermal generation of carriers in barrier regions are other important sources. Detailed modeling of dark current and transport in QDIPs (Lim et al., 2006; Ryzhii, 1996; Ryzhii et al., 2001; Vukmirovi´c et al., 2006) are available. Dark current can be reduced by lowering the operating temperature or by increasing the energy barrier by changing the composition in the barrier material. The latter makes it difficult to extract the higher wavelength carriers out of quantum dots. Hence, in a typical QDIP design, there is a trade-off between longer peak wavelength and lower dark current. Because the density of states in quantum dots should be “atom-like,” the dark current is expected to be lower for similar wavelengths, as compared with QWIPs. This is because carriers confined in the quantum dot ground state do not contribute in bulk dark current, unlike the case of quantum wells, where, due to the continuous density of state even the quantum well ground state contributes to the dark current. Doping concentrations inside quantum dots have to be carefully controlled and optimized in order to have minimum dark current with high photocurrent levels. The dark current can also be reduced by designing resonant tunneling barriers that block the continuum energies contributing to the

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100

Normalized Idk(A/cm2)

10−2 10−4

QWIP

10−6 σens/σQD = 1

10−8

= 10 = 100

10−10 10−12

HgCdTe 5.0

10.0

15.0

20.0

25.0

1000/T(1/K)

FIGURE 3.5 Theoretical Comparisons for dark current for various IR technologies, after Phillips (2002).

dark current while allowing the energy levels of interest to pass through. This allows the dark current to be selectively reduced, while maintaining the same photocurrent. This has enabled far-infrared detection with QDIPs with moderately low dark current levels. It has been predicted, theoretically, that well-designed QDIPs would have lower dark current, and hence higher operating temperature than QWIPs and comparable with HgCdTebased detectors, as shown in Fig. 3.5. This results in background-limited performance (BLIP) at higher temperatures, for the same wavelength. 3.1.2. Responsivity and photoconductive gain Increased carrier lifetime in the QDIPs as compared with QWIPs because of the phonon bottleneck has significant implications. Because the excited states of quantum dots are long-lived, it is easier to extract the carriers out, by the application of an electric field, before they relax back to the groundstate, thereby increasing the quantum efficiency. Longer carrier lifetime also implies higher photoconductive gain to satisfy charge neutrality inside the quantum dots. Photoconductive gain, which is inversely proportional to the capture probability, from 0.1 to 10,000 has been observed in the literature (Barve et al., 2010b; Lim et al., 2006; Tang et al., 2006) for QDIPs. Photoconductive gain originates from the requirement of charge neutrality of the quantum dots after photoexcitation (or thermal excitation) of an electron from the quantum dot. Because pc is the capture probability of the quantum dot, 1/pc carriers are needed for one electron to get captured in

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the quantum dot. If there are N stacks in the active region, approximately, average of g = 1/Npc electrons have to be injected from the contact for each photon absorbed. Note that this formula is highly approximate, as it assumes uniform capture probability (hence uniform electric field) in all the stacks and also neglects the relative position of the stack with respect to the contact and carrier re-excitation from the quantum dots. Experimentally, the photoconductive gain can be estimated from the measured noise and I-V curves (Kochman et al., 2003), g=

1 i2n + 4qIdark 2N

(3.2)

In QDIPs, the last term is negligible as the gain is usually higher than unity because of low capture probability of quantum dots. The equation is valid only when the dark current is mainly generation–recombination (g–r) dominated. The excess noise factor, which would be present in g–r gain has been neglected. In DWELL designs, the photoconductive gain is also affected by the efficiency of carrier capture by the quantum well (Barve et al., 2010b), as can be seen in Fig. 3.6. The quantum dots in all the three structures have been grown in identical conditions, while the thickness of the quantum well in the DWELL region is varied such that the excited state energy is tuned with respect to the barrier energy, leading to different transitions such as bound to continuum (B–C), bound to quasibound (B–Q) and bound to bound (B–B). In B–B devices, the excited energy level is deep inside the barrier, thus has greater carrier capture efficiency, as compared 20

B–C B–Q2 B–B

PC gain

15

10

5

0

−40

−20 0 20 Electric field (kV/cm)

40

FIGURE 3.6 Measured photoconductive gain for different well widths in DWELL detectors, as a function of electric field (Barve et al., 2010b).

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with B–C designs, where the excited energy level falls in the continuum band, preventing electrons from getting captured in the quantum well. These schemes enable the designer to control the photoconductive gain of the detector as a “knob” to control the charge flow into the charge well in the readout circuit. Large variation of photoconductive gain with respect to the applied bias is also apparent from the figure, and has been observed in other QDIP reports (Kochman et al., 2003; Lim et al., 2006; Ye et al., 2003). Photoconductive gain increases the extraction quantum efficiency and hence the responsivity as many electrons flow in the external circuit for a single photon absorbed in the quantum dot. However, the absorption quantum efficiency is not affected by the photoconductive gain. Absorption quantum efficiency of quantum dots tends to be lower than that for quantum wells because of the reduced fill factor and lower absorption coefficient because of size variation of quantum dots. Because both signal and noise currents are amplified by the photoconductive gain, the signal-to-noise ratio remains constant. 3.1.3. Detectivity and noise equivalent temperature difference Specific detectivity (D∗ ) is a widely used figure of merit for describing the signal-to-noise ratio of a detector, normalized with respect to the detector area (A) and measurement bandwidth (1f ). It is defined as, p R(λ) A1f (cm·Hz1/2 /W), D (λ) = in ∗

(3.3)

where, in is the root mean square (RMS) noise current. For λ = λpeak , D∗ is refered to as peak-specific detectivity, which is often quoted as the figure of merit for a single-pixel detector. Primary components of noise current in QDIPs are shot noise because of dark current and photocurrent, and the thermal noise. The expression for the rms noise current is, s in =

4qg(Idark + Iphoto )1f +

4kT , Rd

(3.4)

where q is the electronic charge, g is the photoconductive gain, Idark and Iphoto are the dark current and photocurrents, respectively, k is the Boltzman constant, T is the absolute temperature, and Rd is the differenq tial resistance of the device. The last term 4kT Rd , the thermal noise current, is usually negligible compared with the shot noise. Noise equivalent temperature difference (NETD) is a useful figure of merit for the performance of FPA, which depends on SNR of the detector

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as well as properties of the electronics associated with the readout integrated circuit (ROIC). It determines the minimum temperature difference the detector can distinguish for a given bias, input irradiance, q and tempera2g

ture. In the charge capacity limited regime, NETD scales as Nw where Nw is the storage capacity, in terms of the number of electrons in the storage well, for the readout circuit. Hence, in a charge capacity limited regime, it is better to have lower photoconductive gain. NETD values as low as 5–7 mK have been reported for QWIP FPAs, partly because of much lower photoconductive gain. However, if the dark current is very low, then it is possible to be in storage capacity limited regime only for high irradiance or higher operating temperatures. Because QDIPs can have very-low dark currents, they can demonstrate high temperature operation, or low NETD at lower temperature.

3.2. Design considerations Designing the quantum dot infrared detectors involves optimization of several parameters, such as peak wavelength, spectral width, dark current, operating temperature, signal-to-noise ratio, and photoconductive gain. There are some inherent trade-offs in some of these optimizations in the traditional designs, such as the dark current increases for higher peak wavelengths, resulting in lowering the operating temperature. Various design parameters include quantum dot dimensions and material, barrier material and designs, quantum well material and dimensions (in the case of DWELL detectors), and the number of stacks. This section reviews some of the design methodologies and specific device architectures. 3.2.1. Wavelength selection: QDIP vs DWELL From the intersubband nature of infrared transitions in the quantum dotbased detectors, designing for the particular peak wavelength requires control on both the ground state and the excited state. Depending on the relative position of the excited energy of interest, the transitions can be either from bound to bound, characterized by narrow spectral response or from bound to continuum, characterized by broad spectral response. Resulting from the relatively large size of a self-assembled quantum dot, there are multiple energy levels in it, resulting in the richness of the available intersubband spectrum. Typical quantum dot detectors have multiple wavelength response, which can be tuned by the applied bias. This is in sharp contrast with optimum QWIP designs, in which the quantum well is designed such that there is only one excited energy level supported. In traditional QDIPs, the quantum dot size and shape needs to be controlled in order to control the peak wavelength. Various transition

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Photoresponse (a.u.)

1.0

0.5

Continuum state

T = 80 K

−2.0 V

GaAs conduction band 0.050

−1.0V

Wetting layer state

0.209 0.201 0.171 0.170 0.114

1.5 3.5 5.5 7.5 Wavelength (µm)

In0.4Ga0.6As conduction band edge

0

In0.4Ga0.6As valence band edge

−1.090 −1.134

0

1

6

11 16 21 Wavelength (µm) (A)

26

−1.193

0.067

GaAs valence band

(B)

FIGURE 3.7 (A) Spectral response of the 20-layer, InGaAs–GaAs quantum-dot infrared detector. The inset shows the normalized two-color response at 80 K. (B) Calculated electronic states in a In0.4 Ga0.6 As quantum dot of base and height equal to 25 and 8 nm, respectively, using an eight-band k.p. formulation (Chakrabarti et al., 2005a).

wavelengths are attributed to excitation of electrons from the ground state of the quantum dot to one of the excited states of the quantum dot, or to the continuum energy levels. Figure 3.7A shows a typical spectral response from a QDIP detector (Chakrabarti et al., 2005b), which can be explained from the k.p simulations of the InGaAs/GaAs quantum dot, Fig. 3.7B. The three peaks, at 3.5 µm, 7.5 µm, and 22 µm, are a result of the quantum dot ground state to the continuum, quasibound, and bound states, respectively. This explains the broad spectral width for the 3.5 µm response (1λ/λ ∼ 0.79) and the narrow response for the 7.5 µm and 22 µm (1λ/λ ∼ 0.2). It is to be noted that in QDIP detectors, it is difficult to select an arbitrary peak wavelength response because of the difficulty in accurately controlling the quantum dot shape and size. In DWELL designs, the ground state of the quantum dot can be kept fixed, and the quantum well composition and thickness can be varied in order to control the peak wavelength. This allows precise control on the peak wavelength with availability of “dial-in” recipes. The InGaAs–GaAs quantum well, which surrounds InAs quantum dots has an optimum growth temperature similar to the InAs quantum dots, unlike the QDs capped with GaAs. This, combined with strain-relieving action of the quantum well improves the optical quality of the quantum dot. However, the InGaAs quantum well adds additional compressive strain per stack, thus limiting the maximum number of stacks that can be grown with minimum defects. Figure 3.8A shows the change in peak wavelength of a DWELL detector by simply changing the quantum well thickness (Krishna, 2005b). The peak wavelength and full width half maximum (FWHM)

T = 60 K

F

E

C

B

36

9.5 32

9.0

28

8.5 8.0

24

7.5 20

7.0 A

4.5 7 Wavelength (µm) (A)

9.5

B

C

D

E

F

(B)

A 2

Spectral Width (Δλ/λ)

Peak wavelength (µm)

D

Peak wavelength Spectral width

12

FIGURE 3.8 (A) Progressive red shift in the peak operating wavelength of the detector as the width of the bottom InGaAs layer is increased from 10 to 60A (Krishna, 2005b). (B) Variation of peak wavelength and FWHM of the response for different samples.

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Spectral response (au)

10.0

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of these devices as a function of quantum well thickness is plotted in Fig. 3.8B. 3.2.2. Optimum doping Optimum doping in quantum wells for optimizing QWIP detectors is well understood (Schneider and Liu, 2007). For maximizing the detectivity, the doping should be such that the Fermi level (Ef ) should be Ef = kT. However, to maximize the BLIP temperature, Ef = 2kT. Thus, optimum doping for highest signal-to-noise ratio is lower than the optimum doping required for maximizing the BLIP temperature. In QDIPs, this trend is still applicable, but the exact value of optimum doping for the given temperature is difficult to find. Several groups have optimized the detectors for different doping, but there is no general consensus about the optimum doping in QDIPs. Preferred doping varies from nonintentionally doped quantum dots (Campbell and Madhukar, 2007), one electron per dot (Attaluri et al., 2006) and two electrons per dot (Chakrabarti et al., 2004a). Higher doping results in higher absorption quantum efficiency but higher dark current because of the reduction in the activation energy. 3.2.3. Choice of barrier material AlGaAs current blocking layers (Barve et al., 2010b; Chakrabarti et al., 2004a; Ling et al., 2008; Ye et al., 2002a) have been widely and successfully used for reducing the dark current and increasing the signal to noise ratio of QDIPs, especially with DWELL architecture. Thick AlGaAs barriers can be placed in each stack, which eliminates intradot tunneling between the stacks or it can be placed at the end of the InAs/GaAs device, just before the contacts (Chakrabarti et al., 2004b). In the latter case, the dark current and photocurrents are reduced by equal factors as all the carriers are thermalized before reaching the barrier. This, although, does not increase D∗ of the device, it increases the signal-to-noise ratio (and hence the NETD) for the focal plane array in the charge capacity limit. Placing the barriers just before the contacts also significantly reduces the tunneling between the contact layer and the quantum dots in the first stack. For the barriers between each active stack of the quantum dot, there exists a tradeoff between the dark current and peak wavelength. For high Al concentrations, the photoexcited carriers, as a result of the longwave absorption, cannot escape even for very-high electric fields. Even for lower Al concentrations, extraction of longwave carriers is limited only at higher electric fields. Hence, in the typical DWELL or QDIP with two or more excited energy states, the MWIR response is dominant at lower bias, whereas the LWIR response is typically dominant at higher electric field, thus leading to a bias tunable spectral response. For example,

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Quantum Dot Infrared Photodetectors

+1V

T = 77 K Photocurrent (a.u.)

+5V −3V

4

6

8

10

12

Wavelength (µm)

(A) without AlGaAs

0

10

1010

77 K 100 K

77 K

10−1 100 K 10−2 10−3

with AlGaAs

−4

10

10−5 −2.0 −1.5 −1.0 −0.5 0.0 0.5

1.0 1.5 2.0

Peak detectivity cm • Hz1/2/W

Peak responsivity (A/W)

101

• 10

9

•

•

• • • •

108

•

•

•

•

•

••

• • •• • • •

•

• •

• • •

107

•

••• •• • • • •• • • • •• •• • • •

•

• •

•

with blocking layers without blocking layers

−1.5 −1.0 −0.5

0.0

0.5

Bias (V)

Bias (V)

(B)

(C)

1.0

1.5

2.0

FIGURE 3.9 (A) Spectral response for a quantum dot in a double-well (DWELL) device from UNM (Barve et al., 2010a), showing MWIR-dominated response at low biases and LWIR-dominated response at higher biases. (B)–(C) Reduction in responsivity and improvement in detectivity with AlGaAs current blocking layers (Campbell and Madhukar, 2007).

the measured spectral response of a DWELL device, fabricated at the University of New Mexico (UNM; Barve et al., 2010a), as shown in Fig. 3.9A, clearly shows that at lower bias, the midwave signal is dominant while the longwave absorption is dominant only at larger biases. AlGaAs barriers also typically reduce the responsivity of the device; however, the noise is suppressed more effectively, such that the overall signal-to-noise ratio is larger. This is demonstrated in Fig. 3.9B and 3.9C, taken from the work of Campbell and Madhukar (2007), which shows lowering the responsivity and an increase in the D∗ with AlGaAs current blocking layers. Note that

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the bias for peak D∗ is higher for device with AlGaAs current blocking layers.

3.3. Design examples In this section, we will explore a few examples of specific device architectures. 3.3.1. Low-strain DWELL designs In the first-generation DWELL designs, InAs quantum dots were embedded in InGaAs–GaAs quantum well. This quantum well adds additional compressive strain per stack, thereby reducing the maximum number of stacks that can be grown in the detector. This problem can be solved by confining quantum dots in InGaAs–GaAs–AlGaAs double quantum well (Shenoi et al., 2008), which provides for several confined energy levels in the quantum well region, while drastically reducing the required thickness of InGaAs layer. Because there are several energy levels in the quantum well region, this structure typically has multiple peaks, which can be individually tuned by varying the applied bias (see Fig. 3.9A). In addition, AlGaAs barriers reduce the dark current as explained before. 3.3.2. Resonant tunneling barriers As described earlier, in a traditional detector design with uniform barriers, there is always a trade-off between increasing the peak wavelength and reduction in the dark current. This trade-off can be broken by the use of resonant tunneling (RT) filters in the barriers, which can selectively extract the energy levels corresponding to the excited states of interest, while blocking carriers with energies different than the resonant energies. RT filters have sharp transmission peaks at the resonant energies where the transmission is near unity, while transmission probability for other energies is very small. Because dark current is generated by the thermally generated carriers with a continuum of energy distribution, it is significantly reduced (Su et al., 2005) by the application of a RT-barrier. However, the photocurrent is primarily generated from the carriers excited to the quasibound state of the system. Hence, the photocurrent remains comparable as the RT-barriers have near unity transmission at those energies. This results in a large increase in the signal-to-noise ratio (SNR) of the detector. Resonant tunneling barriers have been used for QDIPs, demonstrating room temperature operation with very long-wavelength (VLW) response (Bhattacharya et al., 2005; Su et al., 2005) and even in the THz range (Bhattacharya et al., 2007; Su et al., 2006). Bias tunable multicolor operation for tunneling QDIP have been demonstrated (Ariyawansa et al., 2008). More recently, the resonant tunneling barriers have been used with

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quantum ring detectors (Huang et al., 2009) for THz detection. Operation of RT-barriers on simple DWELL detectors (Barve et al., 2008) and optimized low-strain DWELL detectors (Barve et al., 2010a) has been reported. Over two to three orders of magnitude reduction in dark current and significant improvement in D∗ has been obtained. Resonant tunneling filters can be designed to extract different bound states of the DWELL detectors, leading to an ability to shape the spectral response of the detector for selective extraction of the designed wavelengths (Barve et al., 2010a). 3.3.3. Confinement-enhanced DWELL detectors In the case of DWELL detectors, the excited state electronic wave function extends to the quantum well region. With the InGaAs quantum well layer, the absorption strength associated with the bound-to-bound transition becomes weaker because of the decreased dipole element. This can be countered by a thin Al0.3 Ga0.7 As layer inserted on top of the InAs QD layer (Ling et al., 2008). This added layer provides better confinement for the excited state wave function in the QD region and also elevates the excited state energy, to increase the escape probability, thus improving the overall quantum efficiency. Using this approach, a factor of 20 improvement in quantum efficiency and an order of magnitude improvement in D∗ , as compared with an unoptimized control sample has been reported. 3.3.4. Bound to quasibound DWELL detectors The systematic study of tuning the excited energy of DWELL detectors (Barve et al., 2010b) with respect to the barrier energy allows for greater tunability in device designs, with the ability to control the peak wavelength, spectral width, absorption coefficient, photoconductive gain, activation energies for a fixed barrier composition. An ability to independently control the ground state and excited state energy in the DWELL architecture offers a unique advantage over QWIP and QDIP detectors for obtaining the optimum bound to quasibound type of transitions, as shown in Fig. 3.10A. The B–B transitions showing highest absorption QE and responsivity have the best response at high-applied biases because most of the photoexcited carriers can be swept out. The B–C devices have the least the absorption QE and responsivity resulting from a poor overlap between the wave functions of the two energy levels, as shown in Fig. 3.10B. However, because of unity extraction probability, these devices are suitable for low bias operation, with broadband response. The B–Q devices show the best overall response as shown in Fig. 3.10C, with the measured f /2 detectivity of 4 × 1011 cm·Hz1/2 W −1 (+3V, f /2 optics) at 77 K and BLIP performance up to 100 K. Very-high detectivities of ∼108 cm·Hz1/2 W −1 were measured at operating temperatures more than 200 K. High-performance FPAs with NEDT of 44 mK at 80 K were fabricated from B–C devices.

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Normalized photocurrent

B–C B–Q1 B–Q2 B–B

4

77 K E = 32 kV/cm

6 Wavelength (µm)

8

10

(A) 1012 B–C B–Q1 B–Q2 B–B

1.2 1.0 0.8

77 K

0.6 0.4 0.2 0.0

0

10 20 30 40 Electric field (kV/cm) (B)

Detectivity (cm•Hz1/2/W)

Responsivity (A/W)

1.4

1011

1010

B–C B–Q1 B–Q2 B–B

77 K f/2 optics 109

−40

−20 0 20 40 Electric field (kV/cm) (C)

FIGURE 3.10 (A) Spectral response obtained from the four devices with varying well thickness to get broadband B–C to narrowband B–B type of response. (B) Measured responsivity against electric field, showing three distinct regions. (C) Measured detectivity at f /2 optics at 77 K (Barve et al., 2010b).

4. REVIEW OF RECENT PROGRESS IN QDIP TECHNOLOGY In this section, we will discuss how QDIPs compare with state-of-the-art QWIPs in terms of device performance, by considering important figures of merit such as dark current, quantum efficiency, detectivity, and noise equivalent temperature difference for focal plane arrays.

4.1. Single pixel It is common to process large-size detectors, with mesa sizes upto a few hundred micron, in order to characterize the detector performance. A typical process flow involved in this fabrication is a simple two-step

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process with mesa definition by dry etching or wet etching, followed by contact metallization. A popular choice of contact metal on n-doped GaAs contacts is Ge/Au/Ni/Au. Rapid thermal annealing is used to form ohmic contacts. Common single-pixel characterization includes dark current and photocurrent measurements, spectral response measurements using Fourier transform infrared spectroscopy (FTIR), calibrated blackbody measurements for measuring responsivity and noise measurements for detectivity and photoconductive gain measurements. 4.1.1. Dark current It has been predicted theoretically that well-designed QDIPs would have lower dark current, and hence higher operating temperature than QWIPs. This results in background limited performance at higher temperatures, for the same wavelength. The dark currents for comparable wavelengths in a typical QDIP and QWIP have been plotted in Fig. 3.11 at similar operating temperatures. Data was extracted from various references on QWIPs (Gunapala et al., 2000; Ozer et al., 2007) and QDIPs (Barve et al., 2010a; Kim et al., 2004). Clearly, QDIPs are beginning to outperform QWIPs in dark current levels as predicted. Figure 3.12 shows quoted BLIP temperatures from various groups for QWIPs (Dupont et al., 2001; Gunapala et al., 2000; Jiang et al., 2001; Kaldirim et al., 2008; Lee et al., 1999; Liu et al., 2001; Luo et al., 2005; Ozer et al., 2007; Shen et al., 2000; Tidrow and Bacher, 1996; Tidrow et al., 1997) and QDIPs (Attaluri et al., 2006; Campbell and Madhukar, 2007; Chou et al., 2006; Gunapala et al., 2007a; Jiang et al., 2004a, 2002, 2003; Kim et al., 2004; 8.3 µm QWIP at 77 K Ozer et al. (2007) 8.5 µm QWIP at 70 K (JPL) (2000)

10−1

Jd (A/cm2)

10−3 10−5 10−7 10−9 10−11 −6

QDIP at 77 K 8.3 µm (−ve bias) 10.0 µm (+ve bias) Barve et al. (2008)

−4

−2

QDIP at 77 K 8.7 µm ( −ve bias) 9.3 µm ( +ve bias) Kim et al. (2004) 0 E(V/µm)

2

4

6

FIGURE 3.11 Comparison of dark current density for various QWIPs and QDIPs.

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300 QDIP 2π FOV

BLIP temperature (K)

QDIP π/2 FOV QWIP 2π FOV

200

QWIP π/2 FOV

100

0

0

5

10 15 Wavelength (µm)

20

FIGURE 3.12 Comparison of BLIP temperatures for QWIPs and QDIPs.

Krishna et al., 2005; Szafraniec et al., 2006; Zhang et al., 2005). The data has been broadly divided based on field of view for fair comparison. It confirms the superiority of QDIPs in terms of higher operating temperatures. Room temperature operation has been demonstrated for QDIPs with highdetectivity values, even in VLWIR wavelengths (Su et al., 2004). This has important consequences in the selection of detector technology for commercial applications; as for higher operating temperatures, the detectors can be cooled by portable thermoelectric coolers. This decreases the cost of cooling and increases the portability. 4.1.2. Detectivity Specific detectivity is a popular figure of merit which describes normalized signal-to-noise ratio (SNR). Figure 3.13 shows recently published D∗ values as a function of wavelength at 77–80 K. As can be seen, QDIPs (Aivaliotis et al., 2007c,d; Ariyawansa et al., 2007, 2005; Attaluri et al., 2007; Barve et al., 2008; Chakrabarti et al., 2005b; Gunapala et al., 2007b, 2006a; Huang et al., 2008; Jiang et al., 2004b, 2002; Kim et al., 2004; Krishna et al., 2005, 2003; Lim et al., 2007a; Ling et al., 2008; Meisner et al., 2008; Raghavan et al., 2002; Shenoi et al., 2008; Su et al., 2005, 2006; Szafraniec et al., 2006; Ye et al., 2002a,b,c; Zhang et al., 2005) have comparable D∗ values as QWIPs (Bois et al., 2001; Gunapala et al., 2005, 2006b; Kaldirim et al., 2008; Levine, 1993; Lu et al., 2007; Ozer et al., 2007; Razeghi et al., 2001). This is very promising, as D∗ values for QDIPs have increased by over two orders of magnitude during the last 7–8 years as seen in Fig. 3.14.

Quantum Dot Infrared Photodetectors

U. Mich. NWU G. State, U. Mich. Misc UNM USC and UT Austin Levine QWIP JPL QWIP Recent QWIP data JPL QDIP

1012

1011 D* (cm • Hz1/2/W)

181

1010

109

108

5

10

15

20 25 30 Wavelength (µm)

35

40

45

FIGURE 3.13 Comparison of specific detectivities of QWIPs and QDIPs. After 2004 Before 2004

Detectivity (cm • Hz1/2/W)

1012 1011 1010 109 108 107 0

5

10

15 20 25 30 Wavelength (µm)

35

40

45

FIGURE 3.14 Improvement in D∗ for QDIP over past few years. Filled symbols are recently quoted detectivities, open symbols are from data published in and before 2004.

4.2. Focal plane arrays Lower dark current, higher operating temperature and spatial uniformity over a large area are some of the prerequisites for the next generation photon-rich imaging applications. QDIPs have the advantage of mature III-V processing technique, which allows highly uniform material

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(Pal and Towe, 2006) and standardized device fabrication. Large QDIP focal plane arrays with high-pixel operability (>99%) have been demonstrated, partially owing to the fact that once the epitaxy is completed, there is no difference in the processing, hybridization, and packaging of a QDIP and QWIP. Focal plane arrays operating at high temperatures upto 200 K have also been demonstrated (Lim et al., 2007b; Tang et al., 2006; Tsao et al., 2007) in MWIR. QDIP FPAs in LWIR range and dual-color operation has also been demonstrated (Krishna et al., 2005, 2007). Noise equivalent temperature difference is a useful figure of merit for the performance of FPA, which is a measure of signal-to-noise ratio of the detector. It determines the minimum temperature difference the detector can distinguish for the given bias, input irradiance, and temperature. QD-based FPA performances have been getting better since early demonstrations. Normalized NETD is plotted as a function of wavelength in Fig. 3.15 for both QDIP (Andrews et al., 2009; Gunapala et al., 2007a; Jiang et al., 2004a; Razeghi et al., 2006; Tang et al., 2007; Tsao et al., 2007; Vaillancourt et al., 2009; Varley et al., 2007) and QWIPs (Bois et al., 2001; Gunapala et al., 2000; Gunapala et al., 2006b; Helander et al., 1999; Jhabvala et al., 2007; Kaldirim et al., 2008; Ozer et al., 2007; Schneider et al., 2004). For fair comparison, all NETD data points were scaled to have f-number ( f ) of 2, using following relation (Gunapala et al., 2007b) √ AB (1 + 4f 2 ) (3.5) NETD = ∗ B DB dP dT 1000 QWIP QDIP

NETD (mK)

120 K 100

66 K 100 K

60 K

65.5 K 40 K 67 K

90 K

10 4

6 8 Wavelength (µm)

10

12

FIGURE 3.15 NETD comparison for QDIP and QWIP FPAs. For fair comparison, NETD is normalized for f#2.

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B where D∗B is background limited detectivity, dP dT is the derivative of integrated blackbody power with respect to the operating temperature, A is the device area, and B is the measurement bandwidth. The data has been measured for different operating temperature of FPAs. Most of the values are for the operating temperature of 70–80 K. The other temperatures are mentioned on the figure. It can be seen that the performance of QDIP FPAs is still inferior to the performance of standard QWIP FPAs in terms of NETD, while the QDIP FPAs are already working at higher operating temperatures as compared with QWIP FPAs. With the optimized designs to reduce the photoconductive gain and increase the escape probability, it can be expected that QDIP FPAs would yield comparable imaging performance as QWIPs, but at higher operating temperatures. The addition of 2D grating in the fabrication of QDIP FPAs can increase the absorption coefficient by a factor of 5–6, resulting in sharp reduction in NETD values. Figure 3.16 shows some of the images obtained from QDIP FPAs for 320×256 (A), fabricated at University of New Mexico and Northwestern University (NWU) (B, C)(Tsao et al., 2007), 640×512 (D) (Gunapala et al., 2007b), and 1024×1024 (E) (Ting et al., 2009) fabricated at JPL.

5. FUTURE DIRECTIONS As the experimentally achieved performance of QDIPs is still inferior to the theoretically predicted performance, especially for the focal plane arrays, there are several key areas where QDIPs need to improve. There is a vast scope for improvement in all the major aspects, such as crystal growth, energy band optimization, device designs, usage of materials, and device modeling. The future research is expected to be focussed on the growth optimization, exploring different material systems and geometries, theoretical modeling of the transport properties and optimum device designs for specific goals (such as multicolor response, high-operating temperature, high-quantum efficiency, lower dark currents, and so on). In this section, we attempt to identify the key areas of improvement in QDIPs and trends for the future research.

5.1. Growth optimization for higher normal incidence absorption Even though QDIPs respond to normal incident light, because of the asymmetry in quantum dot dimensions in lateral plane and vertical plane, the absorption coefficient for s-polarization is much less than that of ppolarization. Typical ratio of s–p polarization absorption is close to 15–20%, as shown in Fig. 3.17B. The data has been measured at UNM, at 77 K, using a linear polarizer and a 45◦ polished sample mounted on a 45◦ holder. In these measurements, the s-polarization corresponds to the electric field in

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(A) T=200K

T=130K

(B)

(C)

(E)

(D)

(F)

FIGURE 3.16 Images taken from QDIP FPAs (A) UNM 320 × 256 FPA, operating at 80 K for 6.1 µm peak wavelength (B)-(C) NWU 320 × 256 FPAs for 4.1 µm peak wavelength (Tsao et al., 2007) (D) JPL 640 × 512 FPA for 8 µm peak wavelength, at 60 K (Gunapala et al., 2007b) (E)-(F) JPL 1024 × 1024 FPA for 7.8 µm peak wavelength at 80 K (Ting et al., 2009).

the growth plane, while p-polarization response has electric field at 45◦ to the growth plane. Similar ratios have been reported by other groups (Gunapala et al., 2006a; Liu et al., 2003a). This results from the shape of self-assembled quantum dot, which typically has a pancake shape, with the base diameter much larger than the height. For InAs quantum dot on GaAs (001) substrates, the typical diameter is ∼15–20 nm while the typical height is 5–10 nm. Because the quantum confinement is weak in the growth plane, the normal incidence absorption is weaker than the lateral absorption. Apart from the use of the gratings to make use of p-polarization absorption, the important avenue for the quantum dot infrared detector research would be to increase the s-polarization (normal incidence)

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1.2

Normalized Photocurrent (a.u.)

Normalized Photocurrent (a.u.)

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1.0 0.8 0.6 0.4 0.2 0 3

4

5

6

7

8

9

10

5

p-polarization s-polarization

4 3 2 1 0 2

3

4

5

Wavelength (µm)

Wavelength (µm)

(A)

(B)

6

7

FIGURE 3.17 Comparison of photocurrents measured from s and p absorption in DWELL detector with InAs quantum dots (A) InGaAs capping, (B) InGaAlAs capping.

absorption. To increase the absorption coefficient in normal direction, the quantum dot base diameter needs be reduced for greater quantum confinement in the lateral plane, as predicted both theoretically (Stoleru and Towe, 2003) and experimentally (Tseng et al., 2008). As pointed out by Liu et al. (2003b), strong lateral confinement also means only one or two energy levels in quantum dots. It is still possible to achieve wavelength selection by using a transition from quantum dot ground state to eigenstate in confining quantum well in dots-in-a-well structure. Stronger quantum confinement will also result in longer carrier lifetime in quantum dots because of widely separated energy levels, which will serve to increase the responsivity and quantum efficiency further, while simultaneously reducing the dark current. Another important topic of research is the study of different strain-bed and capping material compositions surrounding the quantum dots for increasing the quantum confinement in QDs by reducing size and minimizing the migration of species during the growth of subsequent layers. Recently, polarization-dependent photocurrent measurements carried out on a detector with In0.15 Al0.1 Ga0.75 As capping layer on InAs quantum dot have shown s to p polarization ratio ∼50%, as shown in Fig. 3.17B. However, there is a large scope of improvement in capping material research, in order to optimize the QD shape, as well as the quantum mechanical barrier the capping material offers. Absorption coefficient can be further increased by increasing the number of stacks in the active region. Because the cumulative compressive strain prevents the growth of large number of stacks, reducing the strain per stack is an important area of research. Various approaches such as low-strain DWELL detectors and submonolayer quantum dots have demonstrated successfully for reducing the compressive strain per stack. Further reduction is possible by incorporating tensile-strained

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InGaP-based materials for the growth on GaAs, for strain compensation. Use of thick GaP layers for strain compensation has already been demonstrated (Hubbard et al., 2008; Laghumavarapu et al., 2007; Lever et al., 2003), especially for solar cells. However, a thick active region would require a larger applied bias, which may be limited by ROIC design.

5.2. Submonolayer quantum dots In self assembled quantum dots, typically two to three monolayers of InAs is deposited on GaAs (001) substrates, which has ∼7% compressive strain. The cumulative compressive strain buildup limits the number of layers that can be grown, thus limiting the absorption quantum efficiency. More than a monolayer of this material forms the wetting layer, which has no importance in infrared absorption. The novel approach of replacing SK-QDs with SML QDs significantly reduces the InAs deposition required for forming quantum dots, by depositing a fraction of a monolayer of InAs. The quantum dots can be formed by strain-induced vertical coupling of these fractional monolayers. The size and density of the 2–D islands can be controlled to increase the absorption cross-section. Lateral densities as high as 5×1011 /cm2 and lateral dimensions of 5–10 nm (Xu et al., 2003) have been reported. Because only the lateral dimensions are important for absorption of normally incident light, this configuration still retains the advantages of SKQDs, such as normal incident absorption, longer lifetimes, and so on, but reduces the cumulative compressive strain. The s to p polarization ratio can be adjusted just by changing the number of layers that are coupled to each other. Researchers at JPL have demonstrated excellent FPA imaging (Ting et al., 2009) with SML QDIP (see Fig. 3.16E and 3.16F), upto 80 K, with NETD of 22, 28, and 33 mK at 50, 60, and 70 K, respectively.

5.3. Device modeling One of the advantages of QWIPs is their simplicity, which allows precise modeling with coupled Shrodinger-Poisson equation solvers, for understanding the absorption and the transport in the system. Complexity and inhomogeniety of QDIP systems prevents such a modeling, thus energy structure and transport has to be solved independently. Some attempts have been made to combine the two problems (Vukmirovi´c et al., 2006), but they require several critical simplifying assumptions related to the shape and distribution of quantum dots. Emission and capture of electrons in the quantum dots, which is related to the photoconductive gain is not well understood, especially for DWELL system. Many researchers use models developed for QWIPs to understand QDIPs, which results in inaccuracies

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because of presence of multiple energy levels in quantum dots. Although it is clear that the background doping and doping inside the quantum dots results in band bending near the quantum dot-barrier interface, this fact is not taken into consideration while designing the devices. These local variations in doping result in a nonuniform electric field, which would drastically affect the emission and capture phenomenon. Because most of the devices are designed in flatband approximations, it is hard to predict the experimental results from them. Hence, in order to design optimum devices, the quantum dot and transport modeling is expected to be an important area of research.

5.4. Barrier engineering Engineering the barriers around the quantum dots has been the topic of active research in the recent years. By proper barrier designs, such as resonant tunneling barrier, confinement-enhancing barrier, bound to quasibound barrier devices, escape probabilities of photoexcited electrons can be increased without reducing the absorption coefficients. These designs have been discussed in section 3. Detailed theoretical study for band-bending and carrier-transport effects near the quantum dots will allow precise design of these barriers that are expected to improve the performance of these barrier devices. For example, the design of RT barriers is carried out assuming flatband conditions and negligible coupling between the absorber and resonant tunneling filter. This results in nonideal coupling, with nonunity tunneling probabilities at resonant energy. The effect is experimentally observed as the reduction in responsivity (Barve et al., 2010a) and lack of narrowing of the spectral response (Barve et al., 2010a; Su et al., 2005). By solving exact potential profile and the quantum mechanical coupling between the barrier and quantum dot, the designs can be significantly improved. Similarly, AlGaAs current blocking barriers can be designed such that there is only one energy level in the quantum well of DWELL detector, aligned within 10–15 meV of the barrier energy, to obtain bound to quasibound type of response, to increase the escape probability.

6. SUMMARY In this chapter, we discussed the basics of QDIPs to understand some of the important advantages of this technology over QWIPs. The quantum dot infrared photodetectors are predicted to be technologically important, especially for photon-rich LWIR and VLWIR applications. The threedimensional quantum confinement within QDs gives rise to important

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fundamental advantages, such as, normal incidence absorption, highcarrier lifetimes, highquantum efficiency, and low dark currents. This allows QDIPs to operate at higher temperature than QWIPs. However, the nonideal shape of the typical SK-grown quantum dot prevents the QD-based detectors to realize their full potential. The growth of quantum dots plays a crucial role in designing and improving the performance of QDIPs. Research toward optimum growth, such as smaller and more uniform quantum dots, higher dot density, capping materials for better optical, structural as well as electrical properties, optimum doping profile would be expected to yield significant improvement in the performance of QDIPs. Further improvements, such as unity escape probabilities, lower dark current and higher absorption, are possible by clever barrier designs, such as AlGaAs current blocking barriers, resonant tunneling barriers, confinement-enhanced architectures, and so on. Important figures of merit have been compared between QWIP and QDIP technologies, and it can be seen that QDIPs are beginning to match the performance of QWIPs. High-operating temperatures in both MWIR and LWIR, large format and highly sensitive arrays, detection of VLWIR, and THz wavelengths at moderately high temperatures are just some of the demonstrated achievements of quantum dot infrared detectors, proving that great strides have been accomplished since the first detector was published just more than a decade ago. Detailed modeling of the transport and electronic structure of quantum dots, including the effects of nonuniform electric field will play a crucial role in obtaining the theoretically predicted performance of quantum dots. In conclusion, with high-operating temperature, availability of substrates and ease of growth and fabrication leading to large format array, multicolor detection because of richness of electronic spectra in the quantum dots provide all the ingredients of a successful third-generation imaging technology.

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CHAPTER

4 Terahertz Semiconductor Quantum Well Photodetectors J. C. Cao∗ and H. C. Liu†

Contents

1. Introduction 2. Principle of THz QWP 3. Theory and simulation of THz QWP 3.1. Basics of simulation models 3.2. Dark current 3.3. Photocurrent 3.4. Many-body effects 3.5. Simulation and optimization of grating coupler 4. Design and characterization of THz QWP 4.1. Design 4.2. Measurement of photocurrent spectrum 4.3. THz QCL emission spectrum measured by THz QWP 5. Application: THz free space communication 6. Summary Acknowledgments References

195 196 201 201 202 206 211 217 223 223 227 231 234 239 239 239

1. INTRODUCTION THz detectors are one of the key devices in various THz applications, such as THz science research, bio and chemical material identification, medical imaging, security screening, and communication (Ferguson and Zhang, 2002). Early THz detectors are thermal detectors and semiconductor ∗ Key Laboratory of Terahertz Solid-State Technology, Shanghai Institute of Microsystem and Information

Technology, Chinese Academy of Sciences, 865 Changning Road, Shanghai 200050, China † Key Laboratory of Artificial Structures and Quantum Control, Department of Physics, Shanghai Jiao Tong

University, 800 Dongchuan Road, Shanghai 200240, China Semiconductors and Semimetals, Volume 84 ISSN 0080-8784, DOI: 10.1016/B978-0-12-381337-4.00004-8

c 2011 Elsevier Inc.

All rights reserved.

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photoconductive detectors (Haller, 1994). Thermal detectors include Lithium tantalate (LiTaO3 ) pyroelectric detector (Byer et al., 1975; Fukada and Furukawa, 1981), deuterated triglycine sulfate (DTGS) pyroelectric detector (Goss et al., 1984; Lal and Batra, 1993), and Si bolometer (Downey et al., 1984; Richards, 1994). Doped Ge photoconductive detector (Haller, 1994; Haller et al., 1979), n type bulk GaAs detector (Gornik, 1984), and homojunction and heterojunction interfacial workfunction internal photoemission (HIWIP and HEIWIP) far-infrared detectors (Perera, 2006; Perera et al., 2000) are typical semiconductor photoconductive detectors. These devices are used in astronomy and astrophysics (Haller, 1994); besides, DTGS and Si bolometer are used in FTIR to measure the transmission and reflection spectra of materials or the emission spectra of lasers. LiTaO3 detectors are used to calibrate the laser-emission power (Li. et al., 2009a), and the array of which can also be used to characterize and analyze the beam of lasers or image (Yang et al., 2008). Recently, using intersubband transitions in semiconductor quantum structures, THz quantum well photodetectors (THz QWPs) have been demonstrated as fast, compact, and easy integratable THz photon detectors (Cao, 2006; Cao et al., 2006; Chen et al., 2006; Graf et al., 2004; Guo et al., 2009; Lake et al., 1997; Liu et al., 2008, 2004; Luo et al., 2005; Patrashin et al., 2006; Tan and Cao, 2008; Tan et al., 2010, 2009). Compared with THz thermal detectors, THz QWPs are narrowband and fast response, which are suitable for laser-emission characterization and THz communication (Grant et al., 2009). As the extension of quantum well infrared photodetectors (QWIPs) in THz range, THz QWPs have similar device performance and characteristics with QWIPs. Based on GaAs/AlGaAs material system, there are two types of QWIPs: photoconductive QWIP and photovoltaic QWIP. Reported THz QWPs are mostly photoconductive detectors (Guo et al., 2009; Liu et al., 2004; Luo et al., 2005; Patrashin et al., 2006). Because of good responsivity and high sensitivity, photoconductive QWIPs are widely used in focal plane arrays and multicolor detection (Gunapala et al., 2000), while ¨ photovoltaic QWIPs, which are low-dark current (Schonbein et al., 1996), working at zero or near-zero bias and only existing in midinfrared range (Schneider et al., 1996, 1997) so far, can be used to construct high thermal resolution focal plane array (Schneider et al., 2003). In this chapter, the working mechanism, simulation, design, and characterization of THz QWPs are discussed systematically. Then, we introduce some recent applications based on THz QWPs.

2. PRINCIPLE OF THz QWP In 1985, infrared absorption by intersubband transition in GaAs/AlGaAs multiple quantum well was first observed by West and Eglash (1985). After

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that, a new photon-detection technology based on intersubband transition in quantum well was realized and studied by many researchers (Levine, 1993; Levine et al., 1990, 1987; Schneider et al., 2003). THz QWPs are the extension of QWIP to THz range. In 2004, Liu et al. (2004) realize the first THz QWP. Since then, significant improvements in simulation and design of active region (Guo et al., 2009; Liu et al., 2007a; Xiong et al., 2008), device performance (Hewageegana and Apalkov, 2008; Luo et al., 2005; Patrashin and Hosako, 2008; Schneider et al., 2009), and applications (Fathololoumi et al., 2010; Graf et al., 2009; Luo et al., 2006) have been achieved. According to different active region structures, electron distributions, and transport mechanisms, there are two types of quantum well photodetectors: photoconductive and photovoltaic. The active region consists of periodic multiple quantum wells and barriers. Each period include a doped GaAs layer (well) and a AlGaAs layer (barrier). The operation mechanism of THz QWPs is as follows: when THz waves are incident on the active part of the detectors, the electrons on the bond state in the quantum well absorb the THz photons and then get excited to the quasicontinuum state, which is very close to the top of the barrier. With external bias, these excited carriers (electrons) result in a photocurrent. The response peak is determined by the energy-level spacing between the bond state and quasicontinuum state, which can be tailored by barrier height, well width, and doping density in the well. Usually, many wells (10–100) are required for sufficient absorption. Conductive THz QWPs are promising detectors in future high-speed THz wireless communication because of their simple structure and high respond speed. Because of different doping types, conductive THz QWPs can either be n-type or p-type. In quantum wells, electrons are bound to the well only in the growth direction of quantum wells; while in the direction normal to the growth direction, the dispersion relation of electron is parabolic under effective mass approximation for n-type, which is similar to free electrons. Hence, n-type quantum wells can not absorb photons of normal incident light, while p-type quantum wells can as a result of intervalence transitions of holes. So, 45◦ incident, light-coupling geometry or grating coupler is often used in n-type devices, and normal incident can be directly used in p-type ones. However, because of other limitations such as low mobility, the performances of p-type devices are far inferior to n-type ones. Recently, many advances of n-type THz QWPs have been obtained (Guo et al., 2009; Liu et al., 2007a; Luo et al., 2005; Patrashin et al., 2006; Schneider et al., 2009). Detector responsivity is an important performance characteristic, usually written as (Beck, 1993; Liu, 1992)

Ri =

Iphoto e = ηgphoto , ~ω8 ~ω

(4.1)

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where ω and 8 are the frequency and the number of the incident photon per unit time, respectively, η = Nη(1) is the total absorption quantum efficiency, in which η(1) is the absorption quantum efficiency of single quantum well, and N is the number of quantum wells in active region. gphoto is the photoconductive gain, which is gphoto =

τtrans + τc 1 pe 1 τrelax = , τesc + τrelax τtrans N pc N

(4.2)

where τrelax and τesc are the intersubband relaxation time and the escape time from the quantum well, respectively. pc and pe are trapping or capture probability when electrons with higher energy than barrier pass through the quantum wells and the escape probability when excited electrons escape the quantum wells, respectively. Detectivity D? and blip (background limited infrared performance) temperature are the two most important THz QWP characteristics. D? is the signal (per unit incident power) to noise ratio normalized by the detector area and the measurement electrical bandwidth. The relevant noise contributions are from (1) the detector itself (i.e., dark current) and (2) the fluctuation of the photocurrent induced by background photons incident on the detector. When the noise is only because of dark current, using threedimensional (3D) carrier drift model and two-dimensional (2D) emissioncapture model (Schneider and Liu, 2006), we get the detector noise limited D? s τc η λ ? √ , (4.3) Ddet = 2π ~c N N3D Lp and D?det

η λ √ = 2π ~c N

r

τscatt , N2D

(4.4)

where λ is the wavelength, N3D and N2D can be approximated by N3D

mb kB T 3/2 2π ~c Ef =2 exp − + , 2π ~ λc kB T kB T

(4.5)

and N2D =

mkB T 2π ~c Ef exp − + , λc kB T kB T π~2

(4.6)

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where m (mb ) is the effective mass in the well (barrier), and λc is the cutoff wavelength. Fermi energy and the electron density in quantum well satisfy ND = (m/π~2 )Ef .

(4.7)

In view of the balance between scattering escape and capture, Eq. (4.3) and (4.4) are actually equivalent. However, they do show the physical process from different perspectives. While Eq. (4.3) relates the detectivity to the 3D effective carrier concentration and the capture process, Eq. (4.4) addresses a 2D effective carrier concentration and a scattering (or emission) process. From Eqs. (4.3)–(4.6), the expected general behavior for a photoconductor is seen, such as (1) a higher η or lower T lead to a higher D? , and (2) λc and T are the most sensitive parameters, being on the exponent. Noting that η is proportional to the doping density and hence the Fermi energy, there is an optimum value for Ef . The optimum value is found by Ef d ) = 0, (4.8) Ef exp(− dEf 2kB T which gives the maximum D? when Ef = 2kB T (Kane et al., 1992). This condition dictates an optimum value for ND for maximizing D? . The blip condition is defined when the photocurrent caused by the background equals the dark current, and the temperature is called blip temperature (Tblip ). For operations at and lower than Tblip , the detector is said to be under blip condition, and then the maximum detectivity is limited by the background. In the blip regime, the background limited D?det is given by D?blip

λp = 4π ~c

s

ηp φB, ph

,

(4.9)

where λp is the peak detection wavelength, ηp is the peak absorption, and φB,ph is the integrated background photon number flux (per unit area) incident on the detector. For a given wavelength and if a detector is blip, D?det only depends on the absorption quantum efficiency and the background photon flux. The electron lifetime becomes irrelevant in this regime. Using three-dimensional (3D) carrier drift model and twodimensional (2D) emission-capture model, the blip temperature is found to be determined by the following equations: η(1) τscatt φB, ph =

Ef 2π ~c mkB T + , exp − λc kB T kB T π~2

(4.10)

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and η

(1)

τc φB, ph

Ef 2π ~c mb kB T 3/2 + , Lp exp − =2 λc kB T kB T 2π ~2

(4.11)

where η(1) is the peak absorption efficiency for one quantum well. From Eqs. (4.10) and (4.11), the most sensitive parameter is λc , being in the exponent. A high capture velocity (short scattering time), although giving rise to a fast intrinsic response speed, leads to a low Tblip . It is interesting to note that Tblip depends on the one well absorption, not the total absorption, and that improving η(1) has the same effect as improving τc /Lp and τscatt . The practical values of τc for QWIPs fall in the range of 1–10 ps. Given λc , τc , T, and φB, ph , Eq. (4.10) can be rewritten as Ef Ef 2π ~c exp − = (Constant) × exp − . kB T kB T λc kB T

(4.12)

Noting η(1) ∝ ND ∝ Ef , one can adjust Ef to maximize the left-hand-side of the equation, which maximizes Tblip . The optimum condition is Ef = kB T, which is different from the optimum condition for maximizing the detector limited detectivity by a factor of two (i.e., Ef = 2kB T). These predictions have been verified experimentally for QWIPs in the 8–10 µm region (Yang et al., 2009). For completeness, the ideal (blackbody) background photon flux is given by φB, ph =

Z

h i dλ πsin2 (θ/2) η(λ)LB (λ),

(4.13)

where θ is the field of view (FOV) full-cone angle, the photon irradiance is given by LB (λ) =

−1 2π ~c 2c , − 1 exp λkB TB λ4

(4.14)

where TB is the background temperature, and the device spectral lineshape is modeled by 1

η(λ) = 1+

1λ 2λ

−

1λ 2λp

2 .

(4.15)

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Presently, most THz QWPs are photoconductive detectors, covering peak response frequency from 2 to 7 THz. The operation temperature is still not very high, about 30 K or lower (Liu et al., 2007a).

3. THEORY AND SIMULATION OF THz QWP 3.1. Basics of simulation models THz QWPs are designed with the same principle used in midinfrared quantum well photodetectors. Quantum well photodetector is a unipole device, which replies on intersubband transitions of electrons (holes). Understanding the transport is important to predict the detector performance. Several models have been proposed: (1) nonequilibrium Green function based on quantum transport theory (Lake et al., 1997) and (2) Monte Carlo method based on Boltzmann equation. Ryzhii et al. (1998) used this method to study the dark current, I–V characteristic and the nonlinear dynamics of carrier transport; Cellek et al. (2004) applied a microscopic scattering model in the Monte Carlo simulation to solve the problem of transition between local state and extented state; (3) rate equation method based on quasimicroscopic scattering model. Jovanovi´c et al. (2004) used this method to analyze the gain, photocurrent response, and I–V characteristic of quantum well photodetectors. Various scattering mechanisms and physics effects can be easily included in the nonequilibrium Green function method, such as correlation, depolarization and memory effect, and so on. But this method is difficult to solve for complex structures because of its heavy computational demand. Rate equations take into account microscopic scattering mechanisms, but the quantitative results are still difficult to obtain because of phenomenological parameters. Different scattering processes can be conveniently considered with Monte Carlo method. Considering all these factors, Monte Carlo method is an effective method to design quantum well photodetectors. The numerical models for dark current include self-consistent driftdiffusion model, self-consistent emission-capture model, and numerical Monte Carlo model. The self-consistent drift-diffusion model developed by Ershov et al. (1996, 1995) calculates the QWIP characteristics by selfconsistently solving three equations: (1) Poisson equation, (2) continuity equation for electrons in the barriers, and (3) rate equation for electrons in the quantum wells. The inclusion of the Poisson equation is especially important for QWIPs with a small number of wells (<10) because the field can be substantially different (often higher) for the first few periods starting from the emitter in comparison with the rest of the wells. The continuity equation involves the current (expressed in the standard

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drift-diffusion form) and rates of thermal and optical generation and of recombination. Using this numerical model, we were able to account for the observed unusual capacitance behavior (Ershov et al., 1997b) and explain the nonlinear photoconductivity at high excitation power using a CO2 laser (Ershov et al., 1997a). In addition, the model has the capability to predict transient and hence frequency characteristics (Ershov, 1996), as well as photoresponse under localized IR excitation (Ershov, 1998). Thibaudeau et al. (1996) presented a numerical model that extends the simple emission-capture model presented before. The model allows the electric field to be nonuniform, self-consistently determined by Gauss’ law. The authors obtained better agreement with experiments than the simple model. Ryzhii (1997) constructed an analytical model by solving Poisson’s equation and an equation governing the electron balance in the quantum well. Interesting functional dependencies of the responsivity on the number of wells and the photon excitation power were found. Jovanovi´c et al. (2004) constructed a quantum mechanical model considering all scattering processes, including emission and capture. The model results were compared with experimental data on a GaAs/AlGaAs device and good agreement was found. Ryzhii and Ryzhii (1998) and Ryzhii et al. (1998) carried out Monte Carlo simulations on QWIPs, in particular their ultrafast electron-transport properties. Cellek and Besikci (2004) and Cellek et al. (2004) also performed such simulations, analyzing the effects of material properties on the device characteristics. They found the evidence that the L-valley in GaAs/AlGaAs QWIPs plays an important role in determining the responsivity versus voltage behavior. Monte Carlo simulations shed light on the hot electron distribution on top of the barriers, and they should provide guidance to the optimization of QWIPs. To end this section, although several models have been established, with varying degree of complexity, and good agreement between models and experiments has been obtained, to formulate a true first-principle QWIP model is a highly nontrivial task. This is because the QWIP is rather complicated. Given the wide barriers and narrow wells, the transport mechanism falls between ballistic and drift-diffusion; and because of the high doping and high field, realistic calculations of scattering or trapping rates are extremely complicated and have not been performed so far. The situation becomes even more complicated to model for p-type structures (Petrov and Shik, 1998).

3.2. Dark current Photoconductive THz QWPs have features of simple structure, high-speed response, and high sensitivity, which are suitable for high-speed detection

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applications (Cao, 2006). In this section, we will introduce two simple models for the simulation of dark current in photoconductive devices: 3D carrier drift model and 2D emission-capture model; then the dark current curve of a THz QWP is simulated by an improved emission-capture model. A good understanding of the dark current is crucial for design and optimization of QWIPs because dark current contributes to the detector noise and dictates the operating temperature. There are several common assumptions or approximations made to define the physical regime for all the discussions in this subsection. These are as follows: (1) the interwell tunneling contributes negligibly to the dark current, (2) the electron density in each well remains constant (Liu et al., 1991), (3) the heavily doped emitter serves as a perfectly injecting contact (Liu et al., 1997), and (4) mainly one bound state is confined in the quantum well, including the case where the upper state (final state of the ISBT) is in resonance or very close to the top of the barrier. Assumption (1) is satisfied by requiring the barriers to be sufficiently thick. Assumption (2) is a good approximation but is not strictly valid especially at large bias voltages as shown experimentally (Liu et al., 1991). Assumption (3) is expected to be valid for QWIPs with a large number of quantum wells, consistent with experimental results. The effect of contacts becomes important for QWIPs with a small number of quantum wells as shown in simulations (Ershov et al., 1995). To produce good detectors, condition (4) is required (Liu, 1993). Here we first present two simple physical models, and then the simulation results are compared with experimental data. 1. 3D carrier drift model: The first physical model calculates Jdark by directly estimating j3D . A 3D electron density on top of the barriers N3D is estimated with only the drift contribution taken into account (diffusion is neglected). The model was first presented in a very clear and concise article by Kane et al. (1992). The dark current density is given by Jdark = eN3D υ(F),

(4.16)

where υ(F) is the drift velocity as a function of electric field F. The drift velocity takes the usual form υ (F) = h

µF 1 + (µF/υsat )

2

i1/2 ,

(4.17)

where µ is the low field mobility and υsat is the saturated drift velocity. Usually THz QWPs are degenerately doped in the wells, i.e., the top of the Fermi sea is higher than the energy of the lowest subband, so the only 2D quantum well effect comes into the picture for the evaluation of the Fermi

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energy Ef . Assuming a complete ionization, the 2D doping density ND equals the electron density within a given well, as a good approximation. 2. Emission-capture model: Scattering-assisted escape is the dominant process for a typical QWIP, especially at low fields (Schneider and Liu, 2006). Electrons associated with the confined ground state in the well and distributed on the 2D in-plane dispersion curve undergo a scattering event to get out of the well and then become a 3D mobile carrier in the barrier. The escape current density can be written as je =

eN2D , τscatt

(4.18)

where N2D is a 2D electron density which only includes electrons on the upper part (with energy greater than the barrier height) of the ground state subband and τscatt is the scattering time to transfer these electrons from the 2D subband to the nonconfined continuum on top of the barrier. The standard THz QWPs having their barriers much wider than wells, we neglect any superlattice miniband effects. The capture probability is related to the relevant time constants by pc =

τtrans , τtrans + τc

(4.19)

where τc is the capture time for an excited electron back into the well, and τtrans is the transit time for an electron across one quantum well region including the surrounding barriers. In the limit of pc 1, i.e., τc τtrans , as is true for actual devices at operating electric fields, the dark current becomes Jdark = e

N2D τc υ(F), Lp τscatt

(4.20)

where Lp is the period length of the multiple quantum well structure, which is the sum of the well and barrier widths Lp = Lw + Lb . The quantity N2D /τscatt represents the thermal escape or generation of electrons from the quantum well, and 1/pc is directly proportional to the photoconductive gain. We theorectically simulated the dark current curves of THz QWP (ID: V267) (Tan et al., 2009). The bias range is from 0.1 to 30 mV, and the temperatures are from 7 to 20 K. In the simulation, the saturated mobility is taken as υsat = 1 × 107 cm/s; the energy of the ground state is E1 = 4.25 meV; the barrier height is Eb = 0.87x eV; and the effective mass of electron is

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Terahertz Semiconductor Quantum Well Photodetectors

0 100

16

Field (V/cm) 48 64

32

80

96

112

T = 7, 8, 9, 10, 11, 12, 14, 16, 18, 20 K

Current density (A/cm2)

10−1 10−2 10−3 10−4 10−5 Simulation

10−6 10−7

Experiment

0

5

10

15 20 Bias voltage (mV)

25

30

FIGURE 4.1 The I–V curves. Solid lines: mumerical results; dots: experimetal data.

m∗ = 0.067me and mb = (0.067 + 0.083x)me , where x is the Al fraction of the barrier. The dark current curves are shown in Fig. 4.1, where the theoretical results (solid lines) agree well with the experimental measurements (dots) (Tan et al., 2009). In the temperature range of 7 to 20 K, the dark current of V267 increases quickly with increasing temperatures. The range of the current density is from 10−5 to 10−1 A/cm2 within the bias range. The relation between dark current and temperature indicates that the thermionic emission is the mainly dark current mechanism in THz QWP (C ¸ elik et al., 2008; Tan et al., 2009). In the simulating process for the dark currents, it is important to note that a temperature-dependent mobility parameter was used to fit the I–V curves. The fitted mobility versus temperature relation is shown in Fig. 4.2, having a decreasing trend with temperature. This is opposite to the Hall mobility (Stillman et al., 1970), which is of an ionized impurity scattering origin in the relatively pure GaAs materials at the temperature less than 20 K. The reason for the discrepancy is surely related to the simplicity of the model, neglecting processes such as field nonuniformity and self-consistency.

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106

Mobility (cm2/Vs)

105

104

103

102

6

9

12 15 Temperature (K)

18

21

FIGURE 4.2 Vertical electron drift mobilities in the device structure versus device temperatures (Tan et al., 2009).

3.3. Photocurrent The distinct feature of photoconductive QWPs in contrast with the conventional intrinsic and extrinsic photoconductors is the discreteness, i.e., incident photons are only absorbed in discrete quantum wells that are normally much narrower than the inactive barrier regions. In this section, we discuss the photocurrent caused by intersubband excitations in a QWP. The photocurrent spectrum is an important characteristic of the device performance, which gives the peak response frequency and the sensitivity to the radiation. Compared with the wideband IR sources (such as Globar, Hg lamp, and so on), THz QWPs are narrowband detectors. We calculated the spectral response of a THz QWP designed for 7 THz detection peak frequency (Cao et al., 2006). We incorporate the effect of GaAs optical phonons which give rise to a strong absorption in the region of 34–36 meV and result in an increase in reflection because of the large refractive change around this region. Comparing the calculated spectral shape with experiments, we show the improvement over the standard expressions. For QWPs, the total absorption coefficient η is usually defined as the ratio of the absorbed electromagnetic energy per unit time, volume, and the intensity of the incident radiation. For simplicity, we define a dimensionless absorption coefficient normalized by the area A instead of

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the volume. The expression for η is given by η=

~ω X X | < n|(e/m∗ )A · P|n0 > |2 IA 0 n,n k⊥

× [f (En (k⊥ )) − f (En0 (k⊥ ))] × δ(En0 (k⊥ ) − En (k⊥ ) − ~ω),

(4.21)

where I is the intensity of the incident radiation and is given by I = (1/2)ε0 cn0 E20 .

(4.22)

Here n0 is the refractive index of the material, taken to be real and constant, and E0 is the electric field amplitude (Liu and Capasso, 2000). Expressing A by E0 and changing the summation into a two-dimensional integration (Liu and Capasso, 2000), we get X 2 Z πe2 d2 k⊥ | < n|pz |n0 > |2 η= ε0 cn0 ωm∗2 0 (2π)2 n,n

· [f (En ) − f (En0 )]δ(En − En0 − ~ω).

(4.23)

The spectral current responsivity
(4.24)

where 8i is the incident photon number per unit time. The photocurrent Iphoto is given by (1)

Iphoto = iphoto /pc ,

(4.25)

where (1)

iphoto = e8i ηpe /N

(4.26)

is the photoemission current directly ejected from one well, N is the number of quantum wells, pc is the capture probability, and pe is the escape probability for an excited electron from the well (Liu and Capasso, 2000). Using Eqs. (4.25) and (4.26), we get
e ηgphoto , ~ω

where photoconductive gain is gphoto = pe /pc N.

(4.27)

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J. C. Cao and H. C. Liu

Until now, we have assumed that the amount of absorption is the same for all the wells and the absorption by the lattice is negligible (Ershov et al., 1999; Jovanovi´c et al., 2004). However, this assumption does not hold for the present case. In the reststrahlen region (34–36 meV), the absorption by the optical phonons of GaAs is very strong, and the amount of absorption for each well is not the same either. Therefore, 8i in Eq. (4.26) should be replaced by 8(z), to take into account the difference between the incident light and the light propagating in the QWIP. For simplicity, we take the absorption of the middle well as the average absorption, and use the light intensity I instead of the photon number 8, I = ~ω8, then we have
eηI(z) gphoto . ~ωIi

(4.28)

Using the following standard expressions (Klingshirm, 1997), I(z) = I(z = 0)e−2ωk(ω)z/c , I(z = 0) = (1/2)ε0 cn(ω)E20 and Ii = (1/2)ε0 cni E20 , and Ii = (1/2)ε0 cni E20 , where z is the distance from the middle well to the first well, ni is the refractive index of air, and n(ω) is the refractive index of the matter in connection with Snells, law of refraction. If we use a “single oscillator” model to simulate such absorption behavior in the reststrahlen region (Blakemore, 1982), we can easily get the complex refractive index κ ∗ (ω) ≡ (κ1 − iκ2 ) = κ∞ +

2 (κ − κ ) ωTO ∞ 0 2 − ω2 + i2π γ ω ωTO p

,

(4.29)

where κ0 is the low–frequency dielectric constant, κ∞ is the high– frequency (optical) dielectric constant, ωTO is the resonant frequency, and γp is the damping coefficient. In addition, we have √ n(ω) = (1/ 2)[(κ12 + κ22 )1/2 + κ1 ]1/2 ,

(4.30)

√ k(ω) = (1/ 2)[(κ12 + κ22 )1/2 − κ1 ]1/2 .

(4.31)

Figure 4.3 shows the spectral variation of the real refractive index n(ω) and the extinction coefficient k(ω) for GaAs at T = 8 K, yielded from Eqs. (4.30) and (4.31) with ~ωTO = 33.81 × (1 − 5.5 × 10−5 T) meV, κ∞ = 10.88, κ0 = κ∞ × 1.170 × (1 + 3.0 × 10−5 T) (Blakemore, 1982), and 2π ~γp = 0.25 meV. The curves of n(ω) and k(ω) cross at the energy ~ωTO (33.3 meV), and again at the energy ~ωLO (36.2 meV).

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Real refractive index n Extinction coefficient k

14 12 GaAs T=8K

10

n k

8 6 4 2 0 20

30

40 50 60 Photo energy (meV)

70

80

FIGURE 4.3 Spectral variation of the real refractive index and the extinction coefficient for GaAs at 8 K (Cao et al., 2006), modeled by Eqs. (4.30) and (4.31).

Absorption efficiency h

1.0 GaAs/AIGaAs QWIP T = 8K

0.8

Total B–B B–C

0.6 0.4 0.2 0.0 20

30

40 50 60 Photo energy (meV)

70

80

FIGURE 4.4 Calculated absorption quantum efficiency versus photon energy for one well with well width d = 12 nm and electron density 1017 cm−3 (Cao et al., 2006).

In the experiment of THz QWIP (Liu et al., 2004) discussing the reststrahlen region, the device consists of 50 quantum wells made of 12-nm GaAs wells and 40-nm Al0.05 Ga0.95 As barriers. The center 10-nm region of the wells was doped with Si to 1017 cm−3 . The 45◦ edge facet geometry was used for photoresponse measurement and the polarization is p. The applied voltage is only ±0.4 V and the voltage drop across a given well is less than 2 meV, which is negligible compared with the groundstate energy. The absorption spectrum is calculated at zero bias as an approximation (Liu et al., 2004). First, the absorption coefficient is calculated using Eq. (4.23) (Ikonic et al., 1989; Liu, 1993), as shown in Fig. 4.4. Here the ground state energy E0 = 14.2 meV, and the first excited state energy E1 = 43.1 meV is very close to the barrier height Vb . This optimum

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J. C. Cao and H. C. Liu

design (Liu and Capasso, 2000) will bring both a large absorption and a rapid escape for the excited electrons. From the results of the calculation, we can see that the peak detection wavelength (42.5 µm) is in good agreement with the design, and both bound-to-bound and bound-to-continuum intersubband transitions contribute to the absorption. Using Eq. (4.28), we get the calculated detector response shown in Fig. 4.5, where the reststrahlen region (34–36 meV) is clearly seen. Comparing with experiments, the general shapes are similar and our model, therefore, indeed represents an improvement over the standard expressions. As an approximation, the calculated absorption spectrum at zero bias is used. For the experiment, the bias voltage is low (given in Liu et al. (2004). The polarization is p and the angle is 45◦ . Comparing experimental and theoretical results in Fig. 4.5, quantitatively there is still a significant difference in the relative response magnitudes above and below the reststrahlen region. We point out that there are uncertainties in both experiment and calculation. In the experiment, the overall shape and the relative strength depend on how well the spectrometer system response is corrected. This is done by using a reference detector assumed to have a flat response, which is not very accurate over a wide spectral range. For the calculation, the barrier height (band offset) has not been tested in this very-low aluminum fraction regime. The barrier height value will

20

Spectral response (a.u.)

Spectral response (a.u.)

GaAs/AIGaAs THz QWIP, T = 8 K

Calculation

30

20

40

Detector response at 8 K Experiment

30

40 50 60 70 Photo energy (meV)

50 60 Photo energy (meV)

70

80

80

FIGURE 4.5 Calculated and experimental photoresponse spectrum versus photon energy (Cao et al., 2006). The THz QWIP consists of 50 quantum wells made of 12-nm GaAs wells and 40-nm Al0.05 Ga0.95 As barriers.

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change the relative strength of contributions from bound-to-bound and bound-to-continuum transitions, and therefore change the overall shape. Moreover, many-body effects have not been included, which would have moved the overall response to a higher energy and made a better fit in the low-energy region (20–25 meV). In the experimental curve, there are some smaller features, for example, dips at 42 and 45 meV. These may be caused by the weaker absorption of two-zone edge and AlAs-like phonons, and they may also be caused because of the absorption associated with the localized vibrational modes of Si-doped GaAs. A lot of investigations have been done on the absorption induced by Si-related defects in doped GaAs (Chen et al., 1980; Spitzer and Panish, 1969), and the frequencies of all the absorption bands of interest in their study is from 350 to 480 cm−1 (43.4–59.6 meV). In addition, there may be absorption resulting from other localized phonon modes (Shen, 1984). We note that having an intersubband transition in resonance with optical photons may lead to a strong coupling and the formation of intersubband polarons. However, because the doping density in the device analyzed here is not high and the intersubband oscillator strength is not large because of the bound-toquasibound nature, the polaron splitting is expected to be about 1 meV or less (Liu et al., 2003). We, therefore, neglect the effect of strong coupling. A more detailed comment is in order regarding the AlAs-like phonons. For alloys like AlGaAs, a more complex dielectric function should be used to describe a two-mode oscillator for GaAs-like and AlAs-like optical phonons. However, if we take a simple model of either additive or factorized functions for the entire multiple quantum well stack, a very-strong absorption would also result in the AlAs-like phonon region, which does not agree with experiment. This is an issue to be resolved, i.e., how to include the contribution of the AlAs-like phonon. In conclusion, we have calculated and discussed the response spectrum of a THz QWP. Because of the optical phonon absorption in the reststrahlen region, the refractive index n and the extinction coefficient k change strongly. Considering all the changes, we have improved the usual expression for
3.4. Many-body effects Because of the low-doping density, the many-body effects are usually neglected in the design of midinfrared QWPs (Schneider and Liu, 2006). However, for THz QWPs, because the energy difference between the bound subband and the continuum is around 10 meV, notable error of photoresponse peak position will be introduced without considering the many-body effects (Liu et al., 2004; Schneider and Liu, 2006). The many-body effects include the interactions among electrons and between electrons and

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other quasiparticles. Earlier investigations have shown that in QWIPs, the electron–electron interactions can affect the optical response peak position (Schneider and Liu, 2006). The other many-body interactions have influence on the linewidth and line shape of photocurrent spectrum (Xiong et al., 2008). We studied the many-body effects on THz QWPs (Guo et al., 2009). It is found that large differences between theory and experiment are introduced without including the above many-body interactions in the theoretical design. Our numerical results show that it is very important to consider the many-body interactions for designing THz QWPs. In general, because of the large degrees of freedom of a many-particle system, many-body effects can only be treated with various approximation methods. For electron–electron interactions, the static exchangecorrelation and the dynamical depolarization (or local field) (Liu, 1994; Załuzny, 1993) and exciton-like effects are considered with local density ˙ approximation (LDA) within the framework of density functional theory. The depolarization and exciton-like interactions between the ground and excited sublevels are photon-induced many-body contributions (Fung et al., 1999). For the electron–quasiparticle interactions, the electron– phonon and the electron-impurity scatterings are described by using a simple model with two free parameters (Fu et al., 2003; Xiong et al., 2008), the values of which are determined by fitting numerical photocurrent curves to experimental data. Because of the low aluminum concentration in barrier layers, the scattering between electron and interface roughness is not considered. The photocurrent spectra of two THz QWPs are calculated here; the device parameters are the two devices labeled as V266 and V267 reported in the studies of Liu et al. (2004) and Luo et al. (2005). Our numerical results show that there is only one bound subband in the quantum well with only the Hartree potential being considered. When the exchange-correlation potential is taken into account, however, two bound subbands exist in the quantum wells for the two THz QWPs, and the second subband is near the top of the barrier. The static exchange-correlation and the dynamical depolarization electron–electron interactions cause blueshifts of the photoresponse peaks, and the calculated photocurrent peak positions agree with the experimental data quantitatively. The shapes of the photocurrent peaks are well described by the energy-dependent 0 model that represents the effects of the electron–phonon and electron-impurity scatterings. The LDA functional for exchange-correlation potential adopted in this chapter cannot properly describe the exciton-like many-body effect in THz QWPs. The Hamiltonian for an electron in THz QWPs within the effective mass approximation is H=p

1 p + VQW (z) + VH (z) + Vxc (z), 2m∗ (z)

(4.32)

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where m∗ is the electron effective mass, p is the momentum operator, VQW is the well confinement potential, VH is the Hartree potential, and Vxc is the exchange-correlation potential. The wave function of electrons in the THz QWPs is expressed as a two-dimensional plane wave times a one dimensional envelope function along the growth direction, ψk,l r|| , z = exp ir|| ·k|| ϕkz ,l (z), where r|| and k|| are the in-plane coordinate and momentum, kz is the quasimomentum limited to the first Brillouin zone associated with the quantum well period, and l is the subband index. With the above approximation, the Schrodinger equation reads "

~2 ∂ − 2 ∂z

1 ∂ m∗ (z) ∂z

# + VQW (z) + VH (z) + Vxc (z) ϕl,kz (z) = εl,kz ϕl,kz (z). (4.33)

The energy of the electron is Ek,l = ~2 k||2 /2m∗ + εkz ,l . The electron charge density is given by ρe (z) = |e|

X

2 f Ek,l , εF , T ϕkz ,l (z) ,

(4.34)

k,l

where e is the electron charge, f is Fermi distribution function, εF is the Fermi energy, and T is temperature. Once the density is known, the Hartree potential VH can be obtained by solving the Poisson equation ρe (z) − ρd (z) ∂2 , VH (z) = − 2 ∂z

(4.35)

where ρd (z) is the fixed ionized dopant density, and is dielectric constant. In general, it is a difficult task to find the exact exchange-correlation potential Vxc . In this chapter, the widely used LDA based on the density functional theory is adopted through the following formula (Gunnarsson and Lundqvist, 1976; Zhang and Potz, 1990): e2 Vxc (z) = 4π 2 aB rs (z)

9 π 4

1/3

11.4 , (4.36) 1 + 0.0545rs (z) ln 1 + rs (z)

where aB = ~2 /e2 m∗ (z) is the effective Bohr radius and rs = h −1 i1/3 . The band structure of THz QWP is obtained (3/4π ) a3B ρe (z) by self-consistently solving the above set of equations with plane-wave expansion method.

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The absorption efficiency η can be derived from the Fermi’s golden rule X Z dk 2 πe2 j pz 0 η (ω) = 3 0 cn0 ωm∗2 (2π ) j × f Ek,0 , εF , T − f Ek,j , εF , T δ 1e Ek,l,0 − ~ω ,

(4.37)

where 0 is the vacuum permittivity, c is the speed of light, n0 is the refractive index, and 1e Ek,l,0 is the energy difference between the jth and the ground subbands with depolarization and exciton-like effects included. The expression for 1e Ek,l,0 is (Ando et al., 1982) 1e E2k,l,0 = 1E2k,l,0 1 + αk,l,0 − βk,l,0 , 2  z Z∞ Z 2 2e ρ2D dz  dz0 ϕkz ,l z0 ϕkz ,0 z0  , αk,l,0 = 1Ek,l,0 −∞

βk,l,0 = −

2ρ2D 1Ek,l,0

Z∞

−∞

−∞

dzϕkz ,l (z)2 ϕkz ,0 (z)2

∂Vxc [ρ (z)] . ∂ρ (z)

(4.38)

Here αk,l,0 and βk,l,0 describe the depolarization and exciton-like effects, respectively, and 1Ek,l,0 is the energy difference between l and 0 subbands without the two dynamical many-body corrections. The photocurrent is Iphoto = e8ηgphoto , where 8 is the incident photon number per unit time, and gphoto is the photoconductive gain. On the assumption of energyindependant 8 and gphoto , the photon current Iphoto is proportional to the absorption efficiency η. Forhsimplicity, the delta function in Eq. (4.37) is i 2 2 replaced by a Lorentzian 0/ π Ek,j − Ek,0 − ~ω + 0 , where 0 is a small constant. √ In Fu et al. (2003) and Xiong et al. (2008), an energy-dependent 0 = a E − ~ωTO + b is used to take into account the effects of electron– phonon and electron-impurity on the shape of photocurrent peak, where a and b are parameters, and E is the electron energy measured from the conduction band edge of (Al,Ga)As barrier. In this chapter, the same expression of 0 is adopted to fit for the experimental results. The band structures and photocurrents of two THz QWPs are calculated. In order to compare with the experimental results, the parameters of the two THz QWPs, including the barrier and well widths, the barrier height, and the doping concentration and position, are those reported in the studies of Liu et al. (2004) and Luo et al. (2005). The effective electron mass is 0.067m0 with m0 the electron mass. The temperature is 8.0 K. To expand the envelope wave functions, 99 plane waves are used. The

Terahertz Semiconductor Quantum Well Photodetectors

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z (nm) 50

−40 −20

0

20

40

−40 −20

0

20

40

Energy (meV)

40 30 20 10 0 −10 −0.04 −0.02 0.00 (A)

0.02

0.04 −0.04 −0.02 0.00 kz(1/nm)

0.02

0.04

(B)

FIGURE 4.6 Band structures of V266 THz QWP (A) without and (B) with exchange-correlations potential (Guo et al., 2009).

convergent criteria is (εFi − εFi−1 )/εFi 5 0.0005, with εFi being the Fermi energy at the ith iterative step, and the convergence is reached in the condition of i 5 15 for all the calculations. Figure 4.6 shows the band structure of V266 THz QWP with and without the exchange-correlation potential. As shown in Fig. 4.6A, when the Coulomb interaction is taken into account with Hartree approximation, only one localized subband exists in the quantum well. The first excited subband is in resonance with the top of the barrier, which is in accordance with the design rule of bound-to-quasibound QWIPs. However, because the quantum well is very shallow for THz QWPs, the neglect of exchangecorrelation potential will introduce large errors in design of THz QWPs. Because the exchange-correlation potential is negative, for V266 THz QWP, the exchange-correlation interaction deepens the quantum well by about 6.3 meV, which makes the first excited subband fall into the quantum well and be off resonance with the top of the barrier. The energy difference between the ground and the first excited subbands increases by about 3.2 meV for V266 THz QWP. Similar effects of exchange-correlation interaction on the band structure of V267 THz QWP (not shown) are found. The effects of Hartree potential on the band structures of V266 and V267 are also explored. Because the Si dopants are doped in well layers, the electrons and ionized dopants are spatially overlapped, which lowers the Hartree contribution. The energy difference between the ground and the

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J. C. Cao and H. C. Liu

first excited subbands increases by 0.4 meV for V266 and 0.3 meV for V267 with Hartree potential being considered. The calculated results show that the exchange-correlation interaction plays a key role in the design of THz QWPs. The theoretical and experimental photocurrent spectra for V266 and V267 are shown in Fig. 4.7. In order to obtain some physical insights, different many-body interactions are taken into account step-by-step in our calculations. The energy differences of response peak positions between theory and experiment for V266 and V267 THz QWPs are 5.6meV (24.8%) and 4.8 meV (36.0%) without including any many-body interaction. When the static exchange-correlation potentials are taken into account, the differences decrease to 2.4 meV (10.6%) and 2.6 meV (19.4%), respectively. The further improvements of theoretical response peak positions are achieved by considering the dynamical depolarization effects, and the discrepancies are about 0.2 meV (0.9%) and 1.1 meV (8.2%) for V266 and V267, respectively. The exciton-like interaction plays a negative role in our calculations. Earlier investigations show that the value of βk,l,0 is much smaller than that

1.2

Exp. data Without Vxc With Vxc Vxc + Depol.

0.8

Normalized photocurrent

0.4 0.0 4

8

12

16

20

24

28

(B) 1.2

Exp. data Without Vxc With Vxc Vxc + Depol.

0.8 0.4 0.0 10

15

20

25

30

35

Energy (meV) (A) FIGURE 4.7 Calculated and experimental photocurrent spectra of THz QWPs, (A) for V266 THz QWP and (B) for V267 THz QWP (Guo et al., 2009).

Terahertz Semiconductor Quantum Well Photodetectors

217

of αk,l,0 in Eq. (4.38) (Helm, 2000; Liu et al., 2007b). However, our numerical results show that the value of βk,l,0 is in the same order of magnitude as that of αk,l,0 . The overestimate of exciton-like interaction in our work originates from the following two reasons: (1) in the current expression for Vxc in Eq. (4.36), ∂Vxc [ρ (z)] /∂ρ (z) is proportional to ρ (z)−2/3 , which will lead to unreasonably large values of ∂Vxc [ρ (z)] /∂ρ (z) in barrier layers. (2) because of the low barrier height, in comparison with midinfrared QWIPs, more portions of the wave function will extend into the barrier layer. For the above two reasons, the integration value in Eq. (4.38) will be overestimated. The value of βk,l,0 should be much smaller than that of αk,l,0 (Schneider and Liu, 2006). Therefore, for the present work, we leave out the exciton-like contribution. In conclusion, we have investigated the effects of exchange-correlation, depolarization, and exciton-like interactions on the photon response spectra of THz QWPs. Because of the decrease of energy difference between the ground subband and the first excited subband, large relative errors are introduced without including the above many-body interactions in the theoretical design. The exchange-correlation potential deepens the quantum well. As a result, the ground subband and the first excited subband shift to the lower energy region, and the energy difference between them increases. Because the expression for exchange-correlation potential is inadequate in the low electron density region and the leakage of wave function into the barrier layer, the exciton-like interaction is overestimated. The discrepancy between the theoretical and experimental photoresponse peak positions decreases evidently by including the exchange-correlation and depolarization effects. Our numerical results show that it is very important to consider the many-body interactions for designing THz QWPs.

3.5. Simulation and optimization of grating coupler The ISBT selection rule requires a nonzero polarization component in the quantum well direction (the epitaxial growth direction, z) (Schneider and Liu, 2006). As mentioned earlier, 45◦ incident, light-coupling geometry is usually used to acquire a nonzero polarization in z direction. However, this prevents the construction of two-dimensional (2D) focal plane arrays, which need light incident normal to the devices (the QW planes, xy plane). To solve this problem, it is useful to utilize gratings, as exploited by Heitmann et al. (1982) to diffract the light and thus excite ISBT in Si inversion layers. In the midinfrared region, large-format arrays with up to 1024 × 1024 pixels have already been demonstrated (Gunapala et al., 2005). Recently, Patrashin et al. (2006) fabricated one-dimensional (1D) metal gratings on the top of the THz QWP, realizing device response under normal incidence (Patrashin and Hosako, 2008).

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J. C. Cao and H. C. Liu

We utilized Modal method (Todorov and Minot, 2007) to simulate the field distribution in the 1D metal grating THz QWP (Zhang et al., 2011). The average intensity in device active region was obtained. Based on numerical results, the optimizations of the grating including period and fill factor were discussed, which led to high coupling efficiency and device responsivity. Usually, GaAs/AlGaAs material system is used to fabricate THz QWPs. The device is grown on semi-insulating (SI) GaAs substrate. From the bottom to the top, there are bottom contact, multiple quantum wells and top contact, shown in Fig. 4.8. The top and bottom contacts are n-doped GaAs, and the multiple quantum wells consist of several tens of AlGaAs barrier and n-doped GaAs well. The 1D metal grating is made of gold and is defined using standard mirofabrication lift-off techniques. The period of the grating is d, and the width of metal stripe is a. The modal method is proposed by Todorov and Minot (2007). This method combines the Rayleigh expansion method of the diffracted field and the transfer matrix method of the multilayer, by which the electric field distribution in the device can be obtained conveniently. The field appears in the form of a Rayleigh expansion in the homogeneous layers outside the 1D grating: ∞ X eiαn x Pn eiγn z + Qn e−iγn z , ψ x, y, z = eiβy n=−∞

z THz waves

1D metal grating

x

Multilayer

Top contact AIGaAs GaAs AIGaAs GaAs AIGaAs

1st diffractive mode 0th diffractive mode

Bottom contact

P

SI GaAs substrate

FIGURE 4.8 Schematic of 1D grating THz QWP (Zhang et al., 2011).

Q T

(4.39)

Terahertz Semiconductor Quantum Well Photodetectors

αn = α + γn =

2π n , d

q εk02 − αn2 − β 2 ,

219

(4.40) (4.41)

where ψ is any component of the field, ε is the dielectric function of the material, k0 is the wave vector in the vacuum, and αn is the wave vector in x direction. The x, y, and z direction are shown in Fig. 4.8. α0 = α is the wave vector of incident wave in x direction. The conservation of the tangential component of the wave vector at the grating surface leads to Eq. (4.40). β and γn are the wave vectors in y and z direction, respectively. (Pn ,Qn ) is the pair of amplitudes (see Fig. 4.8), and all the pairs in different layers are connected with each other through transfer matrix. For the incident area outside the device, Qn = 0 except Q0 , and Q0 = 1 if the amplitude of incoming wave is set to be 1; while for the transmitted area, Pn = 0 and Qn = Tn . The field distribution can be obtained by solving the simultaneous equations in different areas with the boundary conditions. For normal incidence, only p polarization is need to be considered because no contribution is from s polarization which is in parallel with the QW planes makes no contribution. A typical field distribution (Ez component) in 1D metal grating THz QWP is shown in Fig. 4.9 (only Ez component contributes to the ISBT). Compared with the total thickness of the active region (less than 5 µm), the GaAs substrate is much thicker, normally around 600 µm, which is also much longer than the wavelength. So an approximation of infinite substrate is taken in the calculation for simplicity, which will not affect the diffractive characteristic of the grating. In Fig. 4.9A and B, we can see a pair of stripes beneath the grating. This indicates the diffraction occurs and the nonzero Ez component appears, which will cause the response of the detector. The field distribution in the substrate is also given in Fig. 4.9. The periodic dark and light stripes are similar with the multislit interference. In the following, we will discuss the optimization of the 1D metal grating based on the Ez in the active region. Two THz QWPs are considered here (Liu et al., 2008). The multilayer is sandwiched between 0.4 and 0.8 µm of top and bottom contacts, doped to 1.0 × 1017 . The structures are detailed in Table 4.1. The optimization is discussed from the period d and the fill factor r (i.e., the ratio of metal stripe width a and d). Lw is the quantum well width, Lb is the barrier width, N is the period number of multilayer, [Al] is the Al fraction in the barrier, Nd is the doping density in the well, and f0 is the peak response frequency of the device.

Distribution of Ez

Metal grating Top contact

−0.5

z (µm)

−1.0 −1.5

Multilayer

−2.0 −2.5 −3.0

0.40 0.24 0.08 −0.08 −0.24 −0.40

Bottom contact

−3.5 5

10

15 20 x (µm)

25

(A) Energy distribution of Ez

Metal grating Top contact

−0.5

z (µm)

−1.0 −1.5

Multilayer

−2.0 −2.5

0.40 0.32 0.24 0.16 0.08 0

−3.0 Bottom contact

−3.5 5

10

15 20 x (µm)

25

(B) Energy distribution of Ez Metal grating Device

z (µm)

−5 −10 −15 Substrate

−20

0.50 0.40 0.30 0.20 0.10 0

−25 10

20

30 40 x (µm)

50

(C)

FIGURE 4.9 In a typical 1D metal grating THz QWP, (A) the distribution of Ez (amplitude); (B) the energy distribution of Ez (intensity), without the part of substrate; (C) the energy distribution of Ez (intensity), including the part of substrate. The metal grating is at z = 0, which is the top of the device (Zhang et al., 2011).

Terahertz Semiconductor Quantum Well Photodetectors

TABLE 4.1

The structure parameters of THz QWPs

˚ LW (A) A B

155 221

221

˚ Lb (A) 702 951

[Al]

N 30 23

3% 1.5%

N d (cm−3 ) 16

6 × 10 3 × 1016

f 0 (THz) 5.41 3.21

The dielectric function is taken as follows (Blakemore, 1982): ε(ω) =

"

2 (ε − ε ) ωTO s ∞ 2 − ω2 − iωδ ωTO TO

+ ε∞

ωP2 1− ω (ω + iδP )

# (4.42)

For GaAs, εs = 12.85, ε∞ = 10.88, ωTO = 2π × 8.02 THz, δTO = 2π × 0.06 THz, δP is the damping rate, depending on the doping density NP , Drude frequency ωP is s ωP =

NP e2 , ε0 εs m∗

(4.43)

where e is the charge of electron, and m∗ is the effective mass of free carriers. The Drude model of metal is εM (ω) = 1 −

2 ωM ω (ω + iδM )

(4.44)

For gold, ωM = 1.11 × 104 THz and δM = 83.3 ps−1 . The thickness of 1D metal grating studied here is 0.38 µm, deposited on the top of top contact. With these parameters, we calculate the average intensity Iaverage of Ez in the active region at the peak response frequency f0 , which are 5.41 THz and 3.21 THz for device A and B, respectively. The expression of Iaverage is

Iaverage

R iωt 2 Ez e dV =C V

(4.45)

where C is the constant of proportionality. It should be mentioned that, because of the much smaller thickness of metal grating than the width, most of the metallic losses are expected to occur along the walls parallel to the xy plane. The perfect-metal approximation is not suitable anymore, so we take the surface impedance boundary condition to take into account the dissipation in the metal (Todorov and Minot, 2007). Figure 4.10A gives the relation of Iaverage and the grating period at 50% fill factor. It can be seen that the average intensities reach the maximum at 14.6 µm and 25.7 µm for A and

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J. C. Cao and H. C. Liu

Device A Device B

0.12 0.08 0.04

Device A Device B

0.16 Iaverage (a.u.)

Iaverage (a.u.)

0.16

0.12 0.08 0.04 0.00

0.00 0

5 10 15 20 25 30 35 40 45 d (µm) (A)

0.0

0.2 0.4 0.6 0.8 Filling factor a/d (B)

1.0

FIGURE 4.10 At peak response frequency (A) Iaverage versus the grating period under the condition of 50% fill factor; (B) Iaverage versus the fill factor when the period of grating is set to match the wavelength (Zhang et al., 2011).

B, respectively, which correspond to the wavelength of THz waves at f0 in the device material (in GaAs, 5.41 THz corresponds to 14.6 µm, and 3.21 THz corresponds to 25.7 µm). Therefore, when the period of the grating equals the wavelength in the device material, the coupling efficiency reaches the maximum. Then, we fix the grating period according to the peak response, and study the relation between average intensity and the fill factor. The results are given in Fig. 4.10B. For device A, the maximum occurs at 54.5% when the grating period is 14.6 µm; and for device B, it is 61.5% when the grating period is 25.7 µm. The results are not 50%, which may be related to the transmission and reflection of the multilayer. So the fill factor should be determined according to the specific structure of a THz QWP. To confirm these predictions, we fabricated three grating samples (A-G12 with a 12-µm-period grating, A-G15 with a 15-µm-period grating, and A-G20 with a 20-µm-period grating). At 0.15-V bias, the peak responsivities are 0.128, 0.197, and 0.070 A/W for A-G12, A-G15, and AG20, respectively. It can be seen that, the 15-µm-period grating is the most efficient one, which is in consistent with our prediction. In conclusion, the Modal method is used to analyze the electric field distribution in the 1D metal grating THz QWP, and the optimization of the grating is also discussed based on the simulation. We find that, when the period of the grating equals the wavelength in the material and a proper fill factor is chosen (54.5% for A device, 61.5% for B device), the coupling efficiency reaches a maximum, leading to high field intensity and high detector’s responsivity. Moreover, we find that the thickness of substrate is important for the field distribution, which may be caused by the cavity effect. Further investigation is needed.

Terahertz Semiconductor Quantum Well Photodetectors

223

4. DESIGN AND CHARACTERIZATION OF THz QWP 4.1. Design The detection of THz waves is the one of the key technology of THz applications. To study the THz wave itself and its interaction with other materials, various characterizations should be done, including spectrum measurement, power calibration, beam analysis, and so on. Because of the specific position in the electromagnetic wave spectrum, the study of THz range developed slowly for a long time because of the lack of radiation sources and detectors, and hence limited the methods that could be used for detection. In the recent 10 years, as the development of compact THz sources and the detection methods, the methods for detection of THz waves improved substantially (Tonouchi, 2007). Therefore, different sources and detectors could be chosen, and various physical phenomena could be studied. THz QWP is the extension of QWIP in THz range. The materials are commonly GaAs/AlGaAs. The optimum QW parameter for a standard QWIP is to have the first excited state in resonance with the top of the barrier. Strong ISBT absorption and fast relaxation of excited electrons can be both achieved in this structure. Therefore, the structure parameters should be optimized in design. These strcture parameters are the quantum well width, barrier width, doping density, barrier height (the Al fraction in AlGaAs barrier), and the number of quantum wells. For THz QWP working at longer wavelength than QWIP, smaller barrier height and lower doping density are required (to reduce the absorption by free carriers and the dark current). In 2004, Liu et al. (2004) demonstrated the first THz QWP with a peak response at 7.1 THz (42 µm). The width of quantum well and barrier are 12 nm and 40 nm, respectively. The Al fraction is 5%, and the number of quantum wells is 50. The center 10 nm of the quantum well and the top (400 nm) and bottom (700 nm) GaAs contacts are doped to 1017 cm−3 by Si. The calculated parameters of barrier Al percentage and well width for a given peak detection frequency (wavelength) are shown in Fig. 4.11 (Liu et al., 2004). A word of caution: the parameters used here, although expected to be valid, are proven for midinfrared QWIPs and are not tested in the low aluminum fraction region. From Fig. 4.11, it is predicted that the THz frequency range of 1–8 THz is covered by QWIPs with low aluminum fractions between 0.8 and 5.4%. Figure 4.12 shows the calculated Tblip versus the peak detection frequency (Liu et al., 2004). For achieving the highest dark-current-limited detectivity, if one follows the Ef = 2kB T rule, the density would become very low for low temperatures ( 80 K), making the absorption also low.

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J. C. Cao and H. C. Liu

6 νp= f/7.5 THz (λp = 40 µm)

Aluminum %

5

6.5 (46)

4

5.3 (57) 4.2 (72)

3

2.8 (108)

2

2.1 (144)

1

1.5 (195)

GaAs/AlGaAs QW

0 10

12

14

16

1.05 (285) 18

20

22

24

26

28

30

32

Well width (nm)

Background limited temperature (K)

FIGURE 4.11 Calculated parameters of barrier Al percentage and well width for a given peak detection frequency (wavelength) (Liu et al., 2004). 25

Lower curve: η1 = 0.5% per well at 10 THz Upper curve: scaled by EF = 2kBT 300 K / 90° FOV τlife = 5 ps

20 15 10 5 0

0

2

4 6 8 Peak detection frequency (THz)

10

FIGURE 4.12 Calculated background-limited infrared performance (blip) temperature versus peak detection frequency (Liu et al., 2004).

We, therefore, considered two cases in Fig. 4.12. The upper curve uses the Ef = 2kB T condition, while the lower curve starts with a higher absorption (using higher doping) 0.5% at 10 THz and is reduced linearly down to 0.05% at 1 THz. The trade-off here is that if the operating temperature is desired to be as high as possible, the upper curve should be followed. However, if a high absorption is needed, one should use the lower curve, which will mean a somewhat lower operation temperature. Because for these very farinfrared devices the doping densities are usually low, many-body effects result in small energy corrections. However, because of the transition energies are also small, many-body effects need to be considered. The exact

Terahertz Semiconductor Quantum Well Photodetectors

225

values depend on doping densities. The detection frequency in Fig. 4.12 should, therefore, be shifted to higher values by about 30% if these effects are included. In general, to qualify as a good detector, there must be a sufficiently high absorption. On one hand, a high doping is desirable for achieving high absorption; but on the other hand, high doping leads to a high dark current and low operating temperature. A trade-off must, therefore, be made for a given application. For most applications, it is desirable to operate the detector under the blip condition for detecting weak signals. In some applications involving a strong source such as a THz QCL, the requirement is different. Here as long as the dark current is lower than the signal photocurrent, photon noise limited detection is achieved. In such a case, the detector operating temperature can be raised. Having determined the quantum well and doping parameters, the next design parameter is the barrier width. The barrier width should be sufficiently thick so that the dark current is completely in the thermionic regime, i.e., interwell tunneling should be negligible comparing to the background photocurrent. The barrier thickness was chosen according to Fig. 4.13 so that the interwell tunneling currents are less than 10−5 A/cm2 , which corresponds to the estimated background current. For the number of quantum wells, because the absorption strongly depend on the device geometry and the coupling method, generally a large number of wells would give a high absorption. However, provided

Interwell tunneling current (A/cm2)

100 10−1 10−2 10−3

x = 1.5%

10−4 10−5 10−6

x = 3%

10−7 10−8 10−9

x = 5%

10−10 10−11 40

50

60 70 80 Barrier width (nm)

90

100

FIGURE 4.13 Estimated direct interwell tunneling current versus barrier thickness for three cases of barrier aluminum fractions of x = 1.5, 3, and 5%. Other parameters used for the estimate are E1 = 4.3, 8.6, and 14 meV, n2D = 0.3, 0.6, and 1.0 × 1011 cm−2 , and LW = 22.0, 15.4, and 12.0 nm, for the three x values, respectively (Schneider and Liu, 2006).

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Wavelength (µm) 80 70 60 50

40

Spectral response (a.u.) Transmission (%)

20

Detector response at 8 K

0.02

50 40 30 20 10 0

30

0.03

0.04

0.05 (A)

0.06

0.07

0.08

0.04 0.05 0.06 Photon energy (eV) (B)

0.07

0.08

GaAs substrate transmission

0.02

0.03

FIGURE 4.14 (A) Photoresponse spectrum and (B) low temperature bulk GaAs transmission spectrum (Liu et al., 2004).

a sufficient absorption is reached, a small number of wells is preferred for high gain. The photoresponse spectrum is shown in the upper part of Fig. 4.14 (Liu et al., 2004) for a bias voltage of 0.4 V and a temperature of 8 K. For reference, the bulk GaAs transmission is shown in the lower part of the figure, measured at 15 K on a 400-mm-thick GaAs substrate. The “dark” reststrahlen region from 33 to 37 meV resulting from optical phonon absorption is clearly seen. We simulated the photocurrent spectrum (Cao et al., 2006) theoretically by the improved photo response model, which is in consistent with the experimental data above. As a result of the interaction between electron and phonon, the radiation with frequency in the “dark” region cannot be detected by GaAs/AlGaAs THz QWPs. The measured dark current characteristics at various temperatures are shown in Fig. 4.15 (Liu et al., 2004). The measured dark current slowly decreased to less than 25 K and stopped at about 15 K. These studies confirm that the structure of QWPs is practicable in THz detection.

Terahertz Semiconductor Quantum Well Photodetectors

227

101

Current (A/cm2)

100 10−1 10−2 10−3 10−4 10−5 −1.5

15, 20, 25, 30, 35 K Symbols: measured Lines: model

−1.0

−0.5

0.0 0.5 Field (kV/cm)

1.0

1.5

FIGURE 4.15 Dark current characteristics at various temperatures (Liu et al., 2004).

In addition, Graf et al. (2004) demonstrated a THz quantum well photodetector based on the quantum cascade structure, with the peak response wavelength of 84 µm (3.57 THz), operating at 10–50 K. The responsivity at 10 K is 8.6 mA/w. Although the detectivity and the responsivity are two orders of magnitude smaller than the THz QWP based on photoemission, its noise level is relative low because of the cascade mechanism. Because of the potential of zero bias photovoltaic response, the development of this type of detectors is also very interesting.

4.2. Measurement of photocurrent spectrum Terahertz radiation bridges the gap between the microwave and optical regimes. It is only 5 years since the first demonstration of THz QWP (Liu et al., 2004), and a lot of researches are still needed. Before the measurement of photocurrent spectrum, we test the I–V curves first, then analyze the dark current mechanism and the temperature performance. The temperature-dependent I–V properties are important characteristics for terahertz QWPs. In the following, we measured the I–V curves with 300 K background or the dark condition, and the relation between dark current and temperature is also discussed. The active region of the device is GaAs/AlGaAs multiquantum wells grown by MBE. The parameters of the active region are shown in Table 4.2. It should be mentioned that the doping in Table 4.2 is implemented at the center 10 nm of the quantum well by Si. The purpose of the wide barriers is to reduce the interwell tunneling (Liu et al., 2007a). In a real device, the active region is between the top and bottom contacts. The top and bottom contacts are usually 400 and 800 nm respectively, doped to 1 × 1017 cm−3 with Si, which is relatively low

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TABLE 4.2 Structure parameters for the THz QWIPs (Schneider and Liu, 2006) Sample V265 V267

Lw (nm) 11.9 22.1

Lb (nm) 55.2 95.1

[Al] 0.05 0.015

N d (cm−3 ) 1 × 1017 3 × 1016

N 40 23

to reduce the contact layer free carrier absorption and plasma reflection in the THz region (Schneider and Liu, 2006). Next, we will mainly introduce the measurement and analysis of V267. Mesa devices of different sizes were fabricated using standard GaAs processing techniques. Because low temperatures are required for operation, a close-cycle cryostat with the lowest temperature of 3 K is used to cool the device. A source meter is used to provide the external bias, and the current is also recorded at the same time. The bias range is from 1 to 30 mV during the measurement. The current–voltage curves under dark condition (solid) and under a 90◦ FOV 300-K background (dash) at the temperatures from 3.15 to 20 K are shown in Fig. 4.16. Because thermionic emission and field-assisted tunneling were much stronger than interwell tunneling within the experiment temperature range, we did not observe any current bottom-out behavior (Schneider and Liu, 2006). As in Section 2. Tblip is a good figure-of-merit of a detector. The measured Tblip of V267 is 12 K. Sequential tunneling and thermionic emission are two major dark current mechanisms in GaAs/AlGaAs barrier structures (Levine, 1993), and the latter becomes dominant for thick barrier structures. From the I–V curves in Fig. 4.16A, the I–T curves have been obtained and shown in Fig. 4.16B. The dark current decreased by six to seven orders of magnitude in accordance with the thermally activated character of the thermionic emission (C ¸ elik et al., 2008) when the device was cooled from 20 K down to 3.15 K, which indicates that the use of the emission-capture model, combined with the 3D carrier drift model, is reasonable for describing the dark current of this detector. A steep drop of the I–T curves when the device temperature ≤12 K has been observed, which is consistent with the good performance when the device is operating at and lower than Tblip . Next, we will introduce the measurement and analysis the photocurrent spectra of 2 THz QWPs (V265 and V267). The measured photocurrent spectra of V267 at different bias voltages are given in Fig. 4.17A. The operating temperature is 3.15 K. The peak response is 3.2 THz, corresponding to 93.6-µm wavelength. Strong response also exists in the range from 3 to 5.3 THz, which can be used to characterize the THz radiation source in this region. In addition, the photocurrent spectra at different operating temperatures under 30-mV bias are also measured, see Fig. 4.17B. Upon increasing of the operating temperature, the photocurrent

229

Terahertz Semiconductor Quantum Well Photodetectors

Field (V/cm) 101

−100

−50

0

Current density (A/cm2)

100

T = 3.15, 4.2, 6.0, 8.0, 10, 12, 16, 20 K

Dark

100

50

Background

10−1 10−2 10−3 10−4 10−5 10−6 10−7 −30

−20

−10

0 10 Bias voltage (mV) (A)

20

30

100

Current density (A/cm2)

10−1 10−2 10−3 10−4 30 mV

10−5

20 mV

10−6

5 mV

10 mV 1 mV

10−7 10−8

4

8

12 Temperature (K)

16

20

(B)

FIGURE 4.16 (A) Current–voltage curves of V267 under dark condition (solid) and under a 90◦ FOV 300-K background (dash) at different temperatures; (B) Current–temperature characteristic measured at selected bias voltages.

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J. C. Cao and H. C. Liu

Wavelength (µm) 120 1.0

80

40

(A)

Photocurrent (arb. units)

V267 @ 3.15 K 0.8

32 mV 30 mV 25 mV 20 mV 15 mV 10 mV 8 mV

0.6 0.4 0.2 0.0

Photocurrent (arb. units)

1.0

(B)

0.8 V267 @ 30 mV 3.15 K 4.2 K 5.0 K

0.6 0.4 0.2 0.0 2

4

6

8 10 Frequency (THz)

12

14

FIGURE 4.17 Photocurrent spectra of V267 at (A) different bias voltages and (B) different operating temperatures.

response decreases. The shape of the spectra doesn’t change significantly because of the small temperature range of the measurement. Photocurrent spectra of V265 at different bias voltages at 3.5 K are shown in Fig. 4.18. It can be seen that the peak response is 9.7 THz (wavelength of 31.0 µm). The theoretical peak response is around 7 THz for the structure of V265. The differences are caused by the phonon absorption of GaAs, leading to a dark region from 32 to 37 meV. Stronger photocurrent could be generated with higher bias, so the amplitude of photocurrent spectrum increases when the external bias is increased.

Terahertz Semiconductor Quantum Well Photodetectors

120

Wavelength (µm) 40

80

1.2

V265 @ 3.5 K 600 mV 400 mV 200 mV 100 mV 50 mV

1.0 Photocurrent (arb. units)

231

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FIGURE 4.18 Photocurrent spectra of V265 at different bias voltages at 3.5 K.

4.3. THz QCL emission spectrum measured by THz QWP We use a THz QWP to characterize the emission spectrum of a THz QCL (Tan et al., 2010). The shape and peak of the emission spectrum are acquired, and the relation of the emission power with driving current is estimated, from which the current density range of lasing and the threshold are obtained. The detection performance of THz waves from the THz QCL by THz QWP is also studied at different temperatures. We found that THz QWP is a good detector in characterizing the emission spectrum of THz QCL. The emission spectrum is an important characterization of a laser. Usually to measure the emission spectrum of a THz QCL, a Fourier Transform Spectrometer is used. To reduce the absorption by the water vapor, the spectrometer should be evacuated. A bolometer operating at the liquid helium temperature is often used to measure weak signal. In this section, we will mainly introduce the measurement of the emission spectrum of a continuously THz QCL by a Fourier Transform Far-Infrared Spectrometer operating at linear scan mode. The structure of the active region of the THz QCL is given in the study by Li et al. (2009b), and the sample ID is B1316 PKG3. Because low temperature is required for the laser operation, we use a close-cycle cryostat to cool the laser. The lowest temperature is 9 K. The radiation of the THz QCL enters the FTIR through the windows of the cryostat and the spectrometer. The scan

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speed and the resolution of the FTIR are set to be 1.6 KHz and 0.25 cm−1 , respectively. The beam splitter is 6 µm Mylar, and the detector is DTGS-PE. The range of wave number is 100–160 cm−1 , and the THz QCL is driven by a DC bias at 10 K. We measured the emission spectra of the THz QCL at different driving currents and operation temperatures. THz QCL and THz QWP are both multiquantum well devices. Hosako et al. (2007) suggested that THz QWP could be used to detect the emission of THz QCL. In the following, we will use a THz QWP to characterize the emission spectrum of a THz QCL. Before the characterization of THz QCL using THz QWP, we discuss the feasibility from the spectra (Tan et al., 2010). The photocurrent spectrum of the THz QWP at 3.15 K under the illumination of a Globar is shown in Fig. 4.19. In order to compare with the emission spectrum of the THz QCL, the photocurrent signal is normalized, the inset shows the same spectra on an expanded range. It can be seen that the response peak of the THz QWP is 3.2 THz. The response at 4.13 THz is about 67% of the peak, and strong response occurs in the range of 3–5.3 THz

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FIGURE 4.19 Comparison of the photocurrent spectrum of the THz QWP and the emission spectrum of the THz QCL. The operation temperatures are 3.15 and 10 K for THz QWP and THz QCL, respectively (Tan et al., 2010).

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(normalized amplitude ≥40%). The four emission peaks of the THz QCL are 4.022 THz (134.27 cm−1 ), 4.058 THz (135.48 cm−1 ), 4.094 THz (136.68 cm−1 ), and 4.130 THz (137.89 cm−1 ). The emission peaks are all in the region in which the curve of the response of the THz QWP is relatively flat. Moreover, the responsivity of the THz QWP is about 0.4 A/W (Luo et al., 2005), which is comparable with the mid-infrared QWIP with similar structures (Levine, 1993). Therefore, the characterization of THz QCL with THz QWP is practicable. The characterization by THz QWP is similar to that by DTGS-PE. We simply replace the DTGS-PE with the THz QWP as the FTIR system detector. The I–V curve and the L–I curve of the THz QCL are shown in Fig. 4.20 (Tan et al., 2010). It can be seen that the current density range of lasing and the threshold are the same as those measured by the DTGS-PE. The threshold is 630 A/cm2 . The main differences of the L–I curves are because of the electrical noise. The area marked by pattern is the multipeak operating region. The results indicate that the performance of the THz QWP in characterizing the emission spectrum of the THz QCL is comparable with the DTGS-PE. Improvements could be done on reducing the electrical noise. The emission spectra of THz QCL working at different driving current are shown in Fig. 4.21, where the solid line and the dashed line correspond Current density (A/cm2)

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FIGURE 4.20 The I–V curve (solid line) of the THz QCL and the P–I curves from THz QWP (dashed line) and DTGS-PE (dash-dot line), respectively (Tan et al., 2010).

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FIGURE 4.21 The emission spectra of the THz QCL taken by the THz QWP (dashed line) and the DTGS-PE (solid line) (Tan et al., 2010).

to measurements taken by DTGS-PE and THz QWP, respectively. The spectra are normalized and shifted in vertical axis for clarity. The spectrum in dashed line is sharper than the one in solid line. The difference may be from the artifact caused by the difference in preamplifiers and circuits. The multipeaks and the blue shifts by the Stark effect are seen by both detectors (Bastard et al., 1982; Williams et al., 2003). The results above show that THz QWP is good at characterizing the performance of THz QCL, and its high-speed response is much superior to traditional detectors. The measurements above establish the basis of wireless communication based on THz QCLs and THz QWPs and the time-resolved spectrum applications.

5. APPLICATION: THz FREE SPACE COMMUNICATION It is anticipated that many new applications in the THz spectrum are possible if simple compact sources and detectors were readily available. Many groups around the world are in the process of developing semiconductor

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FIGURE 4.22 The emission spectra of the THz QCL taken by the THz QWP working at different temperatures (Tan et al., 2010).

sources and photodetectors for the THz spectrum (Belkin et al., 2008; Kumar et al., 2009; Liu et al., 2008; Scalari et al., 2009). A demonstration of a sub-THz analog transmission system was reported by Jastrow et al. (2008) at 300 GHz using an electronic system. In this section, we present a demonstration of an all photonic terahertz communication link operating at 3.8 THz using a quantum cascade laser and quantum well photodetector (Grant et al., 2009). The link consists of a quantum cascade laser transmitter and a quantum well photodetector receiver. The link was used to transmit audio frequency signal through 2 m of room air. Carrier strength at the photodetector was 100 times greater than the noise level. Figure 4.23 is a schematic representation of the link. At the left, a quantum cascade laser housed in a vacuum dewar provides 3.8-THz radiation, which is collected and collimated by a parabolic mirror labelled M1. The laser transmitter was constructed from a multiple quantum well structure described earlier (Luo et al., 2007) with a 1-mm-long and 100-µm-wide surface plasmon waveguide formed on a semi-insulating GaAs substrate. A reflecting mirror was formed on the back facet by first coating the facet with an aluminium oxide insulator, to prevent short circuiting the electrodes,

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AM radio

MP3 player

LNA 77k

MOD

M1

M2

2 m path

FIGURE 4.23 Schematic of link showing quantum cascade laser at left and quantum well photodetector on right (Grant et al., 2009).

followed by evaporating a gold layer over the facet. The exit coupler of the laser is the cleaved surface. M1 is a 50-mm focal length off-axis parabolic reflector, whereas M2 is 76-mm focal length. Both mirrors are 50 mm in diameter. The laser was mounted on an aluminum cold finger in a liquid nitrogen dewar with the laser facet approximately 2 mm from the lowdensity polyethylene window. This permitted collecting a large fraction of the diverging beam with an off-axis parabolic mirror. A temperature sensor was mounted near the base of the QCL die and showed that the base temperature was maintained at 78 or 77 K. Care was required to align the four optical components, the QCL, the QWIP, and the two mirrors. The initial alignment was performed in air without the polyethylene windows. The photodetector was displaced by 2 mm using a translation stage and a visible laser beam was passed through the photodetector location to the two mirrors and then to the laser. Crude alignment was performed to ensure that the laser was near the focus of each mirror and that the visible light was arriving at the QCL facet. The optical coupling was quite sensitive to the position of the QCL which was rather small. Sometimes, no coupling could be established after an optical component was moved, and we used a piece of 50-mm diameter Plexiglass pipe 200 cm long as a light guide. The QCL could then be focused on the end of the light pipe, which was only 10 cm away from the mirror. After a signal was established, the light guide could be removed, and there was

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still sufficient signal to allow optimizing alignment of the long path. The position of the larger QW detector was not as critical. A custom-made electronic pulse generator was fabricated to provide low-duty cycle pulses of amplitude VH . The maximum VH required was 17 V at a current of 2.6 A for a peak power of 43 W. The pulse width above threshold was approximately 8 ns. Pulse repetition frequency was 455 kHz. Total power injected was calculated from the recorded voltage waveform and integrated to give an average power of 0.16 W or a peak-to-average ratio of 268 : 1. The generator contained power amplifiers that forced VH to follow the modulation voltage which we wanted to transmit, typically a sine wave at 500 Hz or music. The optimum conditions for VH and modulation amplitude (VM ) were found by transmitting a 455-kHz carrier modulated by a 500-Hz sine wave while measuring the second harmonic at 1 kHz. Clipping by modulating less than threshold or more than saturation rapidly increased the second-harmonic content of the detected signal. It was found that the best VM was about 1 V peak-to-peak with VH of 15 V. Numerical calculation of the Fourier transform of the expected photocurrent indicated that there should be a DC term, a modulation term, and a large number of replications of the pulse repetition frequency. Each replication would have a carrier plus modulation side-bands. The DC term is proportional to the average laser power and for the low-duty cycle pulses that we are using, the carrier amplitudes are equal to each other and to the DC term. This is a central point in the demonstration. Even though the laser was pulsed, the Fourier transform of the photocurrent contains useful continuous-wave (CW) components with amplitude equal to the average photocurrent. Further, the modulation side-bands contain the Fourier transform of the time variations of VM . Experimentally, the 500-Hz basic modulation term could be easily detected using a bolometer and lock-in amplifier. The 455-kHz pulse repetition frequency was also easily detected using the QWIP and could be observed on a spectrum analyzer as a typical amplitude modulated waveform. Figure 4.24 shows a typical nonmodulated spectrum measured at the pulse repetition frequency after the transimpedance amplifier. The left inset in Fig. 4.24 is an expanded spectrum of the laser measured using an Fourier transform infrared (FTIR) spectrometer. Both were measured while the QCL was being pulsed at 455 kHz with no modulation. Although none of the modulation can be resolved using the FTIR, the central emission line width is at the FTIR resolution of 0.04 wavenumbers or 1.2 GHz. The right inset shows the QW photodetector spectral responsivity overlaid with the 126 wavenumber laser spectrum at the left. The RMS photocurrent at the 455 kHz is two orders of magnitude greater than the noise level. The noise level from 450 to 460 kHz originates in the custom-made laser driver electronics and is not a fundamental limitation of the devices. Finally, the

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Photocurrent (nA)

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FIGURE 4.24 Spectrum of photocurrent measured after low-noise amplifier with insets showing laser spectrum at left and photodetector responsivity at right. Photodetector spectrum measured at temperature of 12 K (Grant et al., 2009).

signal could be coupled to the antenna input of an AM radio (Sony ICF 2010) and music recovered. The low-noise amplifier (LNA) has a transimpedance amplifier, a filter, and a buffer amplifier, as well as the photodetector bias circuit. The capacitance of the cable from the cold section to room temperature was measured as 160 pF plus the large QW photodetector capacitance of 88 pF caused instability in high-speed amplifiers that we initially tried to use. A general purpose operational amplifier with a 12-MHz gain bandwidth product could be made stable in a 1-k transimpedance configuration. This was followed by a 455-kHz center frequency, 10-kHz bandwidth filter, and a line driver amplifier to provide an effective transimpedance of 10 k. Detector bias was introduced at the input of the transimpedance amplifier. Typically, our measurements were performed with −20 mV of bias and 2 µA of total photodetector current. DC photocurrent was always less than 0.1 mA, the resolution of the meter, which was used for monitoring bias current. Using the QW detector responsivity measured in (Luo et al., 2005) of 1 A/W and the property of the Fourier transform of a narrow pulse (with its low harmonics having the same amplitude as the average), the average optical power can be determined. The recovered 455-kHz carrier current was 18 nA RMS from which we calculate the average optical power to be 1.414 × 18 = 25 nW. Although there are many atmospheric absorption bands known in the THz frequency region, we observed very little impairment of our link owing to atmospheric absorption. The center frequency of the laser was

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3787 GHz as determined by FTIR measurement of the emission. Empirically, we measured the air in our laboratory in Ottawa, Canada, and observed that this frequency is at the upper edge of an essentially transparent region of the electromagnetic spectrum that extends from 3700 to 3789 GHz. This band is 89 GHz wide and is only one of many which we observe to be essentially transparent in room air. We point out that while there are many absorption bands because of water vapor, as much as 50% of the spectrum space we observe is transparent or of low absorption. We used a 50-mm diameter Plexiglass pipe as a gas cell and compared transmission through room air with transmission through dry nitrogen and found no difference. The only strong absorber that we observed was liquid water.

6. SUMMARY We have introduced the principle, simulation and design method, and device performance of THz QWPs. At the present time, various incoherent detection methods (such as bolometer) and several coherent detection methods (such as THz TDS) are well developed and are used in spectroscopy and imaging fields. Because of easy production of high quality and large area uniform THz QWP materials, THz QWPs have great advantages in high sensitivity and high resolution detection, especially in the construction of focal plane arrays. THz QWPs are also useful in the detection of toxic materials and THz wireless communication. Because the characteristic absorption lines of most molecules are in THz range, under a normal continuous light source (such as high-voltage mercury lamp), monitoring of toxic materials can be achieved by THz QWPs because of their high spectrum resolution and high response speed. The monitoring ability can be improved by multicolor THz QWPs, and multiple identifications at the same time can also be achieved. It can be expected that the development of high-performance, single-element detectors and focal plane arrays will enable the THz communication and THz detection applications.

ACKNOWLEDGMENTS We thank our colleagues and coworkers for their contributions, especially R. Zhang, Z. Y. Tan, X. G. Guo, Y. L. Chen, and F. Xiong in SIMIT, and M. Buchanan, R. Dudek, E. Dupont, M. Graf, P. D. Grant, H. Luo, A. J. SpringThorpe, C. Y. Song, and Z. R. Wasilewski of National Research Council Canada.

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Ryzhii, V. (1997). J. Appl. Phys. 81, 6442. Scalari, G., Walther, C., Fischer, M., Terazzi, R., Beere, H., Ritchie, D., and Faist, J. (2009). Laser & Photon. Rev. 3, 45. Schneider, H., Fleissner, J., Rehm, R., Walther, M., Pletschen, W., Koidl, P., Weimann, G., Ziegler, J., Breiter, R., and Cabanski, W. A. (2003). Proc. SPIE 4820, 297. ¨ Schneider, H., Koidl, P., Schonbein, C., Ehret, S., Larkins, E. C., and Bihlmann, G. (1996). Superlattices Microstruct. 19, 347. Schneider, H., and Liu, H. C. (2006). “Quantum well infrared photodetectors: Physics and applications.” Springer, Berlin. Schneider, H., Liu, H. C., Winnerl, S., Song, C. Y., Walther, M., and Helm, M. (2009). Opt. Express 17, 12279. ¨ Schneider, H., Schonbein, C., Walther, M., Schwarz, K., Fleissner, J., and Koidl, P. (1997). Appl. Phys. Lett. 71, 246. ¨ Schonbein, C., Schneider, H., Bihlmann, G., Schwarz, K., and Koidl, P. (1996). Appl. Phys. Lett. 68, 973. Shen, Y. R. (1984). “The principles of nonlinear optics.” John Wiely & Sons, New York. Spitzer, W. G., and Panish, M. B. (1969). J. Appl. Phys. 40, 4200. Stillman, G. E., Wolfe, C. M., and Dimmock, J. O. (1970). J. Phys. Chem. Solids 31, 1199. Tan, Z. Y., and Cao, J. C. (2008). Physics 37, 199. Tan, Z. Y., Guo, X. G., Cao, J. C., Li, H., and Han, Y. J. (2010). Acta Phys. Sin. 59, 2391. Tan, Z. Y., Guo, X. G., Cao, J. C., Li, H., Wang, X., Feng, S. L., Wasilewski, Z. R., and Liu, H. C. (2009). Semicond. Sci. Technol. 24, 115014. Thibaudeau, L., Bois, P., and Duboz, J. Y. (1996). J. Appl. Phys. 79, 446. Todorov, Y., and Minot, C. (2007). J. Opt. Soc. Am. A 24, 3100. Tonouchi, M. (2007). Nat. Photon. 1, 97. West, L. C., and Eglash, S. J. (1985). Appl. Phys. Lett. 46, 1156. Williams, B. S., Callebaut, H., Kumar, S., Hu, Q., and Reno, J. L. (2003). Appl. Phys. Lett. 82, 1015. Xiong, F., Guo, X. G., and Cao, J. C. (2008). Chin. Phys. Lett. 25, 1895. Yang, J., Ruan, S. C., and Zhang, M. (2008). Chin. Opt. Lett. 6, 29. Yang, Y., Liu, H. C., Shen, W. Z., Li, N., Lu, W., Wasilewski, Z. R., and Buchanan, M. (2009). IEEE J. Quantum Electron. 45, 623. Załuzny, M. (1993). Phys. Rev. B 47, 3995. ˙ Zhang, J., and Potz, W. (1990). Phys. Rev. B 42, 11366. Zhang, R., Guo, X. G., and Cao, J. C. (2011). Acta Phys. Sin. 60, in press.

CHAPTER

5 Homo- and Heterojunction Interfacial Workfunction Internal Photo-Emission Detectors from UV to IR A. G. U. Perera∗

Contents

1. Introduction 1.1. Introduction to infrared detectors 1.2. Semiconductor junctions 1.3. Internal and external photoemission 2. Free Carrier–Based Infrared Detectors 2.1. Types of HIP detectors 2.2. Workfunction dependence on doping concentration above the Mott transition 2.3. Theoretical modeling of light propagation in the multi-layer structure 2.4. Responsivity 2.5. Dark and noise current 2.6. Homojunction detectors 2.7. Light–heavy hole transition effects 2.8. Heterojunction detectors 2.9. Dualband detectors 3. Inter-Valence Band Detectors 3.1. Uncooled SO detectors 3.2. LH-HH transitions for long-wavelength infrared detection 3.3. SO-HH transitions for spectral response extension 3.4. Modeling and optimization of SO detectors

244 244 245 246 247 247 251 254 255 256 258 262 263 270 277 280 284 286 289

∗ Email: [email protected], Tel: (404)413-6037, Fax: (404)413-6025

Semiconductors and Semimetals, Volume 84 ISSN 0080-8784, DOI: 10.1016/B978-0-12-381337-4.00005-X

c 2011 Elsevier Inc.

All rights reserved.

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4. Conclusion 5. Nomenclature Acknowledgments References

295 297 298 298

1. INTRODUCTION 1.1. Introduction to infrared detectors Infrared (IR) radiation was discovered accidently by Sir Frederick William Herschel (1738–1822), a musician and an astronomer who also discovered the Uranus. Since then, various types of IR detectors were studied (Case, 1917; Johnson, 1983; Levinstein, 1965; Rogalski, 2005; Sclar, 1976). Initial efforts focused on detectors based on thermal effects, the thermometers (Herschel, 1800), and the bolometers which are sensitive to all IR wavelengths but with low sensitivity. The Second World War dramatically increased the interest in IR detection in which photon detectors were developed to improve the performance. Various extrinsic semiconductor (e.g., Si:P and Ge:Zn) photon detectors were developed to extend the detection wavelength beyond the wavelength of intrinsic photoconductors (Kruse, 1981). Doped materials, e.g., germanium doped with copper, zinc, or gold (Levinstein, 1965), demonstrated sensitivities in the long-wavelength infrared (LWIR) range (8–14 µm) and the far infrared (FIR) region. Novel growth techniques such as molecular beam epitaxy (MBE; Cho (1979)) and metal organic chemical vapor deposition (MOCVD; Manasevit (1968)) in the twentieth century allowed band-gap tailoring to develop novel IR detectors that transformed the detector technologies. Now the infrared detectors are used in various sectors not only in defense and security but also in manufacturing, medicine, environment, and various other testing/monitoring applications. In this chapter, the focus is on detection using internal photoemission across an interfacial workfunction in a semiconductor homo- or a heterojunction architecture. Although quantum well structures also have a junction and an interface, the energy difference between the two states associated with the transitions are because of the quantization effects in the well material but not at an interface. The detector concepts discussed here can be applied to any semiconductor material where an interface can be formed. Varying the interfacial workfunction will lead to different energy photons to be detected giving rise to different threshold wavelength (λt ) detectors. This idea will be extended to show how multiband detection is achieved in a single detector element. In addition, controlling the operating temperature and the responsivity by adjusting the interfacial workfunction will also be discussed in connection with the spin-orbit

Number of publications

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UV detectors IR detectors

600

400

200

2008

2006

2004

2002

2000

1998

1996

1994

1992

0

Year

FIGURE 5.1 Number of journal publications reported in each year (January to December) as of July 2009 based on a search in the ISI Web of Knowledge database on the term “UV detector(s)” and “IR detector(s)” in the “topic” field.

split-off detectors. A search on the term “UV detector(s)” and “IR detector(s)” in the “topic” of the ISI Web of Knowledge journals indicated a trend showing increasing interest with more than 200 articles per year, published throughout the period as shown in Fig. 5.1. In the last decade, on average, more than one article per day was published which has “UV detector(s)” or “IR detector(s)” in the title. Hence, this clearly shows that the detector development efforts are still continuing in earnest.

1.2. Semiconductor junctions In semiconductor physics a junction is formed when two materials are in contact. The term junction refers to the boundary interface where the two semiconductors meet. If the two materials with the same band gap are in contact, what is known as a homojunction is formed. However, these two materials can still have differences such as a p-type material and an n-type material forming a p–n junction or an n–p–n transistor. This development has been the dawn of the semiconductor age starting with Bardeen, Schokley, and Brattain discovery, leading to a Nobel Prize (Bardeen, 1956). When the two materials have different band gaps, the junction is termed a heterojunction. The advent of the novel growth techniques, such as MBE (Cho, 1979) and MOCVD (Manasevit, 1968), and so on, has lead to the development of various heterojunction devices revolutionizing the semiconductor industry. These techniques allow sharp abrupt junctions of various different material systems, leading to various semiconductor devices, e.g., semiconductor lasers, solar cells, detectors, transistors, and

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so on. One of the significant factors is actually the band offset, which is produced by the difference in either the doping levels in two materials composing a homojunction and/or the band gaps in a heterojunction. The carriers will see a band-offset when transporting across a homo- or hetero-semiconductor junction. Under illumination, the carriers can excite into higher energy states giving a higher probability to pass through the energy barrier. The use of homo- or heterojunctions with a doped emitter leads to a (photocurrent) response to the incident light because of photon absorption in the emitter and escape across the barrier. The collection of excited carriers confirms the detection of the incoming photon. Adjusting the energy barriers can tailor the detection wavelength. Detector development including a variety of spectral ranges will be discussed in this chapter.

1.3. Internal and external photoemission Photoemission, first observed and documented by Hertz in 1887, has been recognized as an important step in the development of devices, earning Albert Einstein the Nobel prize in 1929 for his work on external photoemission, which is also known as photoelectric effect (Einstein, 1905). In the classic photoelectric effect, the photons gets absorbed and the energized carriers come out or get ejected from matter and hence can be classified as external photoemission. In this process, there is a threshold energy that is needed to eject the carriers out. With higher incident energy of the light, carriers will also have a higher energy. Once the photons are absorbed, the carriers come out from the original state and overcome an energy barrier but still stay in the material. Then it can be categorized as internal photoemission. For the carriers to come out of the original state, there is a specific energy requirement, which is historically known as the workfunction (http://hyperphysics.phy-astr.gsu.edu/hbase/mod2.html). At a semiconductor junction, there is also an interface, which is the boundary between the two sections. In general, there is an energy gap between the two materials which could either be resulting from the band gap difference in the case of a heterojunction or band offset coming from band gap narrowing because of doping the material or a combination of the two. This energy gap at the interface of the two semiconductors can be used to detect photons by matching that energy difference with the incoming photons which in turn will provide the required energy for the carriers to overcome the energy gap. The photoexcited carriers, if collected by the collector, provide the photocurrent, whereas thermally excited carriers will give rise to the dark current which is not useful in the detection and usually needs to be kept low. However, a dark current also plays a role in replenishing the depleted carriers which also allows the detector to operate continuously.

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2. FREE CARRIER–BASED INFRARED DETECTORS Internal photoemission (IP) detectors were first proposed by Shepherd et al. (1971) in Schottky barrier structures. Since then, several different types of internal photoemission detectors have been demonstrated (Perera, 2001; Perera et al., 1995; Shepherd, 1992). Among them are metalsemiconductor Schottky barrier IR detectors, such as PtSi/Si detectors (Kosonocky, 1992) operating in 3–5 µm range; semiconductor heterojunction IR detectors, Gex Si1−x /Si detectors (Lin and Maserjian, 1990; Tsaur et al., 1991) developed for 8–14 µm or even longer wavelengths; and a degenerate Si homojunction detector (Tohyama et al., 1991), which has a response in the 1–7 µm range. The absorber and photoemitter can be a metal, a metal silicide, or a degenerate semiconductor in the Schottky barrier, silicide, and degenerate homojunction detectors, respectively. A similar detector concept was proposed and demonstrated by Liu et al. (1992), using Si MBE multilayer structures in the long-wave infrared (LWIR) range. However, the basic operating mechanism is the same, and following the terminology of Lin and Maserjian (1990), all of these detectors including the free carrier–based detectors can be described as Heterojunction or Homojunction Internal Photoemission (HIP) detectors.

2.1. Types of HIP detectors A basic HIP detector consists of a doped emitter layer and an undoped barrier layer. In the homojunction detectors, the absorber/photoemitter will be a doped semiconductor. The doping will cause the bandgap to narrow, forming a barrier at the interface with an undoped layer of the same material. The height and the shape of the barrier will depend on the doping level in the HIP, which can be divided into three types (typeI, -II, and -III; Perera and Shen (1999); Perera et al. (1995)). These basic types of detectors operate similarly for both n- and p-doping (except for the carriers; electrons in n-type and holes in p-type) and will be described here for p-type detectors. Significant effective band-gap shrinkage has been observed for heavily doped p-type Si (Dumke, 1983), Ge (Jain and Roulston, 1991), and GaAs (Harmon et al., 1994). Better carrier-transport properties of GaAs such as higher mobility will translate into a higher gain, which may produce improved performance for these types of detectors. In the heterojunction case, the only difference is the use of different bandgap materials for the emitter and barrier, which will introduce an additional component for barrier formation. p+

2.1.1. Type I HIP detectors: Na < Nc (EF > Ev ) The type I detectors are characterized by an acceptor doping concentration (Na ) in the p+ -layer high enough to form an impurity band but still

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less than the Mott critical value (Nc ), so the Fermi level (EF ) is located in the impurity band at low temperatures. The incident FIR light is absorbed by impurity photo-ionization, with a threshold workfunction given by p+

p+

1 = EF − Ev , where Ev is the valence band edge in the p+ -layer. The photoexcited holes are collected by an electric field formed in the i-layer because of an external bias. Type I HIP detectors are analogous to semiconductor photoemissive detectors (Escher, 1981) in their operation, which can be described by a three-step process (see Fig. 5.2A): (1) holes are photoexcited from impurity band states into valence band states; (2) phonon relaxation rapidly thermalizes the photoexcited holes to the top of the valence band, and then diffuses to the emitter/barrier interface, with the transport probability determined by the hole diffusion length; and (3) the holes tunnel through an interfacial barrier (1Ev ), which is because of the offset of the valance band edge caused by the bandgap-narrowing effect and are collected by the electric field in the i-region. The collection efficiency will depend on the tunneling probability and hence on the i-region electric field. The threshold wavelength (λt ) can be tailored with the doping concentration to some extent because with the increase p+

i

p+ Ev

Impurity band EF hn

F

Δ

p+

Ev

i

h+

Δ hn

Ev

Thermal diffusion (A)

i

EF

Tunneling ΔEv

p+ ΔEv

F

(B) p++

i(p−)

p−

bias EF hn

h+ (C)

FIGURE 5.2 Energy band diagrams for the three different types of HIP detectors for p+

the p-doped case. (A) Type I: Na < Nc (EF > Ev ); (B) Type II: Nc < Na < N0 p+

i

Ev

h+

(Ev > EF > Eiv ); (C) Type III: Na > N0 (EF < Eiv ). Here, Nc is the Mott critical concentration and N0 is the critical concentration corresponding to 1 = 0. In (A) and (B), the valence band edge of the i-layer is represented by a dotted line for Vb = V0 (flatband) and by a solid line for Vb > V0 . Reused with permission from Perera (2001). Copyright 2001, Academic Press.

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of doping concentration, the impurity band broadens and the band edge moves rapidly toward the valance band (Jain et al., 1991). The impurity compensation effect (Perera et al., 1995), which was neglected in the previous discussion, can induce an electric field in the p+ -layer. This field may extend over a wide region of the p+ -layer for very small compensating concentrations. This is the case of blockedimpurity-band (BIB) detectors (Petroff and Stapelbroek, 1986; Szmulowicz and Madarasz, 1987), for which the photoexcited carrier–collection mechanisms ((2) and (3) above) are replaced by field-induced sweep out of the carriers. In contrast to the type I HIP detector, the BIB detector resembles a reverse-biased photovoltaic detector in its operation, with the collection efficiency in the electric field region approaching 100%. However, if the compensated acceptor concentration is high in the majority of the p+ layer, there is no electric field induced when an external voltage is applied, except for a very small depletion region near the p+ -i interface. In this case, the photoresponse mechanism can still be described by the processes developed above for type I HIP detectors. Initial development of Ge BIB detectors by Rockwell scientists (Petroff and Stapelbroek, 1986) led to the development of Si BIBs for LWIR region (15–40 µm). Lately, there has been work on developing GaAs-based BIB detectors (Reichertz et al., 2005; Reichertz et al., 2006; Haller and Beeman, 2002). In GaAs BIB detectors, the low donor-binding energy, giving rise to an impurity transition energy of ∼4.3 meV, is the key for terahertz detection. According to Reichertz et al. (2006), detection of terahertz radiation upto ∼300 µm (1 THz) was expected. However, the material quality in the barriers of BIB structures needs to be very high in order to obtain high performance. This has been one of the problems for GaAs BIB detectors, hence, only preliminary results are presently available. Recently, Cardozo et al. (2005) has reported high absorption of terahertz radiation near ∼300 µm (1 THz) for a GaAs BIB structure grown by liquid phase epitaxy. Also, the absorption coefficient drops to 50% of the maximum at ∼333 µm (0.9 THz). A list of several terahertz BIB detector details are given in Table 5.1. TABLE 5.1 Several terahertz BIB detectors along with their performances. Here, ft is the threshold frequency, λt is the threshold wavelength, λp is the peak wavelength, η is efficiency, and T is the operating temperature Reference Watson and Huffman (1988) Watson et al. (1993) Bandaru et al. (2002) Beeman et al. (2007)

Material System Ge:Ga Ge:Ga Ge:Sb Ge IBIB

ft (THz) 1.6 1.36 1.5 1.35

λt (µm) 187 220 120 222

λp (µm) 150 150 120 104

η (%) 4 14 — 1.2

T (K) 1.7 1.7 2 1.3

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p+

2.1.2. Type II HIP detector: Nc < Na < N0 (Ev > EF > Eiv ) For doping concentrations above the Mott transition, the impurity band merges with the valence band, and the p+ -layer becomes metallic. However, as long as the concentration does not exceed a critical concentration N0 , the Fermi level can still be above the valence band edge of the i-layer (EF > Eiv ) because of the bandgap-narrowing effect. The difference between the Fermi level and the valence band edge in the barrier then forms a workfunction 1d = EF − Eiv at the emitter/barrier interface as seen in Fig. 5.2B. The detectors operate by free-carrier absorption, followed by internal photoemission of the excited carriers and sweep out of the emitted carriers by an externally applied electric field. Because the workfunction in theory can be reduced to a small value as desired by adjusting the doping concentration, no restriction on λt was expected. However, λt was found to be limited by hole transitions (Perera et al., 2003). Although the freecarrier absorption in Type II HIP detectors is less than what is found in Schottky barrier detectors which they resemble, they have a higher internal quantum efficiency as a result of a lower Fermi level and increased hot electron scattering lengths. For heterojunction detectors, the only difference is in the formation of the barrier which has an additional component 1x from the band offset because of the material difference, making the total workfunction 1 = 1d + 1x . The basic absorption, photoemission, and collection will be the same as in the homojunction case.

2.1.3. Type III HIP detector: Na > N0 (EF < Eiv ) When the doping concentration is so high that the Fermi level is above the conduction band edge of the i-layer, the p+ -layer becomes degenerate. The space charge region causes a barrier to form at the p+ − i interface as a result of the electron diffusion, as shown in Fig. 5.2C. The barrier height depends on the doping concentration and the applied voltage, giving rise to an electrically tunable λt . This type of device was first demonstrated by Tohyama et al. (1991) using a structure composed of a degenerate n++ hot carrier emitter, a depleted barrier layer (lightly doped p, n, or i), and a lightly doped n-type hot carrier collector. As the barrier height decreases at higher biases, the spectral response shifts toward the longer wavelength, and the signal increases at a given wavelength. The photoemission mechanism of type III HIP detectors is similar to that of type II HIP detectors, with different response wavelength ranges and different operating temperature ranges resulting from differences in the barrier heights. The type II HIP detector is an FIR detector, and it usually operates at temperatures much lesser than 77 K. In contrast, the type III HIP detectors operate near 77 K and have responses in the MWIR and LWIR ranges (Shepherd, 1992).

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2.2. Workfunction dependence on doping concentration above the Mott transition When the doping concentration is above the metal-insulator transition (Mott transition) concentration value, the detector can be regarded as a metal photoemitter (type II detector). According to the material composition of the two regions of the detectors (i.e., emitter and barrier), the detectors can be further categorized as Homojunction Interfacial Workfunction Internal Photoemission (HIWIP) or HEterojunction Interfacial Workfunction Internal Photoemission (HEIWIP) detectors. The band offset produced by the doping difference alone in HIWIPs is because of the bandgap-narrowing effect, and this offers a detection capability in the FIR region. In contrast, the offset can be controlled by adjusting the bandgap difference between materials forming HEIWIPs. This is also the case of p-doped HEIWIPs using the absorption mechanism by hole transitions between inter-valence bands, showing the capability of uncooled operation in the MWIR spectral range as discussed in Section 3. 2.2.1. Barrier height variation in HIWIPs There are four major contributions to the bandgap narrowing because of doping (Jain et al., 1991): (1) the shift of the majority band edge as a result of the exchange interaction; (2) the shift of the minority band edge because of carrier–carrier interaction or electron–hole interaction; (3) the shift of the majority band edge due to carrier–impurity interactions; (4) the shift of the minority band edge due to carrier–impurity interactions. The majority band denotes the conduction or valence band in n- or p-doped materials, respectively. With increased doping, the enhanced contributions leads to shifting of the conduction (or valence) band edge downward (or upward) in the bandgap region. At the same time, the impurity band becomes broaden and asymmetrical. At a critical doping level, the conduction (or valence) and impurity bands merge making the semiconductor to behave as a metal (Mott transition). Above the Mott transition, with further increasing the doping concentration, the impurity band starts to shrink and finally becomes absorbed into the conduction band (Jain et al., 1991). It has been shown (Perera et al., 1995) that raising of the valence band edge 1Ev (lowering of the conduction band edge, 1Ec ) can be described using the high-density (HD) theory. HD theory (Jain et al., 1991) describes the behavior of heavily doped Si, GaAs and Ge to a fair degree of accuracy in the high-density regimes, i.e., above the Mott critical concentration, and gives reasonable results even at doping concentrations as low as 1018 cm−3 . The main result of this theory is that the electron–electron interaction (manybody effect) causes a rigid upward (downward) shift of the valence (conduction) band, 1Eex , which is also known as the exchange energy.

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The electron–impurity interaction causes an additional shift, 1Ei , and also distorts the density of states function. In this theory, the semiconductor is assumed to be uncompensated with completely ionized impurities so that the free carrier concentration is equal to the donor doping concentration Nd . In principle, this theory is valid close to 0 K. Jain and Roulston (1991) have derived a simple and accurate expression for the shift of the majority band edge, 1Emaj , that can be used for all n- and p-type semiconductors and for any doping concentration in the high-density regime. By introducing a correction factor to take deviations from the ideal band structure (anisotropy of bands for n-type material) into account the workfunction for the homojunction has been obtained (Perera and Shen, 1999). As seen in Fig. 5.3, as the hole doping concentration Na increases more than 1019 cm−3 , λt becomes sensitive to Na ; hence, only a small increase in Na can cause a large increase in λt . It should be pointed out that although the high-density theory is valid in the high-doping range (Na > Nc ), it can not be used for moderately doped semiconductors where Na is in the neighborhood of Nc (Jain et al., 1991). The metal-to-nonmetal transition and several properties of moderately doped semiconductors, such as the Fermi level position, the shape of density-of-states which is highly distorted in this case, cannot be modeled by this theory.

Wavelength (μm)

400

300

p-GaAs

λt

Exp. data λ t ΔEv

EF Δ VB

200

ΔEv EF

100 Δ 0 18

19 log(Na) (cm−3)

20

FIGURE 5.3 Doping concentration dependence of 1Ec (1Ev ), EF , 1, and λt , calculated using the high-density theory for p-type GaAs. The experimental λt obtained from p-GaAs HIWIP detectors are shown by solid circles. The dotted lines indicate concentration (3.2 × 1019 and 3.6 × 1019 cm−3 ) needed to obtain λt = 200 and 300 µm, respectively, at low bias. Reused with permission from Perera and Shen (1999). Copyright 1999, Springer.

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To determine the 1 versus Na relationship in the intermediate doping range, other theories, such as Klauder’s multiple scattering theory (Klauder, 1961), are needed. In theory, the workfunction 1d can be varied almost close to zero by controlling the doping concentration giving rise to wavelength tailorable HIWIP detectors. 2.2.2. Barrier height variation in HEIWIPs HEIWIP detectors which combine the free-carrier absorption of the HIWIP (Homojunction Interfacial Workfunction Internal Photoemission) detectors (Shen et al., 1997) with the material composition of Quantum Well Infrared Photodetectors (QWIPs) have been experimentally demonstrated (Perera et al., 2001), covering the wavelength range from 4 to 124 µm. The typical HEIWIP detector structure consists of a p-doped GaAs emitter (absorber) region followed by an undoped AlGaAs barrier region. Although the structure appears similar to that of a p-type QWIP, the emitter/absorber in a HEIWIP is thicker than the well of a QWIP. As a result, the carriers form a three-dimensional distribution in HEIWIPs rather than being in quantized states as in a QWIP. The basic idea of HEIWIP detectors is to add the valence band offset for the GaAs/AlGaAs interface to the offset from the doping (NA ) in the emitters. The contribution from the doping (1d ) is the same as for HIWIPs. The Al fraction contribution is taken as 1Al = (x ∗ 530) meV where x is the Al fraction. The total barrier at the interface is then 1 = 1d + 1Al . λt can be determined directly from λt = 1.24/1, where λt is in micrometer and the workfunction 1 is in electron volts. A practical lower limit for the Al fraction is around x ≥ 0.005, which corresponds to λt ≤ 110 µm. Further increase in λt beyond 110 µm requires a change in the design because the minimum 1 is limited by the bandgap-narrowing 1d . One possible approach to avoid this limit is to use AlGaAs as the emitter and GaAs as the barrier (Rinzan et al., 2005b). In such a device, the bandgap narrowing in the doped AlGaAs is partially offset by the increased bandgap of the AlGaAs material relative to the GaAs, giving 1 = 1d − 1Al . For example, a λt = 335 µm detector would have an Al fraction of ∼0.01. The FIR absorption in AlGaAs is very similar to GaAs (Rinzan et al., 2005a) because of the very-low Al content giving performances similar to the devices with AlGaAs barriers. Another approach is to increase doping concentrations to reduce the bandgap-narrowing contribution. This has been done in n-type GaAs/AlGaAs structures (Weerasekara et al., 2007) leading to detectors with response out to 94 µm. The variation of λt with the Al fraction for n-type AlGaAs HEIWIPs and p-type HEIWIPs using both GaAs and AlGaAs emitters is shown in Fig. 5.4. The experimentally observed thresholds are represented by symbols, which will be discussed later.

300

1

100 10 p-GaAs emitter n-GaAs emitter p-AlGaAs emitter

10

100 1E-3

Threshold frequency (THz)

A. G. U. Perera

Threshold wavelength (µm)

254

0.01 0.1 Al fraction (x)

FIGURE 5.4 The variation of the threshold frequency with Al fraction for n-type HEIWIPs using GaAs emitters, and for p-type HEIWIPs with GaAs and AlGaAs emitters. The symbols represent the experimentally observed thresholds, which will be discussed later.

2.3. Theoretical modeling of light propagation in the multi-layer structure A semiconductor detector structure consists of multiple layers in which the light propagation can be described (Esaev et al., 2004a) using the transfer matrix method (Klein and Furtac, 1986) with each layers modeled by the complex refractive index and complex permittivity (Blakemore et al., 1982). By applying continuity conditions (the electric field and its derivative for transverse electric [TE] waves, or the magnetic field and its derivative for transverse magnetic [TM] waves) across the interfaces, one can deduce the following transfer matrix M connecting the incoming (E0 ), reflection (rE0 ), and transmission (tE0 ) light:

E0 rE0

= M·

tE0 0

=

M11 M21

M12 M22

tE0 , · 0

(5.1)

where E0 denotes the electric field. The reflection r and transmission t coefficients are calculated by r = M21 /M11 ;

t = 1/M11 .

(5.2)

The reflectance R and transmittance T of the complete structure were defined as R = |r|2 and T = (nout /nin )|t|2 (for TE) or T = (nin /nout )|t|2 (for TM), where nin and nout are the real component of refractive index of the media for light incoming and outgoing, respectively. Total absorption in the structure was calculated as the difference between unity and the sum of the reflectance and transmittance A = 1 − T − R. The depth to which the incident radiation penetrates into the layers, skin depth δ(λ), depends on the wavelength, doping concentration N, and

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Skin depth (µm)

1000 100

p = 1018 cm−3

10

p = 1019 cm−3

1

n = 1018 cm−3 n = 1019 cm−3

0.1 0

20

40 60 80 Wavelength (µm)

100

FIGURE 5.5 Skin depth for infrared radiation in GaAs with both n- and p-type doping of 1018 and 1019 cm−3 . The skin depth is relatively constant at long wavelength and increases rapidly at short wavelength. The feature between 8.5 and 7.5 THz (35 and 40 µm) is because of the reststrahlen effect. Skin depth is least for n-type material. Reused with permission from D. G. Esaev, Journal of Applied Physics, 96, 4588 (2004). Copyright 2004, American Institute of Physics.

effective mass of the free carriers. The variations of δ(λ) with wavelength for an n- and p-type GaAs layers with doping concentrations 1018 and 1019 cm−3 have been calculated (Esaev et al., 2004a) and are shown in Fig. 5.5. At shorter wavelength, δ(λ) is high and has a strong wavelength dependence, whereas at higher wavelength δ(λ) approaches a plateau. Hence, a thin emitter layer will be almost transparent to lower wavelength, providing a negligible contribution to the photocurrent. It is suggested that because of the shorter skin depth of n-type layers at the same doping concentration causing higher reflectivity than p-type, n-type layers are better for mirrors inside the structure, allowing selective increase of absorption of photons at desired wavelength (Esaev et al., 2004a), leading to enhanced detector response. A model for optimizing the response has been suggested (Zhang et al., 2002), with experimental confirmation of enhanced absorption in a device structure (Zhang et al., 2003).

2.4. Responsivity The responsivity of a photodetector at wavelength λ is given by (Esaev et al., 2004a) R = ηgp

q λ, hc

(5.3)

where h is Planck’s constant, η is total quantum efficiency, and gp is the photoconductive gain. The responsivity calculations included effects

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A. G. U. Perera

of photoexcitation of carriers in the emitter, hot carrier transport, thermalization, and photoemission into the barrier. Total quantum efficiency (Perera et al., 1995), which is the product of photon absorption ηa , internal photoemission ηi , and hot-carrier transport probabilities is given as ηt , η = ηa ηi ηt . The ηi , was described by an “escape cone” model (Williams, 1970), and ηt followed the Vickers–Mooney model (Vickers, 1971; Mooney and Silverman, 1985). The absorption probability is proportional to the imaginary part of the permittivity. In determining the absorption for use in responsivity, only the photoexcitation is included, and not the contributions from phonon generation. Radiation absorbed through optical phonon generation is dissipated in the crystal lattice, without producing any hot carriers, and hence does not contribute to the photocurrent. The absorption coefficient is related to the skin depth as α(λ) = 2/δ(λ). As shown in Fig. 5.5, δ(λ) for n-type GaAs is about 10 times lower than for p-type at doping concentrations of 1019 cm−3 for wavelengths longer than 8 µm. This increased absorption is because of the reduced carrier mass of the electrons compared with the holes. Details of the responsivity calculations can be found in the study of Esaev et al. (2004a).

2.5. Dark and noise current The dark current of a detector plays a major role in the device performance. Dark current variation with temperature allow the determination of the workfunction through Arrhenius plots (Sze, 1981). Dark current in the HEIWIP structure is a sum of the thermo-emission current over the barrier and the tunneling current through the barrier (Perera et al., 1995). The thermionic current in the HEIWIP structure can be described in the frame of the 3D carrier drift model (Kane et al., 1992). The measured and calculated dark currents and the 300 K photocurrent for a HEIWIP detector with a λt of 124 µm at various temperatures are shown in Fig. 5.6. As FIR detectors typically operate at low temperatures, the thermal noise is typically negligible in these detectors. Hence, the primary sources of noise in the devices are the shot noise from the injection of carriers into the detector at the contact barrier interface, and the generation– recombination (g–r) noise from the carrier capture and emission from trap states. In most cases, the shot noise will dominate the g–r noise at high frequencies and the noise current is related (Levine, 1993) to the mean current through the detector, I by: 2 Inoise = 4qIgn 1f

where gn is the noise gain and δf is the measurement bandwidth.

(5.4)

257

Homo- and Heterojunction Interfacial Workfunction

31 K 21 K

15 K

10−6

4.2 K 10−5

Exp

I/T3/2

Dark current (A)

10−2

Model

10−10 −1

10−7

300 K background

3 100/T 6

0 Bias (V)

1

FIGURE 5.6 Dark current at various temperatures for the HEIWIP detector. The dark current at 10 K is almost the same as for 4.2 K. Also shown is the 300 K background current (dashed line) indicating BLIP operation at 14 K. Reused with permission from Perera et al. (2001). Copyright 2001, American Institute of Physics.

The noise gain gn and photocurrent gain gp are given by (Ershov and Liu, 1999) gn =

1 − pc/2 1 − (1 − pc )N+1 + pc (N + 1) pc (N + 1)2 [1 − (1 − pc )N ]

(5.5)

1 pc N

(5.6)

gp =

where pc is the capture probability of a carrier traversing an emitter, and N is the number of such emitters. The ratio gn /gp varies from 0.5 to 1 when pc varies from 0 to 1 and N from 1 to infinity. Hence, the difference between them may be ignored in many applications, particularly if the capture probability is low. Typical noise current spectra (Perera and Shen, 1999) of a p-GaAs HIWIP FIR detector at 4.2 K for various forward bias values are presented in Fig. 5.7. Similar noise behavior was observed under reverse bias conditions. All the spectra display 1/f noise dependence at frequencies ( f ) less than 1 kHz and are independent of frequency at higher values. The 1/f noise power density is proportional to Idα with an α value of 2.05 ∼ 2.10. This type of behavior indicates that the origin of the 1/f noise could be interpreted in terms of a random fluctuation in the occupancy of the interface trap centers that can lead to generation–recombination (g–r)

258

A. G. U. Perera

Noise density Si (A2/Hz)

10−14 Bias (mV)

p-GaAs HIWIP T = 4.2 K

190 10−20

89 47 10

10−26

1/f 1

10

100 1000 1200 1400 1600 Frequency (Hz)

FIGURE 5.7 Measured dark current noise spectra of p-GaAs HIWIP far-infrared detector at 4.2 K for various forward biases. The dashed line represents the 1/f dependence of the noise power density Si . Reused with permission from Perera and Shen. (1999). Copyright 1999, Optical Society of America.

1/f noise (Jantsch, 1987). Two representative models of the 1/f noise have been proposed (Shklovskii, 1980; Luo et al., 1988). The noise measurements could also be used for gain determination (Levine, 1993). For frequencies above 1 kHz, the noise was independent of frequency and was dominated by shot noise. The determined gain increases rapidly with bias at low voltages and then saturates (Perera and Shen, 1999). This behavior is similar to the case of QWIPs (Levine, 1993). The highest value of g recorded for this detector was ∼0.95 (Perera and Shen, 1999) at a bias corresponding to the highest responsivity, in good agreement with the estimation of 0.984, by combining the experimental responsivity and quantum efficiency.

2.6. Homojunction detectors HIWIP detectors have been demonstrated based on different material systems. In general, the doping in the emitter of HIWIP detectors is higher than that of HEIWIP detectors. While p+ -Si/Si HIWIPs were developed (Perera et al., 1998) some times ago, p+ -GaAs/GaAs HIWIPs were started to be developed because of the rapid development and growth of GaAs. Presently, HIWIPs based on other materials, such as GaSb (Jayaweera et al., 2007), have also been tested; however, the progress of growth techniques plays a role for these new materials to be used for potential high-performance detectors. In HIWIPs, the active region consists of a

Homo- and Heterojunction Interfacial Workfunction

259

TABLE 5.2 A comparison of different HIWIP detectors. Here, ft is the threshold frequency, λt is the threshold wavelength, RP is the peak responsivity, λP is the peak wavelength, and D∗ is the detectivity Reference

Material System

ft (THz)

λt (µm)

RP (A/W) at λP

T (K)

D∗ (Jones)

Perera et al. (1998) Ariyawansa et al. (2006b) Jayaweera et al. (2007) Shen et al. (1997) Esaev et al. (2004b)

p+ -Si/Si p+ -Si/Si p+ -GaSb/GaSb p+ -GaAs/GaAs p+ -GaAs/GaAs

6.25 8.6 3.1 3.0 4.3

48 35 97 100 70

12.3 at 28 1.8 at 25 31 at36 3.1 at 34 7.4 at 34

4.2 4.6 4.9 4.2 4.2

6.6×1010 1.2×1011 5.7×1011 5.9×1010 3.6×1011

junction formed by a doped layer (emitter) and undoped layer (barrier) made of the same material. The primary detection mechanism in a HIWIP involves free-carrier absorption, internal photoemission across the barrier, and the carrier collection. The interfacial workfunction (1), which arises because of doping different in the emitter and the barrier, determines the terahertz threshold. Several HIWIPs are listed in Table 5.2. 2.6.1. p+ -Si/Si HIWIP detectors Si p-i-n diodes under forward bias has shown various infrared response thresholds from MWIR to FIR. A device (Perera et al., 1992, 1993) with a peak responsivity of 1.5 × 104 V/W at 30 µm showed a threshold of 57 µm, while another Si p-i-n diode (Perera et al., 1992) showed a response up to 220 µm at 1.5 K. Following this, a Silicon p-type HIWIP sample was specifically developed for FIR detection (Perera et al., 1998). The spectral response at 4.2 K measured at different forward biases and having a wide spectrum with high responsivity is shown in Fig. 5.8. The tailing behavior at short wavelengths reflects the nature of internal photoemission. The responsivity has a similar spectral shape and strong bias dependence for both polarities, increasing significantly with increasing bias. However, the bias cannot increase indefinitely as the dark current also increases with bias. Several sharp peaks were seen in the spectra under high biases, becoming stronger with increasing bias. At low biases, the photoconductivity is because of the usual photon capture by the impurity states, where λt of the response is determined by the energy gap 1. At high biases, for high-enough doping concentration, the wave functions of excited impurity states overlap, leading to hopping conduction among ionized dopant sites. These peak positions are in good agreement with the theoretical energies of transitions from the ground states to the first (2P0 ), second (3P0 ), and third (4P0 ) excited states (marked by arrows in Fig. 5.8; Perera et al., 1998). For this device, the λt was reported (Perera et al., 1993) as 50 µm at low biases, decreasing to around 90 µm at a bias of 0.79 V. The highest

260

A. G. U. Perera

Wavelength (µm) 50

20

B

20

10 Id (A)

Responsivity (A/W)

25

15

100

−1

10−7

(c)

10

10−13 −1

(b) ft

5

0 1 Bias (V)

(a) 0 15

6 Frequency (THz)

3

FIGURE 5.8 Spectral response of p-Si HIWIP FIR detector measured at 4.2 K under different forward (top positive) bias Vb (a) 0.377V, (b) 0.539V, and (c) 0.791V. A peak responsivity of 12.3 A/W is observed at 10.9 THz (27.5 µm) in curve (c). The sharp response peaks are associated with excited impurity states with the theoretical energy levels marked by arrows. The other minor features are because of the instrument response function against which the detector output was rationed. The inset shows the variation of the dark current, Id , with bias at 4.2 K. Reused with permission from Perera et al. (1998). Copyright 1998, American Institute of Physics.

responsivity reported was 12.3 ± 0.1 A/W at 27.5 µm and 20.8 ± 0.1 A/W at 31 µm. Hopping conduction can be clearly seen in the I–V data in the inset of Fig. 5.8, where the dark current increases rapidly with bias more than 0.75 V. The highest D∗ (6.6 × 1010 Jones for 4.2 K under a bias of 10 mV at 27.5 µm) occurred at low biases because the dark current increases rapidly with the bias. However, D∗ also increases slightly with the bias because of the rapid increase in responsivity, and finally decreases again because of the onset of hopping conduction. 2.6.2. p+ -GaSb/GaSb HIWIP detectors A p+ -GaSb/GaSb HIWIP detector structure responding up to 97 µm has also been reported (Jayaweera et al., 2007). In a separate publication (Perera et al., 2008), it has been reported that a similar GaSb-based HIWIP detector also responds with a flat response in the terahertz range (100–200 µm) as shown in Fig. 5.9. The sharp dip at ∼43 µm is because of reststrahlen absorption in GaSb. Based on the Arrhenius calculation, the activation energy was reported as 128 meV, which is in good agreement with the observed free carrier threshold of 97 µm. The flat response in the range 100–200 µm is relatively weak compared with the free carrier response, but

Homo- and Heterojunction Interfacial Workfunction

Responsivity (A/W)

101

Wavelength (μm) 100 150

T = 4.9 K

3V 2V 1V

100 10−1

ln(1/T3/2)

50

3.1 THz

−12 −13

261

200

Arrhenius calculation

−14 Δ=128 meV (97 μm) −15 0.03 0.04

0.05

1/T (1/K)

10−2 10−3 10−4 15

6

3 Frequency (THz)

1.5

FIGURE 5.9 The response of a p+ -GaSb/GaSb HIWIP detector in the 15–1.5 THz range at 1, 2, and 3 V bias voltages at 4.9 K. The arrow indicates the free-carrier response wavelength threshold at the 3.1 THz (97 µm). The noise curves at the bottom were obtained under dark conditions, and the dashed line shows the maximum noise level of the spectral response measurement setup. The Arrhenius curve, which translates to an activation energy of 128 meV (97 µm) is also shown in the inset. Reused with permission from Perera et al. (2008). Copyright 2008, Elsevier.

is an order of magnitude higher than the system noise level as shown in Fig. 5.9. Although the mechanism of this response has also not been established yet as in the case of terahertz response in GaN/AlGaN structure, this result also implies the possibility of developing GaSb/InGaSb terahertz HEIWIP detectors, which would provide flexibility in controlling the threshold with the In fraction. Based on the lower band gap offset between GaSb and InSb, it is clear that λt of 300 µm could be achieved, while keeping the In fraction in the practical range. Therefore, GaSb-based HEIWIPs would also be possible substitutions for GaAs, where high accuracy of the alloy fraction (Al fraction in AlGaAs) is needed to control the threshold.

2.6.3. p+ -GaAs/GaAs HIWIP detectors The spectral responses reported at different forward biases for a GaAs HIWIP sample consisting of 20 periods of 4 × 1018 cm−3 doped GaAs emitters and undoped GaAs barriers are shown in Fig. 5.10. This was the highest response as well as the longest λt (100 µm) reported for GaAs HIWIP detectors (Shen et al., 1997). The long tailing behavior in the long wavelength region reflects the nature of internal photoemission. This detector reported a peak response of 3.1 A/W for a bias of 192 mV, and

262

A. G. U. Perera

Wavelength (µm) 70

20

120

4

Responsivity (A/W)

1s

2p

p-GaAs HIWIP T = 4.2 K 192.0 mV 83.0 mV

2

32.0 mV 7.0 mV

0 15

5 Frequency (THz)

2.5

FIGURE 5.10 Spectral response measured at 4.2 K for a p-GaAs HIWIP detector with emitters doped to 8 × 1018 cm−3 at different forward biases. Reused with permission from Shen et al. (1997). Copyright 1997, American Institute of Physics.

the peak D∗ was 5.9 × 1010 Jones for a bias of 83 mV at 4.2 K and 34 µm (Esaev et al., 2004b).

2.7. Light–heavy hole transition effects Although, in principle, the barrier height can be reduced to any desired value by increasing the doping in the emitter, it was reported (Perera et al., 2003) that the transitions between the light and heavy hole states in detectors lead to a decrease in the expected λt . The measured and calculated values (1 and λt ) from HD theory as well as the values predicted from the light-heavy hole transitions are shown in Fig. 5.11. This calculation (Shen et al., 1998) used a modified Fermi level expression, which provides a correction for the difference in the values for the Fermi level determined by the conventional density of state calculation and the values determined by the experimental luminescence spectra (Jain and Roulston, 1991). From this correction, the effect on the workfunction was ∼5 ± 1 meV, as can be observed from a comparison between the curves in Figs. 5.3 and 5.11. The reported values of 1 were obtained using Arrhenius plots of the current versus temperature, whereas λt was obtained from the spectral measurements. For low-doping densities (<1019 cm−3 ), the predicted values of both

263

Homo- and Heterojunction Interfacial Workfunction

p-GaAs

Exp. data Calc from Δ Calc from Δmin

2.5

p-GaAs

10

3

Exp. data Calculated

18

ft (THz)

Δ(meV)

20

7.5

19 log(NA) (cm−3)

20

(A)

18

19 log(NA) (cm−3)

20

(B)

FIGURE 5.11 Plots of (A) calculated and measured (based on from Arrhenius analysis) workfunction 1 and (B) calculated and measured (from response spectra) ft versus doping in HIWIP detectors. The solid line indicates the results from the HD theory while the points (•) are the experimental results. Also shown in (B) are the threshold limit (+) calculated from the heavy–light hole transition. Reused with permission from Perera et al. (2003). Copyright 2003, Elsevier.

quantities were in good agreement with the measured values. However, at higher doping where λt was expected to increase, it remained nearly constant even though the measured 1 decreased as expected. The differences between spectral and Arrhenius results were explained (Perera et al., 2003) in terms of direct excitations from the heavy-to-light hole bands. For highly doped materials, the carriers excited directly into the light hole band can escape leading to reduced population in the heavy hole band, and hence a reduced λt . This is the reported cause for the limit on the effective threshold for p-type detectors even at high doping (Perera et al., 2003).

2.8. Heterojunction detectors In HIWIP detectors, the only way to adjust λt is through the doping concentration, which encounters difficulties in controlling the barrier height and extending the threshold to longer wavelength (Perera et al., 2003). This difficulty has led to the development of the HEIWIP detectors (Perera and Matsik, 2007) which use the Al fraction in one or both of the layers as an additional degree to tailor λt . The band diagram for two different types of p-doped HEIWIP detectors using GaAs and AlGaAs are shown in Fig. 5.12. The choice between these two types of detectors is determined by desired λt . The first type (Fig. 5.12A) is the standard HEIWIP detector, which uses doped GaAs emitters and undoped AlGaAs barriers. The contributions

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A. G. U. Perera

Undoped Alx Ga1–xAs barrier

p++-GaAs emitter

p++-Alx Ga1–xAs emitter

Δd Δx

Δ

(A)

Undoped GaAs barrier Δx Δd

Δ

(B)

FIGURE 5.12 (A) The band diagram for a HEIWIP detector using doped GaAs emitters and undoped AlGaAs barriers. The contributions from both the doping and the Al fraction will increase the workfunction. (B) The band diagram for a HEIWIP detector using doped AlGaAs emitters and undoped GaAs barriers. Here the contribution from doping increases the workfunction while the contribution from the Al fraction decreases it.

from the doping and Al fraction to the workfunction are both in the same direction, i.e., reducing the Al fraction can increase λt from a minimum of ∼2 µm for an AlAs emitter up to a limit of ∼110 µm for an Al fraction of 0.005. The upper limit is due to the Al fraction at which the Al starts to act as an isoelectronic dopant and does not produce a consistent change in the valence band. Although an Al fraction of zero is possible, that would correspond to the HIWIP case which had a limitation in λt . The second type of design uses doped AlGaAs as the emitter, and undoped GaAs as the barrier as shown in Fig. 5.12B. In this approach, the band offset from the Al fraction is used to reduce the band offset from the doping in the emitter. In this approach, the Al fraction must be kept small (x < 0.17) such that the band offset does not exceed the doping offset. In theory, this approach will allow the workfunction to be reduced down to zero. Several HEWIPs are listed in Table 5.3.

2.8.1. p-GaAs emitter/AlGaAs barrier HEIWIP detectors Results were reported (Perera et al., 2001) on a device structure consist˚ GaAs wells and 800 A ˚ Al0.02 Ga0.98 As barriers. ing of 20 periods of 158 A 18 −3 The wells were doped with Be to 3 × 10 cm . The response increased as the bias was increased up to ∼200 mV after which it remained relatively constant. Strong response was reported for wavelength less than 50 µm with a λt of 70 µm. The peak responsivity was ∼6 A/W √ at a wavelength of 32.5 µm. The specific detectivity (D*) was ∼2 × 1013 cm √ Hz/W (Jones), with a Noise Equivalent Power (NEP) of 1.4 × 10−15 W/ Hz (Perera et al., 2001).

Homo- and Heterojunction Interfacial Workfunction

265

TABLE 5.3 A comparison of different HEIWIP detectors. Here, ft is the threshold frequency, λt is the threshold wavelength, RP is the peak responsivity, λP is the peak wavelength, and D∗ is the detectivity Reference

Material System

ft (THz)

λt (µm)

RP (A/W) at λt (µm)

T (K)

D∗ (Jones)

Perera et al. (2001) Matsik et al. (2003) Matsik et al. (2003) Rinzan et al. (2005b) Weerasekara et al. (2007)

p+ -GaAs/ Al0.02 Ga0.98 As p+ -GaAs/ Al0.01 Ga0.99 As p+ -GaAs/ Al0.005 Ga0.995 As p+ -Al0.005 Ga0.995 As/ GaAs n+ -GaAs/ Al0.04 Ga0.96

4.3

70

6 at 32.5

4.2

2×1013

3.6

84

5.4 at 30.7

4.2

4×1010

3.3

92

5.9 at 30.7

4.2

3.6×1010

2.3

130

7.3 at 31

4.8

5.3×1011

3.2

93

6.5 at 42

6

5.5×108

Device structures with different Al fractions from 0.005 to 0.02 showing variations in the threshold from 92 to 68 µm have been reported (Matsik et al., 2003). The Al fraction was varied, with x = 0.02, 0.01, and 0.005, respectively, to adjust λt , with the expected barrier heights of 18, 13.5, and 11.2 meV, respectively. The responsivity results for the three samples at a bias field of 3.5 kV/cm for 4.2 K are shown in Fig. 5.13 with a strong response for wavelengths less than 50 µm. The inset shows the raw response normalized so that the response was 1 at the wavelength where the signal equaled the noise determined from the deviation of multiple measurements. The threshold values (indicated by the arrows) were λt = 65, 84, and 92 µm for samples with x = 0.02, 0.01, and 0.005, respectively. The responsivity at 30 µm was ∼5.6 A/W for samples with x = 0.02 and 0.01, and 6.0 A/W for x = 0.005. The quantum efficiency was 22% for x = 0.02 and D∗ was 4 × 1010 √ 0.01, and 25% for x = 0.005 at 30 µm. The 10 Jones (cm Hz/W) for x = 0.02 and 0.01 and 3.6 × 10 Jones for x = 0.005 at 4.2 K (Matsik et al., 2003). The variation of λt with the Al fraction for p-GaAs/Alx Ga1−x As detectors is summarized in Fig. 5.14. The experimental data from detectors using inter-valence band transitions is also included, which will be discussed in Section 3. 2.8.2. p-AlGaAs emitter/GaAs barrier HEIWIP detectors As discussed earlier, p-type HEIWIP detectors with GaAs emitters have a λt limit because of the limit on Al fraction. One approach to overcome this difficulty is to use AlGaAs emitters with a low aluminum fraction. Absorption measurements have been performed on doped AlGaAs films giving good agreement with the model for the absorption coefficient (Rinzan et al., 2004) as seen in Fig. 5.15A. The model was the same as for the GaAs absorption with the material parameters obtained by a linear interpolation

266

A. G. U. Perera

Wavelength (µm) 6

20

60

100

Responsivity (A/W)

log (Resp.)

10

Wavelength (µm) 60 100

1 5

Frequency (THz)

3 x = 0.02 x = 0.01 x = 0.005

0

15

5 Frequency (THz)

3

FIGURE 5.13 Experimental responsivity spectra for p-GaAs emitter/Alx Ga1−x As barrier HEIWIP detectors at 3.5 kV/cm obtained at 4.2 K. The only difference in the samples was the Al fraction which was x = 0.02, 0.01, and 0.005, respectively. The data shows an increase in λt with decreasing x. The sharp decrease near 8 THz is because of the reststrahlen effect. The inset shows a log plot of the raw response with all curves normalized to have the same noise level indicated by the horizontal line. The threshold (indicated by the arrows) variation, with λt = 65, 84, and 92 µm for samples with x = 0.02, 0.01, and 0.005, respectively, can be clearly seen. Reused with permission from Matsik et al. (2003). Copyright 2003, American Institute of Physics.

of the values for GaAs and AlAs. Based on these results, detectors using AlGaAs emitters were designed and results have been reported (Rinzan et al., 2005b) on a sample consisting of 10 periods of 3 × 1018 cm−3 ˚ thick Al0.005 Ga0.995 As emitters and 2000-A ˚ thick GaAs Be-doped 500- A barriers sandwiched between two contacts. The variation of 1 obtained from Arrhenius plots with the bias field for three devices with different electrical areas are shown in Fig. 5.15B. The 1 decreased from ∼17 meV at zero bias to 10.5 meV at 2 kV/cm (Rinzan et al., 2005b). The source of this decrease is yet to be explained. The variation of responsivity with the bias field at 4.8 K is shown in Fig. 5.16. For wavelengths <50 µm, the responsivity increases with the field with a maximum responsivity of 9 A/W at 1.5 kV/cm. Although further increase in the field increases the shorter wavelength response, the longer wavelength (>50 µm) response increases as well. As expected, 1 decreases with the field, increasing the threshold to 130 µm for a bias field of 2.0 kV/cm.

267

Homo- and Heterojunction Interfacial Workfunction

100 Calc.

λt (µm)

Exp.

50

0 0.0

0.2

0.4

0.6

Al fraction

FIGURE 5.14 The variation of λt in p-GaAs/Alx Ga1−x As heterojunction detectors. The solid square represents the experimentally observed thresholds in which the data from detectors using inter-valence band transitions as discussed in Section 3 is also included. Frequency (THz) 10

1 16

HH/LH to split off p = 8 × 1018 cm−3 x = 0.01

103

Exp. Model

101

2

10 100 Wavelength (μm)

Δ(meV)

α(cm−1)

105

100

1000 × 1000 μm2 800 × 800 600 × 600

12

−2

−1

0 1 Bias (kV/cm)

2

FIGURE 5.15 (A) The measured and calculated absorption coefficient for an Al0.01 Ga0.99 As film with doping of 8 × 1018 cm−3 . For low Al fractions, the experimental results are in good agreement with the model developed for absorption in GaAs. Reused with permission from Rinzan et al. (2004). Copyright 2004, American Institute of Physics. (B) Variation of workfunction, 1 with the bias field for three mesas with different electrical areas. The workfunction at different bias fields were obtained using Arrhenius plots. The zero bias workfunction is ∼17 meV for all the mesas. Reused with permission from Rinzan et al. (2005). Copyright 2005, American Institute of Physics.

The semilog scale of Fig. 5.16 clearly shows the variation of λt with the applied field. A dark current limited peak detectivity of 1.5×1013 Jones was obtained at the bias field of 1.5 kV/cm at 4.2 K. A BLIP temperature of 20 K for a 0.15 kV/cm bias field was recorded (Rinzan et al., 2005b).

268

A. G. U. Perera

Wavelength (µm) 10

101

50

100

0.5 kV/cm 1.0 1.5 2.0

Responsivity (A/W)

4.2 THz

10−1

10−3 30

150

2.8 2.6 2.3

6

3 Frequency (THz)

2

FIGURE 5.16 The variation of responsivity with applied field for p-AlGaAs/GaAs HEIWIP (sample V0207) at 4.8 K. The peak responsivity, 9 A/W at 31 µm was obtained at 1.5 kV/cm. The increase in response with the field around λt is because of threshold shift with the bias. The sharp dip at ∼37.5 µm is because of the interaction of radiation with GaAs-like TO phonons. The bias field decreases the effective workfunction pushing λt toward 150 µm with the increasing field. Reused with permission from Rinzan et al. (2005). Copyright 2005, American Institute of Physics.

2.8.3. n-GaAs emitter/AlGaAs barrier HEIWIP detectors Most of the HIWIP and HEIWIP work has been carried out based on p-type materials. However, results have been recently reported (Weerasekara et al., 2007) on an n-type GaAs/AlGaAs HEIWIP device structure consisting of an undoped 1-µm thick Alx Ga1−x As (x = 0.04) barrier layer sandwiched between two 1×1018 cm−3 Si-doped GaAs contact layers. The 100-nm top contact and a 700-nm bottom contact layers serve as emitters in this design. The 1 was estimated to be 13–14 meV corresponding to a λt of 88–97 µm from Arrhenius analysis (Weerasekara et al., 2007). The calculated 1 should be between ∼10–20 meV, corresponding to a λt of 60–125 µm. The maximum peak response (Rpeak ) of 6.5 A/W at 42 µm (Weerasekara et al., 2007) was seen at a bias field of 0.7 kV/cm in the forward bias operation (top emitter positive) as shown in Fig. 5.17A. The Rpeak obtained in the reversed bias was 1.7 A/W at 0.25 kV/cm. At a bias field of 0.5 kV/cm, The Rpeak in the forward bias was 6.1 A/W while the Rpeak in reverse bias is 1.1 A/W. The responsivity ratio in forward and reverse bias operations agrees with the thickness ratio of the bottom and the top contact layers (Weerasekara et al., 2007). Based on the spectral response, a threshold of 94 µm was observed. The variation of

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Wavelength (µm) 40

60

GaAs phonon

Responsivity (A/W)

10

20

0.1 15.0

100

T=6K 0.7 kV/cm 1.5 ft = 3.2 THz

phonon

AlAs-like

1

80

3.0

7.5

5.0 3.75 Frequency (THz)

Peak responsivity (A/W)

(A)

8

7.1 THz 10.4

6

T=6K

6

Vb = 0.7 kV/cm

4

7.1 THz 10.4

4 2 2 0 0 0 1 2 Bias field (kV/cm) (B)

5 10 15 20 25 Temp (K) (C)

FIGURE 5.17 Responsivity variation of the n-GaAs/AlGaAs HEIWIP for 0.7 and 1.5 kV/cm is shown. The highest Rpeak is 6.5 A/W at 0.7 kV/cm at 6 K. The λt is 94 µm. The λt which is 94 µm was determined by the instrument noise level. The inset shows the device structure. Top and Bottom contacts are 100- and 700-nm thick n-doped GaAs, respectively. The barrier is 1-µm thick undoped GaAs/Al0.04 Ga0.96 As. (B) Variation of Rpeak s at 7.1 and 10.4 THz under different bias fields. (C) The Rpeak variation with temperature at the bias field of 0.7 kV/cm and responsivity vanishes after 25 K. Reused with permission from A. Weerasekara, Optics Letters 32, 1335 (2007), Copyright 2007, Optical Society of America.

the responsivity values at 29 and 42 µm (10.4 and 7.1 THz) with bias are shown in Fig. 5.17B. The Rpeak under 0.7 kV/cm bias field decreases from 6.5 to 0.1 A/W, when the operating temperature increases from 6 to 25 K. The variation of the responsivity values at 29 and 42 µm (10.4 and 7.1 THz) with operating temperature is shown in Fig. 5.17C. The experimentally observed (symbols) and the calculated (lines) thresholds for p-GaAs/AlGaAs, p-AlGaAs/GaAs, and n-GaAs/AlGaAs HEIWIP detectors with different Al fractions are shown in Fig. 5.4. The results for p-GaAs/AlGaAs HEIWIP detectors are based on samples

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with x = 0.02, 0.01, 0.005; the p-GaAs/Al0.12 Ga0.88 As HEIWIP detector reported by Matsik et al. (2004); and p-GaAs/Alx Ga1−x As HEIWIP detectors (x = 0.28, 0.37, and 0.57) reported by Jayaweera et al. (2008). The p-Al0.005 Ga0.995 As/GaAs detector reported by Rinzan et al. (2004) has shown the highest wavelength threshold. Experimental thresholds of most of the p-GaAs/AlGaAs detectors agree with the calculated values. As seen in the plot corresponding to n-GaAs emitter, the threshold of the n-GaAs/Al0.04 Ga0.96 As HEIWIP detector reported by Weerasekara et al. (2007) is also in good agreement with the theoretical calculation. However, the threshold obtained for an n-GaAs/Al0.12 Ga0.88 As HEIWIP detector deviates from the calculated value. In any of the detectors considered for the comparison in Fig. 5.4, the actual Al fraction after the growth of the structure in AlGaAs has not been reported, instead the designed Al fraction has been considered for the plot. Because a deviation in the Al fraction during the growth can occur, one of the possible reasons for the slight deviation in the threshold could be because of this difference. 2.8.4. n-GaN/AlGaN HEIWIP detectors A GaN/AlGaN HEIWIP detector structure responding in the FIR range has also been reported (Ariyawansa et al., 2006c), indicating the feasibility of terahertz detector development with the rapidly developing GaN/AlGaN material system. The detector structure was grown by organo-metallic chemical vapor deposition (OMCVD, same as MOCVD) on a sapphire substrate. The complete response of this detector at 5.3 K is shown in Fig. 5.18 with the response composed of three parts based on three detection mechanisms. The free carrier response exhibits a threshold at 11 µm, while the sharp peak at 54 µm is due to the 1s–2p± transition of silicon (Si)-dopant atoms, which has been observed previously (Moore et al., 1997) with the same energy of ∼23 meV. In addition to the free-carrier and impurity-related responses discussed, there is also a slower mechanism which responds out to 300 µm. This response was reported to be due to either a thermal or pyroelectric effect; however, the exact mechanism has not been confirmed yet. Further studies on the response mechanism will benefit the development of GaN-based terahertz detectors.

2.9. Dualband detectors In both HIWIP and HEIWIP detectors, it has been reported (Ariyawansa et al., 2005) that interband transitions in the undoped barrier and intraband transitions within the emitter lead to dualband response characteristics. Incident radiation with an energy greater than the band gap of the barrier are absorbed, generating an electron–hole pair. The standard detection

Homo- and Heterojunction Interfacial Workfunction

Responsivity (A/W)

12

Wavelength (µm) 10 100

3

1s-2p Impurity transition (23 meV)

271

300

T = 5.3 K Vb = −1 V

8 Flat response

4

0 100

Free-carrier response

10 Frequency (THz)

1

FIGURE 5.18 The response of the GaN/AlGaN HEIWIP detector at 5.3 K and −1 V bias. There are three response mechanisms, which can contribute to the photocurrent: free-carrier response, impurity-related response, and a flat terahertz response.

mechanism in HIWIPs and HEIWIPs including free-carrier absorption leads to the detection of terahertz radiation. Excited carriers are then collected by the applied electric field. The interband response threshold is determined by the band gap of the barrier material. Hence, using different material systems (such as Si, GaAs/AlGaAs, GaN/AlGaN, and so on), the interband response can be tailored to different wavelength regions. 2.9.1. NIR-FIR dualband HIWIP detectors A NIR-FIR dualband detector based on a p-GaAs HIWIP detector has been reported (Ariyawansa et al., 2005). The structure consisted of a bottom contact (p++ ) layer with 1.0 µm thickness, a barrier layer with 1.0 µm thickness, an emitter (p+ ) layer with 0.2 µm thickness, and a top contact layer. The spectral response for different bias voltages in both NIR and FIR regions at 4.6 K is given in Fig. 5.19A. The optimum responsivity at 0.8 µm is ∼9 A/W while the detectivity is ∼2.7×1011 Jones under 100 mV reverse bias at 4.6 K. The response because of intraband transition is observed up to 70 µm with a responsivity of ∼1.8 A/W and a specific detectivity of ∼5.6×1010 Jones at 57 µm under 100-mV reverse bias. The sharp drop around 37 µm was assigned to the strong absorption around the reststrahlen band of GaAs and the peaks at 57 and 63 µm were assigned to transitions of impurity atoms in the barrier region (Esaev et al., 2004b). The spectral responsivity curves resulting from both interband and intraband transitions for temperatures from 4.6 K to 20 K are shown in Fig. 5.19B. An optimum responsivity of ∼8 A/W and a detectivity of ∼6×109 Jones were

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Frequency (THz) 15

12

7.5

5

2

−20 mV −50 mV −100 mV

8

1

4

0 0.7

Responsivity (A/W)

Responsivity (A/W)

T = 4.6 K

0 0.8

2 20 40 Wavelength (µm)

60

(A) Frequency (THz) 15

7.5

5

Vbias = −50 mV

6

4.6 K 10 K 20 K

8

4 4

2

Responsivity (A/W)

Responsivity (A/W)

12

0 0.7

0.8

20

40

60

Wavelength (µm) (B)

FIGURE 5.19 (A) The interband and intraband response of the GaAs-based HIWIP at 4.6 K under different reverse bias values. (B) Shows both interband and intraband response at different temperatures under −50 mV bias. The left and right axes are corresponding to NIR and FIR responsivity, respectively, and a break on the frequency axis at 39 THz has been made in order to expand the view in both regions. Reused with permission from Ariyawansa et al. (2005). Copyright 2005, American Institute of Physics.

obtained at 0.8 µm for interband response, while a responsivity of ∼7 A/W and a detectivity of ∼5×109 Jones were reported at 57 µm, under 100-mV reverse bias at 20 K (Ariyawansa et al., 2005).

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Following the same principle, a second detector operating in both the NIR and FIR ranges has been reported based on a p-type Si HIWIP detector (Ariyawansa et al., 2006b). The NIR response at −1 V bias had a threshold of ∼1.05 µm, agreeing with the ∼1.17 eV bandgap of Si at 4.6 K. A NIR responsivity of 0.024 A/W was obtained at 0.8 µm with a detectivity of ∼1.7×109 Jones at 0.8 µm under −1 V bias at 4.6 K. The FIR response is in the range of 5–35 µm. A responsivity of 157 A/W at 25 µm at −2 V bias was reported, which translates to an efficiency-gain product of 7.8. 2.9.2. UV–IR dualband HEIWIP detectors

0.6

T = 300 K Vb = −0.5 V

T = 5.3 K Vb = −1 V

1.5

1.0

Exp. Model

0.4

0.5

0.2

0.0

Responsivity (A/W)

Responsivity (mA/W)

Recently, a nitride-based dualband detector was also demonstrated which showed response in both the UV and IR ranges (Ariyawansa et al., 2006a; Perera and Matsik, 2007) similar to the previous NIR-FIR detectors as shown in Fig. 5.20, in which a theoretical response is calculated for comparison using a model developed by Matsik and Perera (2008). This detector used interband absorption to detect the UV radiation and intraband absorption to detect the IR radiation. The GaAs was replaced by GaN and the AlGaAs replaced by AlGaN. Although the initial detector using only two contacts required separate modulations to distinguish the UV from the IR, a later design using three contacts and separate active regions for the UV and the IR were able to distinguish UV from IR without separate modulations (Jayasinghe et al., 2008). This approach allows tremendous variations in the thresholds. By using AlGaN in both layers with different

0.0 0.30

0.40 5 λ(µm)

10

15

FIGURE 5.20 Calculated UV/IR responses (dashed line) of the detector, fitted with experimental results (solid line). UV response at 300 K and a −0.5 V bias, and response at −1.0 V and 5.3 K. Note that although the response is only shown in the two ranges of interest, the model calculates the response over the entire range from the UV to the IR. Reused with permission from Matsik and Perera et al. (2008). Copyright 2008, American Institute of Physics.

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Al fractions and adjusting the Al fraction in the barriers, the UV threshold can be tailored, whereas by adjusting the difference between the fractions in the emitters and barriers, the IR threshold can be tailored. However, for high-performance devices, the quality of the GaN/AlGaN material system needs to be improved, which is presently the focus of many researchers. 2.9.3. Simultaneous and separate identification of UV and IR A three-contact design modification for the UV–IR dual-band detector (one common contact for both regions) allowed separate and simultaneous identification of UV (250–360 nm) and IR (5–14 µm) radiation (Jayasinghe et al., 2008). The structure consists of an n+ -GaN top-contact (TC) layer, an undoped Ga0.974 Al0.026 N layer acting as the UV-active region, an n+ -GaN middle-contact (MC) layer, the IR-active region, and a bottom-contact (BC) layer. The IR-active region consists of two periods of an n+ -GaN emitter layer and an undoped Ga0.974 Al0.026 N barrier layer. Depending on the bias either the MC or the BC also acts as an emitter. The dual-band detection is based on two absorption mechanisms in the heterostructure: interband absorption in the top Ga0.974 Al0.026 N layer for UV response and free-carrier absorption in the emitters for IR response. Figure 5.21 shows the device structure and the band diagram and the schematic of the detector. Throughout this discussion, the MC terminal is the common terminal for both UV- and IR-active regions. Hence, forward (reverse) bias denotes that the TC for the UV-active region or the BC for the IR-active region is positive (negative) relative to the MC. When the TC is negatively biased, it also acts as an emitter, making the IR detection possible in the UV-active region. This effect can be decreased by reducing the TC layer thickness, which reduces the IR absorption and the generated photocurrent. Furthermore, this TC layer absorbs UV radiation, suppressing the transmission of UV into the UV-active region, without generating a photocurrent because the excited electron–hole pairs are trapped by the barriers and recombine in the highly doped TC. For an optimum UV response, the TC layer thickness was found to be 0.1 µm, which is thin enough to reduce the IR absorption while still giving uniform electric field distribution across the UV-active region. Furthermore, the generation of IR photocurrent is prominent in the IR-active region, while no UV photocurrent is expected irrespective of the bias configuration because almost all the UV radiation is absorbed within the UV-active region. The spectral response is shown in Fig. 5.22. The solid curves show simultaneously measured photocurrents from the UV-active region (Fig. 5.22A) and the IR-active region (Fig. 5.22B) at 77 K when both IR and UV radiations were incident onto the detector. The dashed curve in Fig. 5.22A represents the photocurrent from the UV active region when only the UV radiation was incident. Comparing the two curves, it is

Homo- and Heterojunction Interfacial Workfunction

TC (−)

275

n − GaN, 0.1 μm 5 × 1018 cm−3

MC i − AI0.026Ga0.974N, 0.6 μm (+) n − GaN, 0.6 μm, 5 × 1018 cm−3 UV-active region i − AI0.026Ga0.974N, 0.6 μm

ΔIR

i − AI0.026Ga0.974N, 0.6 μm

CB ΔUV

n − GaN, 1 μm, 5 × 1018 cm−3 Sapphire substrate

(A)

Top contact

VB h+

Bottom contact

n − GaN, 0.05 μm, 5 × 10 cm BC (−)

e−

−3

Middle contact

18

IR-active region

e−

(B)

FIGURE 5.21 (A) The three contact structure for simultaneous dual-band response measurements. Three contacts allow separate readouts from the UV- and IR-active regions. The labels TC, MC, and BC indicate the top-, middle-, and bottom-contacts, respectively, and (+) or (−) shows the relative potential at which the device was operated. (B) The band diagram of UV–IR dual-band detectors under reverse bias configuration. CB and VB are the conduction and valance bands, respectively. Three contacts allow separate readouts from the UV- and IR-active regions. 1UV and 1IR represent the transition energies for interband and intraband absorption, respectively.

evident that there is no significant effect from IR radiation on the response from the top and middle contacts, indicating the sole UV detection from the UV active region, whereas the response from the IR-active region is because of the fixed IR radiation (9.3 µm), and there is no significant effect from the UV radiation except for a feature at 365 nm, which is probably because of one of the following two reasons: (1) it could be because of a light transmission as a result of a generation–recombination mechanism of an exciton (Jiang et al., 2001). An exciton 365 nm generated in the top GaAlN layer in the UV-active region could relax re-emitting a UV photon, generating another exciton, and so on, allowing a small fraction of photons at 365 nm to pass through to the IR-active region; (2) the low-energy UV radiation that has energy less than the bandgap of Ga0.974 Al0.026 N was absorbed in the MC layer, and the generated photocurrent could be either due to the minority carrier transportation (Chernyak et al., 2001) in the structure where the generated holes were recombined with the electrons in the valence band, or due to electron hopping from the filled impurity acceptor levels above the valence band of GaAlN layers.

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0.30 UV-active region T = 77 K Bias = −2 V

(A)

Responsivity (a.u.)

0.15 UV + IR UV only

0.00 (B)

IR-active region T = 77 K Bias = −2 V

0.030

0.015 UV + IR IR only

0.000 250

IR-active region (MC-BC (−2.0 V) (−2.5 V) UV-action region (TC-MC) (−1.0 V)

50 IR responsivity (mA/W)

300 350 Wavelength (nm)

400

T = 77 K (C)

25

0 5

10 Wavelength (µm)

15

FIGURE 5.22 Simultaneously measured photo currents (solid lines) from (A) UV-active region and (B) IR-active region at 77 K, when both IR and UV radiation were incident onto the detector. The UV wavelength was varied between 250 and 400 nm, while IR was fixed at 9.3 µm (using a CO2 laser). The dashed line in (A) represents the photocurrent when only UV radiation was incident and the dashed line in (B) indicates the response level (which is constant with time), as a reference level for the “UV + IR” response from the IR-active region, when only IR radiation was incident which only corresponds to the bottom axis. The lower and upper x-axes of (A) are also the upper axis of (B). (C) The IR response from IR- and UV-active regions at 77 K. The UV-active region showed almost zero response for IR radiation under reverse bias configuration as expected. Reused with permission from Ranga C. Jayasinghe, Optics Letters 33, 2422–2424 (2008), Copyright 2008, Optical Society of America.

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The broad IR responses from both active regions obtained separately at 77 K are shown in Fig. 5.22C, with the free-carrier response seen as a broad peak with a maximum near 11 µm. The UV-active region did not show a measurable IR response under negative bias but did show a response under positive bias as expected. The observed response in the GaN/GaAlN single-element detector indicates the capability of simultaneously detecting both the UV and IR responses with near-zero spectral cross talk. The detector can be further improved by the addition of more periods of GaN/GaAlN in the IR-active region.

3. INTER-VALENCE BAND DETECTORS Room-temperature or thermoelectrically cooled operation of infrared detectors would greatly reduce the weight and/or power requirements and are of importance for various practical applications. In addition to the InSb and PbSe detectors for the 3–5 µm range, HgCdTe (Gordon et al., 2006), quantum well (Alause et al., 2000), quantum dot (Ariyawansa et al., 2007), and type-II strained superlattice (Plis et al., 2007) detectors are being studied as SWIR–LWIR detectors. Infrared detection based on hole transitions from the light/heavy hole (LH/HH) bands to the spinorbit split-off (SO) band coupled with an interfacial workfunction offers a novel approach for detectors to realize uncooled or near room-temperature operation. The split-off band detection was initially observed in HEIWIP detectors (Perera et al., 2006). The split-off detection mechanism was then confirmed using detectors specifically designed and grown by MBE, which showed response up to 330 K (Jayaweera et al., 2008). The detectors have a similar structure to the standard HEIWIP detectors consisting of alternating pdoped absorbing layers (emitters) and undoped barrier layers sandwiched between two highly doped (1 × 1019 cm−3 ) top and bottom contact layers with thickness of 0.2 and 0.7 µm, respectively. The standard interfacial workfunction in the HEIWIP detectors will still provide a λt . However, this offset (threshold) can be adjusted in comparison with the split-off energy for higher response or higher temperature operation. The highly doped and thick emitters (18.8 nm) will lead to threedimensional energy states as opposed to quantized states. An E–k band diagram around k = 0 in the Brillouin Zone (BZ) for an emitter region is schematically given in Fig. 5.23A and the band diagram for the device is shown in Fig. 5.23B. The SO band is separated from the degenerate point of the LH and HH bands at k = 0 by an energy EE−SO which equals the spin splitting energy 1SO . The detector mechanism consists of three

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HH band

(2)

GaAs emitter

k

AIxGa1−x As barrier

E CB

EF

(1) LH band

EB−L/H EE−SO

SO band (A)

EB−SO (B)

FIGURE 5.23 (A) E − k diagram for an emitter region of the detector and (B) band diagram of the detector structure illustrating the different IR detection threshold mechanisms. The horizontal dashed lines EB−L/H and EB−SO indicate the LH/HH and split-off band maximum (k = 0) positions in the barrier. The horizontal dotted lines EF and EB−SO indicate the Fermi energy and the split-off energy in the emitter at k = 0. The arrows indicate the possible threshold transition mechanisms: (1) a direct transition from LH band to SO band followed by scattering back to LH band (2) an indirect transition followed by scattering back to LH band. Reused with permission from Perera et al. (2009).

main steps: (i) photoabsorption, exciting the carriers from the emitters, (ii) escape of the photoexcited carriers, and (iii) the sweep out and collection of the escaped carriers. Photoexcited carriers in the SO band can escape directly or scatter back into the LH/HH bands and then escape. The lowest barrier for the excited carriers in LH/HH bands is the threshold workfunction 1 as defined for HIP detectors which determines the λt for free-carrier response and thermionic dark current hence controlling maximum operating temperature. Increasing 1 results in a reduction in the free-carrier response making SO transitions become dominant, but large 1 also decreases the escape probability and gain. The optimum value will be determined by the key application requirement of high operating temperature or high performance. Unlike QWIP detectors, SO detectors will detect normal incidence radiation removing the need for light coupling processes and associated costs. The spin-orbit splitting effects result from the coupling of electron spin to the orbital angular momentum via the spin-orbit interaction which is a relativistic effect and scales with the atomic number of the atom. Hence spin-split off based IR detection should be sensitive to the magnetic

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field allowing magnetic tunability and controllability. For semiconductors containing lighter elements, the splitting energy becomes small hence extending the SO transition wavelength into far-infrared (FIR) spectral region. For example, zincblende or wurtzite crystal structures of GaN having the SO splitting energies of 20 meV(∼4.8 THz/62 µm) and 8 meV (∼1.92 THz/156 µm), respectively (Levinshtein et al., 2001) would be a promising material for THz detection. In addition to SO-HH transitions, the selection rule allows hole transitions between the LH and HH bands. These can take place at k values other than the BZ center where the LH-HH energy separation approximately approaches 2/3 of the SO splitting energy. Such a consideration composes a complete scene for inter-valence band absorption (IVBA) in p-type semiconductors. A broad spectral region covering MWIR and LWIR regions can be expected as the LH-HH transition energy has no minimum limitation from the band-structure point of view. Experimental measurements on the absorption properties for p-doped semiconductors have been made over a variety of materials, e.g., GaAs (Braunstein and Magid, 1958; Songprakob et al., 2002; Hu et al., 2005b; Rinzan et al., 2004), GaP (Wiley and DiDomenico, 1971), GaSb (Chandola et al., 2005; Hu et al., 2005a), Ge (Briggs and Fletcher, 1952), InAs (Stern and Talley 1957), InP (Henry et al., 1983), and InSb (Gobeli and Fan, 1960). All these p-type materials show broad absorption extended into the FIR region. The IVBA strength is generally increased with the doping. However, enhanced scattering of carriers by charged centers at higher doping concentrations could relax the selection rule 1k = 0 leading to broad SO-HH peak and reduced intensity (Newman and Tyler, 1957), whereas the LH-HH peak keeps a well-defined shape even at very high doping concentrations (Songprakob et al., 2002). The energy onset of LH-HH absorption band (e.g., 0.25 eV reported by Braunstein and Magid (1958)) approximately approaches the LH-HH separation 11 (3) in the h111i direction (e.g., 0.225 eV reported by Lautenschlager et al. (1987)) for p-GaAs. From the band structure point of view, hole transitions will see the parallel structure of the LH and HH bands along h111i and h100i directions enhancing the transition rate. The use of detection mechanism involving LH-HH transitions is promising for infrared detection to concurrently cover multiband spectral region by using a single structure, e.g., p-type GaAs/AlGaAs detectors (Lao et al., 2010). However, the background from 300 K-blackbody radiation (peak at ∼10 µm) inducing a photocurrent in the p-type GaAs/AlGaAs detector could degrade the detection capability. In this case, it will be desirable to narrow the detection to one specific region, e.g., MWIR. A possible solution is to design the zero-response λt to suppress the long-wavelength response. As it will be discussed in Section 3.4, the

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use of a cavity structure can also enhance the absorption in the MWIR range.

3.1. Uncooled SO detectors The split-off band detection was initially observed in the GaAs/AlGaAs HEIWIP detector (Perera et al., 2006) which was designed for the 10–15 µm range with a 20 µm threshold (Matsik et al., 2004). The detector structure was composed of 16 periods of p-doped 18.8-nm GaAs emitters doped to 1 × 1018 cm−3 and 125-nm Al0.12 Ga0.88 As barriers. Figure 5.24 presents the spectral responsivity at different temperatures. Also shown is the absorption spectra of p-doped Al0.01 Ga0.99 As films indicating stronger split-off absorption above the free-carrier absorption. It has been observed that optimum response occurs at a moderate temperature, which could be the result of thermal-related phonon effects on the escaping rate for excited carriers and increased dark current at higher temperatures. Optimum 0.6

Responsivity (mA/W)

130 K 0.4 100 K

8 × 1018 cm−3

0.10 Absorption

120 K

0.05 3 × 1018 cm−3

0.00 2

0.2

3 4 Wavelength (µm)

5

90 K

80 K 0.0 2

3 Wavelength (µm)

4

5

FIGURE 5.24 Measured responsivity of the HEIWIP detector at various temperatures at 5 kV/cm. The inset shows the measured absorption for Al0.01 Ga0.99 As films. The solid lines are the total absorption in the films, while the dashed lines are the λ2 curves indicating the free-carrier absorption. The difference represents the absorption from the split-off band. Higher doping leads to a large increase in the split-off absorption as seen from the curves. Reused with permission from Perera et al. (2006). Copyright 2006, American Institute of Physics.

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response and the operating temperature are two competing requirements. Smaller 1 giving rise to a longer free-carrier threshold wavelength allows increased collection of the carrier over the split-off barrier, also allowing a higher dark current. In contrast, larger 1 reducing the dark current will lead to an increase in operating temperature but accordingly decreases the photocarrier escape and the response. The two steps seen in the response at 2.8 and 3.4 µm are related to the transitions 1 and 2 as illustrated in Fig. 5.23. This initial results imply that the SO transition-based mechanism could be a novel approach for infrared detection with the capability of highoperating temperatures. Studies have shown that the inter-valence band absorption including the SO transitions was one critical part of optical loss for long-wavelength semiconductor lasers at elevated temperatures (Henry et al., 1983; Piprek et al., 1996), which is related to the temperature behavior of IVBA resulting from a higher amount of thermally populated heavy holes. In contrast, such IVBA behavior will be beneficial for infrared detectors. As discussed above, the threshold workfunction 1 (shown in Fig. 5.23) determines the thermionic dark current hence controlling maximum operating temperature. By designing structures with optimized 1 values, high-operating-temperature SO detectors is thus possible. Such design was demonstrated (Jayaweera et al., 2008; Perera and Matsik, 2010) on three detector structures SP1, SP2, and SP3 which have different 1 values of 155, 207, and 310 meV (corresponding Al fractions are x = 0.28, 0.37, 0.57), respectively. All these detectors were composed of 3 × 1018 cm−3 p-doped 18.8-nm GaAs emitters and 60-nm undoped Alx Ga1−x As barriers. The current voltage (I–V) characteristics were measured with different temperatures from 70 to 300 K. As shown in Fig. 5.25A, dark current density at 1 V bias reached the same order at 140, 190, and 300 K for samples SP1, SP2, and SP3, respectively. The measured dark current densities of SP1, SP2, and SP3 at 150 K temperatures (solid lines) are consistent with a thermionic model (dots) as shown in Fig. 5.25B. The spectral response of SP1, SP2, and SP3 were measured at temperatures up to 140, 190, and 330 K, respectively, as shown in Fig. 5.26. The maximum responsivity of SP3 was observed at 2.5 µm and 4 V bias above which increased dark current (low-dynamic resistance) decreased the response. The λt for the response mechanisms 1 and 2 shown in Fig. 5.23 can be identified in Fig. 5.26 at 2.9 and 3.4 µm, respectively. The higher responsivity was seen for samples (SP1 and SP2) with longer λt , possibly because of impact ionization (gain) and collection efficiency, compared with samples with shorter λt , as shown in the inset of the Fig. 5.26. Based on the noise measurements, the D∗ values are calculated for each sample and listed in Table 5.4.

A. G. U. Perera

Dark current density at 1 V bias (A cm−2)

282

100 SP1

10−2

SP2

SP3

10−4

10−6

10−8

50

100

150 200 Temperature (K)

250

300

Dark current density (A/cm−2)

(A)

100

SP001

10−2

SP002 150 K

10−4

10−6

SP003 Exp. Cal.

10−8 −4

−2

0 Voltage (V)

2

4

(B)

FIGURE 5.25 (A) The dark current density versus temperature for samples SP1, SP2, and SP3 under 1 V applied bias. The dark current densities reached 1 A/cm2 for each sample at 140, 190, and 300 K. (B) The dark current density for the three samples measured at 150 K showing thermionic emission. Reused with permission from Perera et al. (2009).

Also shown in Fig. 5.26 is a comparison with the model response (Matsik et al., 2009), which gives an agreement with the predicted peak response being within 20% of the measured value for all the biases. The

283

Homo- and Heterojunction Interfacial Workfunction

Calc.

Exp. 1V 2V 3V 4V

Responsivity (mA/W)

0.3

SP3 330 K

Responsivity (mA / W)

theoretical analysis gives an understanding to the observed SO response by which related optimization on detector structures can be carried out. The model details will be discussed in Section 3.4.

SP2 190 K

2

1

0.2

SP1 140 K 3 2 Wavelength (µm)

4

0.1

0.0 2

3 Wavelength (µm)

4

FIGURE 5.26 The measured responsivity of the sample SP3 under four different biases at 330 K. The inset shows the responsivity of the samples SP1 and SP2 at 140 and 190 K, respectively. (Reused with permission from P. V. V. Jayaweera et al., Applied Physics Letters, 93, 021105 (2008).) Copyright 2008, American Institute of Physics. Also shown is the comparison of experimental spectra with the calculated response (Matsik et al., 2009) showing good agreement except at the longer wavelengths. The disagreement at long wavelengths is because of the thermal mechanism that is not included in the model. Reused with permission from Matsik et al. (2009). Copyright 2009, American Institute of Physics.

TABLE 5.4 Sample parameters for detectors SP1–3. The dynamic resistance (RDyn ), dark current density (IDark ) at 1 V bias, and D∗ are experimentally measured values. 1L/H is the designed band offset Sample

1L/H (eV)

Tmax (K)

RDyn ()

IDark (A cm−2 )

D∗ (Jones)

SP1 SP2 SP3

0.155 0.207 0.310

140 190 300

787 913 1138

0.663 0.875 0.563

2.1 × 106 1.8 × 106 6.8 × 105

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A. G. U. Perera

3.2. LH-HH transitions for long-wavelength infrared detection In contrast to the SO transitions that give rise to absorption in the spectral region with photon energy larger than the SO splitting energy, the LHHH transitions (as one type of IVB transitions) are allowed by the selection rule producing absorption in the MWIR and LWIR region (Lao et al., 2010). A schematic of IVBA processes and room-temperature absorption spectra for p-GaAs are shown in Fig. 5.27. The IVBA appears as on top of FCA lines, where the broad peak around 4–16 µm is because of the LH-HH transitions. The broad LH-HH feature is related to two factors contributing to the IVBA strength: the difference in hole distribution functions between the initial and final states relating the Fermi level, and the joint density of states − → (JDOS) | k · ∇k (Eki − Ekj )|−1 (i and j represent band indexes). Because of the parallel structure of LH and HH bands, JDOS shows singularities at

1

hh → lh hh → so

Ef

104 2

Energy

hh band

3 103

(3) (2) Δ′0

(1) Δ1

4 lh band

lh → so

so band Λ

Γ

102

Absorption coefficient (cm−1)

lh ← hh

lh ← hh lh ← hh so ← hh so ← lh

Energy (eV) 0.6 0.3 0.2 0.1

101 Δ

4

8

12

Wavevector

Wavelength (μm)

(A)

(B)

16

FIGURE 5.27 (A) Schematic of the valence-band structure along the direction of h111i (3) and h100i (1). Various IVBA transitions are indicated. The (1), (2), and (3) represent LH-HH transitions at different wavevectors. The Fermi level is calculated for 3 × 1018 cm−3 p-doped GaAs at 80 K. (B) Measured room-temperature absorption spectra of p-GaAs compared with the calculated FCA curves plotted by dashed lines. Also shown is data from Songprakob et al. (2002) (curve 1) and Braunstein and Kane (1962) (curve 4); the doping levels for curves 1–4 are 2.7 × 1019 , 8.0 × 1018 , 3.0 × 1018 , and 2.7 × 1017 cm−3 , respectively. Reused with permission from Lao, Pitigala et al. (2010). Copyright 2010, American Institute of Physics.

285

Homo- and Heterojunction Interfacial Workfunction

large k and hence yields considerable absorption in the short-wavelength part of the LH-HH absorption band. Because the SO and LH-HH transitions are all IVBA processes occurring in p-type materials, the LH-HH transition-based response can be observed in SO detectors. Figure 5.28 shows the spectral responsivity for detectors with different zero-response threshold (λt ) and emitter dopings. Sample HE0206 consists of 16 periods of 18.8-nm p-GaAs emitters doped to 1 × 1017 cm−3 and 125-nm undoped Al0.12 Ga0.88 As barriers. Sample 1332 has 12 periodic units with the same thick emitters and barriers as HE0206, but the emitter doping level is at 3 × 1018 cm−3 and the Al fraction of barriers is 0.15. The SO-HH transition-based short-wavelength response in samples SP1–3 have been discussed earlier in this section.

SP2, 80 K λt = 6.5 μm

Responsivity (a.u.)

5.50 μm

SP3 330 K

SP1, 80 K λt = 9.3 μm

6.46 μm

1.0

SP2 240 K

SP1 170 K

1332, 50 K λt = 15.0 μm

0.5

HE0206, 80 K λt = 16.5 μm 4

8

12

16

4

8

12

16

Responsivity (mA / W)

1.5

0.0

Wavelength (μm) (A)

(B)

FIGURE 5.28 (A) Spectral response of detectors with different λt . The curves from top to bottom are measured at the bias of 8, 2, 1, and 2 V, respectively. In comparison with the FCA response (dashed line) calculated for the detector 1332, LH-HH transitions produce response between 4 and 10 µm. (B) High-operating-temperature capability was measured on samples SP1, SP2, and SP3 under 0.2, 0.3, and 3 V, respectively, showing broad range from 4 to 16.5 µm. The wavelength region above designed threshold is because of a thermal detection mechanism. Cavity interference modes are all marked with the arrows in (A) and (B). Reused with permission from Lao, Pitigala et al. (2010). Copyright 2010, American Institute of Physics.

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A. G. U. Perera

The detector with long-wavelength threshold in Fig. 5.28 shows a broad response between 4 and 16.5 µm involving the FCA and IVBA contributions together. The FCA response alone can be calculated by the escape cone model (Esaev et al., 2004) in which the escape rate of holes out of the emitter region is determined by the photoemission process. However, thermally assisted tunneling contribution at high biases will mix in this process deteriorating the model accuracy. Therefore, the model FCA response for low biases was calculated and compared with detector 1332 shown Fig. 5.28A. The comparison indicate LH-HH transitions can produce spectral response up to 10 µm. The LH-HH process is rather prominent in terms of similar responsivity features observed in detector HE0206 although its emitters are relatively low doped at 1 × 1017 cm−3 . Highoperating-temperature capability was measured on detectors SP1, SP2, and SP3 shown in Fig. 5.28B, indicating promising uncooled operation. The range above λt could be because of the thermal detection mechanisms. Thermal-related processes such as phonon scattering increase the response time at high temperatures. Hence, an enhanced responsivity was observed at high temperatures when a lower optical-path-difference (OPD) velocity value was used for the FTIR settings. A minimum OPD velocity below which response is nearly unchanged was thus used. The peak at ∼13 µm is because of the cavity enhancement of the p-GaAs/AlGaAs structure. In the LH-HH response region, two peaks determined by their center positions at 5.50 and 6.46 µm were observed. Their corresponding energy values (0.225 and 0.192 eV, respectively) are matched with reported LHHH separations along the 3 and 1 directions, respectively, e.g., 11 (3) = 0 0.224 eV as reported by Lautenschlager et al. (1987) and 10 (1) = 0.193 eV − → as reported by Zollner (2001). Therefore, hole transitions at points in k space along the 3 and 1 directions are the reason for this result. The LH-HH transition-based concept builds up the factors including the split-off mechanism and the FCA for GaAs being a platform to realize multispectral infrared detection in an internal photoemission detector. In comparison with MCT detectors which have been realized for uncooled operation within the 2–16 µm spectral range and are commercially available (Rogalski, 2005), the discussed GaAs-based device will be a viable alternative with the robustness of the III–V material system. Uncooled operation is also possible for this type of device which is promising for applications where detecting high-intensity radiation is required.

3.3. SO-HH transitions for spectral response extension As the SO splitting energy scales with the atomic number of the atom, extended spectral response range can be achieved by using different materials. For the wavelength range in the 3–5 and 8–14 µm atmospheric

Homo- and Heterojunction Interfacial Workfunction

Direct gap

AIP

Indirect gap

2.4 AIAs

GaP

1.6 GaAs 0.4

0.8

Energy (eV)

Energy gaps (eV)

287

0.3

InP

ΔEv Eso

0.2 0.1 0.0 0.0

0.0 5.4

InAs

0.4 0.8 As fraction y 5.6

5.8 Lattice constants (Å)

6.0

FIGURE 5.29 Band gap and lattice constant of selected III–V semiconductors (data were taken from Levinshtein et al. (1996)). Solid lines represent direct band region and dashed lines represent indirect band region. GaP/AlGaP would be a high-quality, lattice-matched system similar to GaAs/AlGaAs. Also, InGaAs and InGaP can be lattice-matched to InP and GaAs, respectively. The inset shows the variation of the valence band offset energy (1Ev ) and split-off energy (ESO ) of the In1−x Gax Asy P1−y /InP heterostructure with As fraction y, where x = 0.47y. Reused with permission from Perera et al. (2009).

windows arsenide and phosphide would be the best materials because their split-off energies fall in this range. A bandgap versus lattice constant plot of selected arsenide and phosphide materials is shown in Fig. 5.29. The use of GaAs0.4 P0.6 is possible for a full coverage of 3–5 µm range as its split-off threshold is near 5 µm; however, the lattice mismatch with the GaAs substrate is an issue for high-quality epitaxy. The GaP and AlP have ˚ (Levinshtein et al., 1996), respecthe lattice constant at 5.4505 and 5.4510 A tively, and thus the Alx Ga1−x P ternary alloy is naturally lattice matched with the GaP substrate. A SO detector with GaP emitter and Alx Ga1−x P barrier will give rise to 80 meV (16 µm) of split-off threshold energy (wavelength). Growth of Alx Ga1−x P-based structures should not be difficult because characteristics of GaP/AlGaP heterojunctions (Adomi et al., 1992), superlattice (Nabetani et al., 1995), heterostructure-based detectors (Prutskij et al., 1995), and solar cells (Sulima et al., 2003) have already been reported.

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A. G. U. Perera

In1−x Gax Asy P1−y can be lattice matched to InP when x = 0.47y. The SO splitting energy can be tuned from 0.11 to 0.379 eV (3.3–11 µm) by changing the As alloy fraction y from 0 to 1 (1SO = 0.11 + 0.24y; Yamazoe et al., 1981). Because the valence band discontinuity of the In1−x Gax Asy P1−y /InP heterostructure can be expressed as (Levinshtein et al., 1996) 1Ev = 0.502y − 0.152y2 , the free-carrier threshold wavelength will also be tunable. By setting y within 0.5–0.7 range, the 1Ev will correspond to a λt in the 4–5 µm range. The calculated 1Ev and 1SO for different As fractions y is shown in the inset of Fig. 5.29. Another potential application of the SO detection mechanism is to develop detectors for the THz range. The extending of SO response toward THz frequency domain can be possibly achieved by zincblende or wurtzite crystal structures of GaN that have the SO splitting energies of 20 meV(∼4.8 THz/62 µm) and 8 meV (∼1.92 THz/156 µm), respectively (Levinshtein et al., 2001). Using the model reported by Matsik et al. (2009) as developed for GaAs/AlGaAs SO detectors (see Fig. 5.26), a preliminary calculation (Perera et al., 2009) was applied to zincblende crystal p-GaN/AlGaN split-off band detector in Fig. 5.30A which responds up to 4.2 THz as shown in Fig. 5.30B. In comparison with the BiB detectors in this wavelength range which operate at low-temperatures (Table 5.1), the calculation indicates relatively high-temperature operation could be achieved using the SO detection mechanism.

p+-GaN top contact

p+-GaN emitter Al0.03Ga0.97N barrier p+-Gan bottom contact

Responsivity (A / W)

AlxGa1−xN graded barrier x = 0.01−0.1

75 40 30 16

Wavelength (µm) 20

10

V = 0.2 V T = 40 K

12 8 4 0

Substrate (A)

10

20 Frequency (THz)

30

(B)

FIGURE 5.30 (A) Schematic diagram of a preliminary structure of a GaN/AlGaN split-off band detector. The thickness of the emitter and barrier layers are 20 and 400 nm, respectively. The doping concentration of the emitter and contact layers is 1 × 1019 cm−3 . (B) Theoretically predicted response based on the model reported by Matsik et al. (2009). The threshold at 4.2 THz (62 µm) corresponds to the split-off energy (∼20 meV) of p-GaN.

Homo- and Heterojunction Interfacial Workfunction

289

3.4. Modeling and optimization of SO detectors The transport of carriers in the detector involves a series of processes: the excitation of carriers by incident light, the escape over the barriers, and the trapping and refilling injection of carriers. A high quantum efficiency would be expected by increasing the escaping rate while reducing the trapping. Because a detector generally includes multiple emitters to enhance the absorption, a design with each emitter contributing to the response should result in high performance. Therefore, it will be desirable to understand and explain the response observed in detectors mentioned above from a theoretical point of view, in order to improve the performance. In this section, a theoretical analysis on the SO detectors is presented. The model response shows consistency with the measured response. Detector optimization is then suggested based on the model results. Also an analysis on the dark current concerning the electrical uniformity and the absorption enhancement using an optical cavity is presented. 3.4.1. Graded barriers and resonant escape To optimize the SO response, a theoretical modeling has been carried out by Matsik et al. (2009). The calculated responsivity agrees with the predicted peak response being within 20% of the measured value for all the biases as shown in Fig. 5.26. The model involves five steps in the calculations: (1) the absorption in the emitters, (2) the transport of excited carriers to the emitter/barrier interface, (3) the escape probability at the emitter/barrier interface, (4) the capture rate for injected carriers in the emitters, and (5) the dark and photocurrents. In the transport of injected or photo/thermal-excited carriers throughtout the device, various scattering events can occur. A scattering event can cause the transferring of a carrier from one energy state to another which could result in escape over high-energy barrier or capture into low-energy states. Holes excited from the LH/HH bands into the SO band can move forward the emitter/ barrier interface by remaining within the same (SO) band or scattering back into the LH/HH bands and then escape at the interface, contributing to the photo current for SO response. In this modeling, three basic scattering processes are considered: (1) ionized impurity scattering, (2) phonon scattering, and (3) hot/cold carrier scattering. As a preliminary to the model, the energy bands for the emitter layers were calculated using an eight-band k · p approach (Kane, 1966) to calculate the absorption and scattering rates for the various mechanisms. The IR absorption in the emitter layer consists of two components, a direct absorption involving only the photon and the hole, and an indirect absorption involving an additional scattering through phonon or impurity to conserve momentum. The two processes could be calculated separately and

290

A. G. U. Perera

then combined to give the total absorption. The ionized impurity scattering should be significant only in the emitters, and it will be calculated (Brudevoll et al., 1990) including the effects of screening on the scattering rates. The phonon scattering rates will be calculated (Scholz, 1995), including the absorption and emission of both optical and acoustic phonons for transitions both within and between the hole bands. The total escape probability for the photoexcited carriers can be obtained using a Monte Carlo method. The photoexcitation is obtained using the rates for transitions at a specific value of k. A carrier is randomly selected from the excited carrier distribution and made to propagate forward toward the emitter–barrier interface, which is assumed to travel in a straight line until scattered, or to reach the interface. At the interface, the carrier either escapes or is reflected. There are two possible escape mechanisms: (1) direct escape over the barrier while remaining in the same hole band as presently occupied, where the probability can be determined using an escape cone model (Esaev et al., 2004a) or (2) for the carrier to transfer into a different band as it crosses the emitter/barrier interface. This is possible as a result of the mixing that occurs between the light, heavy, and split-off hole states. The motion of the carrier is followed until it either escapes or has an energy level less than that of the barrier when it is retained in the emitter. This model was tested by comparing the calculated results with experimental measurements for detector SP3 as shown in Fig. 5.26. The results gave reasonable agreement with measured responsivity. The deviation seen at long wavelengths beyond ∼3.5 µm appears to be because of a thermal detection mode that is also present, which is not included in the modeling. Because the model response reasonably agrees with the experiments, structure optimizing can be carried out by varying the structural parameters used in the model such as the barrier height, the doping, and the thickness of emitters. The model gives a photocurrent gain of 0.95 ± 0.05 which is in agreement with the predicted value of 1.0 (Shen and Perera, 1998) for a single emitter detector with all the injected current being trapped in the emitter. This theoretical analysis suggested that modifications in the design to activate more emitters would lead to increase gain hence improved response, which can be achieved by grading the top barrier in order to produce an offset between the barriers on the two sides of the emitter. The improved responsivity with increasing barrier offset is shown in Fig. 5.31A. Another potential improvement is the use of a double-barrier structure to increase escape of holes from the split-off to the light/heavy hole bands by bringing the two bands into resonance. Other parameters, such as the doping level, parameters related to antireflection coatings, and so on, can be also optimized using the model results as shown in Table 5.5 and Fig. 5.31B.

Homo- and Heterojunction Interfacial Workfunction

291

Response (A/W)

200 K 250 K

0.15

300 K

0.10

0.05 0

10 20 Barrier offset (meV) (A)

Responsivity (A / W)

7 6

100

5 4

10−2 3 2 1

10−4 2

3 Wavelength (µm) (B)

FIGURE 5.31 (A) The calculated responsivity variation with barrier offset for a detector with a free-carrier threshold of 4 µm at three different temperatures at a bias of 1.0 V. Reused with permission from Matsik et al. (2009). Copyright 2009, American Institute of Physics. (B) The predicted improvement in responsivity of a GaAs/AlGaAs detector as different design modifications are incorporated. The GaAs-based design consisted of 30 periods of 3 × 1018 cm−3 p-doped 18.8-nm GaAs emitters and 60-nm Alx Ga1−x As barriers. Table 5.5 indicates the modifications for each curve and their effects on responsivity. Each curve includes the effects of all modifications for the curves with lower numbers. Curves 3 and 4 have the same responsivity.

3.4.2. Resonant cavity enhancement Because the optical thickness of the structure is comparable with or greater than the operating wavelength (e.g., p-GaAs for MIR detection based on SO-HH transition and for LWIR detection based on LH-HH transitions), embedding the active region in a Fabry–Perot (F–P) resonant cavity can

292

A. G. U. Perera

TABLE 5.5 Design modifications and improvement in SO detector performance where the curve number corresponds to that in Fig. 5.31B Responsivity Curve

Modifications

Improvement factor

Value (mA/W)

1 2 3 4 5 6 7

Measured results Increase doping from 3 × 1018 to 1019 cm−3 Barrier offset of 100 meV Graded barrier offset of 50 meV Increase effective multiple emitters to 30 Resonant escape of carriers Antireflection coatings

×3 ×1.5 ×1 ×30 ×100 ×1.3

0.14 0.42 0.64 0.64 19 1900 2500

¨ u¨ enhance the performance by increasing the optical absorption (Selim Unl and Strite, 1995; Korotkov et al., 2001; Esaev et al., 2003). The F–P cavity can be fabricated by applying a metallic mirror on one side of the structure with the semiconductor/air interface as another mirror. Such a detector has been realized in experiments for a QWIP (Shen et al., 2000). Similarly, this idea can be applied to the p-GaAs detector under discussion. For comparison between different cavity designs, all calculations were made to detectors with the incoming light from the bottom. In this case, a gold film could be deposited on the device surface as the top mirror. Based on an optical transfer-matrix method, cavity optimization on the absorption enhancement was evaluated through calculating the ratio of total squared electric field in emitter layers to that of the incoming light. Results are shown in Fig. 5.32. As the high-reflection wavelength range of the gold film is broad, an overall enhancement can be observed in both the MWIR and LWIR region. However, such improvement could be undesirable for p-GaAs detectors. As mentioned before, unnecessary noise is resulted because of response from other regions (e.g., LWIR) if the detector is specifically designed for MWIR detecting. Thus, it will be desirable to narrow the spectral detection. Increasing the barrier height to reduce λt can be one of methods. Another option is to use an F–P cavity with a localized enhancement region. As shown in Fig. 5.32A, a distributed Bragg reflector (DBR) consisted of alternating layers with equal optical thickness (λ0 /4), but different refractive index can produce a high-reflection range centered at the wavelength λ0 . By using DBR in place of the gold mirror, cavity enhancement localized around λ0 was obtained as seen in curve (III) (Fig. 5.32B). A further enhancement is also possible by using another GaAs/AlGaAs DBR as the bottom mirror. The increase in the reflectivity of the top mirror enhances the standing wave inside the F–P cavity and hence the absorption. However, the full-width at half-maximum (FWHM) is drastically reduced, creating sharp peaks as seen in Fig. 5.32C. Also shown is a structure with two GaAs/Al0.5 Ga0.5 As DBRs (curve V).

293

100

(A)

75

(C)

Au

IV V

4

5 × SiO2/TiO2 pairs

50 25

3

Cavity enhancement factor (×10−4)

0 (B)

III

2.5

II 2

2.0

I

Cavity enhancement factor (×10−4)

Reflectivity (%)

Homo- and Heterojunction Interfacial Workfunction

1.5 1 1.0

2

4 6 8 Wavelength (µm)

10

3

4 Wavelength (µm)

5

FIGURE 5.32 Comparison of calculated cavity-enhancement factors for detector SP3. The cavity-enhancement factor is defined as the total squared electric field for the emitter layers to the incoming light. Curve (I) represents the calculated result for detector SP3 without cavity enhancement, (II) for the structure to optimize SP3 by depositing a gold top mirror, (III) for the structure with a five-pair SiO2 /TiO2 top DBR, (IV) for the structure with a five-pair SiO2 /TiO2 top DBR and a one-pair GaAs/Al0.9 Ga0.1 As bottom DBR, and (V) for the structure with a 20-pair GaAs/Al0.5 Ga0.5 As top DBR and a five-pair GaAs/Al0.5 Ga0.5 As bottom DBR. All calculations assume the light is incoming from the bottom side of the device. This configuration will facilitate the fabrication of metallic (gold) or dielectric (SiO2 /TiO2 ) mirrors. A comparison of reflection spectra between the gold film and a five-pair SiO2 /TiO2 DBR is shown in (A), indicating localized high-reflection wavelength region was obtained using a DBR. The use of two DBRs drastically narrows the enhancement peak with which only one cavity mode can be possible selected, e.g., curve (V) in (C).

The Al0.5 Ga0.5 As DBR has a narrower high-reflection wavelength region than that of SiO2 /TiO2 and GaAs/Al0.9 Ga0.1 As DBRs. Therefore, only one cavity mode (∼4 µm) can be selectively enhanced. In summary, the above-mentioned theoretical calculation schematically shows the idea of cavity enhancement either for the overall spectral region or for a specific wavelength range. 3.4.3. Dark current analysis As the SO detectors work at high temperatures, increased thermal emission currents could bring about the issue of electrical uniformity because

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A. G. U. Perera

Temperature (K) 107

300

200

100 400 × 400 μm 800 × 800 μm

R0A (Ω cm2)

105

SP3

103

SP2

SP1 10−1

10−1

4

6

8

10

12

1000/T (K−1)

FIGURE 5.33 Temperature-dependent R0 A for detectors SP1–3. The solid square and hollow circle are the experimental data for square-mesa devices with sizes of 400 and 800 µm, respectively. A fit to the low-temperature region (solid line) based on thermionic currents is extended to compare R0 A deviation at high temperatures. Reused with permission from Lao, Jayaweera et al. (2010), IEEE Copyright 2010.

of the device configuration under discussion (square mesa with ring metal contacts) (Lao et al., 2010). The temperature-dependent zero-bias differential resistance (R0 A) extracted from the current–voltage–temperature (I–V–T) measurements are plotted in Fig. 5.33 for detectors SP1–3. The cross-sectional geometry area was used to calculate R0 A. The lowtemperature R0 A was fitted (solid lines) by using a thermal emission model. Higher R0 A values than the fitting curves for detectors SP1 and SP2 indicates the actual conduction area has reduced at high temperatures. The temperature effects can be related to a conductivity ratio of the vertical component to the lateral: α = σ z /σ x where σ z and σ x are the averaged vertical and lateral component of conductivity, respectively. The σ x shows temperature dependence through hole mobility, while the σ z is determined by the thermal current across the potential barrier with an exponential behavior over the temperatures. Therefore, α also shows an exponential increase with temperatures as shown in Fig. 5.34A, which is consistent with the R0 A deviation. A clear understanding of this electrical

Homo- and Heterojunction Interfacial Workfunction

1.5 × 10−3

5 SP2

SP2

5.0 × 10−4

Current density (A / cm2)

Conductivity ratio

SP1

1.0 × 10−3

295

210 K

4

3 200 K 2 190 K

0.0

SP3 100 200 300 Temperature (K) (A)

1

0

50

100 150 x(µm) (B)

200

FIGURE 5.34 (A) The calculated conductivity ratio α as a function of operating temperatures. (B) The calculated lateral current distribution for detector SP2 with the mesa 400 × 400 µm at 190, 200, and 210 K, respectively. x = 0 represents the device center. The nonuniformity becomes remarkable when the temperature is increased.

characteristics is to numerically calculate the 2-D current distribution based on the α-T relationship in Fig. 5.34A. The vertical current at the interface between the active region and the bottom contact layer for the sample SP2 was calculated as a function of lateral position x, and shown in Fig. 5.34B. Obviously, the current localization is induced at temperatures more than 190 K. Analysis suggests that high-energy barrier can efficiently reduce the issue of current localization. The detector SP3 shows uniform electrical performance for room-temperature operation. Also better electrical uniformity can be attained in detectors with smaller mesas.

4. CONCLUSION A schematic diagram indicating the spectral response ranges and the peak responsivity values of the internal photoemission detector structures (BIB, HIWIP, HEIWIP, SO, QWIP, QDIP, QRIP) discussed in this chapter is shown in Fig. 5.35. In this figure, the solid lines represent the full response wavelength ranges for each detector, while the peak response wavelengths are indicated by the symbols. The Ge:Ga BIB detector having a λt of 220 µm was reported by Watson et al. (1993). An AlGaAs emitter–based terahertz HEIWIP detector, which has a threshold of 128 µm (2.3 THz), was reported

296

A. G. U. Perera

12 10 8 Peak responsivity (A / W)

[1]

[2] [3]

[4]

[5] [6]

6 1

[10]

[12] [17]

[15]

0.01

[16] [9]

1E-3 [8] 1E-4 1

[9] [9] 10 Wavelength (µm)

HIWIP and HEIWIP SO detector

[7]

[11] 0.1

BIB

LH-HH detector QWIP

[13]

QDIP QRIP

[14] [18] 100

FIGURE 5.35 Summary of the response for different reported detectors. The vertical axis gives the peak responsivity for each detector. The horizontal solid lines represent the response range (ends corresponding to zero-response threshold), while the symbols represent the peak response wavelength. The detectors used in this figure are listed below with their operating temperature (the temperature at which the data was reported at T), reported maximum operating temperature (Tmax ), and BLIP temperature (TBLIP ). [1]: Ge:Ga BIB (T = 1.7 K), Watson et al. (1993); [2]: p-GaSb-HIWIP (T = 4.9 K, Tmax = 15 K), Jayaweera et al. (2007); [3]: p-GaAs HIWIP (T = 4.2 K), Esaev et al. (2004b); [4]: p-AlGaAs HEIWIP (T = 4.8 K, TBLIP = 20 K), Rinzan et al. (2005b); [5]: n-GaAs HEIWIP (T = 6 K, Tmax = 25 K), Weerasekara et al. (2007); [6]: p-GaAs HEIWIP (T = 4.2 K), Matsik et al. (2003); [7] p-Si HIWIP (T = 4.6 K, TBLIP = 25 K, Tmax = 30 K), Ariyawansa et al. (2006b); [8]: SO detector (T = 330 K), Jayaweera et al. (2007); [9]: LH-HH detecors (T = 8 K), Lao et al. (2005); [10]: QWIP (T = 8 K, TBLIP = 12 K), Luo et al. (2005); [11]: QWIP (T = 8 K, TBLIP = 17 K), Luo et al. (2005); [12]: QWIP (T = 8 K, TBLIP = 13 K), Luo et al. (2005); [13]: QCL-like QWIP (T = 10 K, Tmax = 50 K), Graf et al. (2004); [14]: QWIP (T = 3 K), Patrashin and Hosako (2008); [15]: QDIP (T = 80 K, Tmax = 120 K), Huang et al. (2008); [16]: T-QDIP (T = 80 K, Tmax = 150 K), Su et al. (2005); [17]: quantum dot infrared photodetector (QDIP; T = 4.2 K, Tmax = 80 K), Huang et al. (2009); [18]: quantum ring infrared photodetector (QRIP; T = 8 K, TBLIP = 50 K), Lee et al. (2009). The QDIP and QRIP data are reported here for comparison.

by Rinzan et al. (2005b). Other HIWIPs and HEIWIPs are based on the work reported by Jayaweera et al. (2007), Esaev et al. (2004b), Weerasekara et al. (2007), Matsik et al. (2003), and Ariyawansa et al. (2006b). The detectors using IVBA mechanisms are based on the work reported by Jayaweera et al. (2008) and Lao et al. (2010).

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In conclusion, detectors with spectral response as long as ∼220 µm have been reported in BIB detectors and HIWIP detectors (Perera et al., 1992). However, one of the drawbacks associated with BIB detectors is that they require very high quality materials in the barrier in order to achieve the best performance. Also, BIB detectors’ response range is material specific unlike other detectors. AlGaAs/GaAs HEIWIP detectors have shown a broad response with a threshold at 130 µm, while the IVB detectors discussed in this chapter are actually a type of HEIWIP with a detection mechanism based on IVBA processes. The use of this mechanism provides a novel approach realizing uncooled or near room-temperature operation by which greatly reduced weight and/or power requirements are of importance for practical applications.

5. NOMENCLATURE 2D 3D BIB BLIP BZ CB C-V-T D* DWELL FCA FIR FPA f ft FTIR g η HEIWIP HIP HIWIP IR IVB IVBA I–V–T IWIP JDOS

two dimensional three dimensional blocked-impurity-band background limited infrared performance Brillouin Zone conduction band capacitance voltage temperature specific detectivity dots-in-a-well free-carrier absorption far infrared (30–100 µm) focal plane array frequency threshold frequency Fourier Transform Infrared photoconductive gain quantum efficiency Heterojunction Interfacial Workfunction Internal Photoemission Heterojunction/Homojunction Internal Photoemission Homojunction Interfacial Workfunction Internal Photoemission infrared inter-valence-band inter-valence-band absorption current voltage temperature Interfacial Workfunction Internal Photoemission joint density of states

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Jones λ λp λt LWIR MBE MWIR NIR SO SWIR T Tmax TBLIP THz T-QDIP UV VB VLWIR

√ units of specific detectivity, cm Hz/W wavelength peak wavelength threshold wavelength long-wavelength infrared (5–14 µm) molecular beam epitaxy midwavelength infrared (3–5 µm) near infrared (0.8–5 µm) Split-off short-wavelength infrared (3–5 µm) operating temperature maximum operating temperature background limited infrared performance temperature terahertz, 1012 Hz tunneling quantum dot infrared photodetector ultraviolet valence band very-long-wavelength infrared (14–30 µm)

ACKNOWLEDGMENTS This work was supported in part by the U.S. NSF Grant Nos. ECS-0553051 and U.S. Army Grant No. W911NF-08-1-0448. The authors acknowledge the contributions of Dr H. C. Liu and his group at NRC, Canada, Prof. P. Bhattacharya and his group at the University of Michigan, Prof. S. Krishna and his group at the University of New Mexico, Prof. V. I. Gavrilenko and his group at Institute for Physics of Microstructures, Russia, Prof. E. Linfield and his group at the University of Leeds, United Kingdom, and Prof. Yossi Paltiel and his group at Hebrew University of Jerusalem, Israel. Important contributions made by Dr Ian Ferguson’s group at Georgia Institute of Technology, Dr N. Dietz’s group at Georgia State University, Dr S. G. Matsik at NDP Optronics, LLC and the past and present members of the Optoelectronics Laboratory at Georgia State University are also acknowledged. Some of the work reported here were carried out under the support from U.S. Air Force (SBIR and STTR awards to NDP Optronics LLC) and the Georgia Research Alliance. Special thanks are due to Dr Yan-feng Lao and Dr Gamini Ariyawansa for manuscript preparation.

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CHAPTER

6 HgCdTe Long-Wave Infrared Detectors David R. Rhiger ∗

Contents

1. Introduction 2. Material Properties 2.1. Advantages of HgCdTe 2.2. Fundamental properties 2.3. Control of composition 3. Single Wavelength Ellipsometry For Surface Monitoring 3.1. Basic principles 3.2. Material parameters 3.3. Calculated ellipsometric values 4. Current–Voltage Curve Analysis 4.1. Overview 4.2. Experimental procedure 4.3. Current components 4.4. Curve fitting results 4.5. InAs/GaSb superlattice device for comparison 4.6. Summary 5. Published Resources of Broad Interest 5.1. Selected books References

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1. INTRODUCTION Mercury cadmium telluride is a nearly ideal material for infrared sensor applications because of its strong IR absorption, its adjustable wavelength sensitivity, and its favorable semiconductor properties. Since the first ∗ Raytheon Vision Systems, 75 Coromar Drive, Goleta, California 93117, USA

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investigation of this material system, more than fifty years ago (Lawson et al., 1959), a great amount of resources has been devoted to the development and application of HgCdTe-based sensors. Today HgCdTe focal plane arrays are widely used for both military and civil purposes. Many institutions continue to carry out significant efforts aimed at improving the material quality and the methods of device fabrication, as well as developing new device architectures based on HgCdTe. In this chapter, we address selected aspects of HgCdTe technology pertinent to long-wavelength infrared (LWIR) applications. We consider materials having a cutoff of the sensitivity in the wavelength range of 8–14 µm. We emphasize the material properties but discuss some characteristics of individual diodes. Challenges and limitations to the technology are also addressed. For brevity, this chapter does not discuss the performance of focal plane arrays or IR systems. Also, it is confined to the detectors operating in the photovoltaic mode. HgCdTe is a pseudobinary alloy between the binary compounds HgTe and CdTe. The composition is specified by the mole fraction of CdTe, which is the x-value as in Hg1−x Cdx Te. The forbidden energy gap, when measured at a temperature of T = 78 K, extends from −0.26 eV at x = 0 (in HgTe, a semimetal) to 1.61 eV at x = 1 (in CdTe). Within our defined LWIR interval, at 78 K, x ranges from 0.244 (8 µm cutoff) to 0.203 (14 µm cutoff). Although this span of composition may seem narrow, several properties, in addition to the energy gap, exhibit strong variations within this range. A survey of the material properties of LWIR HgCdTe is presented first. After this, some selected topics will be discussed in detail. Finally, we present a list of books that will be of help to the reader who wishes to delve further into the science and technology of LWIR HgCdTe IR detectors.

2. MATERIAL PROPERTIES 2.1. Advantages of HgCdTe HgCdTe has been called the ultimate IR semiconductor (Kinch, 2010). Its well-known advantages are that: • The bandgap energy can be varied continuously over a wide range from zero to more than 1.6 eV. • There is a relatively small lattice mismatch between HgTe and CdTe. The lattice parameter is therefore not a strong function of the composition x, enabling bandgap-engineered structures to be grown with minimal strain.

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• The material has a large absorption coefficient for IR photons, so that devices with a thickness of only about 10 µm can have an internal quantum efficiency close to 100%. • Electrons and holes have high mobilities. • Carrier lifetimes are relatively long, especially when dominated by intrinsic mechanisms, leading to relatively low dark currents, or enabling higher operating temperatures. • The material (at least for x < 0.5) can be doped either n-type or p-type with good control. • The technology has advanced to the point that practical methods have been well established for device fabrication. Considering the LWIR composition range, there are some challenges to the development of detectors because of the narrow gap, which will be discussed in the following section.

2.2. Fundamental properties The fundamental properties of the HgCdTe alloy system are briefly presented. The most commonly used formula for bandgap energy Eg as a function of the CdTe mole fraction x and the temperature T is Hansen et al. (1982) Eg = −0.302 + 1.93x − 0.81x2 + 0.832x3 + 5.35 × 10−4 (1 − 2x)T

(6.1)

When a layer of HgCdTe is sufficiently thick (> 5µm), an IR transmission spectrum will show a well-defined cutoff wavelength, which is given by λ=

1.2398 eVµm hc = Eg Eg

(6.2)

where h is Planck’s constant and c is the speed of light. According to the temperature term in Eq. (6.1), when x < 0.5, Eg decreases as temperature falls, in contrast to nearly all other semiconductors. The most commonly used formula for the intrinsic carrier concentration (units of cm−3 ) is Hansen et al. (1983) 3/4

ni =(5.585 − 3.82x + 0.001753T − 0.001364xT) × 1014 Eg T3/2 Eg exp − 2kB T

(6.3)

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The electron effective mass ratio relative to the free electron mass m0 is Weiler (1981) Ep m0 = 1 + 2F + m∗e 3

1 2 + Eg Eg + 1

(6.4)

where Ep = 19 eV, 1 = 1 eV, and F = −0.8. There are both heavy and light holes in the valence band. However, the heavy holes are dominant because of their much greater density of states. The heavy-hole effective mass ratio m∗hh /m0 is independent of x to a good approximation. Values in the literature show considerable variance (Capper, 1994), but the two most commonly used values are 0.443 (Hansen et al., 1983) and 0.55 (Rogalski, 2011). For other parameters, the reader is directed to the books that are briefly reviewed in Section 6 and the review article by Rogalski (2005).

2.3. Control of composition In the LWIR range, the cutoff wavelength of HgCdTe is a sensitive function of the composition x. Fig. 6.1 shows this relationship at three temperatures. Also evident is the increase in cutoff when the temperature is lowered, due to the temperature dependence of the bandgap. When a layer of HgCdTe 16

Sensitivity-to-x-3.qpc

T = 110 K Cutoff wavelength (µm)

14 78K

55 K

12

10

8

6 0.18

0.20

0.22 0.24 Composition x

0.26

0.28

FIGURE 6.1 Cutoff wavelength versus alloy composition for LWIR HgCdTe. The cutoff changes rapidly with x at the smaller x-values and gets longer as temperature decreases.

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is grown for detector fabrication, both the desired cutoff wavelength and the planned operating temperature must be taken into account to specify the targeted x-value. In growth by liquid phase epitaxy (LPE) (Tobin et al., 1999; Tung et al., 1992) the desired x-value is achieved by careful control of the melt composition and the temperature–time ramp. When layers are grown by molecular beam epitaxy (MBE), the best composition control is achieved by feedback from a spectroscopic ellipsometer mounted on the growth chamber (Edwall et al., 2001). The curves in Fig. 6.1 become steeper as x decreases. Thus, to obtain the desired cutoff wavelength with minimal error, one must achieve more precise control of the composition as the targeted x value decreases. The curves in Fig. 6.2, obtained by differentiating Eq. (6.1) with respect to x, illustrates this effect quantitatively (at T = 78 K). For example, if the target cutoff is 10.2 µm and x increases by 0.0030, then the cutoff becomes shorter by 0.40 µm. Another requirement on the composition is uniformity across the wafer. After several years of effort, significant improvements have been demonstrated. We consider the results of Reddy et al. (2010), who grew LWIR HgCdTe layers on 6 cm × 6 cm CdZnTe substrates by MBE. The cutoff at 78 K was 10.7 µm. The composition was measured by IR transmission at 121 evenly-spaced locations across the wafer. Figure 6.3 shows the distributions of composition x on two wafers, one before, and the other one after a process improvement. On this kind of probability graph, the fact that a 0.00

Sensitivity-to-x-2.qpc

Change in cutoff wavelength (μm)

Δx = 0.0003 −0.10 Δx = 0.0010 −0.20

−0.30 Δx = 0.0030 −0.40 T = 78 K −0.50

6

7

8

9 10 11 Cutoff wavelength (μm)

12

13

14

FIGURE 6.2 Sensitivity of the cutoff wavelength to changes in composition x. This is a challenge to material growers when targeting a specific cutoff wavelength.

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0.227 Cutoff-bef and aft-LW-HCT-1.qpc

0.226

Composition x

0.225

After

0.224 0.223 0.222

Before

0.221 0.220 0.01 0.1

1

5 10 20 30 50 70 80 90 95 Percent of the population

99

99.9 99.99

FIGURE 6.3 Demonstration of improved compositional uniformity in the MBE growth of HgCdTe. Composition was measured at multiple locations across a pair of 36 cm2 wafers, one grown before and the other after a significant process improvement. On this probability plot the less steep curve indicates a narrower distribution. Data from Reddy et al. (2010).

plot is nearly a straight line indicates that the distribution is approximately gaussian. A flatter slope indicates a narrower distribution with respect to the parameter on the vertical axis. The process improvement in the MBE growth technique has reduced the standard deviation of the composition x from 0.0014 to 0.0003. We can convert the latter to a standard deviation in cutoff by referring to the highest curve in Fig. 6.2. The standard deviation in cutoff turns out to be slightly less than 0.05 µm, which should be satisfactory for LWIR focal planes. With growth of HgCdTe on CdZnTe by the LPE method, a similar achievement has been reported by Tobin et al. (1999). They measured composition at 35 locations on wafers with an area of 12 cm2 having a cutoff of 15.1 µm. Within each wafer, the standard deviation of x was 0.0003.

3. SINGLE WAVELENGTH ELLIPSOMETRY FOR SURFACE MONITORING 3.1. Basic principles When processing HgCdTe wafers, it is necessary to monitor the surface conditions. In particular, it is very desirable to determine the degree of surface cleanliness after etching or removal of photoresist. Deposited

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dielectric films should also be characterized. Ellipsometry is appropriate for this purpose, provided that the measurements can be interpreted. Here we present calculations of the ellipsometry parameters representative of the HgCdTe surface having some very thin films of typical compositions, and give a framework for interpreting the measured data. Ellipsometry is an optical technique for characterizing surfaces and thin films with sensitivity at the angstrom level. Bench-top ellipsometers are commonly available in IR semiconductor processing laboratories, and provide nondestructive feedback on the sample characteristics. Ellipsometry involves the reflection of elliptically polarized light from the surface of a sample, causing a change in the state of polarization, shown symbolically in Fig. 6.4. By measuring this change, one may infer certain characteristics of the sample. Ellipsometers are available in spectroscopic and single-wavelength modes. We address the case of the single-wavelength ellipsometer operating at the He-Ne laser line of 632.8 nm, with an angle of incidence of 70◦ (Fig. 6.4) for HgCdTe samples at T = 300 K. This is more often used for wafer process monitoring than the spectroscopic kind because of its simplicity and lower cost. Single wavelength measurements are very convenient and may be performed quickly. The results can often be interpreted in a straightforward manner (Rhiger, 1993). At any wavelength, each measurement can be expressed in terms of the two parameters ψ and 1, defined below. The modification of the polarized beam due to interaction with the sample can be written in terms of the two complex reflectance coefficients rp = E0p /Ep

(6.5)

E0s /Es

(6.6)

rs =

where the first is the ratio of the parallel component of the electric field vector of the light wave after reflection to that before reflection, and the second is the corresponding relationship for the perpendicular components. Parallel and perpendicular components are defined with respect to

70° Film Substrate

FIGURE 6.4 Simplified representation of the ellipsometry measurement. The sample is probed by measuring the change in the state of polarization of the light beam. The angle of incidence is typically 70◦ .

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the plane of incidence, which is the plane containing the incoming and outgoing rays and the normal to the surface. Combining the reflectance coefficients gives the complex reflectance ratio ρ. ρ = rp /rs = tan ψ exp i1

(6.7)

√ where i = −1. Physically, tan ψ is the factor by which the ratio of the p-component amplitude to the s-component amplitude changes upon reflection, and 1 is the change in the phase difference between the two components upon reflection. For each ellipsometric reading, the instrument gives the values of ψ and 1. An attached computer may also calculate some material characteristics, such as a film thickness, when given ˚ films, it is appropriate input parameters. However, for very thin (< 100 A) more convenient to deal directly with ψ and 1. We show in the following how the ellipsometry measurement can be compared with calculated curves for known materials on a plot of 1 versus ψ.

3.2. Material parameters For any isotropic material, the optical properties can be expressed in terms of the complex refractive index n˜ = n − ik

(6.8)

where n is the ordinary refractive index, and k is the extinction coefficient. Both n and k are positive real numbers, which are independent of the angle of incidence but depend on the wavelength of the light. To proceed, we need the values of n and k for HgCdTe. Ellipsometry measurements are available for samples of HgCdTe over the full range of compositions, in which care has been taken to minimize the amounts of surface films (Aspnes and Arwin, 1984; Rhiger, 1993; Vina et al., 1984). When no film is present on the surface, the components of the complex refractive index can be deduced from ψ and 1. Fig. 6.5 shows the resulting experimental data at 300 K for n versus x with a least squares fit of a quadratic curve. We find n = 3.9234 − 0.96618x + 0.095905x2

(6.9)

A quadratic dependence on composition is the standard approach (Chen and Sher, 1995) for representing a great many parameters of semiconductor

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n and k-data-T3-2.qpc

4.0 HgCdTe T = 300 K

Refractive index n

3.8

3.6

3.4

3.2

Rhiger, 1993 Vina, 1984 Aspnes, 1984 Fit to data

3.0 0.0

0.2

0.4 0.6 Composition x

0.8

1.0

FIGURE 6.5 Refractive index as a function of composition for the HgCdTe alloy series. The fit to the data is slightly bowed. This is for a wavelength of 632.8 nm and a temperature of 300 K.

alloys. Eq. (6.9) in more general form can be written as n = (1 − x)nHgTe + xnCdTe − x(1 − x)b

(6.10)

This is the linear average between the two end compounds minus a bowing term for the deviation from a straight line. The bowing parameter b is positive, corresponding to a downward curvature, a condition that applies for most semiconductor alloy properties—including n and k of HgCdTe. The coefficient of x2 in Eq. (6.9) is the same as the bowing parameter. The corresponding plot for k appears in Fig. 6.6 with a fit to the data giving k = 1.1954 − 1.6309x + 0.67713x2

(6.11)

Additional material parameters are needed to complete the analysis. When a typical etchant such as a bromine solution is applied to the surface of HgCdTe, it leaves behind a layer of elemental Te (Arwin and Aspnes, 1984; Rhiger and Kvaas, 1982). The Te layer is amorphous with values n = 4.1 and k = 1.7 (Rhiger, 1993). In addition, air exposure of the etched surface can produce native oxides, for which n = 2.2 and k = 0. Another surface phenomenon is microscopic roughness. This is difficult to quantify, but it can be modeled approximately as a surface film consisting of a

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Extinction coefficient k

1.2

n and k-data-T3-4.qpc

1.4

HgCdTe T = 300 K

1.0 0.8 0.6 0.4 0.2 0.0 0.0

Rhiger, 1993 Vina, 1984 Aspnes, 1984 Fit to data

0.2

0.4 0.6 Composition x

0.8

1.0

FIGURE 6.6 Extinction coefficient as a function of composition for the HgCdTe alloy series. The fit to the data has a pronounced bow. This is for a wavelength of 632.8 nm and a temperature of 300 K.

two-phase mixture, one phase being the same as the underlying substrate material and the other phase being void spaces for which n = 1 and k = 0. The roughness layer is assumed to have a uniform composition at all points between its upper and lower interfaces. It is convenient to assume that the volume of the roughness layer is divided equally between the two phases and its effective optical parameters are then calculated by an averaging method (Rhiger, 1993). The assumptions and approximations required for roughness layers in single wavelength ellipsometry do not permit any quantitative evaluations of the void fraction and thickness, but qualitative interpretations are often sufficient for wafer process monitoring.

3.3. Calculated ellipsometric values The ellipsometric parameters for film-free surfaces of HgCdTe can be calculated as a function of composition from the n and k values of Eqs. (6.9) and (6.11). The result is displayed in Fig. 6.7 as a plot of 1 versus ψ, with the composition x as a parameter along the curve. The LWIR alloys occupy a part of the interval between x = 0.3 and 0.2. The next step is to show how the film-free ellipsometry reading is altered by the presence of very thin surface films. Results for amorphous tellurium (a-Te) are presented in Fig. 6.8. The lowest curve (labeled by x) is part of the film-free HgCdTe curve of the previous figure. The curves

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HgCdTe Long-Wave Infrared Detectors

149

0.7

0.8

0.6 0.5

Δ (degrees)

148

0.4

0.9

147

psi and delta-T3-1.qpc

150

0.3 0.2

146

0.1

0=x

145 1.0 144

HgCdTe T = 300 K Angle of incidence = 70° Wavelength = 632.8 nm

143 142

4

6

8

10 ψ (degrees)

12

14

16

FIGURE 6.7 Plot of the ellipsometric parameters ψ and 1, calculated from n and k, for clean surfaces of HgCdTe, with composition x as a parameter. The LWIR alloys are near x = 0.2.

151

Δ (degrees)

150

20

a-Te-on-HgCdTe(T3)-1.qpc

152

149 10 148 0.38 147 146 10.0

10.5

0.34

0.30

11.0

0.26

11.5

0.22

0.18

12.0 12.5 ψ (degrees)

0.14 13.0

x = 0.10 13.5 14.0

FIGURE 6.8 Calculated values of ψ and 1 for very thin films of amorphous tellurium (a-Te) on the surface of HgCdTe in the LWIR composition range. Bromine etching can leave a-Te on the surface. This chart is useful for qualitative interpretations of ellipsometric readings during wafer processing. The markers on each trajectory are at ˚ thickness intervals of 1 A.

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David R. Rhiger

rising up from this represent the trajectories of the readings for films of ˚ Assuming a-Te of increasing thickness. The markers are at intervals of 1 A. a HgCdTe substrate with x = 0.18, for example, when a film of a-Te is assumed to grow, starting at zero thickness, the (ψ, 1) points follow the upward trajectory from the point labeled 0.18. Measurements in our laboratory on freshly etched LWIR HgCdTe samples have occasionally given ˚ of a-Te is present. 1 values as high as 151◦ , suggesting that about 20 A Knowing the x-value and the chemical history of a HgCdTe sample, one can use this graph to estimate the amount of a-Te on the surface. It turns out that a-Te is relatively easy to identify because it causes a rise in 1 due to its very high extinction coefficient k, whereas most other surface films cause 1 to decrease. Trajectories for thin native oxides on HgCdTe are shown in Fig. 6.9. The upper curve represents film-free HgCdTe, the same as in the previous figure, but now the film trajectories proceed to lower 1 values. The ˚ In general, a 1◦ drop in 1 corresponds to markers are at intervals of 2 A. ˚ in the oxide thickness. Experimentally, we find that an increase of 3.5 A after etching and a few hours of air exposure a typical oxide, thickness on ˚ Another common surface film is a residue of phoHgCdTe is about 20 A. toresist. Its n and k are not uniquely defined. But because it is composed of organic molecules, we would expect the k to be small and the n to be

0.38

0.34

0.30

0.26

0.22

0.18

0.14

x = 0.10

Δ (degrees)

145

20

140

40

135

130 10.0

Nativeox-on-HgCdTe(T3)-1.qpc

150

10.5

11.0

11.5

12.0 12.5 ψ (degrees)

13.0

13.5

14.0

FIGURE 6.9 Calculated values of ψ and 1 for very thin films of native oxide on the surface of HgCdTe in the LWIR composition range. Air exposure oxidizes the surface. This chart is useful for qualitative interpretations of ellipsometric readings during wafer ˚ processing. The markers on each trajectory are at thickness intervals of 2 A.

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HgCdTe Long-Wave Infrared Detectors

0.38

0.34

0.30

0.26

0.22

0.18

0.14

x = 0.10

Δ (degrees)

145 Native oxide

140

nativeox-on-HgCdTe(T3)-2.qpc

150

Roughness

135

130 10.0

10.5

11.0

11.5

12.0 12.5 ψ (degrees)

13.0

13.5

14.0

FIGURE 6.10 Calculated values of ψ and 1 for very thin films of native oxide and microscopic roughness on the surface of HgCdTe starting with two particular HgCdTe x-values as examples. This shows that roughness can mimic an oxide layer, but they can be distinguished by appropriate chemistry.

about 1.5. Our experiments show that its ellipsometric signature approximately resembles the native oxide, but the thickness calibration should be somewhat different. Figure 6.10 shows two calculations of microscopic ˚ Unfortunately, the trajectoroughness, with markers at intervals of 2 A. ries are very close to those for native oxides on the same substrate. This ambiguity can be resolved by etching the sample briefly in very dilute hydrochloric acid, which readily dissolves the native oxide but does not alter the roughness, and then re-measuring. In summary, single wavelength ellipsometry at 632.8 nm has proven to be very effective for rapid, nondestructive monitoring of HgCdTe surfaces when processing wafers for device fabrication. If the sample history and x-value are known, the (ψ, 1) measurements can be readily interpreted by reference to the graphs presented here.

4. CURRENT–VOLTAGE CURVE ANALYSIS 4.1. Overview Most LWIR photovoltaic HgCdTe detectors consist of an n-type absorbing region adjacent to a p-type collecting layer. The current–voltage (I–V) characteristics of the p–n junction when measured in the dark (in the

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David R. Rhiger

absence of any IR flux other than that due to the surroundings at the same temperature) can be analyzed to diagnose problems and improve our understanding of how the device functions. It is particularly helpful to discern the origins of the dark current in order to guide efforts to minimize detector noise. Although I–V characteristics of LWIR HgCdTe devices have been analyzed on several occasions, the treatment of the generation-recombination (GR) current has not been optimum. We have used a more thorough treatment of GR current (Rhiger et al, 2008) (Rhiger et al, 2009) than most previous analyses applied to HgCdTe, by employing the same equation with the same fitting parameters on both sides of zero bias. This contrasts with most other treatments in which separate equations with unrelated parameters have been used to model the GR current in forward and reverse biases. In the following sections, we apply the improved fitting method to a HgCdTe diode having a 78 K cutoff wavelength of 10.5 µm, analyzing its I–V curves over a wide temperature range. We find that, although the diffusion current is dominant, the GR current is not negligible. Evidence that we are indeed observing a GR current component is that the GR amplitude (defined below) exhibits the expected temperature dependence from 250 to 38 K. Also, we define a parameter called the dynamic ideality factor, representing the slope at any point on the forward bias curve, to help reveal GR current.

4.2. Experimental procedure The HgCdTe material was grown by Hg-melt liquid phase epitaxy (LPE) from two successive melts in the p-on-n configuration on a (111) CdZnTe substrate. Indium was used for doping the n-type absorber layer and arsenic for the p-type collector layer, which had a wider bandgap. Growth and processing were performed at Raytheon Vision Systems. Mesas were etched with bromine solution by conventional photolithography and the surface was passivated with a layer of CdTe. Cutoff wavelength at the 50% response point was measured to be 10.5 µm at 78 K by back side illumination of the same diode as the I–V measurements. Fig. 6.11 shows the I–V curves for the HgCdTe diode. The forward (positive) bias region shows an exponential voltage dependence, except for the higher currents where series resistance is important. In reverse (negative) bias, we observe that between 250 and 86 K, the curves appear to flatten out and to fall with temperature, while for T < 86 K the curves show a pronounced reversal of the temperature dependence. The latter, as we show below, is a manifestation of band-to-band tunneling (BBT), which increases exponentially as the HgCdTe bandgap decreases with falling temperature. The resistance-area product at zero bias (R0 A) at 78 K is 400 ohm cm2 .

HgCdTe Long-Wave Infrared Detectors

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10−2

Current (A)

10−4 10−6 10−8 10−10 10−12 10−14 −0.6

317

−0.5

−0.4

−0.3

−0.2

−0.1

0.0

0.1

0.2

T (K) 250 197 163 138 120 106 94.8 86.0 78.7 72.2 66.9 62.3 58.3 55.6 51.7 46.5 42.2 38.6 35.6 33.0

Bias (V)

FIGURE 6.11 Absolute value of current versus bias for the HgCdTe diode. Temperatures range from 33 to 250 K.

4.3. Current components Gilmore et al. (2006) developed a method for fitting I–V curves and applied it to HgCdTe. They allowed the following current mechanisms: diffusion, generation-recombination (GR), band-to-band tunneling (BBT), trap-assisted tunneling (TAT), series resistance, and shunt resistance. In a very long wavelength IR diode, for example, they found that in reverse bias, diffusion was dominant near 70 K with a minor contribution from TAT, while TAT and BBT accounted for most of the reverse current near 30 K. Current through a shunt resistance was found to be negligible, and avalanching was not present. In summary, Gilmore et al. (2006) demonstrated that HgCdTe I–V curves could be analyzed in a clearly defined manner and established a robust method for doing so. We briefly summarize the equations used in this method. The voltage V on the junction is positive for forward bias. The diffusion and GR currents are written in combined form as Idiff = I0 (eqV/nkB T − 1)

≈

I0 eqV/nkB T

(6.12)

where I0 is the saturation current, n is the ideality factor, q is the unit charge, kB is Boltzmann’s constant, and T is the temperature. The approximation on the right-hand side applies when qV >> nkB T and describes the exponential behavior in forward bias. It is typically assumed that a purely diffusion current is represented by n = 1, while a GR current

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would correspond to n = 2 and a mixture of these mechanisms would give 1 < n < 2. The BBT current is parameterized according to

IBBT = ABBT V(Vbi − V)m exp

−RBBT (Vbi − V)m

(eqV/kB T − 1)

(6.13)

in which physical variables have been consolidated into an amplitude ABBT , a rate RBBT , and an exponent m to be determined by the fit. The built-in voltage of the junction is Vbi , where qVbi is the difference in the conduction band edge between the two sides of the junction, and is usually smaller than the bandgap Eg . The parameterized TAT current is 1/2

ITAT = ATAT (Vbi − V)

S 1+S

(eqV/kB T − 1)

(6.14)

with 1/2

S = FTAT (Vbi − V)

−RTAT exp (Vbi − V)1/2

(6.15)

where ATAT is the amplitude, RTAT is the rate, and FTAT is called the form. The model also assumes a resistor in series with the junction. The voltage dropped across this resistor is subtracted from the externally applied voltage to obtain the junction voltage V used above. For LWIR detectors, other authors (Tobin, 2006; Zemel et al., 2005) have fitted I–V curves of HgCdTe diodes with varying treatments of the specific current mechanisms and varying procedures for optimizing the parameters. In addition, Krishnamurthy et al. (2006) have eliminated some simplifying assumptions in the analysis of TAT, deriving a more general form that takes into account the linearly varying electric field in the depletion region and improves the handling of trap occupation. The GR current originates in the depletion region of the p-n junction where trap sites within the forbidden gap facilitate the transition of carriers between the bands. In reverse bias there is a net generation of carriers, with electrons going from the valence band to the trap sites, and from trap sites to the conduction band in two thermally-activated jumps. In forward bias, excess carriers are injected from the neutral regions on either side into the depletion region, where they recombine through the same traps. No tunneling is involved. The most thorough treatment of the GR current is found in the original paper by Sah et al. (1957). Their equation was discussed for application to

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319

HgCdTe early by Reine et al. (1981). The equation is qni WA IGR = √ τno τpo

qV 1 sinh f (b) q 2kB T 2k T (Vbi − V)

(6.16)

B

where W is the depletion width, ni is the intrinsic carrier concentration, τno and τpo are the electron and hole lifetimes, A is the junction area, and other parameters have been defined earlier. The function f (b) is given by f (b) =

Z∞ u2

du + 2bu + 1

0

(6.17)

where b

−qV = exp 2kB T

CGR

(6.18)

and CGR = cosh

τpo 1 Et − Ei + ln kB T 2 τno

(6.19)

where Et is the trap energy level and Ei is the intrinsic level. Some observations from these equations are as follows. First, CGR ≥ 1. Second, the parameter b is always positive and the function f (b) is also always positive, as we show below. Third, the hyperbolic sine function makes the current go through zero at V = 0, which is physically appropriate. Fourth, the current blows up when V = Vbi in forward bias, placing a bound on the domain of applicability. It turns out that Eq. (6.16) applies for any reverse bias, and into positive bias up to Vmax = Vbi − z(kB T/q)

where z ≈ 2

(6.20)

As an example we assume a built-in voltage of 0.100 volts (for LWIR detectors) and a temperature of 78 K. In this case, the maximum forward bias at which Eq. (6.16) can be applied is approximately 0.086 volts. Considering the function f (b) the integral in Eq. (6.17) gives p 1 ln 2b2 + 2b b2 − 1 − 1 f (b) = √ 2 b2 − 1

for b > 1

(6.21)

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and 1

tan f (b) = √ 1 − b2

−1

! √ 1 − b2 b

for

b<1

(6.22)

In both Eqs. (6.21) and (6.22), taking the limit as b → 1 we find f (b) = 1

and

df db = −1/3

at b = 1

(6.23)

Thus the function and its derivative are continuous at b = 1. For small b, f (b) levels off at π/2, while for large b it falls as (1/b) ln b, but always remains positive. It is crucial to recognize that GR current, if it is present, occurs in both forward and reverse bias. Any improved modeling method should require the GR current in reverse bias to be consistent with that in forward bias. This is accomplished by applying Eq. (6.16), with bias-independent parameters. To this end, we have modified the I–V curvefitting method of Gilmore et al. (2006) to incorporate GR current according to Eq. (6.16). For convenience this current is parameterized as qV 1 sinh f (b) IGR = AGR √ 2kT Vbi − V

(6.24)

where AGR is the amplitude to be determined by the fit. The only other adjustable parameter is CGR , introduced in Eq. (6.18), which enters through f (b). Another modification was to hold the ideality factor at n = 1 in Eq. (6.12) for pure diffusion. The BBT and TAT formulas are unchanged. The ideality factor (in forward bias) can help distinguish between GR and diffusion currents. However, the relative weight of the two can vary with bias. In silicon diodes, it is often the case that GR and diffusion dominate in the lower and higher forward bias ranges, respectively (Sah et al., 1957). We have found it useful to consider a dynamic ideality factor as a representation of the slope on any short interval of the forward bias curve. Considering a pair of neighboring points on a forward bias curve, and applying the approximation on the right-hand side of Eq. (6.12), we define the dynamic ideality factor to be n=

q (V2 − V1 ) kB T

1 ln(I2 /I1 )

(6.25)

The subscripts 1 and 2 label the coordinates of the two points on the I–V curve. Moving the pair of points along the curve we obtain n as a function

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3.0 HgCdTe

Dynamic ideality factor n

2.5

2.0

T (K) 30.8 38.6 46.5 58.3

72.2 94.8 120

1.5

1.0 R series influence

0.5

0.0 10−12

10−11

10−10

10−9 10−8 10−7 Forward current (A)

10−6

10−5

10−4

FIGURE 6.12 Dynamic ideality factor n versus forward current for the HgCdTe diode. Due to the influence of series resistance, results are valid only for current less than 10−6 A. Dominant diffusion current is evidenced by clustering of the curves near n = 1. GR current is a secondary contributor at the lower temperatures. Each curve is for a different temperature.

of bias or current. As expected, 1 < n < 2 and the regions of different behavior can be identified. The dynamic ideality factor for the HgCdTe diode is shown in Fig. 6.12 for several temperatures. Values are not reliable for I > 10−6 A where series-resistance influences the characteristic. For I < 10−6 A, we find n close to 1 except when T < 46 K, suggesting the dominance of diffusion current with a minor GR contribution.

4.4. Curve fitting results The new I–V curve fitting method was applied to the curves in Fig. 6.11. Figure 6.13 gives the result, showing diffusion dominance over most of the range. BBT appears only at the most negative bias region where it becomes very significant. Although TAT and a shunt resistance were allowed in the fits, no contributions were found at 78 K. The fraction of total current due to each mechanism at 78 K is plotted versus bias in Fig. 6.14, where diffusion dominates through most of the bias range, but GR is not negligible. These results are consistent with our observations above based on the dynamic ideality factor. The temperature dependence of the GR current amplitude AGR offers a good test of the GR behavior. Comparing Eqs. (6.16) and (6.24), we find

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10−4

615277-C23

Current measured Total of fit Diffusion GR BBT

Current (A)

10−6 10−7 10−8 10−9

Diff GR

10−10 10

615277-C23-78K-comp-1-f11.qpc

HgCdTe 78K

10−5

BBT

−11

10−12 −0.7

−0.6

−0.5

−0.4

−0.3 −0.2 Bias (V)

−0.1

0.0

0.1

FIGURE 6.13 Results of the fit of dark current components to the I–V curve of the HgCdTe diode at 78K.

615277-C23-Icomp-78Ka-f14.qpc

1.0 HgCdTe 78 K Fraction of total current

0.8

0.6

diffusion

BBT

0.4 GR 0.2

0.0 −0.7

−0.6

−0.5

−0.4

−0.3

−0.2

−0.1

0.0

−0.1

Bias (V)

FIGURE 6.14 Fraction of the total current attributable to each dark current mechanism versus bias on the junction, for the HgCdTe diode at 78K. This corresponds to Figure 6.13.

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HgCdTe Long-Wave Infrared Detectors

that AGR should vary with temperature as ni T. As a general rule, the intrinsic carrier concentration varies as ni = CT3/2 exp(−Eg / 2kB T)

(6.26)

where C is a constant. Then AGR ∼ T5/2 exp(−Eg / 2kB T)

(6.27)

To test this, we plot AGR /T5/2 versus reciprocal temperature from 250 to 38 K as shown in Fig. 6.15. The activation energy on this graph matches the expected Eg / 2 = 0.059eV (based on the bandgap at 78 K). This result supports the idea that we are in fact seeing the GR mechanism in our analysis of dark currents. It also shows that we can extract the parameters of GR current even when it is not dominant. With decreasing temperature, the BBT amplitude in Fig. 6.16 rises rapidly for HgCdTe due to the shrinking bandgap and the BBT rate behaves similarly.

AGR /T 5/2

10−11

Select-Sb1159-E2-C26 and 615277-C23-params3a-f16.qpc

10−9

SL

SL: Ea = 0.066eV

10−13 HCT

10−15

HCT: Ea = 0.059eV

10−17

10−19

0

5

10

15 1000/T

20

25

30

FIGURE 6.15 Temperature-adjusted amplitude of the GR current for both diodes determined by our fitting method. The activation energy revealed by the slope in both cases is very close to half the bandgap, as expected, over a wide temperature range. This supports the conclusion that we are indeed seeing the GR current. The superlattice has a significantly higher GR current than HgCdTe, most likely because of a greater density of trap sites that facilitate the GR mechanism.

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BBT amplitude

100

HCT

10−2 10−4 10−6 10−8 10−10

SL

0

5

10

15

20

25

30

Select-615277-C23 and Sb1159-E2-C26-1-f17.qpc

102

35

1000/T

FIGURE 6.16 BBT amplitude versus temperature determined by our fitting method, for both diodes. It rises rapidly at low temperatures for HgCdTe because of the decreasing bandgap.

It should be noted that the failure to find a TAT component does not prove that it is absent. If present, the TAT of the form included in our model can turn on significantly in reverse bias, but it vanishes at zero bias and is not allowed in forward bias. Given these constraints and the fact that its voltage dependence roughly resembles that of the GR current in reverse bias, it is possible that the TAT current is buried in the apparent GR component. A further improvement in the analysis might thus lead to a correction of the GR component to reveal the TAT. In any case, the GR contribution is difficult to deny because it is evident in the forward characteristic (especially for T < 78 K) and its amplitude shows the expected temperature dependence.

4.5. InAs/GaSb superlattice device for comparison Because InAs/GaSb superlattice materials are now under development as a potential replacement for HgCdTe for some applications, it is instructive to compare the HgCdTe diode with a superlattice diode having the same size and cutoff wavelength. The results of the I–V curve analysis are presented here. The material was grown by MBE with an IR-absorbing layer doped n-type between 5 × 1015 and 1 × 1016 cm−3 , composed of ˚ 200 InAs/GaSb periods, each period being 65.1-A-thick. The p–n junction was formed by contact with an adjacent p-type superlattice region.

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HgCdTe Long-Wave Infrared Detectors

Sb1159-E2-C26-IV-2-f1.qpc

10−2 10−4

Current (A)

10−6 10−8 10−10 10−12 10−14 Sb1159-E2-C26 −0.6 −0.5 −0.4

−0.3

−0.2 −0.1 Bias (V)

0

0.10

0.2

T (K) 250 197 162 138 120 106 94.8 85.9 78.5 72.3 67.0 62.5 58.4 54.9 51.8 46.5 42.1 38.7 35.7 33.0

FIGURE 6.17 Absolute value of current versus bias for the InAs/GaSb type-II superlattice diode. Temperatures range from 33 to 250K.

All superlattice regions had the same period and there were no intentional barriers. The cutoff wavelength at 78 K was 10.5 µm and the diode was part of a mini-array with a 40-µm pitch. Figure 6.17 shows the I–V curves for the superlattice diode. In forward bias (positive voltage), the straight regions of the curves indicate an exponential voltage dependence, while the curvature above 10−6 A is due to the series resistance. In reverse bias, the curves do not saturate but continue to rise as bias becomes more negative. The R0 A at 78 K is 40 ohm cm2 . The dynamic ideality factor for the InAs/GaSb superlattice diode is shown in Fig. 6.18 for several temperatures. Values are not reliable for I > 10−6 A due to the series resistance. For I < 10−6 A, we find n ranging from about 1.3 to about 2.0, implying a significant GR contribution. The I–V curve fitting method was applied to the curves in Fig. 6.17. Figure 6.19 displays the result for the InAs/GaSb superlattice diode at 78 K. GR accounts for most of the current in reverse bias. As with HgCdTe at 78 K, BBT appears at the most negative bias region, but at the lower temperatures it is much less prominent than in the HgCdTe. Although TAT and a shunt resistance were allowed in the fits, no contributions were found at 78 K. The fraction of total current due to each mechanism at 78 K is plotted versus bias for the superlattice in Fig. 6.20, showing the GR dominance. Diffusion dominates only above the crossover at 0.05 volts forward bias. These results support our earlier observations based on the dynamic ideality factor. The GR amplitude is plotted in Fig. 6.15. along with that of the HgCdTe device. Again, the activation energy here is close to half

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Sb1159-E2-C26-dyn-n-7-f8.qpc

3.0 InAs/GaSb SL

Dynamic ideality factor n

2.5

2.0

1.5

1.0

0.5

0.0 10−12

T (K) 30.7 40.3 51.8 62.5

10−11

R series influence

78.5 85.9 94.8 106

10−10

10−9 10−8 10−7 Forward current (A)

10−6

10−5

10−4

FIGURE 6.18 Dynamic ideality factor n versus forward current for the InAs/GaSb superlattice diode. Due to the influence of series resistance, results are valid only for current less than 10−6 A. GR current is evidenced by values of n above 1 up to approximately 2. Each curve is for a different temperature.

10−5

InAs/GaSb 78 K

Current measured Total of fit Diffusion GR BBT

10−6 Current (A)

Select-Sb1159-E2-78K-comp-1-f10.qpc

10−4

10−7 10−8

GR

10−9 Diffusion

10−10 BBT 10−11 10−12 −0.6

−0.5

−0.4

−0.3 −0.2 Bias (V)

−0.1

0.0

0.1

FIGURE 6.19 Results of the fit of dark current components to the I–V curve of the InAs/GaSb superlattice diode at 78K.

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HgCdTe Long-Wave Infrared Detectors

Fraction of total current

GR

InAs/GaSb 78K

0.8

Sb1159-lcomponents-78Ka-f13.qpc

1.0

0.6

0.4

0.2 Diffusion BBT 0.0 −0.5

−0.4

−0.3

−0.2 Bias (V)

−0.1

0.0

0.1

FIGURE 6.20 Fraction of the total current attributable to each dark current mechanism versus bias on the junction, for the InAs/GaSb superlattice diode at 78K. This corresponds to Figure 6.19.

the bandgap, as expected for a GR current mechanism. Figure 6.16 shows the BBT amplitude, which drops as the temperature decreases, opposite to HgCdTe, most likely because of an increasing superlattice bandgap. The material and device technology for InAs/GaSb superlattice IR detectors is continuing to advance rapidly. See the chapter by Ting in this volume. The superlattice device we have analyzed here is not of the most recent vintage and should therefore not be taken as representative of the best performance attained by InAs/GaSb IR detectors.

4.6. Summary We have modified the treatment of generation-recombination (GR) in an existing good model for fitting dark current I–V curves (Gilmore et al., 2006). Our method requires the same GR function to apply in both forward and reverse bias and involves two voltage-independent fitting parameters for GR. The TAT and BBT functions are unchanged from Gilmore. We have applied this method to sets of I–V curves at multiple temperatures for diodes of the type-II InAs/GaSb superlattice and HgCdTe. The GR component is clearly defined in both materials, being dominant in the superlattice for most bias and temperature conditions, while being smaller than diffusion current but not negligible in HgCdTe. The GR current amplitude

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AGR in both materials shows the appropriate temperature dependence, exhibiting activation energy of Eg /2 when AGR /T5/2 is plotted versus reciprocal temperature. This helps confirm that our analysis is indeed seeing GR current. Also, the dynamic ideality factor (in forward bias) is found to be useful as a qualitative indicator of the relative weights of diffusion and GR contributions to the dark current. The diffusion current appears to be approximately equal in the two materials for most of the temperature range. However, the GR current is definitely greater in the superlattice than HgCdTe. Referring to Eq. (6.16), the only factors likely to be responsible for this difference would be the carrier lifetimes in the depletion region τno and τpo . A higher trap density is the probable cause of shorter lifetimes. Therefore, efforts at improving type-II superlattice IR detector performance should include the goal of reducing the trap density. Measurements of the minority carrier lifetimes (Donetsky et al., 2010) in both materials are consistent with the differences in dark current between the superlattice and HgCdTe.

5. PUBLISHED RESOURCES OF BROAD INTEREST There exists a great body of literature on the science and technology of HgCdTe because of its importance in both civil and military applications. The technologies of material growth and device fabrication have matured to the point that HgCdTe-based sensors are now being manufactured and deployed in large numbers. Also, further advances in HgCdTe device design and performance continue to be vigorously pursued at many institutions. Moreover, material in the Hg-rich composition range has drawn the attention of scientific investigators to study phenomena originating from the very narrow energy gap and the unusually small electron effective mass. The five-decade history of scientific progress and technology development in HgCdTe has given rise to the publication of numerous review articles and books that aim to cover certain aspects. Here we list several of the books and describe the particular emphasis of each.

5.1. Selected books Rogalski (2011) has written a 900-page survey of the entire field of infrared detectors, covering all practical IR-sensitive materials and reviewing the fundamentals of radiometry, detector characterization, and detector performance limitations. The book explains the physics of photon detectors, both photoconductive and photovoltaic, as well as thermal detectors, and reviews the technology of focal plane arrays (FPAs). It includes a 119-page section on HgCdTe IR detectors, reviewing crystal growth, band structure, typical device architectures, methods of fabrication, and examples

HgCdTe Long-Wave Infrared Detectors

329

of device performance. The coverage of other detector materials allows the reader to make comparisons. The subject matter is presented in a tutorial style. Capper (1994) has assembled a very useful and broad-ranging reference book entitled Properties of Narrow Gap Cadmium-based Compounds. There are 58 sections by various authors summarizing published data on the properties of HgCdTe, including growth methods, mechanical and optical properties, diffusion rates, defects, band structure, carrier transport, lifetimes, and surface characteristics. Methods of measurement are discussed. When data are in conflict or of unequal reliability, the authors indicate the recommended values. The book also contains many sections on properties of CdTe, CdZnTe, and CdTeSe. The tutorial book by Kinch (2007) explains the device physics of nearly all kinds of IR detectors. A key concept presented for evaluating the relative merits of photon detectors is to compare the density of carriers generated by photons with those generated thermally. This can be quantified by defining the normalized thermal generation rate per unit area (cm−2 ) of the detector G∗th =

nth ατ

=

Gth αt

(6.28)

where nth is the density (cm−3 ) of thermally generated carriers, α is the IR absorption coefficient (units of cm−1 ), τ is the carrier lifetime, and t is the thickness of the absorbing region. Also Gth is the ordinary thermal generation rate. Issues of carrier lifetime, detector geometry, noise, and dark current are presented in detail. The author concludes that HgCdTe is the material of choice for most IR detector applications. Chu and Sher (2008) have written a detailed review of the properties of HgCdTe and related materials from a theorist’s point of view, with abundant comparisons to experimental data. The book explains the physics behind each material property. It also provides brief histories of the development of some of the applicable theories. Topics covered include dynamics of crystal growth, phase diagrams, defects, band structure calculation methods and results, band-related properties of HgCdTe, carrier transport, and optical characteristics of HgCdTe. Numerical tables and analytical formulas for HgCdTe properties are also provided. The book by Chen and Sher (1995) addresses the properties of compound semiconductors and their pseudobinary alloys. The authors explain the methods of calculating band structures, as well as crystal bonding, carrier transport, elasticity, and phase diagrams. Both II-VI and III-V material families are covered. Full lists of the experimental and theoretical parameter values of the band structures are given for many compounds and

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alloys, along with tables of elastic and thermodynamic quantities for the materials. Rogalski et al. (2000) have written a comprehensive account of the physics and technology of photovoltaic IR detectors. HgCdTe is emphasized but other materials are also addressed. The published literature is thoroughly covered and many examples of material and device data are reviewed in detail. Of particular interest are the section on the fundamental limits of HgCdTe photodetector performance and the review of current HgCdTe detector technology. The chapter by Reine et al. (1981) has become a standard reference throughout the photovoltaic HgCdTe community. The authors explain the basic physics of the detector and derive the equations for current as a function of device geometry and surface recombination. Dornhaus and Nimtz (1983) have written a treatise on the basic physics of the HgCdTe material system. Although many topics are addressed, the emphasis is on magneto-optical methods and the physical phenomena related to smallest values of the band gap.

REFERENCES Arwin, H., and Aspnes, D. E. (1984). J. Vac. Sci. Technol. A 2, 1316–1323. Aspnes, D. E., and Arwin, H. (1984). J. Vac. Sci. Technol. A 2, 1309–1315. Capper, P. (Ed.) (1994). “Properties of Narrow Gap Cadmium-based Compounds.” INSPEC, the Institution of Electrical Engineers, London. Chen, A., and Sher, A. (1995). “Semiconductor Alloys Physics and Materials Engineering.” Plenum Press, New York. Chu, J., and Sher, A. (2008). “Physics and Properties of Narrow Gap Semiconductors.” Springer Science and Business Media, New York. Donetsky, D., Belenky, G., Svensson, S., and Suchalkin, S. (2010). Appl. Phys. Lett. 97, 052108– 1–052108–3. Dornhaus, R., and Nimtz, G. (1983). The properties and applications of the Hg1−x Cdx Te alloy system. in: “Narrow-Gap Semiconductors,” Springer Tracts in Modern Physics, edited by Hohler, G. vol. 98, Springer-Verlag, Berlin, pp. 119–300. Edwall, D., Phillips, J., Lee, D., and Arias, J. (2001). J. Electron. Mater. 30, 643–646. Gilmore, A. S., Bangs, J., and Gerrish, A. (2006). J. Electron. Mater. 35, 1403–1410. Hansen, G. L., and Schmidt, J. L. (1983). J. Appl. Phys. 54, 1639–1640. Hansen, G. L., Schmidt, J. L., and Casselman, T. N. (1982). J. Appl. Phys. 53, 7099–7101. Kinch, M. A. (2007). “Fundamentals of Infrared Detector Materials.” SPIE Press, Bellingham, WA. Kinch, M. A. (2010). J. Electron. Mater. 39, 1043–1052. Krishnamurthy, S., Berding, M. A., Robinson, H., and Sher, A. (2006). J. Electron. Mater. 35, 1399–1402. Lawson, W. D., Nielsen, S., Putley, E. H., and Young, A. S. (1959). J. Phys. Chem. Solids 9, 325–329. Reddy, M., Peterson, J. M., Lofgreen, D. D., Vang, T., Patten, E. A., Radford, W. A., and Johnson, S. M. (2010). J. Electron Mater. 39, 974–980. Reine, M. B., Sood, A. K., and Tredwell, T. J. (1981). Photovoltaic Infrared Detectors. in: “Semiconductors and Semimetals vol. 18,” edited by Willardson, R. K., and Beer, A. C., Academic Press, New York, 201–231.

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Rhiger, D. R. (1993). J. Electron. Mater. 22, 887–898. Rhiger, D. R., Gerrish, A., and Hill, C. J. (2008). Analysis of dark current mechanisms in LWIR InAs/GaSb superlattice diodes with comparison to HgCdTe. Unpublished. Rhiger, D. R., and Kvaas, R. E. (1982). J. Vac. Sci. Technol. 21, 168–171. Rhiger, D. R., Kvaas, R. E., Harris, S. F., and Hill, C. J. (2009). Infrared Phys. Technol. 52, 304–309. Rogalski, A. (2005). Rep. Prog. Phys. 68, 2267–2336. Rogalski, A. (2011). “Infrared Detectors,” second edition. CRC Press, Boca Raton, FL. Rogalski, A., Adamiec, K., and Rutkowski, J. (2000). “Narrow-Gap Semiconductor Photodiodes.” SPIE Press, Bellingham, WA. Sah, C.-T., Noyce, R. N., and Shockley, W. (1957). Proc. IRE 45, 1228–1243. Tobin, S. P. (2006). J. Electron. Mater. 35, 1411–1416. Tobin, S. P., Weiler, M. H., Hutchins, M. A., Parodos, T., and Norton, P. W. (1999). J. Electron. Mater. 28, 596–602. Tung, T., DeArmond, L. V., Herald, R. F., Herning, P. E., Kalisher, M. H., Olson, D. A., Risser, R. F., Stevens, A. P., and Tighe, S. J. (1992). Proc. SPIE 1735, 109–134. Vina, L., Umbach, C., Cardona, M., and Vodopyanov, L. (1984). Phys. Rev. B 29, 6752–6760. Weiler, M. H. (1981). Magnetooptical Properties of Hg1−x Cdx Te Alloys. in: “Semiconductors and Semimetals vol. 16,” edited by Willardson, R. K., and Beer, A. C., Academic Press, New York, 119–191. Zemel, A., Lukomsky, I., and Weiss, E. (2005). J. Appl. Phys. 98, 054504–1–054504–7.

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INDEX

A Absorption efficiency, 214 vs. photon energy, 210 Absorption spectra, 75–77 AFM, see Atomic force microscopy Antimonide, arsenide, and arsenide-antimonide III–V semiconductors, 15 Atomic force microscopy (AFM), 158 Auger reduction, 19

B Background-limited performance (BLIP), 168 Band diagram, 61 edge energy positions, strained, 7 gap, 287 structures, 215 Band-to-band tunneling (BBT), 316 amplitude vs. temperature, 324 parameterization, 318 Barrier engineering, 187 infrared detector, 32–37 material, 174–176 BBT, see Band-to-band tunneling BIB detectors, see Blocked-impurity-band detectors BLIP, see Background-limited performance Blocked-impurity-band detectors (BIB detectors), 249 Boltzmann equation, 201 Bound-to-bound (B-B) QWIPs, 74 Bound-to-continuum (B-C) QWIPs, 74 Bound-to-quasibound (B-QB) QWIPs, 74 Brillouin Zone (BZ), 277 Bromine solution, 311 BZ, see Brillouin Zone

C Capture probability, 204 Carrier distribution, 154 CB, see Conduction band CBIRD, see Complementary barrier infrared detector Complementary barrier infrared detector (CBIRD), 11 energy band diagrams of, 33, 35 Complex band structure in InAs and GaSb, 17 Conduction band (CB), 3, see also Valence band (VB) bound-to-bound QWIP, 63 bound-to-continuum QWIP, 66 in bound-to-quasibound QWIP, 67 in broadband QWIP, 68 Contrast, see Modulation Current–voltage (I–V), 315 current components, 317–321 curve analysis, 315 curve fitting results, 321–324 experimental procedure, 316–317 InAs/GaSb superlattice device, 324–327 intrinsic carrier concentration, 323 for superlattice diode, 325 Current–voltage curve analysis, 315–328 Current–voltage–temperature (I–V–T), 294

D Dark current, 77–79, 82–83, 166–168, 179–180, 202–206, 256–258 analysis, 293–295 bias voltage, 78–79 comparisons for, 168 densities, 36, 203 noise vs. bias voltage, 82 reduction, 26–30 DBR, see Distributed Bragg reflector

333

334

Index

Density of states (DOS), 154 Detectivity, see also Responsivity vs. bias voltage, 90 vs. cutoff energy, 90 detector operating temperature, 123 for QWIP, 92 Detector fabrication, 37–39 Deuterated triglycine sulfate (DTGS), 196 pyroelectric detector, 196 DH, see Double heterojunction Dielectric function, 221 Distributed Bragg reflector (DBR), 292 DOS, see Density of states Double heterojunction (DH), 11 flat-band energy band diagrams of, 33 Double heterostructure (DH), 12 Drift velocity, 203 Drude frequency, 221 DTGS, see Deuterated triglycine sulfate Dual-band energy band diagram, 138 focal planes, 136–143 nBn structure, 33 NE1T histogram, 144 QWIP, 138 QWIP device, 95, 137 DWELL, see Quantum dots-in-a-well Dynamic ideality factor, 320

E EL, see Electroluminescence Electroluminescence (EL), 39, 40 Electron absorption and relaxation, 223 drift mobilities, 206 effective mass ratio, 306 energy and diagram, 26 Electronic pulse generator, 237 Elements in solar system, 145 solar abundance, covalent radii, and hardness, 146 Ellipsometry, 309 film-free, 312 measurement, 309 single wavelength, 308–315 values, 312–315 Emission spectra, 232–234 Emission-capture model, 204–206 Energy band diagrams, 33, 35, 138, 248 Escape current density, 204 Etchant, 311

F Fabry–Perot (F–P), 291 Far infrared (FIR), 154, 162 Fermi distribution function, 213 energy, 199, 215 FIR, see Far infrared Focal plane arrays (FPAs), 2, 8–11, 154, 328 Four-band QWIP device, 97 Fourier Transform Infrared (FTIR), 139, 237 Fourier transform PL excitation (FTPLE), 42 F–P, see Fabry–Perot FPAs, see Focal plane arrays Free carrier–based infrared detectors, 247–277 FTIR, see Fourier Transform Infrared FTPLE, see Fourier transform PL excitation Full-width at half-maximum (FWHM), 292 FWHM, see Full-width at half-maximum

G GaAs/AlGaAs material system, 218 GaAs-based HIWIP interband and intraband response, 272 GaN/AlGaN split-off band detector, 288 Generation-recombination (G-R), 2, 26 Generation-recombination current (GR current), 316 current amplitude, 321 diffusion and, 317 origination, 318 parameterization, 320 temperature-adjusted amplitude, 323 G-R, see Generation-recombination Graded barriers and resonant escape, 289–291 Gratings, 95–97 coupler optimization, 217–222 1D, 218, 220 periodic, 92–95

H hB, see Hole-barrier Heavy-hole (HH), 6, see also Light-hole (LH)

Index

HEMT, see High-electron mobility transistor Heterojunction detectors, 263–270 HEterojunction Interfacial Workfunction Internal Photoemission detectors (HEIWIP detectors), 251 band diagram, 264 barrier height variation, 253–254 comparison, 265 n-GaAs emitter/AlGaAs barrier, 268–270 n-GaN/AlGaN HEIWIP detectors, 270 p-AlGaAs emitter/GaAs barrier, 265–268 p-GaAs emitter/AlGaAs barrier, 264–265 responsivity of, 280 UV–IR dualband detectors, 273–274 Heterojunction/Homojunction Internal Photoemission detectors (HIP detectors), 247 BIB detectors, 249 dark current, 256, 257 dualband detectors, 270–277 energy band diagrams, 248 HIP detectors, 247, 250 interband and intraband response, 272 light–heavy hole transition effects, 262–263 measured workfunction, 263 n-GaN/AlGaN HEIWIP detectors, 270 NIR-FIR dualband HIWIP detectors, 271–273 p-AlGaAs emitter/GaAs barrier HEIWIP detectors, 265–268 p+ -GaAs/GaAs HIWIP detectors, 261–262 p+ -GaSb/GaSb HIWIP detectors, 260–261 p+ -Si/Si HIWIP detectors, 259–260 p-GaAs emitter/AlGaAs barrier HEIWIP detectors, 264–265 photo currents, 276 response, 296 spectral response, 285 UV/IR responses, 273 UV–IR dual-band detector, 273–274 HH, see Heavy-hole High-electron mobility transistor (HEMT), 16

335

HIP detectors, see Heterojunction/Homojunction Internal Photoemission detectors HIWIP, see Homojunction Interfacial Workfunction Internal Photoemission Hole-barrier (hB), 34 Homojunction, 245 detectors, 258–262 Homojunction Interfacial Workfunction Internal Photoemission (HIWIP), 251 barrier height variation in, 251–253 comparison of, 259 doping concentration dependence, 252 p+ -GaAs/GaAs, 261–262 p+ -GaSb/GaSb, 260–261 spectral response, 260

I ICIP, see Infrared photodetector ICL, see Interband cascade laser ICP, see Inductively coupled plasma IDCA, see Integrated Dewar Cooler Assembly InAs quantum dot growth, 158–159 InAs/GaAs system, 161 energy level structure, 167 InAs/GaSb superlattice attributable total current fraction, 327 band structure, 19, 21 conduction and valence band DOS, 24 dark current components fit, 326 dynamic ideality factor vs. forward current, 326 energy band diagrams, 22, 31 heavy-hole 1 subband, 23 I–V curves, 325 materials, 324 unstrained band edge energy positions, 7 InAs/GaSb/AlSb energy band alignment, 16 Incident radiation intensity, 207 Inductively coupled plasma (ICP), 12 Infinite periodic grating, absorption QE of, 99 Infrared (IR), 244 radiation in GaAs, 255

336

Index

Infrared photodetector (ICIP), 37 InGaAlAs capping photocurrent comparison, 185 InGaAs capping photocurrent comparison, 185 InGaAs–GaAs quantum-dot infrared detector red shift, 173 spectral response, 172 Integrated Dewar Cooler Assembly (IDCA), 117 Interband cascade laser (ICL), 37 Internal photoemission (IP), 247 Inter-valence band absorption (IVBA), 279 Inter-valence band detectors, 277–295 current density vs. temperature, 282 LH-HH transitions, 284–286 parameters for detectors, 283 response, 296 SO detectors, 289–295 uncooled SO detectors, 280–283 valence-band structure, 284 Intrinsic carrier concentration, 305 Intrinsic infrared photodetector band diagram, 60 IP, see Internal photoemission IR, see Infrared ISBT electrons absorption and relaxation, 223 final state of, 203 nonzero polarization component, 217 I–V, see Current–voltage I–V curves, 205, 229, 233 IVBA, see Inter-valence band absorption I–V–T, see Current–voltage–temperature

J JDOS, see Joint density of states Jet Propulsion Laboratory (JPL), 160 Joint density of states (JDOS), 20, 284 JPL, see Jet Propulsion Laboratory

L LCAO, see Linear combination of atomic orbital LDA, see Local density approximation LH, see Light-hole

LH-HH transitions, 284 Light coupling, 91–104 Light-hole (LH), 7, see also Heavy-hole (HH) Linear combination of atomic orbital (LCAO), 4 Liquid phase epitaxy (LPE), 307, 316 LiTaO3 , see Lithium tantalate Lithium tantalate (LiTaO3 ), 196 LNA, see Low-noise amplifier LO, see Longitudinal optical Local density approximation (LDA), 212 Longitudinal optical (LO), 156 Long-wave infrared (LWIR), 2, 13, 154 detector, 304 GaAs/Alx Ga1 —As band diagram for, 70 HgCdTe diode I–V curves, 318 Low-noise amplifier (LNA), 238 LPE, see Liquid phase epitaxy LWIR, see Long-wave infrared

M Many-body effects, 211–217 MBE, see Molecular beam epitaxy MCT, see Mercury cadmium telluride [HgCdTe] MEE, see Migration-enhanced epitaxy Mercury cadmium telluride [HgCdTe] (MCT), 5, 303 cutoff wavelength vs. alloy composition, 306 extinction coefficient, 312 focal plane arrays, 304 long-wave infrared detectors advantages, 304–305 composition control, 306–308 current–voltage curve analysis, 315–328 fundamental properties, 305–306 material properties, 304–308 published resources, 328–330 single wavelength ellipsometry, 328–330 MBE growth, 308 plot of ellipsometric parameters, 313 refractive index, 311 trajectories for thin native oxides, 314, 315 wafer processing, 308

Index

Metal organic chemical vapor deposition (MOCVD), 244, see also Organo-metallic chemical vapor deposition (OMCVD) Metal organic molecular beam epitaxy (MOMBE), 73 Mid-wave infrared (MWIR), 2, 13, 164 Migration-enhanced epitaxy (MEE), 161 Minimum resolvable differential temperature (MRDT), 136 ML, see Monolayers MOCVD, see Metal organic chemical vapor deposition Modulation, 128 Modulation transfer function (MTF), 126 Molecular beam epitaxy (MBE), 5, 121, 138, 307 MOMBE, see Metal organic molecular beam epitaxy Monolayers (ML), 158 Monolithic grating structures, 91 Monte Carlo method, 201 MQWs, see Multi-quantum-wells MRDT, see Minimum resolvable differential temperature MTF, see Modulation transfer function Multi-quantum-wells (MQWs), 60, 136 MWIR, see Mid-wave infrared MWIR imaging system, 134 MWIR:LWIR dual-band image, 143

N n-doped bound-to-bound miniband QWIPs, 69–70 n-doped bound-to-continuum miniband QWIPs, 70–71 n-doped bound-to-continuum QWIPs, 65–66 n-doped bound-to-miniband QWIPs, 71–72 n-doped bound-to-quasibound QWIPs, 66–67 n-doped broadband QWIPs, 67–69 n-doped In0.53 Ga0.47 As/In0.52 Al0.48 As QWIPs, 72–73 n-doped In0.53 Ga0.47 As/InP QWIPs, 73–74 n-doped QWIPs, 62–64 NEI, see Noise equivalent intensity NEP, see Noise Equivalent Power

337

NE1T, see Noise equivalent temperature difference n-GaAs emitter/AlGaAs barrier HEIWIP detectors, 268–270 n-GaN/AlGaN HEIWIP detectors, 270 NIR-FIR dualband HIWIP detectors, 271–273 Noise current, 170 Noise equivalent intensity (NEI), 44 Noise Equivalent Power (NEP), 264 Noise equivalent temperature difference (NE1T), 10, 113 bias voltage, 116 comparison, 182 detectivity and, 170–171 FPA uniformity, 116, 126 InP/InGaAs QWIP, 120 Noise measurement, 44–47 Normalized thermal generation rate, 329 Northwestern University (NWU), 12 NWU, see Northwestern University

O OMCVD, see Organo-metallic chemical vapor deposition 1D grating, 218, 220 periodic, 92–93 OPD, see Optical-path-difference Optical coupling structures, 97 Optical-path-difference (OPD), 286 Optimum doping, 174 Organo-metallic chemical vapor deposition (OMCVD), 270, see also Metal organic chemical vapor deposition (MOCVD)

P p-AlGaAs emitter/GaAs barrier HEIWIP detectors, 265–268 Parameterization, 318, 320 p+ -GaAs/GaAs HIWIP detectors, 261–262 p+ -GaSb/GaSb HIWIP detectors, 260–261 p+ -Si/Si HIWIP detectors, 259–260 p-doped QWIPs, 64–65 p-GaAs emitter/AlGaAs barrier HEIWIP detectors, 264–265 p-GaAs/Alx Ga1−x As heterojunction detectors, 268

338

Index

Photoconductive gain, 198, 207 vs. bias voltage, 84, 88 for different well widths, 169 estimation, 169 and noise gain, 83–86 and responsivity, 168–170 Photocurrent, 124, 206, 207, 216, 230, 232, 238, 276 spectrum measurement, 227 Photodetector, 255 Photoemission, 246 Photoemission detector response, 296 structures, 295 Photoexcitation, 290 Photoluminescence (PL), 39, 158 spectroscopy, 39–40 Photoluminescence excitation (PLE), 157 Photon energy, 210 Photon flux, see Photocurrent Photoresponse spectrum, 226 P–I curves, 233 PIG, see Punctuated island growth Pixel dual-band QWIP, 142 finite width QWIP pixel mesa, 101 finite-size pixel effect, 98–100 NE1T histogram, 134 pitch, 98 signal strength of, 129 thin QWIP, 102 PL, see Photoluminescence PLE, see Photoluminescence excitation Point spread functions (PSF), 128 PSF, see Point spread functions Punctuated island growth (PIG), 160 Pyroelectric detector, 196

Q QDIPs, see Quantum dot infrared photodetectors QE, see Quantum efficiency Quantum cascade laser, 236 Quantum dot infrared photodetectors (QDIPs), 154 annealing effect, 160–161 barrier, 174–176, 187 BLIP temperature comparison, 180 dark current, 166–168, 179 detectivity, 180–181 detectivity and NETD, 170–171

device modeling, 186–187 doping, optimum, 174 DWELL detectors, 177 electronic structure, 163, 166 epitaxial self assembled quantum dots, 158 FPA, 181 growth modes for, 159–160 growth optimization, 183–186 growth rate and temperature effect, 160 growth trade-offs, 162 images from, 184 InAs quantum dot growth, 158–159 low-strain DWELL designs, 176 material systems for, 161–162 progress in, 178 responsivity and photoconductive gain, 168–170 RT barriers, 176 single pixel, 178–179 strain calculations, 164–166 submonolayer quantum dots, 186 wavelength selection, 171–174 Quantum dots, submonolayer, 186 Quantum dots-in-a-well (DWELL), 156, 175 confinement-enhanced detectors, 177 low-strain DWELL designs, 176 photocurrent comparison, 185 spectral response for, 175 Quantum efficiency (QE), 11, 40, 86–89 Quantum-well infrared photodetectors (QWIPs), 60, 119, 154 absorption spectra, 75–77 band diagram, 61 bound-to-quasibound LWIR QWIP, 109–110 camera, long wavelength, 111 corrugated structure, 102–104 dark current, 77–79, 82–83 detectivity, 89–91 dualband focal planes, 136 dual-band QWIP device structure, 137 finite width QWIP pixel mesa, 101 finite-size pixel effect, 98–100 FPA, 108, 124, 127 gratings, 95–97 IDCA, 117 imaging array effect of non-uniformity, 105–106

Index

light coupling, 91 LWIR focal planes, 108–110 and VLWIR dualband QWIP detector, 117 MWIR imaging system, 134 and LWIR focal planes, 121 n-doped bound-to-bound miniband QWIPs, 69–70 n-doped bound-to-continuum miniband QWIPs, 70–71 n-doped bound-to-continuum QWIPs, 65–66 n-doped bound-to-miniband QWIPs, 71–72 n-doped bound-to-quasibound QWIPs, 66–67 n-doped broadband QWIPs, 67–69 n-doped In0.53 Ga0.47 As/In0.52 Al0.48 As QWIPs, 72–73 n-doped In0.53 Ga0.47 As/InP QWIPs, 73–74 n-doped QWIPs, 62–64 noise gain and photoconductive gain, 83–86 p-doped QWIPs, 64–65 periodic gratings, 92, 93–95 quantum efficiency, 86–89 random reflectors, 100–102 residual non-uniformity, 115 responsivity, 79–82 thin QWIP pixel, 102, 117 VGA format LWIR focal planes, 110 VLWIR focal planes, 106–108 QWIPs, see Quantum-well infrared photodetectors

R Random reflectors, 100–102 Readout circuit (ROC), 111 Red shift, 173 Reflectance coefficients, 309 Reflectance ratio, 310 Reflection high energy electron diffraction (RHEED), 158 Refractive index, 310 as function of composition, 311 Resonant cavity enhancement, 291–293 Resonant interband tunneling diodes (RITD), 16

339

Resonant tunneling (RT), 176 Responsivity, 79–82, see also Detectivity Responsivity spectra, 79, 207 bias dependent, 81 corrugated QWIP, 104 enhancement, 95 of four bound-to-quasibound VLWIR, 108 function of grating period, 94 p-GaAs emitter/Alx Ga1−x As barrier HEIWIP detectors, 266 and photoconductive gain, 168 photodetector, 255 pixel pitch, 98 spectral parameter, 81 variation of, 268, 269 vs. wavelength, 80 well thickness, 178 Reverse-bias energy diagrams, 28, 29 RHEED, see Reflection high energy electron diffraction RITD, see Resonant interband tunneling diodes RMS, see Root mean square ROC, see Readout circuit Root mean square (RMS), 170 RT, see Resonant tunneling

S Scanning Electron Microscopic (SEM), 95 Schulman diode, 17 SEM, see Scanning Electron Microscopic SEMI, see Shallow-etch mesa isolation Semiconductor band gap and lattice constant, 287 junctions, 245–246 Shallow-etch mesa isolation (SEMI), 12 Shockley-Read-Hall (SRH), 25, 28, 29 recombination, 41 Short-wave infrared (SWIR), 16 Si bolometer, 196 Signal-to-noise ratio (SNR), 180 Single wavelength ellipsometry, 308 ellipsometric values, 312–315 material parameters, 310–312 principles, 308–310 SLS, see Strained layer superlattice SNR, see Signal-to-noise ratio SO band, see Split-off band

340

Index

SO detectors modeling and optimization, 289 dark current analysis, 293–295 design modifications and improvement, 292 graded barriers and resonant escape, 289–291 resonant cavity enhancement, 291–293 response, 296 Specific detectivity, 170 of QWIPs and QDIPs, 181 Spectral current responsivity, 207 Spectral parameter, 81 Spectral response, 172, 285, see also Responsivity spectra well thickness, 178 Spectral variation of refractive index, 209 Split-off band (SO band), 277 s-polarization, 184 SRH, see Shockley-Read-Hall Strain energy, 164 tensor components, 165 Strained layer superlattice (SLS), 2 homojunction LWIR, 36 Submonolayer quantum dots, 186 Superlattice infrared detectors, 25 barrier infrared detector, 32–37 dark current reduction, 26–30 detector fabrication, 37–39 lifetime and dark current, 49 lifetime measurement, 47–49 noise measurement, 44–47 optical characterization, 39–44 unipolar barriers, 25–26 SWIR, see Short-wave infrared

T TAT, see Trap-assisted tunneling Te layer, 311 TEM, see Transmission electron microscopy Temperature-adjusted amplitude, 323 Terahertz (THz), 154 Terahertz Semiconductor Quantum Well Photodetectors (THz QWP), 195 absorption efficiency, 214 absorption quantum efficiency vs. photon energy, 209 applications, 234–239

band structures, 215 barrier Al percentage and well width, 224 blip temperature vs. peak detection frequency, 224 bulk GaAs transmission spectrum, 226 dark current, 202–205 design of, 223–227 detectivity and blip, 198 dielectric function, 221 Drude frequency, 221 electron drift mobilities, 206 electronic pulse generator, 237 emission spectra, 231–234, 235 emission-capture model, 204–205 fabrication, 218 GaAs/AlGaAs material system, 218 high doping, 225 interwell tunneling current vs. barrier thickness, 225 I–V curves, 205, 229, 233 manybody effects, 211 1D grating, 218, 220 photoconductive gain, 207 photocurrent, 206–211, 216, 230, 232, 238 photocurrent spectrum measurement, 227–230 photon energy, 210 photoresponse spectrum, 226 P–I curves, 233 principle, 196–201 quantum cascade laser and, 236 response frequency vs. grating period, 222 simulation and optimization of grating coupler, 217–222 simulation models, 201–202 spectral current responsivity, 207 spectral variation of refractive index, 209 structure parameters for, 228 3D carrier drift model, 203–204 Thermal detectors, 195 Thermal noise current, 170 Thermophotovoltaics (TPV), 17 3D carrier drift model, 203–204 THz, see Terahertz THz QWP, see Terahertz Semiconductor Quantum Well Photodetectors TIR, see Total internal reflection

Index

TM waves, see Transverse magnetic waves Total escape probability, 290 Total internal reflection (TIR), 98 Total quantum efficiency, 256 TPV, see Thermophotovoltaics Transmission electron microscopy (TEM), 158 Transverse electric waves (TE waves), 254 Transverse magnetic waves (TM waves), 254 Trap-assisted tunneling (TAT), 317 parameterization, 318 Tunneling suppression, 17–19 2D periodic gratings, 93–95 Type II, see Type-II broken gap Type-II broken gap, 5 InAs/Ga(In) Sb superlattice, 32 Type-II superlattice Auger reduction, 19 developments in, 11–13 effective masses and transport, 20–25 InAs/GaSb, 2 for infrared detection, 5–8 infrared detectors and focal plane arrays, 8–11 ˚ material system, 13–17 6.1A and the broken-gap band alignment, 3–5 tunneling suppression, 17–19

341

U Unipolar barriers, 25–26 building, 30–32 dark current reduction, 26–30 University of New Mexico (UNM), 12 UNM, see University of New Mexico UV/IR responses, 273 UV–IR dual-band detector, 273–274 contact structure, 275 response, 296

V Valence band (VB), 3 structure, 284 VB, see Valence band Very long-wavelength infrared (VLWIR), 11, 154, 162 Video frame cutoff, 127, 135 VLWIR, see Very long-wavelength infrared

W W superlattice (WSL), 31 Wetting layer, 158 WSL, see W superlattice

Z Zone center, 15

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CONTENTS OF VOLUMES IN THIS SERIES

Volume 1 Physics of III–V Compounds C. Hilsum, Some Key Features of III–V Compounds F. Bassani, Methods of Band Calculations Applicable to III–V Compounds E. O. Kane, The k-p Method V. L. Bonch–Bruevich, Effect of Heavy Doping on the Semiconductor Band Structure D. Long, Energy Band Structures of Mixed Crystals of III–V Compounds L. M. Roth and P. N. Argyres, Magnetic Quantum Effects S. M. Puri and T. H. Geballe, Thermomagnetic Effects in the Quantum Region W. M. Becker, Band Characteristics near Principal Minima from Magnetoresistance E. H. Putley, Freeze-Out Effects, Hot Electron Effects, and Submillimeter Photoconductivity in InSb H. Weiss, Magnetoresistance B. Ancker-Johnson, Plasma in Semiconductors and Semimetals

Volume 2 Physics of III–V Compounds M. G. Holland, Thermal Conductivity S. I. Novkova, Thermal Expansion U. Piesbergen, Heat Capacity and Debye Temperatures G. Giesecke, Lattice Constants J. R. Drabble, Elastic Properties A. U. Mac Rae and G. W. Gobeli, Low Energy Electron Diffraction Studies R. Lee Mieher, Nuclear Magnetic Resonance B. Goldstein, Electron Paramagnetic Resonance T. S. Moss, Photoconduction in III–V Compounds E. Antoncik and J. Tauc, Quantum Efficiency of the Internal Photoelectric Effect in InSb G. W. Gobeli and I. G. Allen, Photoelectric Threshold and Work Function P. S. Pershan, Nonlinear Optics in III–V Compounds M. Gershenzon, Radiative Recombination in the III–V Compounds F. Stern, Stimulated Emission in Semiconductors

Volume 3 Optical Properties of III–V Compounds M. Hass, Lattice Reflection W. G. Spitzer, Multiphonon Lattice Absorption

343

344

Contents of Volumes in This Series

D. L. Stierwalt and R. F. Potter, Emittance Studies H. R. Philipp and H. Ehrenveich, Ultraviolet Optical Properties M. Cardona, Optical Absorption Above the Fundamental Edge E. J. Johnson, Absorption Near the Fundamental Edge J. O. Dimmock, Introduction to the Theory of Exciton States in Semiconductors B. Lax and J. G. Mavroides, Interband Magnetooptical Effects H. Y. Fan, Effects of Free Carries on Optical Properties E. D. Palik and G. B. Wright, Free-Carrier Magnetooptical Effects R. H. Bube, Photoelectronic Analysis B. O. Seraphin and H. E. Benett, Optical Constants

Volume 4 Physics of III–V Compounds N. A. Goryunova, A. S. Borchevskii and D. N. Tretiakov, Hardness N. N. Sirota, Heats of Formation and Temperatures and Heats of Fusion of Compounds of AIII BV D. L. Kendall, Diffusion A. G. Chynoweth, Charge Multiplication Phenomena R. W. Keyes, The Effects of Hydrostatic Pressure on the Properties of III–V Semiconductors L. W. Aukerman, Radiation Effects N. A. Goryunova, F. P. Kesamanly, and D. N. Nasledov, Phenomena in Solid Solutions R. T. Bate, Electrical Properties of Nonuniform Crystals

Volume 5 Infrared Detectors H. Levinstein, Characterization of Infrared Detectors P. W. Kruse, Indium Antimonide Photoconductive and Photoelectromagnetic Detectors M. B. Prince, Narrowband Self-Filtering Detectors I. Melngalis and T. C. Hannan, Single-Crystal Lead-Tin Chalcogenides D. Long and J. L. Schmidt, Mercury-Cadmium Telluride and Closely Related Alloys E. H. Putley, The Pyroelectric Detector N. B. Stevens, Radiation Thermopiles R. J. Keyes and T. M. Quist, Low Level Coherent and Incoherent Detection in the Infrared M. C. Teich, Coherent Detection in the Infrared F. R. Arams, E. W. Sard, B. J. Peyton and F. P. Pace, Infrared Heterodyne Detection with Gigahertz IF Response H. S. Sommers, Jr., Macrowave-Based Photoconductive Detector R. Sehr and R. Zuleeg, Imaging and Display

Volume 6 Injection Phenomena M. A. Lampert and R. B. Schilling, Current Injection in Solids: The Regional Approximation Method R. Williams, Injection by Internal Photoemission

Contents of Volumes in This Series

345

A. M. Barnett, Current Filament Formation R. Baron and J. W. Mayer, Double Injection in Semiconductors W. Ruppel, The Photoconductor-Metal Contact

Volume 7 Application and Devices Part A J. A. Copeland and S. Knight, Applications Utilizing Bulk Negative Resistance F. A. Padovani, The Voltage-Current Characteristics of Metal-Semiconductor Contacts P. L. Hower, W. W. Hooper, B. R. Cairns, R. D. Fairman, and D. A. Tremere, The GaAs Field-Effect Transistor M. H. White, MOS Transistors G. R. Antell, Gallium Arsenide Transistors T. L. Tansley, Heterojunction Properties

Part B T. Misawa, IMPATT Diodes H. C. Okean, Tunnel Diodes R. B. Campbell and Hung-Chi Chang, Silicon Junction Carbide Devices R. E. Enstrom, H. Kressel, and L. Krassner, High-Temperature Power Rectifiers of GaAs1−x Px

Volume 8 Transport and Optical Phenomena R. J. Stirn, Band Structure and Galvanomagnetic Effects in III–V Compounds with Indirect Band Gaps R. W. Ure, Jr., Thermoelectric Effects in III–V Compounds H. Piller, Faraday Rotation H. Barry Bebb and E. W. Williams, Photoluminescence I: Theory E. W. Williams and H. Barry Bebb, Photoluminescence II: Gallium Arsenide

Volume 9 Modulation Techniques B. O. Seraphin, Electroreflectance R. L. Aggarwal, Modulated Interband Magnetooptics D. F. Blossey and Paul Handler, Electroabsorption B. Batz, Thermal and Wavelength Modulation Spectroscopy I. Balslev, Piezooptical Effects D. E. Aspnes and N. Bottka, Electric-Field Effects on the Dielectric Function of Semiconductors and Insulators

Volume 10 Transport Phenomena R. L. Rhode, Low-Field Electron Transport J. D. Wiley, Mobility of Holes in III–V Compounds

346

Contents of Volumes in This Series

C. M. Wolfe and G. E. Stillman, Apparent Mobility Enhancement in Inhomogeneous Crystals R. L. Petersen, The Magnetophonon Effect

Volume 11 Solar Cells H. J. Hovel, Introduction; Carrier Collection, Spectral Response, and Photocurrent; Solar Cell Electrical Characteristics; Efficiency; Thickness; Other Solar Cell Devices; Radiation Effects; Temperature and Intensity; Solar Cell Technology

Volume 12 Infrared Detectors (II) W. L. Eiseman, J. D. Merriam, and R. F. Potter, Operational Characteristics of Infrared Photodetectors P. R. Bratt, Impurity Germanium and Silicon Infrared Detectors E. H. Putley, InSb Submillimeter Photoconductive Detectors G. E. Stillman, C. M. Wolfe, and J. O. Dimmock, Far-Infrared Photoconductivity in High Purity GaAs G. E. Stillman and C. M. Wolfe, Avalanche Photodiodes P. L. Richards, The Josephson Junction as a Detector of Microwave and Far-Infrared Radiation E. H. Putley, The Pyroelectric Detector – An Update

Volume 13 Cadmium Telluride K. Zanio, Materials Preparations; Physics; Defects; Applications

Volume 14 Lasers, Junctions, Transport N. Holonyak, Jr., and M. H. Lee, Photopumped III–V Semiconductor Lasers H. Kressel and J. K. Butler, Heterojunction Laser Diodes A. Van der Ziel, Space-Charge-Limited Solid-State Diodes P. J. Price, Monte Carlo Calculation of Electron Transport in Solids

Volume 15 Contacts, Junctions, Emitters B. L. Sharma, Ohmic Contacts to III–V Compounds Semiconductors A. Nussbaum, The Theory of Semiconducting Junctions J. S. Escher, NEA Semiconductor Photoemitters

Volume 16 Defects, (HgCd)Se, (HgCd)Te H. Kressel, The Effect of Crystal Defects on Optoelectronic Devices C. R. Whitsett, J. G. Broerman, and C. J. Summers, Crystal Growth and Properties of Hg1−x Cdx Se Alloys

Contents of Volumes in This Series

347

M. H. Weiler, Magnetooptical Properties of Hg1−x Cdx Te Alloys P. W. Kruse and J. G. Ready, Nonlinear Optical Effects in Hg1−x Cdx Te

Volume 17 CW Processing of Silicon and Other Semiconductors J. F. Gibbons, Beam Processing of Silicon A. Lietoila, R. B. Gold, J. F. Gibbons, and L. A. Christel, Temperature Distributions and Solid Phase Reaction Rates Produced by Scanning CW Beams A. Leitoila and J. F. Gibbons, Applications of CW Beam Processing to Ion Implanted Crystalline Silicon N. M. Johnson, Electronic Defects in CW Transient Thermal Processed Silicon K. F. Lee, T. J. Stultz, and J. F. Gibbons, Beam Recrystallized Polycrystalline Silicon: Properties, Applications, and Techniques T. Shibata, A. Wakita, T. W. Sigmon and J. F. Gibbons, Metal-Silicon Reactions and Silicide Y. I. Nissim and J. F. Gibbons, CW Beam Processing of Gallium Arsenide

Volume 18 Mercury Cadmium Telluride P. W. Kruse, The Emergence of (Hg1−x Cdx )Te as a Modern Infrared Sensitive Material H. E. Hirsch, S. C. Liang, and A. G. White, Preparation of High-Purity Cadmium, Mercury, and Tellurium W. F. H. Micklethwaite, The Crystal Growth of Cadmium Mercury Telluride P. E. Petersen, Auger Recombination in Mercury Cadmium Telluride R. M. Broudy and V. J. Mazurczyck, (HgCd)Te Photoconductive Detectors M. B. Reine, A. K. Soad, and T. J. Tredwell, Photovoltaic Infrared Detectors M. A. Kinch, Metal-Insulator-Semiconductor Infrared Detectors

Volume 19 Deep Levels, GaAs, Alloys, Photochemistry G. F. Neumark and K. Kosai, Deep Levels in Wide Band-Gap III–V Semiconductors D. C. Look, The Electrical and Photoelectronic Properties of Semi-Insulating GaAs R. F. Brebrick, Ching-Hua Su, and Pok-Kai Liao, Associated Solution Model for Ga-In-Sb and Hg-Cd-Te Y. Ya. Gurevich and Y. V. Pleskon, Photoelectrochemistry of Semiconductors

Volume 20 Semi-Insulating GaAs R. N. Thomas, H. M. Hobgood, G. W. Eldridge, D. L. Barrett, T. T. Braggins, L. B. Ta, and S. K. Wang, High-Purity LEC Growth and Direct Implantation of GaAs for Monolithic Microwave Circuits C. A. Stolte, Ion Implantation and Materials for GaAs Integrated Circuits C. G. Kirkpatrick, R. T. Chen, D. E. Holmes, P. M. Asbeck, K. R. Elliott, R. D. Fairman, and J. R. Oliver, LEC GaAs for Integrated Circuit Applications J. S. Blakemore and S. Rahimi, Models for Mid-Gap Centers in Gallium Arsenide

348

Contents of Volumes in This Series

Volume 21 Hydrogenated Amorphous Silicon Part A J. I. Pankove, Introduction M. Hirose, Glow Discharge; Chemical Vapor Deposition Y. Uchida, di Glow Discharge T. D. Moustakas, Sputtering I. Yamada, Ionized-Cluster Beam Deposition B. A. Scott, Homogeneous Chemical Vapor Deposition F. J. Kampas, Chemical Reactions in Plasma Deposition P. A. Longeway, Plasma Kinetics H. A. Weakliem, Diagnostics of Silane Glow Discharges Using Probes and Mass Spectroscopy L. Gluttman, Relation between the Atomic and the Electronic Structures A. Chenevas-Paule, Experiment Determination of Structure S. Minomura, Pressure Effects on the Local Atomic Structure D. Adler, Defects and Density of Localized States

Part B J. I. Pankove, Introduction G. D. Cody, The Optical Absorption Edge of a-Si: H N. M. Amer and W. B. Jackson, Optical Properties of Defect States in a-Si: H P. J. Zanzucchi, The Vibrational Spectra of a-Si: H Y. Hamakawa, Electroreflectance and Electroabsorption J. S. Lannin, Raman Scattering of Amorphous Si, Ge, and Their Alloys R. A. Street, Luminescence in a-Si: H R. S. Crandall, Photoconductivity J. Tauc, Time-Resolved Spectroscopy of Electronic Relaxation Processes P. E. Vanier, IR-Induced Quenching and Enhancement of Photoconductivity and Photoluminescence H. Schade, Irradiation-Induced Metastable Effects L. Ley, Photoelectron Emission Studies

Part C J. I. Pankove, Introduction J. D. Cohen, Density of States from Junction Measurements in Hydrogenated Amorphous Silicon P. C. Taylor, Magnetic Resonance Measurements in a-Si: H K. Morigaki, Optically Detected Magnetic Resonance J. Dresner, Carrier Mobility in a-Si: H T. Tiedje, Information About Band-Tail States from Time-of-Flight Experiments A. R. Moore, Diffusion Length in Undoped a-S: H W. Beyer and J. Overhof, Doping Effects in a-Si: H H. Fritzche, Electronic Properties of Surfaces in a-Si: H

Contents of Volumes in This Series

349

C. R. Wronski, The Staebler-Wronski Effect R. J. Nemanich, Schottky Barriers on a-Si: H B. Abeles and T. Tiedje, Amorphous Semiconductor Superlattices

Part D J. I. Pankove, Introduction D. E. Carlson, Solar Cells G. A. Swartz, Closed-Form Solution of I–V Characteristic for a s-Si: H Solar Cells I. Shimizu, Electrophotography S. Ishioka, Image Pickup Tubes P. G. Lecomber and W. E. Spear, The Development of the a-Si: H Field-Effect Transistor and its Possible Applications D. G. Ast, a-Si: H FET-Addressed LCD Panel S. Kaneko, Solid-State Image Sensor M. Matsumura, Charge-Coupled Devices M. A. Bosch, Optical Recording A. D’Amico and G. Fortunato, Ambient Sensors H. Kulkimoto, Amorphous Light-Emitting Devices R. J. Phelan, Jr., Fast Decorators and Modulators J. I. Pankove, Hybrid Structures P. G. LeComber, A. E. Owen, W. E. Spear, J. Hajto, and W. K. Choi, Electronic Switching in Amorphous Silicon Junction Devices

Volume 22 Lightwave Communications Technology Part A K. Nakajima, The Liquid-Phase Epitaxial Growth of InGaAsP W. T. Tsang, Molecular Beam Epitaxy for III–V Compound Semiconductors G. B. Stringfellow, Organometallic Vapor-Phase Epitaxial Growth of III–V Semiconductors G. Beuchet, Halide and Chloride Transport Vapor-Phase Deposition of InGaAsP and GaAs M. Razeghi, Low-Pressure, Metallo-Organic Chemical Vapor Deposition of Gax In1−x AsP1−y Alloys P. M. Petroff, Defects in III–V Compound Semiconductors

Part B J. P. van der Ziel, Mode Locking of Semiconductor Lasers K. Y. Lau and A. Yariv, High-Frequency Current Modulation of Semiconductor Injection Lasers C. H. Henry, Special Properties of Semi Conductor Lasers Y. Suematsu, K. Kishino, S. Arai, and F. Koyama, Dynamic Single-Mode Semiconductor Lasers with a Distributed Reflector W. T. Tsang, The Cleaved-Coupled-Cavity (C3 ) Laser

350

Contents of Volumes in This Series

Part C R. J. Nelson and N. K. Dutta, Review of InGaAsP InP Laser Structures and Comparison of Their Performance N. Chinone and M. Nakamura, Mode-Stabilized Semiconductor Lasers for 0.7–0.8- and 1.1–1.6-µm Regions Y. Horikoshi, Semiconductor Lasers with Wavelengths Exceeding 2 µm B. A. Dean and M. Dixon, The Functional Reliability of Semiconductor Lasers as Optical Transmitters R. H. Saul, T. P. Lee, and C. A. Burus, Light-Emitting Device Design C. L. Zipfel, Light-Emitting Diode-Reliability T. P. Lee and T. Li, LED-Based Multimode Lightwave Systems K. Ogawa, Semiconductor Noise-Mode Partition Noise

Part D F. Capasso, The Physics of Avalanche Photodiodes T. P. Pearsall and M. A. Pollack, Compound Semiconductor Photodiodes T. Kaneda, Silicon and Germanium Avalanche Photodiodes S. R. Forrest, Sensitivity of Avalanche Photodetector Receivers for High-Bit-Rate LongWavelength Optical Communication Systems J. C. Campbell, Phototransistors for Lightwave Communications

Part E S. Wang, Principles and Characteristics of Integrable Active and Passive Optical Devices S. Margalit and A. Yariv, Integrated Electronic and Photonic Devices T. Mukai, Y. Yamamoto, and T. Kimura, Optical Amplification by Semiconductor Lasers

Volume 23 Pulsed Laser Processing of Semiconductors R. F. Wood, C. W. White and R. T. Young, Laser Processing of Semiconductors: An Overview C. W. White, Segregation, Solute Trapping and Supersaturated Alloys G. E. Jellison, Jr., Optical and Electrical Properties of Pulsed Laser-Annealed Silicon R. F. Wood and G. E. Jellison, Jr., Melting Model of Pulsed Laser Processing R. F. Wood and F. W. Young, Jr., Nonequilibrium Solidification Following Pulsed Laser Melting D. H. Lawndes and G. E. Jellison, Jr., Time-Resolved Measurement During Pulsed Laser Irradiation of Silicon D. M. Zebner, Surface Studies of Pulsed Laser Irradiated Semiconductors D. H. Lowndes, Pulsed Beam Processing of Gallium Arsenide R. B. James, Pulsed CO2 Laser Annealing of Semiconductors R. T. Young and R. F. Wood, Applications of Pulsed Laser Processing

Volume 24 Applications of Multiquantum Wells, Selective Doping, and Superlattices C. Weisbuch, Fundamental Properties of III–V Semiconductor Two-Dimensional Quantized Structures: The Basis for Optical and Electronic Device Applications

Contents of Volumes in This Series

351

H. Morkoc¸ and H. Unlu, Factors Affecting the Performance of (Al,Ga)As/GaAs and (Al,Ga)As/InGaAs Modulation-Doped Field-Effect Transistors: Microwave and Digital Applications N. T. Linh, Two-Dimensional Electron Gas FETs: Microwave Applications M. Abe et al., Ultra-High-Speed HEMT Integrated Circuits D. S. Chemla, D. A. B. Miller and P. W. Smith, Nonlinear Optical Properties of Multiple Quantum Well Structures for Optical Signal Processing F. Capasso, Graded-Gap and Superlattice Devices by Band-Gap Engineering W. T. Tsang, Quantum Confinement Heterostructure Semiconductor Lasers G. C. Osbourn et al., Principles and Applications of Semiconductor Strained-Layer Superlattices

Volume 25 Diluted Magnetic Semiconductors W. Giriat and J. K. Furdyna, Crystal Structure, Composition, and Materials Preparation of Diluted Magnetic Semiconductors W. M. Becker, Band Structure and Optical Properties of Wide-Gap AII1−x Mnx BIV Alloys at Zero Magnetic Field S. Oseroff and P. H. Keesom, Magnetic Properties: Macroscopic Studies T. Giebultowicz and T. M. Holden, Neutron Scattering Studies of the Magnetic Structure and Dynamics of Diluted Magnetic Semiconductors J. Kossut, Band Structure and Quantum Transport Phenomena in Narrow-Gap Diluted Magnetic Semiconductors C. Riquaux, Magnetooptical Properties of Large-Gap Diluted Magnetic Semiconductors J. A. Gaj, Magnetooptical Properties of Large-Gap Diluted Magnetic Semiconductors J. Mycielski, Shallow Acceptors in Diluted Magnetic Semiconductors: Splitting, Boil-off, Giant Negative Magnetoresistance A. K. Ramadas and R. Rodriquez, Raman Scattering in Diluted Magnetic Semiconductors P. A. Wolff, Theory of Bound Magnetic Polarons in Semimagnetic Semiconductors

Volume 26 III–V Compound Semiconductors and Semiconductor Properties of Superionic Materials Z. Yuanxi, III–V Compounds H. V. Winston, A. T. Hunter, H. Kimura, and R. E. Lee, InAs-Alloyed GaAs Substrates for Direct Implantation P. K. Bhattacharya and S. Dhar, Deep Levels in III–V Compound Semiconductors Grown by MBE Y. Ya. Gurevich and A. K. Ivanov-Shits, Semiconductor Properties of Supersonic Materials

Volume 27 High Conducting Quasi-One-Dimensional Organic Crystals E. M. Conwell, Introduction to Highly Conducting Quasi-One-Dimensional Organic Crystals I. A. Howard, A Reference Guide to the Conducting Quasi-One-Dimensional Organic Molecular Crystals

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Contents of Volumes in This Series

J. P. Pouqnet, Structural Instabilities E. M. Conwell, Transport Properties C. S. Jacobsen, Optical Properties J. C. Scolt, Magnetic Properties L. Zuppiroli, Irradiation Effects: Perfect Crystals and Real Crystals

Volume 28 Measurement of High-Speed Signals in Solid State Devices J. Frey and D. Ioannou, Materials and Devices for High-Speed and Optoelectronic Applications H. Schumacher and E. Strid, Electronic Wafer Probing Techniques D. H. Auston, Picosecond Photoconductivity: High-Speed Measurements of Devices and Materials J. A. Valdmanis, Electro-Optic Measurement Techniques for Picosecond Materials, Devices and Integrated Circuits J. M. Wiesenfeld and R. K. Jain, Direct Optical Probing of Integrated Circuits and High-Speed Devices G. Plows, Electron-Beam Probing A. M. Weiner and R. B. Marcus, Photoemissive Probing

Volume 29 Very High Speed Integrated Circuits: Gallium Arsenide LSI M. Kuzuhara and T. Nazaki, Active Layer Formation by Ion Implantation H. Hasimoto, Focused Ion Beam Implantation Technology T. Nozaki and A. Higashisaka, Device Fabrication Process Technology M. Ino and T. Takada, GaAs LSI Circuit Design M. Hirayama, M. Ohmori, and K. Yamasaki, GaAs LSI Fabrication and Performance

Volume 30 Very High Speed Integrated Circuits: Heterostructure H. Watanabe, T. Mizutani, and A. Usui, Fundamentals of Epitaxial Growth and Atomic Layer Epitaxy S. Hiyamizu, Characteristics of Two-Dimensional Electron Gas in III–V Compound Heterostructures Grown by MBE T. Nakanisi, Metalorganic Vapor Phase Epitaxy for High-Quality Active Layers T. Nimura, High Electron Mobility Transistor and LSI Applications T. Sugeta and T. Ishibashi, Hetero-Bipolar Transistor and LSI Application H. Matsuedo, T. Tanaka, and M. Nakamura, Optoelectronic Integrated Circuits

Volume 31 Indium Phosphide: Crystal Growth and Characterization J. P. Farges, Growth of Discoloration-Free InP M. J. McCollum and G. E. Stillman, High Purity InP Grown by Hydride Vapor Phase Epitaxy

Contents of Volumes in This Series

353

I. Inada and T. Fukuda, Direct Synthesis and Growth of Indium Phosphide by the Liquid Phosphorous Encapsulated Czochralski Method O. Oda, K. Katagiri, K. Shinohara, S. Katsura, Y. Takahashi, K. Kainosho, K. Kohiro, and R. Hirano, InP Crystal Growth, Substrate Preparation and Evaluation K. Tada, M. Tatsumi, M. Morioka, T. Araki, and T. Kawase, InP Substrates: Production and Quality Control M. Razeghi, LP-MOCVD Growth, Characterization, and Application of InP Material T. A. Kennedy and P. J. Lin-Chung, Stoichiometric Defects in InP

Volume 32 Strained-Layer Superlattices: Physics T. P. Pearsall, Strained-Layer Superlattices F. H. Pollack, Effects of Homogeneous Strain on the Electronic and Vibrational Levels in Semiconductors J. Y. Marzin, J. M. Ger´ard, P. Voisin, and J. A. Brum, Optical Studies of Strained III–V Heterolayers R. People and S. A. Jackson, Structurally Induced States from Strain and Confinement M. Jaros, Microscopic Phenomena in Ordered Superlattices

Volume 33 Strained-Layer Superlattices: Material Science and Technology R. Hull and J. C. Bean, Principles and Concepts of Strained-Layer Epitaxy W. J. Shaff, P. J. Tasker, M. C. Foisy, and L. F. Eastman, Device Applications of Strained-Layer Epitaxy S. T. Picraux, B. L. Doyle, and J. Y. Tsao, Structure and Characterization of Strained-Layer Superlattices E. Kasper and F. Schaffer, Group IV Compounds D. L. Martin, Molecular Beam Epitaxy of IV–VI Compounds Heterojunction R. L. Gunshor, L. A. Kolodziejski, A. V. Nurmikko, and N. Otsuka, Molecular Beam Epitaxy of I–VI Semiconductor Microstructures

Volume 34 Hydrogen in Semiconductors J. I. Pankove and N. M. Johnson, Introduction to Hydrogen in Semiconductors C. H. Seager, Hydrogenation Methods J. I. Pankove, Hydrogenation of Defects in Crystalline Silicon J. W. Corbett, P. D´eak, U. V. Desnica, and S. J. Pearton, Hydrogen Passivation of Damage Centers in Semiconductors S. J. Pearton, Neutralization of Deep Levels in Silicon J. I. Pankove, Neutralization of Shallow Acceptors in Silicon N. M. Johnson, Neutralization of Donor Dopants and Formation of Hydrogen-Induced Defects in n-Type Silicon M. Stavola and S. J. Pearton, Vibrational Spectroscopy of Hydrogen-Related Defects in Silicon

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Contents of Volumes in This Series

A. D. Marwick, Hydrogen in Semiconductors: Ion Beam Techniques C. Herring and N. M. Johnson, Hydrogen Migration and Solubility in Silicon E. E. Haller, Hydrogen-Related Phenomena in Crystalline Germanium J. Kakalios, Hydrogen Diffusion in Amorphous Silicon J. Chevalier, B. Clerjaud, and B. Pajot, Neutralization of Defects and Dopants in III–V Semiconductors G. G. DeLeo and W. B. Fowler, Computational Studies of Hydrogen-Containing Complexes in Semiconductors R. F. Kiefl and T. L. Estle, Muonium in Semiconductors C. G. Van de Walle, Theory of Isolated Interstitial Hydrogen and Muonium in Crystalline Semiconductors

Volume 35 Nanostructured Systems M. Reed, Introduction H. van Houten, C. W. J. Beenakker, and B. J. Wees, Quantum Point Contacts G. Timp, When Does a Wire Become an Electron Waveguide? ´ M. Buttiker, The Quantum Hall Effects in Open Conductors W. Hansen, J. P. Kotthaus, and U. Merkt, Electrons in Laterally Periodic Nanostructures

Volume 36 The Spectroscopy of Semiconductors D. Heiman, Spectroscopy of Semiconductors at Low Temperatures and High Magnetic Fields A. V. Nurmikko, Transient Spectroscopy by Ultrashort Laser Pulse Techniques A. K. Ramdas and S. Rodriguez, Piezospectroscopy of Semiconductors O. J. Glembocki and B. V. Shanabrook, Photoreflectance Spectroscopy of Microstructures D. G. Seiler, C. L. Littler, and M. H. Wiler, One- and Two-Photon Magneto-Optical Spectroscopy of InSb and Hg1−x Cdx Te

Volume 37 The Mechanical Properties of Semiconductors A.-B. Chen, A. Sher, and W. T. Yost, Elastic Constants and Related Properties of Semiconductor Compounds and Their Alloys D. R. Clarke, Fracture of Silicon and Other Semiconductors H. Siethoff, The Plasticity of Elemental and Compound Semiconductors S. Guruswamy, K. T. Faber, and J. P. Hirth, Mechanical Behavior of Compound Semiconductors S. Mahajan, Deformation Behavior of Compound Semiconductors J. P. Hirth, Injection of Dislocations into Strained Multilayer Structures D. Kendall, C. B. Fleddermann, and K. J. Malloy, Critical Technologies for the Micromatching of Silicon J. Matsuba and K. Mokuya, Processing and Semiconductor Thermoelastic Behavior

Contents of Volumes in This Series

355

Volume 38 Imperfections in III/V Materials U. Scherz and M. Scheffler, Density-Functional Theory of sp-Bonded Defects in III/V Semiconductors M. Kaminska and E. R. Weber, E12 Defect in GaAs D. C. Look, Defects Relevant for Compensation in Semi-Insulating GaAs R. C. Newman, Local Vibrational Mode Spectroscopy of Defects in III/V Compounds A. M. Hennel, Transition Metals in III/V Compounds K. J. Malloy and K. Khachaturyan, DX and Related Defects in Semiconductors V. Swaminathan and A. S. Jordan, Dislocations in III/V Compounds K. W. Nauka, Deep Level Defects in the Epitaxial III/V Materials

Volume 39 Minority Carriers in III–V Semiconductors: Physics and Applications N. K. Dutta, Radiative Transition in GaAs and Other III–V Compounds R. K. Ahrenkiel, Minority-Carrier Lifetime in III–V Semiconductors T. Furuta, High Field Minority Electron Transport in p-GaAs M. S. Lundstrom, Minority-Carrier Transport in III–V Semiconductors R. A. Abram, Effects of Heavy Doping and High Excitation on the Band Structure of GaAs D. Yevick and W. Bardyszewski, An Introduction to Non-Equilibrium Many-Body Analyses of Optical Processes in III–V Semiconductors

Volume 40 Epitaxial Microstructures E. F. Schubert, Delta-Doping of Semiconductors: Electronic, Optical and Structural Properties of Materials and Devices A. Gossard, M. Sundaram, and P. Hopkins, Wide Graded Potential Wells P. Petroff, Direct Growth of Nanometer-Size Quantum Wire Superlattices E. Kapon, Lateral Patterning of Quantum Well Heterostructures by Growth of Nonplanar Substrates H. Temkin, D. Gershoni, and M. Panish, Optical Properties of Ga1−x Inx As/InP Quantum Wells

Volume 41 High Speed Heterostructure Devices F. Capasso, F. Beltram, S. Sen, A. Pahlevi, and A. Y. Cho, Quantum Electron Devices: Physics and Applications P. Solomon, D. J. Frank, S. L. Wright and F. Canora, GaAs-Gate Semiconductor-InsulatorSemiconductor FET M. H. Hashemi and U. K. Mishra, Unipolar InP-Based Transistors R. Kiehl, Complementary Heterostructure FET Integrated Circuits T. Ishibashi, GaAs-Based and InP-Based Heterostructure Bipolar-Transistors H. C. Liu and T. C. L. G. Sollner, High-Frequency-Tunneling Devices H. Ohnishi, T. More, M. Takatsu, K. Imamura, and N. Yokoyama, Resonant-Tunneling HotElectron Transistors and Circuits

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Contents of Volumes in This Series

Volume 42 Oxygen in Silicon F. Shimura, Introduction to Oxygen in Silicon W. Lin, The Incorporation of Oxygen into Silicon Crystals T. J. Schaffner and D. K. Schroder, Characterization Techniques for Oxygen in Silicon W. M. Bullis, Oxygen Concentration Measurement S. M. Hu, Intrinsic Point Defects in Silicon B. Pajot, Some Atomic Configuration of Oxygen J. Michel and L. C. Kimerling, Electrical Properties of Oxygen in Silicon R. C. Newman and R. Jones, Diffusion of Oxygen in Silicon T. Y. Tan and W. J. Taylor, Mechanisms of Oxygen Precipitation: Some Quantitative Aspects M. Schrems, Simulation of Oxygen Precipitation K. Simino and I. Yonenaga, Oxygen Effect on Mechanical Properties W. Bergholz, Grown-in and Process-Induced Effects F. Shimura, Intrinsic/Internal Gettering H. Tsuya, Oxygen Effect on Electronic Device Performance

Volume 43 Semiconductors for Room Temperature Nuclear Detector Applications R. B. James and T. E. Schlesinger, Introduction and Overview L. S. Darken and C. E. Cox, High-Purity Germanium Detectors A. Burger, D. Nason, L. Van den Berg, and M. Schieber, Growth of Mercuric Iodide X. J. Bao, T. E. Schlesinger, and R. B. James, Electrical Properties of Mercuric Iodide X. J. Bao, R. B. James, and T. E. Schlesinger, Optical Properties of Red Mercuric Iodide M. Hage-Ali and P. Siffert, Growth Methods of CdTe Nuclear Detector Materials M. Hage-Ali and P. Siffert, Characterization of CdTe Nuclear Detector Materials M. Hage-Ali and P. Siffert, CdTe Nuclear Detectors and Applications R. B. James, T. E. Schlesinger, J. Lund, and M. Schieber, Cd1−x Znx Te Spectrometers for Gamma and X-Ray Applications D. S. McGregor, J. E. Kammeraad, Gallium Arsenide Radiation Detectors and Spectrometers J. C. Lund, F. Olschner, and A. Burger, Lead Iodide M. R. Squillante and K. S. Shah, Other Materials: Status and Prospects V. M. Gerrish, Characterization and Quantification of Detector Performance J. S. Iwanczyk and B. E. Patt, Electronics for X-ray and Gamma Ray Spectrometers M. Schieber, R. B. James and T. E. Schlesinger, Summary and Remaining Issues for Room Temperature Radiation Spectrometers

Volume 44 II–IV Blue/Green Light Emitters: Device Physics and Epitaxial Growth J. Han and R. L. Gunshor, MBE Growth and Electrical Properties of Wide Bandgap ZnSe-based II–VI Semiconductors S. Fujita and S. Fujita, Growth and Characterization of ZnSe-based II–VI Semiconductors by MOVPE

Contents of Volumes in This Series

357

E. Ho and L. A. Kolodziejski, Gaseous Source UHV Epitaxy Technologies for Wide Bandgap II–VI Semiconductors C. G. Van de Walle, Doping of Wide-Band-Gap II–VI Compounds – Theory R. Cingolani, Optical Properties of Excitons in ZnSe-Based Quantum Well Heterostructures A. Ishibashi and A. V. Nurmikko, II–VI Diode Lasers: A Current View of Device Performance and Issues S. Guha and J. Petruzello, Defects and Degradation in Wide-Gap II–VI-based Structure and Light Emitting Devices

Volume 45 Effect of Disorder and Defects in Ion-Implanted Semiconductors: Electrical and Physiochemical Characterization H. Ryssel, Ion Implantation into Semiconductors: Historical Perspectives You-Nian Wang and Teng-Cai Ma, Electronic Stopping Power for Energetic Ions in Solids S. T. Nakagawa, Solid Effect on the Electronic Stopping of Crystalline Target and Application to Range Estimation G. Miller, S. Kalbitzer, and G. N. Greaves, Ion Beams in Amorphous Semiconductor Research J. Boussey-Said, Sheet and Spreading Resistance Analysis of Ion Implanted and Annealed Semiconductors M. L. Polignano and G. Queirolo, Studies of the Stripping Hall Effect in Ion-Implanted Silicon J. Sroemenos, Transmission Electron Microscopy Analyses R. Nipoti and M. Servidori, Rutherford Backscattering Studies of Ion Implanted Semiconductors P. Zaumseil, X-ray Diffraction Techniques

Volume 46 Effect of Disorder and Defects in Ion-Implanted Semiconductors: Optical and Photothermal Characterization M. Fried, T. Lohner, and J. Gyulai, Ellipsometric Analysis A. Seas and C. Christofides, Transmission and Reflection Spectroscopy on Ion Implanted Semiconductors A. Othonos and C. Christofides, Photoluminescence and Raman Scattering of Ion Implanted Semiconductors. Influence of Annealing C. Christofides, Photomodulated Thermoreflectance Investigation of Implanted Wafers. Annealing Kinetics of Defects U. Zammit, Photothermal Deflection Spectroscopy Characterization of Ion-Implanted and Annealed Silicon Films A. Mandelis, A. Budiman, and M. Vargas, Photothermal Deep-Level Transient Spectroscopy of Impurities and Defects in Semiconductors R. Kalish and S. Charbonneau, Ion Implantation into Quantum-Well Structures A. M. Myasnikov and N. N. Gerasimenko, Ion Implantation and Thermal Annealing of III–V Compound Semiconducting Systems: Some Problems of III–V Narrow Gap Semiconductors

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Contents of Volumes in This Series

Volume 47 Uncooled Infrared Imaging Arrays and Systems R. G. Buser and M. P. Tompsett, Historical Overview P. W. Kruse, Principles of Uncooled Infrared Focal Plane Arrays R. A. Wood, Monolithic Silicon Microbolometer Arrays C. M. Hanson, Hybrid Pyroelectric-Ferroelectric Bolometer Arrays D. L. Polla and J. R. Choi, Monolithic Pyroelectric Bolometer Arrays N. Teranishi, Thermoelectric Uncooled Infrared Focal Plane Arrays M. F. Tompsett, Pyroelectric Vidicon T. W. Kenny, Tunneling Infrared Sensors J. R. Vig, R. L. Filler, and Y. Kim, Application of Quartz Microresonators to Uncooled Infrared Imaging Arrays P. W. Kruse, Application of Uncooled Monolithic Thermoelectric Linear Arrays to Imaging Radiometers

Volume 48 High Brightness Light Emitting Diodes G. B. Stringfellow, Materials Issues in High-Brightness Light-Emitting Diodes M.G. Craford, Overview of Device Issues in High-Brightness Light-Emitting Diodes F. M. Steranka, AlGaAs Red Light Emitting Diodes C. H. Chen, S. A. Stockman, M. J. Peanasky, and C. P. Kuo, OMVPE Growth of AlGaInP for High Efficiency Visible Light-Emitting Diodes F. A. Kish and R. M. Fletcher, AlGaInP Light-Emitting Diodes M. W. Hodapp, Applications for High Brightness Light-Emitting Diodes J. Akasaki and H. Amano, Organometallic Vapor Epitaxy of GaN for High Brightness Blue Light Emitting Diodes S. Nakamura, Group III–V Nitride Based Ultraviolet-Blue-Green-Yellow Light-Emitting Diodes and Laser Diodes

Volume 49 Light Emission in Silicon: from Physics to Devices D. J. Lockwood, Light Emission in Silicon G. Abstreiter, Band Gaps and Light Emission in Si/SiGe Atomic Layer Structures T. G. Brown and D. G. Hall, Radiative Isoelectronic Impurities in Silicon and SiliconGermanium Alloys and Superlattices J. Michel, L. V. C. Assali, M. T. Morse, and L. C. Kimerling, Erbium in Silicon Y. Kanemitsu, Silicon and Germanium Nanoparticles P. M. Fauchet, Porous Silicon: Photoluminescence and Electroluminescent Devices C. Delerue, G. Allan, and M. Lannoo, Theory of Radiative and Nonradiative Processes in Silicon Nanocrystallites L. Brus, Silicon Polymers and Nanocrystals

Volume 50 Gallium Nitride (GaN) J. I. Pankove and T. D. Moustakas, Introduction S. P. DenBaars and S. Keller, Metalorganic Chemical Vapor Deposition (MOCVD) of Group III Nitrides

Contents of Volumes in This Series

359

W. A. Bryden and T. J. Kistenmacher, Growth of Group III–A Nitrides by Reactive Sputtering N. Newman, Thermochemistry of III–N Semiconductors S. J. Pearton and R. J. Shul, Etching of III Nitrides S. M. Bedair, Indium-based Nitride Compounds A. Trampert, O. Brandt, and K. H. Ploog, Crystal Structure of Group III Nitrides H. Morkoc¸, F. Hamdani, and A. Salvador, Electronic and Optical Properties of III–V Nitride based Quantum Wells and Superlattices K. Doverspike and J. I. Pankove, Doping in the III-Nitrides T. Suski and P. Perlin, High Pressure Studies of Defects and Impurities in Gallium Nitride B. Monemar, Optical Properties of GaN W. R. L. Lambrecht, Band Structure of the Group III Nitrides N. E. Christensen and P. Perlin, Phonons and Phase Transitions in GaN S. Nakamura, Applications of LEDs and LDs I. Akasaki and H. Amano, Lasers J. A. Cooper, Jr., Nonvolatile Random Access Memories in Wide Bandgap Semiconductors

Volume 51A Identification of Defects in Semiconductors G. D. Watkins, EPR and ENDOR Studies of Defects in Semiconductors J.-M. Spaeth, Magneto-Optical and Electrical Detection of Paramagnetic Resonance in Semiconductors T. A. Kennedy and E. R. Claser, Magnetic Resonance of Epitaxial Layers Detected by Photoluminescence K. H. Chow, B. Hitti, and R. F. Kiefl, µSR on Muonium in Semiconductors and Its Relation to Hydrogen K. Saarinen, P. Hautoj¨arvi, and C. Corbel, Positron Annihilation Spectroscopy of Defects in Semiconductors R. Jones and P. R. Briddon, The Ab Initio Cluster Method and the Dynamics of Defects in Semiconductors

Volume 51B Identification Defects in Semiconductors G. Davies, Optical Measurements of Point Defects P. M. Mooney, Defect Identification Using Capacitance Spectroscopy M. Stavola, Vibrational Spectroscopy of Light Element Impurities in Semiconductors P. Schwander, W. D. Rau, C. Kisielowski, M. Gribelyuk, and A. Ourmazd, Defect Processes in Semiconductors Studied at the Atomic Level by Transmission Electron Microscopy N. D. Jager and E. R. Weber, Scanning Tunneling Microscopy of Defects in Semiconductors

Volume 52 SiC Materials and Devices K. J¨arrendahl and R. F. Davis, Materials Properties and Characterization of SiC V. A. Dmitiriev and M. G. Spencer, SiC Fabrication Technology: Growth and Doping V. Saxena and A. J. Steckl, Building Blocks for SiC Devices: Ohmic Contacts, Schottky Contacts, and p-n Junctions

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Contents of Volumes in This Series

M. S. Shur, SiC Transistors C. D. Brandt, R. C. Clarke, R. R. Siergiej, J. B. Casady, A. W. Morse, S. Sriram, and A. K. Agarwal, SiC for Applications in High-Power Electronics R. J. Trew, SiC Microwave Devices J. Edmond, H. Kong, G. Negley, M. Leonard, K. Doverspike, W. Weeks, A. Suvorov, D. Waltz, and C. Carter, Jr., SiC-Based UV Photodiodes and Light-Emitting Diodes H. Morkoc¸, Beyond Silicon Carbide! III–V Nitride-Based Heterostructures and Devices

Volume 53 Cumulative Subjects and Author Index Including Tables of Contents for Volumes 1–50 Volume 54 High Pressure in Semiconductor Physics I W. Paul, High Pressure in Semiconductor Physics: A Historical Overview N. E. Christensen, Electronic Structure Calculations for Semiconductors Under Pressure R. J. Neimes and M. I. McMahon, Structural Transitions in the Group IV, III–V and II–VI Semiconductors Under Pressure A. R. Goni and K. Syassen, Optical Properties of Semiconductors Under Pressure P. Trautman, M. Baj, and J. M. Baranowski, Hydrostatic Pressure and Uniaxial Stress in Investigations of the EL2 Defect in GaAs M. Li and P. Y. Yu, High-Pressure Study of DX Centers Using Capacitance Techniques T. Suski, Spatial Correlations of Impurity Charges in Doped Semiconductors N. Kuroda, Pressure Effects on the Electronic Properties of Diluted Magnetic Semiconductors

Volume 55 High Pressure in Semiconductor Physics II D. K. Maude and J. C. Portal, Parallel Transport in Low-Dimensional Semiconductor Structures P. C. Klipstein, Tunneling Under Pressure: High-Pressure Studies of Vertical Transport in Semiconductor Heterostructures E. Anastassakis and M. Cardona, Phonons, Strains, and Pressure in Semiconductors F. H. Pollak, Effects of External Uniaxial Stress on the Optical Properties of Semiconductors and Semiconductor Microstructures A. R. Adams, M. Silver, and J. Allam, Semiconductor Optoelectronic Devices S. Porowski and I. Grzegory, The Application of High Nitrogen Pressure in the Physics and Technology of III–N Compounds M. Yousuf, Diamond Anvil Cells in High Pressure Studies of Semiconductors

Volume 56 Germanium Silicon: Physics and Materials J. C. Bean, Growth Techniques and Procedures D. E. Savage, F. Liu, V. Zielasek, and M. G. Lagally, Fundamental Crystal Growth Mechanisms R. Hull, Misfit Strain Accommodation in SiGe Heterostructures M. J. Shaw and M. Jaros, Fundamental Physics of Strained Layer GeSi: Quo Vadis? F. Cerdeira, Optical Properties

Contents of Volumes in This Series

361

S. A. Ringel and P. N. Grillot, Electronic Properties and Deep Levels in Germanium-Silicon J. C. Campbell, Optoelectronics in Silicon and Germanium Silicon K. Eberl, K. Brunner, and O. G. Schmidt, Si1−y Cy and Si1−x−y Ge2 Cy Alloy Layers

Volume 57 Gallium Nitride (GaN) II R. J. Molnar, Hydride Vapor Phase Epitaxial Growth of III–V Nitrides T. D. Moustakas, Growth of III–V Nitrides by Molecular Beam Epitaxy Z. Liliental-Weber, Defects in Bulk GaN and Homoepitaxial Layers C. G. Van de Walk and N. M. Johnson, Hydrogen in III–V Nitrides W. G¨otz and N. M. Johnson, Characterization of Dopants and Deep Level Defects in Gallium Nitride B. Gil, Stress Effects on Optical Properties C. Kisielowski, Strain in GaN Thin Films and Heterostructures J. A. Miragliotta and D. K. Wickenden, Nonlinear Optical Properties of Gallium Nitride B. K. Meyer, Magnetic Resonance Investigations on Group III–Nitrides M. S. Shur and M. Asif Khan, GaN and AIGaN Ultraviolet Detectors C. H. Qiu, J. I. Pankove, and C. Rossington, II–V Nitride-Based X-ray Detectors

Volume 58 Nonlinear Optics in Semiconductors I A. Kost, Resonant Optical Nonlinearities in Semiconductors E. Garmire, Optical Nonlinearities in Semiconductors Enhanced by Carrier Transport D. S. Chemla, Ultrafast Transient Nonlinear Optical Processes in Semiconductors M. Sheik-Bahae and E. W. Van Stryland, Optical Nonlinearities in the Transparency Region of Bulk Semiconductors J. E. Millerd, M. Ziari, and A. Partovi, Photorefractivity in Semiconductors

Volume 59 Nonlinear Optics in Semiconductors II J. B. Khurgin, Second Order Nonlinearities and Optical Rectification K. L. Hall, E. R. Thoen, and E. P. Ippen, Nonlinearities in Active Media E. Hanamura, Optical Responses of Quantum Wires/Dots and Microcavities U. Keller, Semiconductor Nonlinearities for Solid-State Laser Modelocking and Q-Switching A. Miller, Transient Grating Studies of Carrier Diffusion and Mobility in Semiconductors

Volume 60 Self-Assembled InGaAs/GaAs Quantum Dots Mitsuru Sugawara, Theoretical Bases of the Optical Properties of Semiconductor Quantum Nano-Structures Yoshiaki Nakata, Yoshihiro Sugiyama, and Mitsuru Sugawara, Molecular Beam Epitaxial Growth of Self-Assembled InAs/GaAs Quantum Dots Kohki Mukai, Mitsuru Sugawara, Mitsuru Egawa, and Nobuyuki Ohtsuka, Metalorganic Vapor Phase Epitaxial Growth of Self-Assembled InGaAs/GaAs Quantum Dots Emitting at 1.3 µm

362

Contents of Volumes in This Series

Kohki Mukai and Mitsuru Sugawara, Optical Characterization of Quantum Dots Kohki Mukai and Milsuru Sugawara, The Photon Bottleneck Effect in Quantum Dots Hajime Shoji, Self-Assembled Quantum Dot Lasers Hiroshi Ishikawa, Applications of Quantum Dot to Optical Devices Mitsuru Sugawara, Kohki Mukai, Hiroshi Ishikawa, Koji Otsubo, and Yoshiaki Nakata, The Latest News

Volume 61 Hydrogen in Semiconductors II Norbert H. Nickel, Introduction to Hydrogen in Semiconductors II Noble M. Johnson and Chris G. Van de Walle, Isolated Monatomic Hydrogen in Silicon Yurij V. Gorelkinskii, Electron Paramagnetic Resonance Studies of Hydrogen and HydrogenRelated Defects in Crystalline Silicon Norbert H. Nickel, Hydrogen in Polycrystalline Silicon Wolfhard Beyer, Hydrogen Phenomena in Hydrogenated Amorphous Silicon Chris G. Van de Walle, Hydrogen Interactions with Polycrystalline and Amorphous Silicon– Theory Karen M. McManus Rutledge, Hydrogen in Polycrystalline CVD Diamond Roger L. Lichti, Dynamics of Muonium Diffusion, Site Changes and Charge-State Transitions Matthew D. McCluskey and Eugene E. Haller, Hydrogen in III–V and II–VI Semiconductors S. J. Pearton and J. W. Lee, The Properties of Hydrogen in GaN and Related Alloys J¨org Neugebauer and Chris G. Van de Walle, Theory of Hydrogen in GaN

Volume 62 Intersubband Transitions in Quantum Wells: Physics and Device Applications I Manfred Helm, The Basic Physics of Intersubband Transitions Jerome Faist, Carlo Sirtori, Federico Capasso, Loren N. Pfeiffer, Ken W. West, Deborah L. Sivco, and Alfred Y. Cho, Quantum Interference Effects in Intersubband Transitions H. C. Liu, Quantum Well Infrared Photodetector Physics and Novel Devices S. D. Gunapala and S. V. Bandara, Quantum Well Infrared Photodetector (QWIP) Focal Plane Arrays

Volume 63 Chemical Mechanical Polishing in Si Processing Frank B. Kaufman, Introduction Thomas Bibby and Karey Holland, Equipment John P. Bare, Facilitization Duane S. Boning and Okumu Ouma, Modeling and Simulation Shin Hwa Li, Bruce Tredinnick, and Mel Hoffman, Consumables I: Slurry Lee M. Cook, CMP Consumables II: Pad Franc¸ois Tardif, Post-CMP Clean Shin Hwa Li, Tara Chhatpar, and Frederic Robert, CMP Metrology Shin Hwa Li, Visun Bucha, and Kyle Wooldridge, Applications and CMP-Related Process Problems

Contents of Volumes in This Series

363

Volume 64 Electroluminescence I M. G. Craford, S. A. Stockman, M. J. Peansky, and F. A. Kish, Visible Light-Emitting Diodes H. Chui, N. F. Gardner, P. N. Grillot, J. W. Huang, M. R. Krames, and S. A. Maranowski, HighEfficiency AIGaInP Light-Emitting Diodes R. S. Kern, W. G¯otz, C. H. Chen, H. Liu, R. M. Fletcher, and C. P. Kuo, High-Brightness NitrideBased Visible-Light-Emitting Diodes Yoshiharu Sato, Organic LED System Considerations V. Bulovi´c, P. E. Burrows, and S. R. Forrest, Molecular Organic Light-Emitting Devices

Volume 65 Electroluminescence II V. Bulovi´c and S. R. Forrest, Polymeric and Molecular Organic Light Emitting Devices: A Comparison Regina Mueller-Mach and Gerd O. Mueller, Thin Film Electroluminescence Markku Leskel´a, Wei-Min Li, and Mikko Ritala, Materials in Thin Film Electroluminescent Devices Kristiaan Neyts, Microcavities for Electroluminescent Devices

Volume 66 Intersubband Transitions in Quantum Wells: Physics and Device Applications II Jerome Faist, Federico Capasso, Carlo Sirtori, Deborah L. Sivco, and Alfred Y. Cho, Quantum Cascade Lasers Federico Capasso, Carlo Sirtori, D. L. Sivco, and A. Y. Cho, Nonlinear Optics in CoupledQuantum- Well Quasi-Molecules Karl Unterrainer, Photon-Assisted Tunneling in Semiconductor Quantum Structures P. Haring Bolivar, T. Dekorsy, and H. Kurz, Optically Excited Bloch Oscillations–Fundamentals and Application Perspectives

Volume 67 Ultrafast Physical Processes in Semiconductors Alfred Leitenstorfer and Alfred Laubereau, Ultrafast Electron-Phonon Interactions in Semiconductors: Quantum Kinetic Memory Effects Christoph Lienau and Thomas Elsaesser, Spatially and Temporally Resolved Near-Field Scanning Optical Microscopy Studies of Semiconductor Quantum Wires K. T. Tsen, Ultrafast Dynamics in Wide Bandgap Wurtzite GaN J. Paul Callan, Albert M.-T. Kim, Christopher A. D. Roeser, and Eriz Mazur, Ultrafast Dynamics and Phase Changes in Highly Excited GaAs Hartmut Hang, Quantum Kinetics for Femtosecond Spectroscopy in Semiconductors T. Meier and S. W. Koch, Coulomb Correlation Signatures in the Excitonic Optical Nonlinearities of Semiconductors Roland E. Allen, Traian Dumitric˘a, and Ben Torralva, Electronic and Structural Response of Materials to Fast, Intense Laser Pulses E. Gornik and R. Kersting, Coherent THz Emission in Semiconductors

364

Contents of Volumes in This Series

Volume 68 Isotope Effects in Solid State Physics Vladimir G. Plekhanov, Elastic Properties; Thermal Properties; Vibrational Properties; Raman Spectra of Isotopically Mixed Crystals; Excitons in LiH Crystals; Exciton–Phonon Interaction; Isotopic Effect in the Emission Spectrum of Polaritons; Isotopic Disordering of Crystal Lattices; Future Developments and Applications; Conclusions

Volume 69 Recent Trends in Thermoelectric Materials Research I H. Julian Goldsmid, Introduction Terry M. Tritt and Valerie M. Browning, Overview of Measurement and Characterization Techniques for Thermoelectric Materials Mercouri G. Kanatzidis, The Role of Solid-State Chemistry in the Discovery of New Thermoelectric Materials B. Lenoir, H. Scherrer, and T. Caillat, An Overview of Recent Developments for BiSb Alloys Citrad Uher, Skutterudities: Prospective Novel Thermoelectrics George S. Nolas, Glen A. Slack, and Sandra B. Schujman, Semiconductor Clathrates: A Phonon Glass Electron Crystal Material with Potential for Thermoelectric Applications

Volume 70 Recent Trends in Thermoelectric Materials Research II Brian C. Sales, David G. Mandrus, and Bryan C. Chakoumakos, Use of Atomic Displacement Parameters in Thermoelectric Materials Research S. Joseph Poon, Electronic and Thermoelectric Properties of Half-Heusler Alloys Terry M. Tritt, A. L. Pope, and J. W. Kolis, Overview of the Thermoelectric Properties of Quasicrystalline Materials and Their Potential for Thermoelectric Applications Alexander C. Ehrlich and Stuart A. Wolf, Military Applications of Enhanced Thermoelectrics David J. Singh, Theoretical and Computational Approaches for Identifying and Optimizing Novel Thermoelectric Materials Terry M. Tritt and R. T. Littleton, IV, Thermoelectric Properties of the Transition Metal Pentatellurides: Potential Low-Temperature Thermoelectric Materials Franz Freibert, Timothy W. Darling, Albert Miglori, and Stuart A. Trugman, Thermomagnetic Effects and Measurements M. Bartkowiak and G. D. Mahan, Heat and Electricity Transport Through Interfaces

Volume 71 Recent Trends in Thermoelectric Materials Research III M. S. Dresselhaus, Y.-M. Lin, T. Koga, S. B. Cronin, O. Rabin, M. R. Black, and G. Dresselhaus, Quantum Wells and Quantum Wires for Potential Thermoelectric Applications D. A. Broido and T. L. Reinecke, Thermoelectric Transport in Quantum Well and Quantum Wire Superlattices G. D. Mahan, Thermionic Refrigeration Rama Venkatasubramanian, Phonon Blocking Electron Transmitting Superlattice Structures as Advanced Thin Film Thermoelectric Materials G. Chen, Phonon Transport in Low-Dimensional Structures

Contents of Volumes in This Series

365

Volume 72 Silicon Epitaxy S. Acerboni, ST Microelectronics, CFM-AGI Department, Agrate Brianza, Italy V.-M. Airaksinen, Okmetic Oyj R&D Department, Vantaa, Finland G. Beretta, ST Microelectronics, DSG Epitaxy Catania Department, Catania, Italy C. Cavallotti, Dipartimento di Chimica Fisica Applicata, Politecnico di Milano, Milano, Italy D. Crippa, MEMC Electronic Materials, Epitaxial and CVD Department, Operations Technology Division, Novara, Italy D. Dutartre, ST Microelectronics, Central R&D, Crolles, France Srikanth Kommu, MEMC Electronic Materials inc., EPI Technology Group, St. Peters, Missouri M. Masi, Dipartimento di Chimica Fisica Applicata, Politecnico di Milano, Milano, Italy D. J. Meyer, ASM Epitaxy, Phoenix, Arizona J. Murota, Research Institute of Electrical Communication, Laboratory for Electronic Intelligent Systems, Tohoku University, Sendai, Japan V. Pozzetti, LPE Epitaxial Technologies, Bollate, Italy A. M. Rinaldi, MEMC Electronic Materials, Epitaxial and CVD Department, Operations Technology Division, Novara, Italy Y. Shiraki, Research Center for Advanced Science and Technology (RCAST), University of Tokyo, Tokyo, Japan

Volume 73 Processing and Properties of Compound Semiconductors S. J. Pearton, Introduction Eric Donkor, Gallium Arsenide Heterostructures Annamraju Kasi Viswanatli, Growth and Optical Properties of GaN D. Y. C. Lie and K. L. Wang, SiGe/Si Processing S. Kim and M. Razeghi, Advances in Quantum Dot Structures Walter P. Gomes, Wet Etching of III–V Semiconductors

Volume 74 Silicon-Germanium Strained Layers and Heterostructures S. C. Jain and M. Willander, Introduction; Strain, Stability, Reliability and Growth; Mechanism of Strain Relaxation; Strain, Growth, and TED in SiGeC Layers; Bandstructure and Related Properties; Heterostructure Bipolar Transistors; FETs and Other Devices

Volume 75 Laser Crystallization of Silicon Norbert H. Nickel, Introduction to Laser Crystallization of Silicon Costas P. Grigoropoidos, Seung-Jae Moon and Ming-Hong Lee, Heat Transfer and Phase Transformations in Laser Melting and Recrystallization of Amorphous Thin Si Films ˇ y and Petr Pˇrikryl, Modeling Laser-Induced Phase-Change Processes: Theory and Robert Cern´ Computation Paulo V. Santos, Laser Interference Crystallization of Amorphous Films Philipp Lengsfeld and Norbert H. Nickel, Structural and Electronic Properties of LaserCrystallized Poly-Si

366

Contents of Volumes in This Series

Volume 76 Thin-Film Diamond I X. Jiang, Textured and Heteroepitaxial CVD Diamond Films Eberhard Blank, Structural Imperfections in CVD Diamond Films R. Kalish, Doping Diamond by Ion-Implantation A. Deneuville, Boron Doping of Diamond Films from the Gas Phase S. Koizumi, n-Type Diamond Growth C. E. Nebel, Transport and Defect Properties of Intrinsic and Boron-Doped Diamond Miloˇs Nesl´adek, Ken Haenen and Milan Vanˇecˇ ek, Optical Properties of CVD Diamond Rolf Sauer, Luminescence from Optical Defects and Impurities in CVD Diamond

Volume 77 Thin-Film Diamond II Jacques Chevallier, Hydrogen Diffusion and Acceptor Passivation in Diamond ¨ Jurgen Ristein, Structural and Electronic Properties of Diamond Surfaces John C. Angus, Yuri V. Pleskov and Sally C. Eaton, Electrochemistry of Diamond Greg M. Swain, Electroanalytical Applications of Diamond Electrodes Werner Haenni, Philippe Rychen, Matthyas Fryda and Christos Comninellis, Industrial Applications of Diamond Electrodes Philippe Bergonzo and Richard B. Jackman, Diamond-Based Radiation and Photon Detectors Hiroshi Kawarada, Diamond Field Effect Transistors Using H-Terminated Surfaces Shinichi Shikata and Hideaki Nakahata, Diamond Surface Acoustic Wave Device

Volume 78 Semiconducting Chalcogenide Glass I V. S. Minaev and S. P. Timoshenkov, Glass-Formation in Chalcogenide Systems and Periodic System A. Popov, Atomic Structure and Structural Modification of Glass V. A. Funtikov, Eutectoidal Concept of Glass Structure and Its Application in Chalcogenide Semiconductor Glasses V. S. Minaev, Concept of Polymeric Polymorphous-Crystalloid Structure of Glass and Chalcogenide Systems: Structure and Relaxation of Liquid and Glass

Volume 79 Semiconducting Chalcogenide Glass II M. D. Bal’makov, Information Capacity of Condensed Systems ˇ A. Cesnys, G. Juˇska and E. Montrimas, Charge Carrier Transfer at High Electric Fields in Noncrystalline Semiconductors Andrey S. Glebov, The Nature of the Current Instability in Chalcogenide Vitreous Semiconductors A. M. Andriesh, M. S. Iovu and S. D. Shutov, Optical and Photoelectrical Properties of Chalcogenide Glasses V. Val. Sobolev and V. V. Sobolev, Optical Spectra of Arsenic Chalcogenides in a Wide Energy Range of Fundamental Absorption Yu. S. Tver’yanovich, Magnetic Properties of Chalcogenide Glasses

Contents of Volumes in This Series

367

Volume 80 Semiconducting Chalcogenide Glass III Andrey S. Glebov, Electronic Devices and Systems Based on Current Instability in Chalcogenide Semiconductors Dumitru Tsiulyanu, Heterostructures on Chalcogenide Glass and Their Applications E. Bychkov, Yu. Tveryanovich and Yu. Vlasov, Ion Conductivity and Sensors Yu. S. Tver’yanovich and A. Tverjanovich, Rare-earth Doped Chalcogenide Glass M. F. Churbanov and V. G. Plotnichenko, Optical Fibers from High-purity Arsenic Chalcogenide Glasses

Volume 81 Conducting Organic Materials and Devices Suresh C. Jain, Magnus Willander and Vikram Kumar, Introduction; Polyacetylene; Optical and Transport Properties; Light Emitting Diodes and Lasers; Solar Cells; Transistors

Volume 82 Semiconductors and Semimetals Maiken H. Mikkelsen, Roberto C. Myers, Gregory D. Fuchs, and David D. Awschalom, Single Spin Coherence in Semiconductors Jairo Sinova and A. H. MacDonald, Theory of Spin–Orbit Effects in Semiconductors K. M. Yu, T. Wojtowicz, W. Walukiewicz, X. Liu, and J. K. Furdyna, Fermi Level Effects on Mn Incorporation in III–Mn–V Ferromagnetic Semiconductors T. Jungwirth, B. L. Gallagher, and J. Wunderlich, Transport Properties of Ferromagnetic Semiconductors F. Matsukura, D. Chiba, and H. Ohno, Spintronic Properties of Ferromagnetic Semiconductors C. Gould, G. Schmidt, and L. W. Molenkamp, Spintronic Nanodevices J. Cibert, L. Besombes, D. Ferrand, and H. Mariette, Quantum Structures of II–VI Diluted Magnetic Semiconductors Agnieszka Wolos and Maria Kaminska, Magnetic Impurities in Wide Band-gap III–V Semiconductors Tomasz Dietl, Exchange Interactions and Nanoscale Phase Separations in Magnetically Doped Semiconductors Hiroshi Katayama-Yoshida, Kazunori Sato, Tetsuya Fukushima, Masayuki Toyoda, Hidetoshi Kizaki, and An van Dinh, Computational Nano-Materials Design for the Wide Band-Gap and High-TC Semiconductor Spintronics Masaaki Tanaka, Masafumi Yokoyama, Pham Nam Hai, and Shinobu Ohya, Properties and Functionalities of MnAs/III–V Hybrid and Composite Structures

Volume 83 Semiconductors and Semimetals T. Scholak, F. Mintert, T. Wellens, and A. Buchleitner, Transport and Entanglement P. Nalbach and M. Thorwart, Quantum Coherence and Entanglement in Photosynthetic LightHarvesting Complexes ¨ Richard J. Cogdell and Jurgen K¨ohler, Sunlight, Purple Bacteria, and Quantum Mechanics: How Purple Bacteria Harness Quantum Mechanics for Efficient Light Harvesting

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