Zinc Oxide: From Fundamental Properties Towards Novel Applications (Springer Series in Materials Science)

Springer Series in

materials science

120

Springer Series in

materials science Editors: R. Hull C. Jagadish R.M. Osgood, Jr. J. Parisi Z. Wang H. Warlimont The Springer Series in Materials Science covers the complete spectrum of materials physics, including fundamental principles, physical properties, materials theory and design. Recognizing the increasing importance of materials science in future device technologies, the book titles in this series ref lect the state-of-the-art in understanding and controlling the structure and properties of all important classes of materials.

Please view available titles in Springer Series in Materials Science on series homepage http://www.springer.com/series/856

Claus F. Klingshirn Bruno K. Meyer Andreas Waag Axel Hoffmann Jean Geurts

Zinc Oxide From Fundamental Properties Towards Novel Applications

With 226 Figures

123

Professor Dr. Claus F. Klingshirn

Professor Dr. Bruno K. Meyer

Institute for Applied Physics Karlsruhe Institute of Technology (KIT) Wolfgang-Gaede-Str. 1 76131 Karlsruhe, Germany E-mail: [email protected]

Universit¨at Gießen, Physikalisches Institut Heinrich-Buff-Ring 16 35392 Gießen, Germany E-mail: [email protected]

Professor Dr. Andreas Waag

TU Berlin, Fakut¨at II Mathematik und Naturwissenschaften Institut f¨ur Festk¨orperphysik Hardenbergstr. 36 10623 Berlin, Germany E-mail: [email protected]

TU Braunschweig Institut f¨ur Halbleitertechnik Hans-Sommer-Str. 66 38106 Braunschweig, Germany E-mail: [email protected]

Professor Dr. Axel Hoffmann

Professor Dr. Jean Geurts ¨ Wurzburg, ¨ Universitat Physikalisches Institut, LS Experimentelle Physik 3 Am Hubland, 97074 W¨urzburg, Germany E-mail: [email protected]

Series Editors:

Professor Robert Hull

Professor J¨urgen Parisi

University of Virginia Dept. of Materials Science and Engineering Thornton Hall Charlottesville, VA 22903-2442, USA

Universit¨at Oldenburg, Fachbereich Physik Abt. Energie- und Halbleiterforschung Carl-von-Ossietzky-Straße 9–11 26129 Oldenburg, Germany

Professor Chennupati Jagadish

Dr. Zhiming Wang

Australian National University Research School of Physics and Engineering J4-22, Carver Building Canberra ACT 0200, Australia

University of Arkansas Department of Physics 835 W. Dicknson St. Fayetteville, AR 72701, USA

Professor R. M. Osgood, Jr.

Professor Hans Warlimont

Microelectronics Science Laboratory Department of Electrical Engineering Columbia University Seeley W. Mudd Building New York, NY 10027, USA

DSL Dresden Material-Innovation GmbH Pirnaer Landstr. 176 01257 Dresden, Germany

Springer Series in Materials Science ISSN 0933-033X ISBN 978-3-642-10576-0 e-ISBN 978-3-642-10577-7 DOI 10.1007/978-3-642-10577-7 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2010930168 © Springer-Verlag Berlin Heidelberg 2010 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specif ically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microf ilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specif ic statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: eStudio Calamar Steinen Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

Preface

After the invention of semiconductor-based rectifiers and diodes in the first half of the last century, the advent of the transistor paved the way for semiconductors in electronic data handling starting around the mid of the last century. The transistors widely replaced the vacuum tubes, which had even been used in the first generation of computers, the Z3 developed by Konrad Zuse in the 1940s of the last century. The first transistors were individually housed semiconductor devices, which had to be soldered into the electric circuits. Later on, integrated circuits were developed with increasing numbers of individual elements per square inch. The materials changed from, e.g., PbS and Se in rf-detectors and rectifiers used frequently in the first half of the last century over the group IV element semiconductor Ge with a band gap of 0.7 eV at room temperature to Si with a value of 1.1 eV. The increase of the gap reduced the leakage current and its temperature dependence significantly. Therefore, the logical step was to try GaAs with a band gap of 1.4 eV next. However, the technology of this semiconductor from the group of III–V compounds proved to be much more difficult, though beautiful device concepts had been developed. Therefore, GaAs and its alloys and nano structures with other III–V compounds like AlGaAs or InP remained restricted in electronics to special applications like transistors for extremely high frequencies, the so-called high electron mobility transistors (HEMT). The IT industry is still mainly based on Si and will remain so in the foreseeable nearer future. The story up to the mid 1980s of the last century has been written up, e.g., by H. Queisser in his book “Kristallene Krisen,” 2nd ed., Piper, M¨unchen (1987). However, the III–V compounds mentioned above found their place in the field of light-emitting semiconductor devices like light-emitting diodes (LED) or laser diodes (LD), since many of the III–V compounds are direct gap materials, while the group IV element and compound semiconductors like Ge, Si, SiC, or C (diamond) have all an indirect band gap with intrinsically low luminescence yield. This property could not yet be overcome, not even by the use of nano crystals, or porous or amorphous Si. The use of inorganic and organic semiconductors (LEDs and O-LEDs) for lighting purposes is envisaged, while the use of the former in data storage and reading (CD, DVD, and blue ray discs), in scanners, displays, traffic lights, in data transmission through glass fibres, etc., is already well established. Some scientists even tend to call the last century the “century of electronics” v

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Preface

while the present one is expected to develop into a “century of optics” or at least of optoelectronics. LEDs exist for the whole visible spectral range including the near IR for glass fibre data transmission and the near UV, but for LDs, there is still a gap in the yellowgreen spectral range, which prevents the use of LDs in full color, high brightness displays, e.g., in projectors. On the other hand, the (near) UV is technically very attractive since shorter wavelengths allow increasing the data density in optical storage, to write smaller structures for the masks of integrated circuits and to excite a wide variety of phosphors covering the whole visible spectrum and being used already as one possibility to produce white light LEDs. The first successful attempt to produce short wavelength LDs was based on the II–VI compound ZnSe with its alloys with other II–VI semiconductors like CdSe, ZnS, MgS, ZnTe, CdTe, or even the very poisonous Be compounds. Though optical output powers of several 10 mW under cw operation at room temperature (RT) have been reached, the ZnSe-based LDs never made it to a successful commercial product, because the lifetime of the prototypes never exceeded a few hundred hours, while a few 10,000 h are expected for a commercial device. Then the group III-nitrides made it. The story of this partly unexpected success is documented, e.g., by S. Nakamura, S. Pearton, and G. Fasol in their book “The Blue Laser Diode: the Complete Story,” 2nd ed., Springer, Heidelberg (2000). A main problem to solve was ambipolar doping. Many of the wide gap semiconductors are easily doped one way, e.g., n-type, but very difficultly the other, e.g., p-type. But still, GaN and the related group III-nitrides have their problems: large GaN single crystals for homoepitaxy do not yet exist, the technology is still very difficult, the material is expensive and poisonous, etc. Therefore, there is a trend to look for alternative materials. An obvious choice is the II–VI semiconductor ZnO. It has a band gap and carrier mobilities comparable to GaN and an exciton binding energy, which is with 60 meV, roughly twice that of GaN. This fact is stressed by many authors as big advantage. Indeed, it allows doing nice basic exciton physics but is much less important for the applications in optoelectronics in contrast to what is claimed by many authors. The real advantages of ZnO are, among others, the facts, that it is much less poisonous (and even used as additive to human and animal food), that it is cheap and already produced by some 100,000 tons per year, that it can be grown as large single crystals by various methods, or that it has a strong tendency to grow in a self-organized way in the form of nano- and microrods with diameters ranging from a few ten nanometers to a micrometer and lengths of several to beyond ten micrometers. These nanorods hold big promises in miniaturized optoelectronics and sensing. By alloying with MgO or CdO, the band gap can be shifted either further into the UV or down into the green spectral ranges, respectively. Additionally, there are many other existing or emerging applications of ZnO. The big drawback of ZnO is still the difficulty to obtain high, stable, and reproducible p-type doping. In this book, we give an overview of fundamental properties of ZnO like its growth or its electronic, phononic, magnetic, and optical properties, with some emphasis on the latter since the hope for optoelectronic devices based on ZnO is the main motivation for the present research boom. Another prominent topic of this

Preface

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book is past, present, emerging, and visions of future applications of ZnO-based devices. More details about the contents of this book and the philosophy behind are given in the introduction. The book is equally well suited for graduate students and scientists in physics who have a good background in solid state physics and are entering the field of ZnO research and development and for those coming from engineering disciplines who frequently do not yet have this background. For them, the book by one of the co-authors (CK) on “Semiconductor Optics,” 3rd ed., Springer, Heidelberg (2007) might be additionally helpful. Karlsruhe, Gießen, Braunschweig, Berlin, W¨urzburg, May 2010

Claus Franz Klingshirn Bruno K. Meyer Andreas Waag Axel Hoffmann Jean Geurts

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Contents

1

2

Introduction .. . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . C. Klingshirn 1.1 History of ZnO Research and Contents of This Book .. . . . . . . .. . . . . . . 1.2 Aim of This Review .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . References .. . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . Crystal Structure, Chemical Binding, and Lattice Properties .. . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . J. Geurts 2.1 Crystal Structure and Chemical Binding .. . . . . . . . . . . . . . . . . . . . . .. . . . . . . 2.1.1 ZnO Polytype Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 2.1.2 Phase Transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 2.1.3 Crystal Axis Polarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 2.2 Thermal Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 2.2.1 Thermal Expansion Coefficients . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 2.2.2 Specific Heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 2.2.3 Thermal Conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 2.3 The Piezoelectric Effect .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 2.3.1 Principle and Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 2.3.2 The Piezoelectric Tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 2.4 Lattice Dynamics .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 2.4.1 Phonon Symmetry and Eigenvectors of the Wurtzite Lattice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 2.4.2 Phonon Dispersion Relations . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 2.4.3 Infrared Optical Phonon Spectroscopy . . . . . . . . . . . . . . .. . . . . . . 2.4.4 Raman Spectroscopy of Phonon Modes .. . . . . . . . . . . . .. . . . . . . 2.4.5 Vibration Modes in Doped ZnO . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 2.4.6 Incorporation of Transition Metal Atoms in ZnO .. . .. . . . . . . 2.4.7 Raman Scattering from ZnO Nanoparticles . . . . . . . . . .. . . . . . . 2.5 Phonon–Plasmon Mixed States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 2.5.1 Collective Charge-Carrier Oscillations . . . . . . . . . . . . . . .. . . . . . . 2.5.2 Coupling to Polar Longitudinal Phonons .. . . . . . . . . . . .. . . . . . . References .. . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .

1 2 4 5

7 8 8 10 10 11 11 12 13 14 14 15 16 17 18 21 23 26 28 30 31 32 33 35 ix

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Growth .. . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . Andreas Waag 3.1 Bulk Growth .. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 3.1.1 Vapor Phase Transport.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 3.1.2 Solvothermal Growth .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 3.2 Epitaxial Growth Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 3.2.1 Metal Organic Chemical Vapor Deposition . . . . . . . . . .. . . . . . . 3.2.2 Molecular Beam Epitaxy .. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 3.2.3 Pulsed Laser Deposition.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 3.3 Growth of Self-Organized Nanostructures .. . . . . . . . . . . . . . . . . . . .. . . . . . . 3.3.1 Growth Techniques for Nano Pillars. . . . . . . . . . . . . . . . . .. . . . . . . 3.3.2 Properties of Nanopillars .. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . References .. . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . Band Structure .. . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . B.K. Meyer 4.1 The Ordering of the Bands at the Valence Band Maximum in ZnO . 4.2 ZnO and Its Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 4.2.1 Cationic Substitution: Mg, Cd, Be in ZnO . . . . . . . . . . .. . . . . . . 4.2.2 Anionic Substitution: S, Se in ZnO . . . . . . . . . . . . . . . . . . .. . . . . . . 4.3 Valence and Conduction Band Discontinuities . . . . . . . . . . . . . . . .. . . . . . . 4.3.1 Iso-Valent Hetero-Structures .. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 4.3.2 Hetero-Valent Hetero-Structures .. . . . . . . . . . . . . . . . . . . . .. . . . . . . References .. . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .

39 40 40 41 42 46 53 65 66 67 67 73 77 77 84 85 89 91 91 92 93

5

Electrical Conductivity and Doping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 95 Andreas Waag 5.1 Introduction .. . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 95 5.2 Hydrogen in ZnO .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 97 5.3 Donors in ZnO: Al, Ga, In . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 98 5.4 Acceptors in ZnO.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 99 5.5 Mobility .. . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .104 5.6 Ohmic and Schottky Contacts on ZnO . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .105 5.7 Two-Dimensional Electron Gas and Quantum Hall Effect .. . .. . . . . . .108 5.8 High-Field Transport and Varistors.. . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .110 5.9 Photoconductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .114 References .. . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .117

6

Intrinsic Linear Optical Properties Close to the Fundamental Absorption Edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .121 C. Klingshirn 6.1 Free Excitons in Bulk Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .121 6.1.1 Free Excitons in Bulk Samples, Epitaxial Layers, and NanoRods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .125 6.1.2 Experimental Observations . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .129 6.2 ZnO-Based Alloys.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .145

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6.3 6.4

Surface Exciton Polaritons .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .150 Excitons in Structures of Reduced Dimensionality .. . . . . . . . . . .. . . . . . .153 6.4.1 Excitons in Quantum Wells and Superlattices . . . . . . .. . . . . . .153 6.4.2 Quantum Wires . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .155 6.4.3 Quantum Dots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .158 6.4.4 Cavity Polaritons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .162 References .. . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .163

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Bound Exciton Complexes .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .169 B.K. Meyer 7.1 ZnO Luminescence: An Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .169 7.2 Neutral Donor Bound Excitons (A-Valence Band) and Their Two Electron Satellites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .172 7.3 Ionized Donor Bound Excitons (A-Valence Band) . . . . . . . . . . . .. . . . . . .177 7.4 A Comparison of the Localization Energies with Theoretical Predictions (the Haynes Rule) . . . . . . . . . . . . . . . . . . . . .. . . . . . .180 7.5 Excited State Properties of the Bound Excitons . . . . . . . . . . . . . . .. . . . . . .183 7.6 Donor–Acceptor Pair Transitions.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .189 References .. . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .197

8

Influence of External Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .201 M.R. Wagner and A. Hoffmann 8.1 Excitons in Magnetic Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .201 8.1.1 Zeeman Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .202 8.1.2 Free and Bound Excitons.. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .203 8.1.3 Selection Rules for Zeeman Splitting of Exciton States in Magnetic Fields . . . . . . . . . . . . . . . . . . . .. . . . . . .212 8.1.4 Symmetry of Exciton Hole States . . . . . . . . . . . . . . . . . . . .. . . . . . .213 8.2 Excitons in Strain Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .215 8.2.1 Uniaxial Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .217 8.2.2 Hydrostatic Pressure .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .219 8.2.3 Biaxial In-Plane Strain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .225 References .. . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .229

9

Deep Centres in ZnO .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .233 A. Hoffmann, E. Malguth, and B.K. Meyer 9.1 The Green and Yellow Emission Bands . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .233 9.2 Transition Metal Ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .239 9.2.1 ZnO/V .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .241 9.2.2 ZnO/Fe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .244 9.2.3 ZnO/Fe3C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .245 9.2.4 ZnO/Fe2C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .249 9.2.5 ZnO/Co.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .253 9.2.6 ZnO/Ni . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .254 9.2.7 ZnO/Cu.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .258 9.3 Outlook . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .264 References .. . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .264

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10 Magnetic Properties .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .267 Andreas Waag 10.1 General Overview of the Topic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .267 10.2 Short Overview of the Situation in ZnO . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .269 References .. . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .272 11 Nonlinear Optics, High Density Effects and Stimulated Emission . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .275 C. Klingshirn 11.1 Nonlinear Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .275 11.2 High Excitation Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .277 11.2.1 The Intermediate Density Regime . . . . . . . . . . . . . . . . . . . .. . . . . . .277 11.2.2 Electron–Hole Plasma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .282 11.3 Processes for Stimulated Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .285 11.3.1 Bulk Samples and Epilayers . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .286 11.3.2 Quantum Wells and Superlattices .. . . . . . . . . . . . . . . . . . . .. . . . . . .293 11.3.3 Nano Rods and Their Cavity Modes .. . . . . . . . . . . . . . . . .. . . . . . .294 11.3.4 Quantum Dots and Random Lasing . . . . . . . . . . . . . . . . . .. . . . . . .296 11.3.5 Cavity Modes, Photonic Crystals and Polariton Lasers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .299 References .. . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .302 12 Dynamic Processes . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .307 C. Klingshirn 12.1 Dephasing Dynamics.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .308 12.2 Relaxation Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .311 12.3 Recombination Dynamics.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .314 References .. . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .320 13 Past, Present and Future Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .325 C. Klingshirn 13.1 Past Applications .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .325 13.1.1 The Electro Fax Copy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .325 13.1.2 Ferrite Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .326 13.2 Present and Emerging Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .326 13.2.1 Cement, Rubber, Paint and Glazes . . . . . . . . . . . . . . . . . . . .. . . . . . .326 13.2.2 Catalysts, Pharmaceutics, Cosmetics and Food Additives ..327 13.2.3 Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .327 13.2.4 Gas Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .330 13.2.5 TCO, Solar Cells and Some Further Applications . . .. . . . . . .331 13.3 Visions of Future Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .332 13.3.1 pn Junctions .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .333 13.3.2 Light Emitting Diodes .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .334 13.3.3 Field Emitters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .338 13.3.4 Spintronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .338 References .. . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .339

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14 Conclusion and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .347 C. Klingshirn 14.1 Conclusions .. . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .347 14.2 Outlook . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .348 References .. . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .349 Index . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .351

Chapter 1

Introduction C. Klingshirn

Abstract The purpose of this introduction is – after a few general words on ZnO – to inform the reader about the history of ZnO research, the contents of this book and the intentions of the authors. Zinc oxide (ZnO) is a IIb –VI compound semiconductor. This group comprises the binary compounds of Zn, Cd and Hg with O, S, Se, Te and their ternary and quaternary alloys. The band gaps of these compounds cover the whole band gap range from Eg  3:94 eV for hexagonal ZnS down to semimetals (i.e., Eg D 0 eV) for most of the mercury compounds. ZnO itself is also a wide gap semiconductor with Eg  3:436 eV at T D 0 K and (3:37 ˙ 0:01) eV at room temperature. For more details on the band structure, see Chaps. 4 and 6 or for a recent collection of data on ZnO, for example, [R¨ossler et al. (eds) Landolt-B¨ornstein, New Series, Group III, Vols. 17 B, 22, and 41B, 1999]. Like most of the compounds of groups IV, III–V, IIb –VI and Ib –VII, ZnO shows a tetrahedral coordination. In contrast to several other IIb –VI compounds, which occur both in the hexagonal wurtzite and the cubic zinc blende type structure such as ZnS, which gave the name to these two modifications, ZnO occurs almost exclusively in the wurtzite type structure. It has a relatively strong ionic binding (see Chap. 2). The exciton binding energy in ZnO is 60 meV [Thomas, J. Phys. Chem. Solids 15:86, 1960], the largest among the IIb –VI compounds, but by far not the largest for all semiconductors since, for example, CuCl and CuO have exciton binding energies around 190 and 150 meV, respectively. See, for example, [R¨ossler et al. (eds) Landolt-B¨ornstein, New Series, Group III, Vols. 17B, 22, and 41B, 1999; Thomas, J. Phys. Chem. Solids 15:86, 1960; Klingshirn and Haug, Phy. Rep. 70:315, 1981; H¨onerlage et al., Phys. Rep. 124:161, 1985] and references therein. More details on excitons will be given in Chap. 6. ZnO has a density of about 5:6 g=cm3 corresponding to 4:2  1022 ZnO molecules per cm3 [Hallwig and Mollwo, Verhandl. DPG (VI) 10, HL37, 1975]. ZnO occurs naturally under the name zinkit. Owing to the incorporation of impurity atoms such as Mn or Fe, zinkit looks usually yellow to red. Pure, synthetic ZnO

C. Klingshirn Institut f¨ur Angewandte Physik, Karlsruher Institut f¨ur Technologie KIT, Karlsruhe, Germany e-mail: [email protected] 1

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is colourless and clear in agreement to the gap in the near UV. The growth of ZnO and ZnO-based nano-structures is treated in Chap. 3. ZnO is used by several 100,000 tons per year, for example, as additive to concrete or to the rubber of tires of cars. In smaller quantities, it is used in pharmaceutical industries, as an additive to human and animal food, as a material for sensors and for varistors or as transparent conducting oxide. For more details and aspects of present and forthcoming applications, see Chap. 13.

1.1 History of ZnO Research and Contents of This Book The data collections INSPEC and Web of Science give more than 26,000 (July 2009) entries for the key word ZnO. During the past few years, the rate of papers on ZnO per annum has exceeded 2,000. This fact, however, does not mean that ZnO is a “new” semiconductor; indeed, it is an “old” semiconductor. The research on ZnO goes back to the first half of the last century and started, for example, with investigations of ion radii and crystal structure, the specific heat, even at low temperatures, its density or its optical properties [1–10] and references given therein. Early examples of ZnO growth, even in the form of thin (partly epitaxial) layers or of tetrapods can be found, for example, in [11–18] and first reviews on ZnO including the electronic transport (see Chap. 5) and optical properties (see Chaps. 6–9, 11 and 12) appeared starting in the 1950s with a few examples going back to the 1930s [19–25]. A first research peak occurred for ZnO from the end of the 1960s to the mid 1980s, driven by the availability of good bulk single crystals and first epitaxial layers [14–18]. The central topics at that time were, apart from the growth, doping and electric transport (see Chap. 5), the band structure and free or bound excitons (Chaps. 4 and 6–8, respectively), deep centres investigated in luminescence or electron spin resonance (Chap. 9) and nonlinear optics and stimulated emission (Chap. 11). For example, the state of knowledge at that time is documented in various reviews, which are partly or completely dedicated to ZnO and entered also as examples in some textbooks [26–32]. In the mid of the 80s, the interest in ZnO faded away essentially for two reasons: One was the problem of ambipolar doping of ZnO. Although ZnO can be easily n-type doped by Al, Ga or In on Zn site up to the range of n  1020 cm3 [33–37], p-type doping could not be realized apart from some hardly reproduced claims, e.g. [38]. However, ambipolar doping is an indispensable prerequisite for most semiconductor applications in opto-electronics. The absence of p-doping at that time destroyed the hope to obtain with ZnO a material for semiconductor laser-diodes in the blue, violet, or near UV spectral ranges. The other reason was the advent of structures of reduced dimensionality such as quantum wells and superlattices and later on of quantum wires and dots. In their early years, these structures were almost exclusively based on III–V compounds, especially on the lattice matched system GaAs=Al1y Gay As. For recent textbooks or data collections of this topic see for example [32, 39].

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The need for blue/UV laser-diodes (LD) remained and after an intermezzo with ZnSe-based LD structures, which unfortunately never exceeded a lifetime of a few 100 h, the group III nitrides made it [40]. However, gradually it became evident that GaN and its alloys with AlN and InN are rather difficult materials because patents concerning LD are in the hands of a few companies with partly rather restrictive licence politics and ZnO and its alloys with MgO, BeO or CdO have partly similar properties as GaN (e.g., concerning band gap, crystal structure, carrier mobilities or heat conductivity) and also some advances, for example, the availability of large single crystals for homo epitaxy, the insensitivity against radiation damage, the fact that ZnO is cheaper and not poisonous or the fact that magnetic dopants such as Co, Mn or Fe do not introduce simultaneously carrier doping as is the case in III–V semiconductors. Finally, the patent situation is for ZnO still more open. Additionally ZnO has a strong tendency for self-organized growth of nanostructures, above all of nano-rods (see Chap. 3) but also of many other types of nano-structures like tetrapods (or fourlings), nano-belts, -ribbons, -nails, -combs, -flowers, -walls, -castles, -tubes, -wool, -corals, or -cabbage, etc., depending on the imagination of the respective author and from which especially the last mentioned ones are frequently nothing but an unsuccessful (and often hardly reproducible) attempt to grow high quality epitaxial layers. By doping or alloying with magnetic ions such as Mn2C , Co2C or Fe2C , diluted magnetic ZnO-based samples may be formed, which possibly show weak ferromagnetism up to RT (see Chap. 10). All these partly application-oriented aspects, for example, progress in the growth of nano-structures such as quantum wells and nano-rods, progress in p-type doping and first reports of light emission from electrically pumped ZnO-based homo or hetero junctions (e.g., see the reviews [41–52] and the references given therein) and some more application aspects, which we present in Chap. 13, are the reason for the renaissance of ZnO research during the last decade. The progress of the field can be seen in the contributions to and proceedings of international or national conferences and workshops such as the proceedings of the International Conference on II–VI Compounds and ICPS or the International ZnO Workshops and in recent reviews [41–53]. During this present renaissance of ZnO research, not only the long known properties of ZnO are being rediscovered – but also beautiful new results are obtained by research groups from all over the world – and this is the main aspect. The topics of research and development are partly the same as in the 1970s and 1980s (and thus partly to some extent a kind of repetition), such as growth, doping, linear and nonlinear optics, including the aspects of stimulated emission; new ones are also added such as the growth of nano-structures, p-type doping and the development of light emitting or even laser diodes (L(E)Ds), the investigation of semi magnetic alloys, the use of ZnO as transparent conducting oxide (TCO) in solar cells, as sensor material or the investigation of the dynamic properties of electron-hole pairs. See Chap. 12 for the last topic.

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1.2 Aim of This Review The aim of this review is twofold: first, to present the basic physical properties of ZnO in a didactical way without too much of theoretical ballast, especially those that are relevant for present and possible future applications, and second to review just these applications. The topics that we shall treat to this end have been already mentioned in the subsection above. Despite of the numerous recent review articles, books or conference proceedings listed above and some other ones, which will be most probably under way during the writing of this book by other authors (actually the recent, over large parts also very good book [53] or [55,56] are example for this expectation), the authors of this book think that it is worthwhile to publish this work because there is, apart from the two aims mentioned above, a third one, namely, to really critically review of the old and new data concerning, for example, the valence band structure, magnetic properties or the laser processes at room temperature. If a new field is started or, as in the case of ZnO, an old one is revived, a certain amount of enthusiasm is necessary and helpful. However, the authors feel that not a too small fraction of papers or conference contributions is too euphoric and overoptimistic in the sense that (frequently good) data are over interpreted, without taking too much care about consistency or plausibly of their interpretations nor of past results. This aspect can be especially annoying when reviewing some of the recently submitted papers. The other aspect is that ambitious young scientists frequently either simply do not know or do not bother about the fact that many things, which they enthusiastically want to present as new, are actually known since decades. For example, it is not acceptable that a group cites a paper for the exciton binding energy of 60 meV, which is just about 5 years old (possibly even from their own group) without giving credit to much earlier work (in this case, e.g., by Thomas and Hopfield and other authors [1, 54]) who published this value already more than 40 years ago. The authors think that this phenomenon touches the boarder of scientific correctness. The team of the authors of this book comprises young scientists, who started to work on ZnO only several years ago, and others, who are familiar with this material since over three decades. On the one hand, this combination may help to reach the above aims. On the other hand, the authors are aware of the fact that they themselves will make in this book their own mistakes and will inevitably miss relevant results and references. Concerning the first aspect, the authors will appreciate comments from critical readers. The second point is an inherent problem. Nobody can read or know the over 26,000 ZnO-relevant publications mentioned at the beginning of this section nor the 2,000 new ones appearing every year. Therefore, the references of this book are necessarily limited and their choice is partly arbitrary or even accidental. Concerning the (co-) authors of the cited references, we give in all chapters all of them up to a maximum number of three, while some of the authors give only the first one followed by et al. (et alii/aliae) in cases of more than three co-authors. These authors apologize for this possible shortcoming.

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5

Another aspect concerns the figures in this book. A large fraction is taken from the own work of the authors of the respective chapters. Figures from other authors are frequently modified for the purpose of this book, for example, by adding a photon energy scale to a wave length scale to make the data of different figures comparable, but in all cases the proper references are given. The authors like to thank their colleagues and various publishing houses for the permission to use their material in this book. As a few minor final comments, it should be noted that every chapter, including this one, has at its beginning under the headline “abstract” a short summary of and partly also an introduction to the topics of this chapter. The references for each chapter are given directly at the end of this chapter. A collection of keywords and the pages, where they appear, are given at the end of this book excluding generally references to keywords appearing in the headlines of chapters or sections.

References 1. U. R¨ossler et al. eds., Landolt-B¨ornstein, New Series, Group III, Vols. 17B, 22, and 41B (Springer, Berlin, 1999) 2. M.V. Goldschmidt, Chem. Ber. 60, 1263 (1927) 3. J. Ewles, Proc. R. Soc. Lond. A Biol. Sci. 167, 34 (1938) 4. H. Schulz, K. H. Thiemann, Solid State Commun. 32, 783 (1979) 5. D. Hallwig, E. Mollwo, Verhandl. DPG (VI) 10, HL37 (1975) 6. C.G. Maier, J. Am. Chem. Soc., 48, 364 and 2564 (1926) 7. L. Pauling, J. Am. Chem. Soc. 49, 765 (1927) 8. F.A. Kr¨oger, Physica, 7, 1 (1940) 9. F.A. Kr¨oger, H.J. Meyer, Physica, 20, 1149 (1954) 10. C.W. Bunn, Proc. Phys. Soc. Lond. A Math. Phys. Sci. 47, 835 (1935) 11. Landolt-B¨ornstein, New Series, Group III, Vol. 8 (1972) 12. E. Mollwo, Physik 1, 1 (1944) 13. M.L. Fuller, J. Appl. Phys. 15, 164 (1944) 14. E. Scharowski, Z. Physik 135, 138 (1953) 15. E.M. Dodson, J.A. Savage, J. Mat. Sci. 3, 19 (1968) 16. R. Helbig, J. Cryst. Growth 15, 25 (1972) 17. R.A. Laudise, A.A. Ballmann, J. Phys. Chem. 64, 688 (1960) 18. H. Schneck, R. Helbig, Thin Solid Films 27, 101 (1975) 19. W. Jander, W. Stamm, Anorg. Allgem. Chem. 119, 165 (1931) 20. H.E. Brown, Zinc Oxide Rediscovered (The New Jersey Zinc Company, New York, 1957) 21. H. Heiland, E. Mollwo, F. St¨ockmann, Solid State Phys 8, 191 (1959) 22. H.H. Baumbach, C.Z. Wagner, Phys. Chem. B 22, 199 (1933) 23. P.H. Miller Jr., in Proc. Intern. Conf. on Semiconducting Materials, Reading (1950) 24. H.K. Henisch (ed.), p. 172, Butterworths Scientific Publications, London (1951) 25. H.E. Brown, Zinc Oxide, Properties and Applications (The New Jersey Zinc Company, New York, 1976) 26. C. Klingshirn, H. Haug, Phy. Rep. 70, 315 (1981) 27. B. H¨onerlage et al. Phys. Rep. 124, 161 (1985) 28. W. Hirschwald et al. Curr. Top Mater. Sci. 7, 143 (1981) 29. R. Helbig, Freie und Gebundene Exzitonen in ZnO, Habilitation Thesis, Erlangen (1975) 30. K. H¨ummer, Exzitonische Polaritonen in einachsigen Kristallen, Habilitation Thesis, Erlangen (1978)

6 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56.

C. Klingshirn M. Ueta et al. Excitonic Processes in Solids, Springer Series in Solid State Science, 60 (1986) C. Klingshirn, Semiconductor Optics, 3rd edn. (Springer, Berlin, 2007) M. Ataev et al. Thin Solid Films 260, 19 (1995) M. G¨oppert et al. J. Lumin. 72–74, 430 (1997) S.Y. Myong et al. Jpn. J. Appl. Phys. 36, L1078 (1997) H. Kato et al. J. Cryst. Growth 237–239, 538 (2002) T. Makino et al. Appl. Phys. Lett. 85, 759 (2004) T.V. Butkhuzi et al. J. Cryst. Growth 117, 366 (1992) Landolt-B¨ornstein, New Series, Group III, Vol. 34C C. Klingshirn ed., Springer, Berlin (2001) S. Nakamura, G. Fasol, The Blue Laser Diode (Springer, Heidelberg, 1997) D.C. Look et al. Phys. Stat. Sol. A 201, 2203 (2004) C. Klingshirn et al. Adv. Solid State Phys. 45, 261 (2005) ¨ ur et al. J. Appl. Phys. 98, 041301 (2005) ¨ Ozg¨ U. C. Klingshirn et al. Phy. J. 5(1), 33 (2006) A. Osinsky, S. Karpov in ZnO Bulk, Thin Films and Nanostructures, ed. By C. Jagadish, S.J. Pearton p525 (Elsevier, London, 2006), p. 525 N.H. Nickel and E. Terukov eds., Zinc Oxide – A Material for Micro- and Optoelectronic Applications, NATO Science Series II, 194 (2005) C. Jagadish, S.J. Pearton (eds.) Zinc Oxide Bulk, Thin Films and Nanostructures (Elsevier, Amsterdam, 2006) C. Klingshirn, Chem. Phys. Chem. 8, 782 (2007) C. Klingshirn et al. Superlattice Microst. 38, 209 (2005) C. Klingshirn et al. NATO Sci Series II 231, 277 (2006) S. T¨uzemen, E. G¨ur, Opt. Mater. 30, 292 (2007) C. Klingshirn, Phys. Stat. Sol. B 244, 3027 (2007) ¨ ur, Zinc Oxide (Wiley-VCH, Weinheim, 2009) ¨ Ozg¨ H. Morkoc¸, U. D.G. Thomas, J. Phys. Chem. Solids 15, 86 (1960) M. Willander et al. Nanotechnology 20, 332001 (2009) C. Klingshirn et al. Phys. Stat. Sol. B 247, 1424 (2010)

Chapter 2

Crystal Structure, Chemical Binding, and Lattice Properties J. Geurts

Abstract This chapter starts with an overview of the ZnO crystal structure and its conjunction to the chemical binding. ZnO commonly occurs in the wurtzite structure. This fact is closely related to its tetrahedral bond symmetry and its prominent bond polarity. The main part of the first section deals with the ZnO wurtzite crystal lattice, its symmetry properties, and its geometrical parameters. Besides wurtzite ZnO, the other polytypes, zinc-blende and rocksalt ZnO are also briefly discussed. Subsequently, lattice constant variations and crystal lattice deformations are treated. This discussion starts with static lattice constant variations, induced by temperature or by pressure, as well as strain-induced static lattice deformation, which reduces the crystal symmetry. The impact of this symmetry reduction on the electrical polarization is the piezo effect, which is very much pronounced in ZnO and is exploited in many applications. See also Chap. 13. Dynamic lattice deformations manifest themselves as phonons and, in case of doping, as phonon–plasmon mixed states. The section devoted to phonons starts with a consideration of the vibration eigenmodes and their dispersion curves. Special attention is paid to the investigation of phonons by optical spectroscopy. The methods applied for this purpose are infrared spectroscopy and, more often, Raman spectroscopy. The latter method is very common for the structural quality assessment of ZnO bulk crystals and layers; it is also frequently used for the study of the incorporation of dopant and alloying atoms in the ZnO crystal lattice. Thus, it plays an important role with regard to possible optoelectronics and spintronics applications of ZnO. The final section of this chapter focuses on phonon–plasmon mixed states. These eigenstates occur in doped ZnO due to the strong coupling between collective freecarrier oscillations and lattice vibrations, which occurs due to the high bond polarity. Owing to the direct correlation of the plasmon–phonon modes to the electronic doping, they are an inherent property of ZnO samples, when applied in (opto-) electronics and spintronics. See also Chap. 12.

J. Geurts Physikalisches Institut der Universit¨at W¨urzburg, W¨urzburg, Germany e-mail: [email protected]

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2.1 Crystal Structure and Chemical Binding ZnO is a semiconducting compound of the group-IIb element 30 Zn and the groupVI element 8 O. Zinc has five stable isotopes, the prevalent ones are 64 Zn (48.89%), 66 Zn (27.81%), and 68 Zn (18.57%), while oxygen almost purely consists of the isotope 16 O (99.76%) [1]. Zinc has the electron configuration (1s)2 (2s)2 (2p)6 (3s)2 (3p)6 (3d)10 (4s)2 ; the oxygen configuration is (1s)2 (2s)2 (2p)4 . The ZnO binding in its crystal lattice involves an sp3 hybridization of the electron states, leading to four equivalent orbitals, directed in tetrahedral geometry. In the resulting semiconducting crystal, the bonding sp3 states constitute the valence band, while the conduction band originates from its antibonding counterpart. The resulting energy gap is 3.4 eV, i.e. in the UV spectral range, which has triggered interest in ZnO as a material for transparent electronics. The cohesive energy per bond is as high as 7.52 eV [2], which also leads to a very high thermal stability: The melting temperature, Tm D 2;242 K. For comparison, the melting temperature of ZnSe is considerably lower: Tm;ZnSe D 1;799 K [1].

2.1.1 ZnO Polytype Structures The tetrahedrally coordinated bonding geometry determines the ZnO crystal structure. Each zinc ion has four oxygen neighbour ions in a tetrahedral configuration and vice versa. This geometrical arrangement, which is well known from, for example, the group-IV elements C (diamond), Si, and Ge, is also common for II–VI and III–V compounds. It is referred to as covalent bonding, although the bonds may have a considerable degree of polarity when partners with different electronegativity are involved. The tetrahedral geometry has a rather low space filling and is essentially stabilized by the angular rigidity of the binding sp3 hybrid orbitals. In a crystal matrix, the neighbouring tetrahedrons form bi-layers in the ZnO case, each one consisting of a zinc and an oxygen layer. Generally, this arrangement of tetrahedrons may result either in a cubic zinc-blende-type structure or in a hexagonal wurtzite-type structure, depending on the stacking sequence of the bi-layers. The zinc-blende structure is shown in Fig. 2.1a. It may be regarded as an arrangement of two interpenetrating face-centred cubic sub-lattices, displaced by 1=4 of the body diagonal axis. The bonding orbitals are directed along the four body diagonal axes. Note that the cubic unit cell is not the smallest periodic unit of a zinc-blende crystal, i.e. it is not a primitive unit cell. See also the comment in [3]. The primitive unit cell of zinc-blende is an oblique parallelepiped and contains only one pair of ions, in our case, Zn2C and O2 . In group theory, this lattice is classified by its point group Td (Schoenflies notation) or 4N 3m (international notation) and by its space group, denoted as T2 d or F 4N 3m, respectively [4]. In contrast to the cubic geometry, the hexagonal wurtzite lattice shown in Fig. 2.1b is uniaxial. In Fig. 1 of [3], the primitive unit cell has erroneously been printed upside down. Its distinct axis, referred to as c-axis, is directed along one of

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Crystal Structure, Chemical Binding, and Lattice Properties

9

b a

Fig. 2.1 The cubic zinc-blende-type lattice (a), and hexagonal wurtzite-type lattice (b). In the wurtzite lattice, the atoms of the molecular base unit (2  ZnO) are marked by red full circles and the primitive unit cell by green lines

the tetrahedral binding orbitals. This implies that the hexagonal c-axis corresponds to a body diagonal axis of the cubic structure. In the plane perpendicular to the c-axis, the primitive translation vectors a and b have equal length and include an angle of 120ı. In contrast to zinc-blende, the wurtzite primitive unit cell contains two pairs of ions, in our case, two ZnO units. In group theory, this lattice type is classified by its point group 6 mm (international notation) or C6v (Schoenflies notation) and by its space group P 63 mc or C 4 6v , respectively. The orientation of axes and faces in a wurtzite lattice is denoted by four-digit Miller indices hkil. The c-axis direction is referred to as [0001], the surface perpendicular to the c-axis is the hexagonal (0001) plane. The natural crystal structure of ZnO is the hexagonal wurtzite structure. At ambient conditions, it has the lattice constants a D b D 0:3249.6/ nm and c D 0:52042 .20/nm. The specific mass density d D 5:675 g cm3 [5]. The ZnO bond has a considerable degree of polarity. The bond polarity is caused by the very strong electronegativity of the oxygen, which is as high as 3.5 on the Pauling scale [6]. This is the second highest value of all chemical elements, it comes after the fluorine value of 4.0. Together with the quite low zinc electronegativity value of 0.91, this leads to an ionicity of 0.616 on the Phillips scale [7]. Therefore, zinc and oxygen in ZnO may well be considered as ionized Zn2C and O2 , i.e. the ZnO binding is at the border between the semiconductors, the binding of which is commonly classified as (predominantly) covalent, while the (predominantly) ionic binding occurs e.g. for the insulating alkali halides. According to Pauling scale, the ionic bond radii of Zn2C and O2 amount to 0.074 and 0.140 nm, respectively, i.e. their ratio is roughly 1:2 [1]. The bond polarity manifests itself in an effective charge Z  . The reported values are within the range Z  D 1:15 ˙ 0:15 [1].

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The high bond polarity is responsible for the favouring of the wurtzite structure instead of the zinc-blende structure, which occurs for tetrahedrally oriented bonds with lower polarity (e.g. in many II–VI compounds and in almost all III–V compounds, such as GaAs). The cubic zinc-blende-type structure of ZnO is obtained only by epitaxial growth on a zinc-blende type substrate, e.g. GaAs(100) with a ZnS buffer or Pt(111)/Ti/SiO2 /Si [8, 9]. Calculations by HF-LCAO (Hartree–Fock linear combination of atomic orbitals) yield the lattice constant a D 0:4614 nm for pressure p D 0 [10]. The experimentally observed preference for the wurtzite structure is confirmed by theoretical results. Among the various methods, best agreement with the experiment was obtained for DFT calculations within the generalized gradient approximation (GGA), yielding the ZnO bond energy values 7:692 eV for wurtzite, 7:679 eV for zinc-blende, and 7:455 eV for rocksalt. This result underscores the preference of the wurtzite structure, although the energy difference to the zinc-blende structure is quite low. While numerical values of the reported theoretical results depend on the applied method, they consistently favour the wurtzite structure [2].

2.1.2 Phase Transitions Owing to the near-ionic bond character of ZnO, it is plausible that the application of a hydrostatic pressure p leads already at a quite modest value of p  10 GPa to a phase transition from the wurtzite to the close-packed rocksalt type structure (space group Fm3m), which is the common crystal structure for the class of alkali halide ionic crystals [11]. The NaCl structure has a sixfold coordination and a considerably enhanced space-filling factor. The volume shrinkage at the ZnO phase transition is about 17% [1]. The experimental values reported for the cubic lattice constant are between 0.4271 and 0.4283 nm, confirming the results of calculations with various models [2]. Calculations also predict a further phase transition to the CsCl structure at considerably higher pressure values beyond 250 GPa [12]. A detailed discussion of the wurtzite-to-rocksalt transition behaviour, reported by various experimental groups, as well as theoretical results, is found in [13] and in an extended ZnO review article [2]. Moreover, the latter article comprises a very detailed general discussion of the ZnO crystal structure and binding properties with a rich survey of experimental results as well as modelling calculations according to different methods.

2.1.3 Crystal Axis Polarity Because of the prominent bond polarity of ZnO, the c-axis [0001] has a pronounced polar character. The corresponding electrostatic forces are responsible for a small

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Crystal Structure, Chemical Binding, and Lattice Properties

11

deviation from the ideal wurtzite geometry: The tetrahedrons are slightly distorted. The bond directed along the c-axis has the angle ˛ D 109:46ı towards the other bonds [1], whereas the ideal tetrahedron value is ˛ D 109:47ı. Therefore, the axis lengths ratio amounts to c=a D 1:602, which is about 2% below the value for the ideal wurtzite geometry c=a D .8=3/1=2 D 1:633. As a further consequence, the ratio u between the bond length and the length of the c-axis is uZnO D 0:3820, which is enhanced by about 2% with respect to the ideal wurtzite value u D 0:375 [1]. The deviation of the c=a ratio from the ideal wurtzite value for ZnO is the largest of all wurtzite-type semiconductors, together with the high-polarity III–V compound GaN. This underscores the crucial role of the bond polarity. For comparison, the wurtzite polytype of the much less polar ZnSe has the ideal c=a ratio within 0:5  103 . A systematic analysis of this parameter and its trend among the various wurtzite compounds was presented by Lawaetz [14]. Furthermore, the sequence of positively charged Zn2C and negatively charged O2 ions in planes perpendicular to the c-axis implies two faces of opposite polarity for a c-cut ZnO crystal: the Zn-terminated (0001) face on one side and the N face on the other. In contrast, a non-polar character occurs for O-terminated (0001) N plane (perpendicular to faces with equal numbers of Zn and O ions, e.g. the (1120) N plane. The opposite polarity of the (0001) and the (0001) N the a-axis) and the (1010) face is reflected e.g. in different etching behaviour, defect characteristics and epitaxial growth properties. Further consequences of the bond polarity are (1) a strong infrared activity of some of the ZnO lattice vibration modes, and (2) a pronounced piezoelectricity. The latter is caused by the bond polarity together with the noncentrosymmetric crystal structure. These aspects will be discussed in more detail in the following sections of this chapter.

2.2 Thermal Properties 2.2.1 Thermal Expansion Coefficients The thermal expansion of ZnO in its common wurtzite structure clearly reflects the uniaxial character of its crystal structure: As shown in Fig. 2.2, the thermal expansion coefficients ˛ are strongly direction-dependent. The ˛-values at 300 K, ˛kc D 2:9  106 K1 for expansion along the c-axis, and ˛? c D 4:7  106 K1 perpendicular to the c-axis differ by a factor of 1.6 [15]. Decreasing temperature brings a reduction of the expansion coefficients. Even negative ˛-values occur at T -values below T  127 K for ˛kc , and below T  95 K for ˛? c [1,15]. The negative thermal expansion coefficient in the temperature range between roughly 20 and 120 K is a common feature of the tetrahedrally coordinated semiconductors. For its explanation, one must take into consideration that generally the origin of thermal expansion is the anharmonicity of the phonon eigenmodes. The volume dependence of the vibration frequency !i (i D mode-index)

12

J. Geurts 8

ZnO

th (10

–6

K–1)

6

c

|| c

4 2 0 0

200

400 600 Temperature (K)

800

1000

Fig. 2.2 ZnO thermal expansion coefficients ˛ as a function of temperature (after [15])

of each mode is expressed quantitatively in terms of the Gr¨uneisen parameter i D @.ln !i /[email protected] V /. For each temperature region, the expansion coefficient is governed by the Gr¨uneisen parameters of the modes activated at these temperatures. Now, low-frequency phonon modes in the energy range around 100–150 cm1 have an inverted Gr¨uneisen parameter, resulting in a negative expansion in the corresponding temperature region. For possible future applications of the wide-gap material ZnO in hightemperature electronics, the thermal expansion coefficients at elevated temperatures are of relevance. Ibach presented data up to T D 800 K. As shown in Fig. 2.2, ˛kc and ˛? c strongly increase with temperature, to saturate near 800 K, yielding the high-temperature values ˛kc D 4:98  106 K1 , and ˛? c D 8:30  106 K1 [15], i.e. an enhancement factor of about 1.7 with respect to the 300 K values.

2.2.2 Specific Heat Specific heat data were published (1) for the low temperature range T D 1:7 to 25 K [16], (2) for the region between 20 and 900 K [1], and (3) from 250 to 1,800 K [17]. The low temperature data show a Debye-like behaviour (cDebye D 234R.T=D/3 /, with a Debye temperature D D 399:5 K [16]. Slight deviations from the ideal Debye theory were explained by contributions from interstitials (Einstein-term with E D 56 K), the ordering of which is possibly responsible for a Schottky contribution below 4 K [16]. Further reported values of the ZnO Debye temperature D range up to D D 440 K, derived from the specific heat data at T D 300 K [17]. For comparison, the D values, measured for ZnS, ZnSe, and CdO amount to D  350 K, 300 K and 250 K, respectively. At T D 300 K, both specific heat data sets (2) and (3) fairly consistently give the value cp D 9:66 cal mol1 K1 and 41:086 J mol1 K1 , respectively. In agreement with the quantum mechanical oscillator model, the specific heat increases with increasing temperature to level

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Crystal Structure, Chemical Binding, and Lattice Properties

13

Cp (cal mol-1 K-1)

12 10 8 6 4 2 0

200

400 600 temperature (K)

800

1000

Fig. 2.3 Temperature dependence of the ZnO specific heat. Data taken from [17]

off towards the classical limit, as shown in Fig. 2.3. Actually, the 900 K value, 12:3 cal mol1 K1 , is slightly beyond the Dulong–Petit value, which amounts to 11:92 cal mol1 K1 D 49:90 J mol1 K1 .

2.2.3 Thermal Conductivity From the application point of view, the thermal conductivity  is a crucial parameter for high-power and/or high-temperature electronics. In semiconductors, heat transport essentially takes place by lattice vibrations. It is described by the relation  D cv vs =3, where cv is the specific heat, vs the sound velocity, and  the mean free path of the phonons. In the temperature range above T  50 K, the main limiting factor for the thermal conductivity by lattice vibrations is anharmonicityinduced phonon–phonon scattering. More specifically, with increasing temperature “Umklapp”-processes gain relevance, in which the sum of the involved phonon wave vectors exceeds the Brillouin zone edge, resulting in a decrease of . For ZnO, the uniaxial character also dominates the thermal conductivity: it manifests itself in the tensor components 11 for a temperature gradient ? c and 33 for a temperature gradient kc, as shown in Fig. 2.4. In the temperature range from 30 to 300 K, the relation is 11  1:233 [19]. The average thermal conductivity is obtained as av D .1=3/.211 C 33 /. Typical values reported for T D 300 K are in the range av  0:6–1 Wcm1 K1 [19,20]. With decreasing T ,  increases by about one order of magnitude to its maximum value av  0:55 to 10 Wcm1 K1 slightly below T D 30 K. In the low-temperature range, a decrease of  with decreasing temperature is observed, because the T -dependence of  D cv vs =3 essentially corresponds to cv  .T =Debye /3 . The numerical value of  strongly depends on the sample quality because of the -limitation by crystal defects, disorder, grain boundaries, etc.

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k ii

103 W Km

Zn0 k33 k11

102

10

∇T II C

1

∇T ⊥ C

102

10

K 103

T

Fig. 2.4 Temperature dependence of the ZnO thermal conductivity for different directions of the T-gradient (from [1, 18])

This leads to a scattering in the reported values, although the T 3 -depencence is well confirmed [2, 16].

2.3 The Piezoelectric Effect 2.3.1 Principle and Applications Generally, the piezoelectric effect describes the connection between an externally applied mechanical stress and a macroscopic polarization at zero external electric field, and vice versa. For ZnO, this effect is extraordinarily prominent. Its piezoeffect is the most pronounced one of all tetrahedrally coordinated semiconductors. The ZnO piezoelectric tensor coefficients are at least twice as high as for other II– VI compounds with wurtzite structure, like ZnS, CdS, CdSe. Only for group-III nitrides, values comparable to ZnO are obtained [21]. Therefore, since many years ZnO is extensively exploited for electromechanical coupling applications. See also Sect. 13.2 in Chap. 13. Its realizations include a wide variety of micro- and nanoelectromechanical systems (MEMS and NEMS), sensors, and applications in signal processing and telecommunications. Among the most ubiquitous applications are ZnO acoustic wave devices, especially exploiting surface acoustic waves (SAW) in interdigital transducers (IDT) for electronic band filtering. In such an IDT, the signal processing through a SAW delay line device relies on the generation of a SAW in a piezoelectric ZnO film by a voltage signal (up to 10 GHz) through a lithographically deposited interdigital metal double-comb structure. This wave travels as a mechanical distortion along the film, and its electrical polarization induces a voltage response in an adjacent similar receiver comb structure. The ZnO film deposition may take place by a variety of techniques, such as sputtering, chemical vapour deposition, or pulsed laser deposition. See Chap. 3. Because of their cheap and compact

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Crystal Structure, Chemical Binding, and Lattice Properties

15

filtering function, these devices, invented already about 50 years ago, have found a wide market in consumer electronics. Recent developments are Mgx Zn1x O ternary films (0  x  0:3) and ZnO=Mgx Zn1x O multilayer structures, which allow the tuneable enhancement of the acoustic wave velocity and the tuning of the piezoelectric coupling coefficient. A very detailed discussion of the widespread applications is given e.g. in an extended review by Y. Lu [22]. In this section, the fundamental physical reasons for the outstanding piezoelectric activity of ZnO are discussed, and its piezoelectric tensor coefficients are listed and compared with other materials.

2.3.2 The Piezoelectric Tensor The ZnO piezoelectricity properties reflect the strong bond polarity and the 6mm wurtzite crystal structure. The piezoelectric tensor components eij , which are called piezoelectric stress coefficients or stress moduli, give the polarization components Pi as a result of the strain "j . For reasons of symmetry, the wurtzite piezoelectric tensor has three independent nonzero components. For comparison, only one non-vanishing component exists for zinc-blende. In Voigt notation, the wurtzite piezoelectric stress moduli are labelled e33 , e31 , and e15 (cf. zinc-blende: e14 /, yielding the wurtzite piezoelectric tensor E: 0

0 ED @ 0 e31

0 0 e31

0 0 e33

0 e15 0

e15 0 0

1 0 0A 0

(2.1)

Two of these components, e33 and e31 , represent the contributions to the c-directed polarization P3 , induced by a strain "3 D .c  c0 /=c0 along the c-axis, and by a strain "1;2 D .a  a0 /=a0 in one of the basal planes, respectively: P3 D e33 "3 C e31 ."1 C "2 /:

(2.2)

The sign convention is such that the positive c-axis direction points from Zn to O. The third independent tensor component e15 describes the polarization P1 (or equivalently P2 ) perpendicular to the c-axis, induced by a shear strain "5 . Microscopically, the polarization P is the superposition of two contributions: (1) the contribution P .1/ due to the lattice deformation, assuming a rigid parameter u (D bond length-to-c-axis ratio, as discussed in Sect. 2.1.3), therefore called “clamped-ion” contribution, and (2) an additional contribution P .2/ due to internal relaxation, called “internal-strain” contribution. The internal-strain contribution P .2/ occurs because a strain " induces not only a change of the lattice constants c or a but also an internal displacement of the sublattices with respect to each other, i.e. a change of the parameter u. Because of the strong ZnO bond polarity, this displacement gives rise to the additional polarization term P .2/ ; which scales with the effective bond charge Z  (cf. LO phonon modes).

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All tetrahedrally coordinated compound semiconductors have in common opposite signs of the polarization contributions P .1/ and P .2/ . Besides, for most of these materials the absolute values of P .1/ and P .2/ are nearly equal, which results in a rather effective cancellation. Therefore, II–VI compounds generally exhibit only a very weak positive piezoelectric effect. For ZnO, an ab initio study of the piezoelectric effect calculating the tensor elements e33 and e31 within the FLAPW method (full-potential linearized augmented-plane-wave method), was presented by Dal Corso et al. [23]. It shows that ZnO forms an exception in the sense that the clamped-ion contribution P .1/ is extraordinarily low, which yields a reduced compensation of the internal-strain contribution P .2/ by P .1/ (as low as 50%). This is the reason for the very pronounced piezoeffect in ZnO. The piezoelectric activity may be expressed in terms of an effective piezoelectric charge eP  . The experimental result for ZnO is eP  D 1:04, while e.g. for ZnSe eP  D 0:13 was observed. The experimentally obtained results of the ZnO piezoelectric stress coefficients eij are: e15 D 0:35 to 0:59 C=m2 , e31 D 0:35 to 0:62 C=m2 and e33 D 0:96 to 1:56 C=m2 [1]. In reasonable agreement with these experimental results are the calculated values e31 D 0:51 C=m2 and e33 D 0:89 C=m2 [21]. As an alternative for the piezoelectric stress coefficients eij  dPi =d"j [C=m2 ], which correlate the polarization with the relative changes of the lattice constants, the piezoelectric behaviour may also be described in terms of the piezoelectric strain coefficients dij  dPi =dXj [C/N] (D ŒV1 m). In this notation, the polarization is expressed with respect to the externally applied stress. Therefore, the set of coefficients dij is connected with the set of coefficients eij through the elastic moduli cij . The ZnO piezoelectric strain coefficients are d33  12  1012 C=N, d31  5  1012 C=N, and d15  10  1012 C=N [1]. For the application in SAW devices, an essential parameter is the conversion efficiency between electrical and mechanical energy. A measure for this efficiency is the electromechanical coupling coefficient K. It is defined by K 2 D e 2 =c", where e, c, and " are the piezoelectric, elastic, and dielectric constants, respectively, along the propagation direction of the acoustic wave.

2.4 Lattice Dynamics The ZnO lattice vibration dynamics is essentially determined by three key parameters: (1) the uniaxial crystal structure, (2) the pronounced mass difference of the zinc and oxygen ions, and (3) the strong bond polarity. The uniaxial structure induces a classification of the vibration eigenmodes according to their symmetry (ion displacement either parallel or perpendicular to the c-axis). Furthermore, the pronounced mass difference is reflected in rather high frequencies of the oxygendominated modes, considerably beyond those of the zinc-dominated ones. Finally, the bond polarity results in a strongly polar character for some eigenmodes, which makes them readily accessible for far-infrared spectroscopy. Besides, almost all modes appear in Raman spectroscopy. Therefore, the latter technique has become

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Crystal Structure, Chemical Binding, and Lattice Properties

17

a standard method for the analysis of ZnO. It will be treated in some detail in Sect. 2.4.4.

2.4.1 Phonon Symmetry and Eigenvectors of the Wurtzite Lattice The wurtzite-type lattice structure of ZnO implies a base unit of four atoms in the primitive unit cell: two ZnO molecular units. The number of N D 4 atoms in the unit cell leads to 3N D 12 vibration eigenmodes. Following the rules of group theory, these modes are classified according to the following irreducible representations:  D 2A1 C 2B1 C 2E1 C 2E2 [24]. This summation corresponds to 12 eigenmodes because of the onefold degeneracy of the A and B modes, and the twofold E modes. One A1 mode and one E1 mode pair are the acoustical phonons. Therefore, opt D A1 C 2B1 C E1 C 2E2 represents the optical phonon eigenmodes, the number of which amounts to 3N  3 D 9. For a translation of the present notation (A1 , B1 , etc.) to the i , see [3]. The eigenvectors (displacement patterns) of the optical phonon modes are shown in Fig. 2.5. For the A1 and B1 modes, the displacements are directed along the caxis, and they are distinct in the following way: The A1 mode pattern consists of an oscillation of the rigid sublattices, Zn vs. O. Owing to the bond polarity, this oscillating sublattice displacement results in an oscillating polarization. In contrast, for the B1 modes one sublattice is essentially at rest, while in the other one the neighbouring atoms move opposite to each other. For the B1 .1/ mode, the prominent displacements occur in the heavier sublattice (Zn), for the B1 .2/ mode in the lighter one (oxygen). No net polarization is induced by the B modes because the displacements of the ions within each sublattice sum up to zero. Thus, the three modes with displacement along the c-axis are classified as one polar phonon mode A1 and two non-polar modes B1 . The same scheme applies for the E modes with their atom displacement directions perpendicular to the c-axis. The E1 mode is an oscillation of rigid sublattices and consequently induces an oscillating polarization. In contrast, the E2 modes (E2 .1/ and E2 .2/ ) are non-polar because of the mutual compensation of O

Zn

A1

B1 (1)

B1 (2)

E1

E2 (1)

E2 (2)

Fig. 2.5 Eigenvectors of the ZnO optical phonon modes. For each mode, the bold arrows represent the dominating displacement vectors. The A1 , B1 .2/ , E1 , and E2 .2/ modes are oxygen-dominated, the B1 .1/ and E2 .1/ mode are dominated by the Zn-displacement. The quantitative displacement ratio Zn:O is given in the text

18

J. Geurts

the displacement vectors within each sublattice. The correspondence of the notation above and the i is found e.g. in [3]. Quantitative values for the ratio eZn =eO of the Zn- and O-displacement eigenvector lengths eZn and eO were obtained from DFT calculations, and for some modes also from its frequency shift with isotope variation (e.g. substitution of 16 O by 18 O) [13]. For the rigid-sublattice modes A1 and E1 , the displacement ratio amounts to eZn =eO  1=.2:02/ (conservation of the centre of mass). The E2 .1/ mode is O-dominated (ratio 0.415), while the reverse case applies for E2 .2/ (ratio 2:4). Along the same scheme, the Zn:O displacement ratios for the B1 .1/ and B1 .2/ mode were calculated to 0:137 and 7.30, respectively. Thus, for the latter mode pair the displacement nearly quantitatively occurs either within the Zn- or within the O-sublattice. While group theory is confined to purely vibrational non-propagating eigenmodes (i.e. to phonon wave vectors q D 0 or to the  point), experimental investigations always imply propagating optical phonon modes, i.e. finite phonon wave vectors q in propagation direction. Therefore, the above mode scheme must be refined to distinguish between two geometry arrangements: (1) the ion displacement vectors parallel to the propagation wave vector q (Longitudinal Optical phonon wave  LO) and (2) displacements and q-vector perpendicular to each other (T ransverse Optical phonon wave  TO). For the non-polar modes B1 and E2 , this distinction is of no relevance for the mode frequency. However, for the polar modes A1 and E1 the longitudinal optical phonon frequency exceeds that of the transverse optical phonon mode due to the polarity-induced macroscopic electric field, which acts as an additional restoring force for the ion oscillation [25]. As a result of this frequency split of polar modes into LO and TO eigenfrequency, a higher number of eigenfrequency values occurs than predicted by group theory. The LO–TO splitting of both the A1 and the E1 mode yields two additional eigenfrequencies, i.e. the total number increases to eight: A1 (LO), A1 (TO), E1 (LO), E1 (TO), two B1 , and two E2 .

2.4.2 Phonon Dispersion Relations After several earlier considerations on the ZnO force constant [26–28], the first semi-empirical calculations of the wurtzite ZnO lattice dynamics were presented in 1974 [29]. Rather recently, Serrano et al. [13] presented an ab initio calculation of the lattice dynamics, obtained in a two-step procedure: First, the electronic structure of ZnO and its lattice properties were derived from first-principles calculations based on density functional theory. Subsequently, the dynamical properties and their dependence on pressure were calculated within the linear response formalism. The dynamical matrices were obtained not only for the common wurtzite ZnO structure but also for the zinc-blende and rocksalt modifications, together with the pressure dependence of several lattice parameters up to 12 GPa. The resulting phonon dispersion relations for high-symmetry directions in the first Brillouin zone (BZ) are displayed in Fig. 2.6 for the wurtzite structure and the

Crystal Structure, Chemical Binding, and Lattice Properties 600

Γ

Κ M

Γ B1

500 Wavenumber [cm-1]

A A1(LO)

Γ

19 Κ Χ

Γ

L

LO

500

E2

400

A1(TO)

300

E1(TO) B1

200 E2

100 0

600

E1(LO)

0

.2 .4 [αα0]

.4

.2 [α00]

0 .2 .4 [00α]

Wavenumber [cm-1]

2

400

TO

300 200 100 0

LA TA 0 .2 .4 .6 .8 1 .8 .6 .4 .2 0 .2 .4 Wavevector

Fig. 2.6 Ab initio calculated ZnO phonon dispersion relations along directions of high symmetry (after [13]). (a) wurtzite structure and (b) zinc-blende structure. For the wurtzite structure, the solid and open circles represent inelastic neutron data at room temperature from [30] and [29], respectively, and the open diamonds represent Raman data for natural ZnO at 6 K [31]

zinc-blende structure together with the experimental data for wurtzite ZnO from Raman scattering [31] and from inelastic neutron scattering [29, 31]. As a consequence of the very different extent of the achievable q-transfer range for these two experimental techniques, the optical data are essentially confined to the BZ centre ( -point), while the neutron-derived data cover the entire BZ. Remarkably, inelastic neutron scattering data have been reported only for the acoustic branches. Overall, a very nice agreement occurs between the calculated results and the experimental data. The comparison of the zinc-blende (ZB) and the wurtzite dispersion results in Fig. 2.6 is quite instructive for a deeper understanding of the assignment of the eight wurtzite ZnO eigenmodes in the BZ centre. The cubic ZB symmetry implies the equivalence of the three perpendicular spatial directions x, y, and z. According to group theory, this results in a threefold degenerate optical phonon mode with F-symmetry. For finite q-vectors, this triple optical phonon mode is frequencysplit into two degenerate TO modes (400 cm1 ) and one LO (550 cm1 /. The LO–TO-frequency difference is a measure of the bond polarity. In contrast to the ZB F-symmetry, the hexagonal wurtzite structure requires the distinction between the c-axis and the two symmetrically equivalent axes ? c. This implies for the optical phonon modes a symmetry splitting of the triple degenerated F mode into one mode with its atomic displacement along c (A1 symmetry) and a degenerate pair of modes, the atomic displacements of which are ? c (E1 -symmetry). The E1 –A1 frequency splitting directly reflects the bond strength anisotropy, and is referred to as hexagonal crystal field splitting.

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It is independent of the bond polarity. Additionally, for both modes, the polarity induces the above-mentioned splitting into A1 (LO) and A1 (TO), and into E1 (LO) and E1 (TO), respectively. Their appearance is directly correlated with the phonon propagation direction: Phonons propagating along the c-axis ( -A direction in the BZ) are A1 (LO) and E1 (TO), while those propagating perpendicular to the c-axis are A1 (TO), E1 (TO) and E1 (LO). As obviously shown in Fig. 2.6, for ZnO the LO–TO frequency splitting (200 cm1 / exceeds by far that between A1 and E1 (<30 cm1 ). This is a consequence of the rather pronounced bond polarity, which distinctly exceeds the bond strength anisotropy. The six additional modes of opt in wurtzite, i.e. the non-rigid-sublattice modes B1 .1/ , B1 .2/ , E2 .1/ , and E2 .2/ , have no counterpart in the centre of the ZB Brillouin zone. As already pointed out in the early days of wurtzite phonon research [32], they may be regarded as a result of the back folding of the (111)-directed  -to-L ZB phonon branches (longitudinal acoustic (1), transverse acoustic (2), longitudinal optic (1), and transverse optic (2)) into the zone centre, when turning from ZB to wurtzite. This back folding in reciprocal space directly results from the doubling of the atomic periodicity length in real space along the wurtzite c-axis with respect to the periodicity length in the corresponding ZB (111) direction (2 molecular ZnO-units in wurtzite instead of molecular unit in ZB). The new zone centre modes from the back-folded optical modes are called B1;high and E2;high , whereas those from the acoustical ones are referred to as B1;low and E2;low . The back folding of these modes appears strikingly clear when comparing the wurtzite phonon branches in  -A direction (Dc-direction) with the  –L branches of the ZB (111)-direction. All these backfolded modes are non-polar, as deduced from their eigenvector patterns in Fig. 2.5. Therefore, they exhibit no LO–TO frequency splitting. Thus, in summary, the occurrence of opt D A1 C 2B1 C E1 C 2E2 with eight different optical mode frequencies in the wurtzite BZ centre region, as compared to 2 in ZB, is explained in terms of (1) the anisotropy-induced splitting of the F-mode from the ZB  -point, leading to A1 C E1 , (2) the back folding of the ZB zone-edge modes, resulting in 2B1 C 2E2 , and (3) the bond-polarity-induced LO–TO splitting of the polar modes A1 and E1 . Further discussion of ZnO the lattice dynamics is confined to the wurtzite crystal structure. The data of Fig. 2.6a give a broad spectrum of information on wurtzite ZnO. The acoustical branches allow a direct access to the elastic moduli. The slope of their linear regions, starting from the BZ centre, represents the sound velocity vs . Besides the scanning of these branches with neutron scattering, optical access to their low-frequency range is provided by inelastic light scattering with extremely high resolution; Brillouin scattering. The neutron-scattering data as well as the calculated branches show that the most relevant criterion for the sound velocity vs is the distinction between longitudinal waves (upper acoustical branch) and shear waves (lower acoustical branch). The direction with respect to the c-axis plays only a minor role. The sound velocities for longitudinal waves were determined as vs3;kc D 6:0961  105 cm s1 and vs1;?c D 6:0776  105 cm s1 , whereas the considerably lower values for shear waves amount to vs4;kc D 2:73530  105 cm s1 ; vs4;?c D 2:73505  105 cm s1 , and vs6;?c D 2:79328  105 cm s1 [33]. The corresponding elastic

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Crystal Structure, Chemical Binding, and Lattice Properties

21

moduli were determined as c11 D 206.4/ GPa, c13 D 118.10/ GPa, c33 D 211.4/ GPa, c44 D 44:3.10/ GPa, and c66 D 44:0.10/ GPa [34]. The optical modes give access to the bond force constants and their anisotropy, as well as to the effective bond charge, as will be discussed in the following sections. The zone centre optical mode frequencies are in the range between about 100 cm1 (12:5 meV) and 600 cm1 (75 meV). Obviously, in the highest frequency range (550–600 cm1 ) a closely spaced group of three mode frequencies occurs: E1 (LO), A1 (LO), and B1 .2/ (Dback-folded A1 (LO)). Similarly, the triple group of E1 (TO), A1 (TO), and E2.high/ (DE2 .1/ , back-folded TO) appears between 370 and 440 cm1 . Finally, the eigenfrequencies 100 and 250 cm1 belong to the E2.low/ (DE2 .2/ / and the B1 .1/ modes, respectively. The exact mode frequencies are listed in Table 2.2.

2.4.3 Infrared Optical Phonon Spectroscopy For the experimental analysis of the zone-centre phonon modes of ZnO, the methods of choice are far-infrared (FIR) and Raman spectroscopy. Group theory considerations determine which modes may be accessed by either method. Their results are referred to as selection rules. For IR spectroscopy, the arguments are quite straightforward: Polarized infrared radiation interacts with those polar modes the ion displacement vectors of which are parallel to the IR polarization direction. Thus, IR spectroscopy of ZnO is applicable for the A1 and E1 modes, which are therefore called IR-active modes. For IR radiation polarized along the ZnO c-axis (1 symmetry), the A1 mode is observed, while IR polarization ? c (5 symmetry) excites the E1 modes instead. The dipole interaction of the IR radiation with the lattice causes a spectral interval of high reflectance, i.e. a stop band, called Reststrahlenbande, which extends from the TO to the LO phonon frequency. Effectively, a complete screening of the oscillating electric field of the incident radiation occurs in this interval because here the frequency-dependent dielectric function ".!/ is negative. This behaviour is readily explained in terms of a Lorentz oscillator model for the lattice vibration response function, superimposed on the dielectric function "b from the excitonic and interband excitations (see Chap. 6), which induce no dispersion in the IR range and acts as a constant background. A more detailed description is presented in [36]. The lower and upper edge frequencies of the Reststrahlenbande allow the direct unambiguous assignment of the TO and LO mode frequencies. Moreover, its spectral width reflects the Lorentz oscillator strength, which allows the evaluation of the dynamical bond polarity and the corresponding effective charge. Figure 2.7 shows an FIR reflectance spectrum for polarization ? c of ZnO with a quite low doping level of the order 1016 cm3 [36]. (The effect of increasing doping will be discussed in Sect. 2.5.) The dominant feature is the Reststrahlenbande. By comparing the Lorentz-model fit of the E ? c polarized reflectance spectrum to the one for E k c, the TO and LO eigenfrequencies of the E1 and the A1 mode were derived, as well as the corresponding phonon oscillator strength. The eigenfrequencies, obtained at T D 10 (295) K are E1 .LO/ D 593.589/ cm1 , A1 .LO/ D 582:5.578:5/ cm1 , E1 .TO/ D 411.412/ cm1 , and A1 .TO/ D 381.378:5/ cm1 ,

22

J. Geurts 20

1.0

R

C

0.8

photon energy (meV) 40 60

80

ZnO:Ga

0.6 0.4 0.2 0.0

100

200

300 400 500 wavenumber (cm-1)

600

Fig. 2.7 Infrared Reflectance spectrum of ZnO with a very low Ga doping level. Temperature T D 10 K. IR polarization direction perpendicular to the c-axis. The high-reflectance band is referred to as stop band or Reststrahlenbande (after [36])

which implies a rather small, but yet clearly detectable anisotropy due to the hexagonal crystal field. The first report of ZnO FIR spectra by Collins et al. already had mentioned this effect, but due to the lack of sufficient spectral resolution it could not yet be quantified at that time [26]. The phonon oscillator strength f is quantified in terms of the transverse effective charge eT  . The term “transverse” originates from the eT  -induced coupling between the transverse optical phonon mode and the infrared light wave, resulting in phonon-polariton states. The transverse effective charge eT , also referred to as Born effective charge eT , is defined to give the local polarization induced by a relative displacement of the sublattices. The oscillator strength f is given by f D ŒN.eT  /2 =Œ"0 . Here, N is the volume density of the ZnO molecular units, and  the reduced ZnO molecular mass; ZnO D 12:89u. The oscillator strength is also denoted as f D !p 2 , where !p is referred to as “plasma frequency” of the phonon mode. This notation will become plausible in conjuncture with doped samples, discussed in Sect. 2.5. For each polar excitation, the plasma frequency !p is connected to the LO and TO frequencies by the relation !LO 2 D !TO 2 C !p 2 . The ZnO dielectric function ".!/ in the infrared range consists of the background contribution "b and the additive contribution Ph .!/ of the phonon Lorentz oscillator, resulting in !p2 ".!/ D "b C Ph .!/ D "b C 2 ; (2.3) !TO  ! 2  i ! where  is the phonon damping constant. The experimentally derived transverse charge eT  of ZnO amounts to 2.09 [37], which corresponds very well to the results of ab initio calculations [21, 23]. As for many other materials, also for ZnO the transverse charge eT  is considerably larger than the effective bond charge Z  . This difference is due to the dynamical charge redistribution which accompanies the lattice vibration. In this sense, the effective bond charge Z  is the static contribution to the transverse charge eT  . For ZnO, the multiplication factor by the dynamical charge redistribution is about two.

2

Crystal Structure, Chemical Binding, and Lattice Properties

23

2.4.4 Raman Spectroscopy of Phonon Modes The first experimental observation of the ZnO Raman spectrum, including a polarization analysis, dates back to 1966 [38]. Soon after, a complete assignment of all phonon modes was enabled from the results of different scattering geometries [39]. Already, prior to the first experimental Raman data, a systematic treatment of the lattice dynamics of zinc-blende- and wurtzite-type crystals was performed, including the determination of normal coordinates and the correlation between the force constants and the eigenmode frequencies [27]. By combining this model calculation with the experimental Raman data, in 1968, a quantitative distinction between the short-range phonon restoring forces and the long-range polarization forces of the polar modes was presented [28]. Presently, Raman spectroscopy is by far the most widespread technique for the ZnO phonon analysis. Beyond the observation of ZnO phonon modes, the main purposes are the analysis of the incorporation of dopant and transition metal atoms in the ZnO host lattice through their local vibration modes, as well as the study of ZnO nanoparticles. After a brief survey of ZnO Raman fundamentals in this section, these application-related aspects will be discussed in the following Sects. 2.4.5 to 2.4.7. Raman-active phonon modes interact with the incident visible light indirectly: They modulate the dielectric polarizability in the visible spectral region, in contrast to the direct oscillating infrared polarization of the IR-active modes. The phonon-induced polarizability modulation by the lattice deformation is referred to as deformation potential (DP) scattering. Furthermore, LO phonons may additionally modulate the polarizability through their macroscopic electric field. Owing to the indirect interaction between the phonons and the light in the Raman scattering process, the Raman selection rules are more complicated than those of IR spectroscopy. They are summarized in a (3  3) Raman tensor for each phonon mode. The non-vanishing tensor elements connect the electric field of the incident laser light with that of the phonon-induced inelastically scattered light, the redshift of which reflects the phonon frequency. In ZnO, being a non-centrosymmetric material, IR activity and Raman activity are not mutually exclusive properties. The polar modes A1 and E1 are IR- as well as Raman active. Furthermore, Raman activity applies for the non-polar modes E1 , E2;low and E2;high . The B1 modes are neither Raman- nor IR-active. They are called silent modes. The Raman tensors of the ZnO phonons for DP scattering are listed in Table 2.1 [24]. The x,y,z coordinate system is chosen such that the z-direction is the wurtzite c-axis. The tensors for Fr¨ohlich scattering from the polar modes A1 (LO) and the E1 (LO) have only diagonal elements and reflect the dielectric tensor symmetry: ˛xx D ˛yy ¤ ˛zz . The implications of the Raman tensors are shown in Table 2.2. The crosses denote the scattering configurations which are required for the observation of the respective modes. These configurations are abbreviated by the q vector directions q i and q s of the incident and the scattered light, as well as the corresponding E -vectors E i and E s , in the form q i .E i ; E s /q s (Porto-notation). As an example, the E2 modes, the non-vanishing tensor elements of which are the xy, xx, and yy components (see

24

J. Geurts

Table 2.1 Raman tensors for deformation potential scattering of the ZnO phonon modes. For the polar modes A1 and E1 , the notation x, y, z represents the phonon polarization direction. The z-direction is the wurtzite c-axis 0 1 0 1 0 1 0 1 a0 0 00c 000 d d 0 @ A @ A @ A @ A1 .z/ D 0 a 0 E1 .x/ D 0 0 0 E1 .y/ D 0 0 c E2 D d d 0 A 0 0b c 00 0c 0 0 0 0

Table 2.2 Frequencies of the ZnO lattice vibration modes for T D 300 K (from [35]), together with the selection rules for their observation by infrared spectroscopy (IR) or Raman spectroscopy. The Raman scattering geometries are denoted according to the Porto notation (see text) Mode Frequency IR Raman scattering [cm1 ] Backscattering 90ı scattering

A1 B1 .1/ B1 .2/ E1 E2 .1/ E2 .2/

TO LO

378 574 261 552 TO 410 LO 590 low 99 high 438

c-face face ?c z.x; x/  z z.x; y/  z x.y; y/  x x.y; z/  x x.y; z/y z.y; y/  z y.x; x/  y kc X X – – ?c X X X – X X X – X X X

Table 2.1), are allowed in the following configurations: (1) incident light polarized along y (E i ky) and scattered light polarized along x (E s kx) and vice versa, or (2a) (E i kE s kx) or (2b) (E i kE s ky). In backscattering geometry, owing to the transversal character of the electromagnetic radiation, all configurations (1) and (2) may be realized on the z-oriented sample face. Furthermore, configurations (2a) or (2b) are possible for face orientation y or z, respectively. Thus, for this example the Porto notations are z.y; x/-z, z.x; y/-z, z.x; x/-z z.y; y/-z (c-face backscattering) and x.y; y; /-x, y.x; x/-y (face orientation ? c). In Fig. 2.8, ZnO phonon backscattering Raman spectra are shown for different scattering configurations. The lower pair of the spectra originates from the basal cface, while for the others the sample surface is perpendicular to the c-face. Besides, polarized (E i k E s ) and depolarized (E i ?E s ) geometry was applied. In accordance with the selection rules in Table 2.2, the c-face spectra show essentially the E2 .1/ (low) and the E2 .2/ (high) modes. Perpendicular to the c-face, the E2 modes appear only for the polarization geometries yy and yz. For the yy and zz polarizations, the A1 (TO) is observed, while the E1 (TO) appears for zy. The peak at 333 cm1 plays a special role and will be discussed in the following section. Interestingly, the A1 (LO) has nearly vanishing intensity also for the polarized configurations, although it is symmetry allowed. This is due to the virtual compensation of its two scattering terms: (1) the deformation potential and (2) the electro-optic coupling

2

Crystal Structure, Chemical Binding, and Lattice Properties

25

Fig. 2.8 Raman spectra of a ZnO single crystal, recorded for various scattering configurations. Excitation wavelength:  D 514:5 nm (2.409 eV). Temperature T D 300 K (after [40])

coefficient, which results for the LO phonon from its macroscopic electric field [41]. Thus, comparing the LO and TO scattering efficiencies allows the separation of both coupling terms. The peak at 333 cm1 is explained in terms of second-order Raman scattering, in which process the restriction to BZ centre phonons is released. When two phonons are simultaneously created (sum process), the constraint of the nearly vanishing qvector is restricted to the sum of their q-vectors. The individual q-vectors may cover the whole Brillouin zone. The same applies for the creation of one phonon simultaneous with the annihilation of another (difference process). Along this line, the prominent peak in the ZnO Raman spectrum, occurring at 333 cm1 , is assigned to difference E2 high  E2 low in the Brillouin zone centre (437 cm1  104 cm1 ). This assignment was substantiated by the temperature dependence of its intensity [35]. The availability of very high quality ZnO bulk crystals also has enabled detailed investigations of very weak second-order Raman features. An experimental study with a very sophisticated assignment of numerous second-order features was presented recently in an excellent review article on temperature-dependent Raman spectroscopy on ZnO [35]. Because of the phonon contributions throughout the Brillouin zone, the secondorder Raman spectra are essentially governed by the phonon density of states. The selection rules for second-order Raman scattering in wurtzite-type crystals can be found in [42]. The knowledge of the second-order Raman features is essential when searching for Raman signatures from incorporated impurities, such as local vibration modes (LVM), because many spectral features can be ruled out as LVM candidates, because they are due to second-order scattering from the ZnO host lattice. Second-order phonon features in Raman spectra of ZnO were presented together with a study of the resonant enhancement of Raman scattering in ZnO [43].

26

J. Geurts

In Resonant Raman scattering, a substantial enhancement of the scattering efficiency occurs when tuning the incident photon energy towards the energy of an allowed electronic transition. Besides an enhanced sensitivity, this technique allows to study the relevant interaction mechanisms (electron-phonon deformation potentials and electro-optic coefficients) in great detail [44, 45]. For ZnO, the knowledge about the cancellation of the A1 (LO) scattering mechanisms for excitation in the visible range originates from a resonant Raman scattering study in 1977 [43]. Furthermore, for resonant excitation in the UV, the electro-optic scattering is predominantly due to the large polarity-induced coupling coefficient. Multiple LO phonon peaks up to the eighth order appear in the Raman spectrum for UV excitation at 325 nm (3.814 eV) [46]. The anharmonic phonon–phonon interaction may be studied by high-resolution temperature-dependent Raman scattering through the evaluation of the phonon peak half-width and line shape in high-quality samples. In this way, the asymmetric lineshape of the E2 (high) mode and the essentially symmetric Lorentzian shape of the A1 (LO) and E1 (LO) are explained through their different decay channels into acoustic phonons [35]. For this purpose, recent calculations of the two-phonon density of states (DOS) [13] were invoked. Furthermore, the considerable effect of isotope scattering was shown by comparing the E2 (high) mode of ZnO with isotopically pure oxygen (either 16 O or 18 O) with mixed O-isotope samples (16 O:5 18 O:5 / [47]. The experiments on isotopically pure samples show how the low-frequency modes are essentially affected by the Zn mass while the high-frequency modes essentially reflect the oxygen mass. As a very remarkable feature, the E2 (low) peak (100 cm1 ) is extremely sharp, i.e. this mode has an extremely high lifetime or more precisely dephasing time . Already, at room temperature, it amounts to about D 29:2 ps [48], which is about an order of magnitude longer than typical lifetimes for phonons in semiconductors, while at T D 5 K even D 211 ˙ 7 ps was reported [49]. These data were deduced from impulsive Raman scattering. Most interestingly, the authors expect even lifetimes in the ns range in ZnO samples with isotopically pure Zn, since the decay seems to be essentially determined by the Zn isotopic disorder.

2.4.5 Vibration Modes in Doped ZnO Optical vibration spectroscopy is frequently employed to investigate the incorporation of dopant atoms in ZnO. Doping is a hot issue with regard to applications in (opto-)electronics and spintronics and the current challenge for ZnO is especially p-type doping (see Chap. 5). While heavy n-type doping (n > 1020 cm3 ) is state of the art, extensive efforts towards p-doping are performed with group-V elements, especially with nitrogen as a promising candidate for substitutional incorporation on oxygen sublattice sites. The incorporated atoms and related complexes should give rise to local vibration modes (LVMs). Actually, five additional modes at 275, 510, 582, 643, and 856 cm1 are observed in the Raman spectrum of N -doped ZnO. The first reports date from the early years of this millennium [50, 51].

Crystal Structure, Chemical Binding, and Lattice Properties

Raman scattering intensity (a.u.)

a

27

b E2(high)

E2(h) 582

275 510

||

200

582

ZnO:N

643

856

intensity (arb.u.)

2

E2(high) –E2(low)

ZnO impl. with 4 at.% N after 800 °C ann.

644 511

275 860

400

600

Wavenumber (cm–1)

800

300

400 500 600 700 wavenumber (cm–1)

800

Fig. 2.9 Raman spectra of Nitrogen-doped ZnO. (a) CVD-grown ZnO-layer on GaN N -concentration ŒN   1019 cm3 (after [51]), (b) N -implanted bulk ZnO with N -concentration 4 at.% and vacuum-annealed at 800ı C (from [40])

The Raman spectra of Fig. 2.9a originate from the c-face of a ZnO layer with an N -concentration ŒN   1019 cm3 [51]. The scattering configurations were polarized and depolarized, respectively. The additional peaks are clearly observed, although some of them are very weak. They appear much stronger in the Raman spectrum of Fig. 2.9b, taken from the N -implanted bulk ZnO, with a nominally very high N concentration of 4 at% (1021 cm3 ), vacuum-annealed at 800ı C during 30 min [40]. The N -concentration chosen here corresponds to the value, for which an effective carrier concentration p  1016 cm3 was reported [52]. That means that only a very small fraction below 104 of N acts as acceptor. The investigations consistently show that the peak intensities scale with the nitrogen concentration. This dependence had also been shown in earlier investigations on N -implanted samples for much lower N -concentrations (ŒN   1019 cm3 ) [53]. In literature, a dispute has arisen about the origin of the additional vibration modes. First of all, the experimental results give no consistent picture. While in many of the investigations most of the peaks do not occur for incorporated species different from nitrogen [40,53–56], few others claim their occurrence also for incorporated aluminium [57–59], and even for a wide variety of other incorporated species [60]. Furthermore, their assignment to local vibration modes of nitrogen or nitrogen complexes [51, 53, 55] has been questioned because of their insensitivity for the exchange of 14 N by 15 N [54]. This gave rise to their assignment as disorder-induced Raman scattering [60], disorder/defects favoured in the presence of N [54], resonantly enhanced LO scattering [56], and impurity-activated silent B modes and their combinations [61]. The latter interpretation is supported by the close correspondence of the peak positions to the B-mode frequencies and their combinations. The strongest peaks (275 and 582 cm1 ) are assigned to B1 (low) and B1 (high). Within this scheme, the 856 cm1 peak originates from the B1 .low/ C B1 .high/ second-order scattering process. Along the same line, the

28

J. Geurts

peaks at about 511 and 644 cm1 are assigned to 2  B1 (low) and B1 .high/ C TA, respectively. The frequently used alternative assignment of the 582 cm1 peak to the disorder-induced A1 (LO) mode [56] is seriously queried by polarized Raman scattering results from N -implanted samples as compared to disordered ones without nitrogen [40]. As a possible reason for the selective N -induced activation of the B1 silent modes, the strong difference of the electronic properties between the substituting nitrogen and the substituted host material oxygen was suggested [61]. This difference occurs due to central-cell corrections, which especially affect elements of the first row of the table of the elements.

2.4.6 Incorporation of Transition Metal Atoms in ZnO The investigation of transition metal (TM)-alloyed ZnO has been triggered by its predicted potential for room temperature (RT) ferromagnetism within the class of diluted magnetic semiconductors (DMS), however, assuming partly completely unrealistic p-type doping levels [62, 63]. In DMS, free-carrier-mediated exchange interaction induces a ferromagnetic coupling of the TM ion spins. A detailed description of the interaction model as well as the theoretical and experimental progress for ZnO doped with various TM elements (Mn, Fe, Co, Ni, V, Cr, Cu) is presented in [64]. Ferromagnetic behaviour at room temperature was reported actually [65], which, however, led to a vivid discussion about its origin. A short (critical) discussion about RT ferromagnetism is also given in Chap. 10. The specific dispute is whether the ferromagnetism arises from substitutionally incorporated TM ions or it is due to the clusters or precipitates of other phases. In this debate, Raman spectroscopy plays a prominent role because it offers in principle the ability to distinguish substitutional ions and precipitate phases by their local vibration modes and lattice vibrations, respectively. Because of its virtue to probe the local atomic arrangement, it has proved in several systems an enhanced sensitivity for nanosize inclusions as compared to the interference-based X-ray diffraction [40, 66]. Moreover, it allows a fast and non-destructive study of disorder in the host lattice. As an example for ZnO:TM, nanocrystalline Co-alloyed ZnO shows ferromagnetism at 300 K for Co-content >5%, while lower Co concentrations result in paramagnetism [66]. Frequently, the issue of solubility of TM and other dopants is not considered, even if the concentration is in the range of percents. Although XRD patterns of these samples give no hint to secondary phases, the Raman spectra in Fig. 2.10 clearly reveal for [Co] > 5% the occurrence of additional bands, which are assigned to Co3 O4 , and with further increasing Co content they evolve to sharp peaks, labelled I1 to I5 . The very weak additional peaks with question marks are tentatively assigned to CoO. Furthermore, the weakening and broadening of the ZnO modes reflects the deterioration of the host lattice by the distortion of the local atomic arrangement around the magnetic impurities. Although these results underscore the ability of Raman spectroscopy for very sensitive second-phase detection, they do not explain the ferromagnetic behaviour, because neither Co3 O4 nor

Crystal Structure, Chemical Binding, and Lattice Properties

Raman intensity (a.u.)

2

A1(TO) E2(h)-E2(l )

E2(high) 484

29

A1(LO)

ZnO

200

300

400 500 600 Wavenumber (cm–1)

700

800

Fig. 2.10 Raman spectra of Co-doped ZnO thin films, in comparison with Raman spectra of undoped ZnO and Co3 O4 thin films. The measurements were performed at RT with Laser D 514:5 nm and 2.409 eV (after [66])

CoO is ferromagnetic at 300 K. The most probable source for ferromagnetism, nanoclustered elementary Co, cannot be detected by Raman spectroscopy, because an elementary crystal lattice has no optical phonons. Rocksalt-type crystallites are also invisible, because their optical phonons are not Raman-active. Thus, it must be kept in mind that the sensitivity of Raman spectroscopy for nano-inclusions applies for a wide variety of compounds, but not for all, and that its detection does not include elementary materials. Another very commonly employed TM element is Mn, containing a half-filled 3d-shell with angular momentum L D 0 and spin S D 5=2. Numerous reports on Raman spectroscopic studies of Zn1x Mnx O exist, e.g. refs 5–13 in [67]. Most of the reported Raman peaks directly reflect the wurtzite lattice vibration modes of pure ZnO. However, additional features occur. The most prominent one is a broad weakly structured band in the spectral range between 500 and 600 cm1 with a quite high scattering efficiency. Already, for Mn concentrations in the range of some percent this band may dominate the Raman spectrum. Similar to N -doped ZnO, also in the Mn case, controversial discussions exist on the origin of this feature (vibrational modes (LVMs), disorder-induced ZnO vibrations, or phonon modes by precipitates). As one path towards a systematic assessment of the disorder contribution, several groups applied Mn implantation with subsequent stepwise annealing; see e.g. [67] and refs 6–8 therein. Especially, very low implantation doses yield an improved spectral structure which allows an easier assignment. In Fig. 2.11, spectra of low-concentration implanted ZnO are compared with the pure host material. The rich peak structure, in the range above the E2 mode (peak a), essentially originates from multi-phonon peaks of the host material, which were assigned by Cusco et al. [35] and are denoted as a, b, d : : :. k. Their intensities are enhanced due to residual disorder. The only non-ZnO feature is peak c at 519 cm1 . Therefore, only this structure is a candidate for a Mn vibration. This assignment is confirmed by the strong appearance of this peak in bulk ZnMnO. Thus, only a very small fraction

30

J. Geurts

Raman Intensity (a.u.)

ZnO : 0.8 at% Mn ZnO : 0.2 at% Mn x x ZnO pure

400

500 600 700 Wavenumber (cm–1)

800

Fig. 2.11 From bottom to top: Raman spectra taken at 300 K from pure ZnO, 0.2 and 0.8 at % Mn-implanted ZnO (700ı C annealing), normalized to the E2 (high) mode (peak a) (after [67])

of the broad band is intrinsically Mn-induced. Therefore, the overall intensity of the left shoulder at about 515–530 cm1 (peaks c and d) in the Raman spectra of Mn-alloyed ZnO should not be taken uncritically as evidence for a substitutional incorporation of Mn on Zn sites or even for an estimation of the actual content of substitutional Mn. Finally, it should also be noted that for high-concentration Mn incorporation micro-Raman spectroscopy has proved its strong potential for localizing and identifying secondary phase inclusions. In 700ıC-annealed ZnO samples with Mn concentrations in the range from 16 to 32%, an increasing concentration of inclusions appears, which is identified in terms of ZnMn2 O4 and non-stoichiometric Znx Mn3x O4 phases [68].

2.4.7 Raman Scattering from ZnO Nanoparticles Nanostructuring of ZnO is considered as an extremely promising road towards a wide field of new applications [36, 69]. It is exploiting the materials’ tendency to self-organized growth, enabling a variety of nanostructures with very different morphology, e.g. nanorods, nanowires, nanobelts, etc. See also Chap. 3. Among the possible applications is e.g. photovoltaics in hybrid solar cells of nano ZnO and a conjugated polymer [70]. Generally, in Raman spectra from samples with reduced dimensionality the observation of size-induced effects is a well-established phenomenon. Spatial confinement of the lattice vibrations implies finite q-vectors, penetrating into the BZ far beyond the relevant q-region of bulk samples. Owing to the phonon branch dispersion, this usually leads to a redshift of the phonon peaks. In addition, replica modes may occur at multiple q-values, i.e. geometrical overtones. In semiconductor superlattices, they allowed the optical study of the phonon dispersion throughout

2

Crystal Structure, Chemical Binding, and Lattice Properties

31

the Brillouin zone (see e.g. [71, 72]). An overview of Raman studies of phonon confinement effects in II–VI systems is given e.g. in [73]. An analytical expression, derived for confined and interface polar optical phonons in wurtzite quantum dots, yields a series of mode patterns with different geometrical symmetry [74]. They are catalogued according to their radial and angular symmetry index, in analogy with the electronic wave functions of atoms. The spectrum of mode frequencies is discrete. Within the experimental resolution, observable differences from bulk modes occur for nanoparticle diameters below 8 nm. An additional feature to be considered for nanoparticle samples is the orientation distribution of the nanocrystallites. Because of the stochastic tilting of the crystallite c-axes in the ensemble with respect to the light propagation direction and its polarization plane, in the Raman spectrum a distribution of mixed symmetries between A1 and E1 occurs, the so-called quasimodes Q, the propagation and displacement vectors of which are between the c-axis and the axes ? c. Thus, they correspond to the mixed mode exciton polaritons discussed in Sect. 6.1. For purely random orientation, the resulting average frequency of the LO quasimode Q(LO) amounts to D Œ1=3  .!A1 .LO/2 C 2!E1 .LO/2 /1=2 , which is slightly above 580 cm1 [75]. Reported observations of phonon confinement effects in the resonant Raman spectrum of ZnO nanoparticles must be considered with great caution. Owing to the extremely flat phonon dispersion curves, only marginal confinement-induced peak shifts (few cm1 ) may be expected. In contrast, a much more distinct thermal phonon shift (redshift of phonon lines >10 cm1 ) due to extensive heating may occur, resulting from the resonant UV-laser irradiation already at very moderate power densities [76, 77], because of the strongly reduced thermal conductivity of the nanoparticle samples because of air gaps between the individual nanoparticles. Therefore, for nanoparticle studies visible laser lines are strongly recommended. Owing to their non-resonant interaction with the ZnO, heating effects are essentially reduced. Even in this case, the interpretation of peak shifts is not totally straightforward. Seemingly confinement-induced shifts may actually originate from a disorder-induced broadening of the relevant q-vector range. The relative impact of the different effects discussed here on the ZnO nanoparticle Raman spectrum may depend on the experimental parameters (temperature, laser power density) and on the sample details, such as nanoparticle average size and dispersion, possible preferential orientation, and degree of crystalline disorder in the nanoparticles. As an example, for ZnO nanocolumns on SnO2 substrates, broad phonon bands were reported that correlate perfectly with the one-phonon density of states obtained from ab initio calculations [78].

2.5 Phonon–Plasmon Mixed States A prerequisite for (opto-)electronic applications of ZnO is the availability of mobile charges (electrons and/or holes). These charges may either originate from chemical doping or from optical excitation. Doping induces a unipolar charge carrier gas,

32

J. Geurts

which is up to now essentially restricted to n-type. In contrast, optical excitation simultaneously generates electrons and holes with equal concentrations and resulting at sufficiently high densities or temperatures in an electron-hole plasma. See Sect. 12.2. The free-carrier gas gives rise to a new type of elementary excitation: the collective charge-carrier oscillation, called plasma oscillation. In this section, we will first derive the eigenfrequency of this plasma oscillation and consider its similarity with the phonon excitations, which were discussed before. Subsequently, the formation of phonon–plasmon mixed states will be explained. In ZnO, the plasmon–phonon coupling is extraordinarily strong because of the high bond polarity. Examples will illustrate the study of the plasmon–phonon coupling by infrared reflectance and Raman spectroscopy.

2.5.1 Collective Charge-Carrier Oscillations For a free electron gas (concentration n), just like for any harmonic oscillator, upon displacement a carrier oscillation is driven by a linear restoring force: The electrons experience the Coulomb force F c D  eE of the electrical dipole field E , which directly scales with the displacement of the negatively charged electrons with respect to their immobile counterpart, the ionized donors. In addition, the field E also has a scaling factor which is essentially governed by the charge density  D ne. Moreover, it is weakened because of the dielectric screening by the valence electrons of the host lattice and, if applicable, by the host lattice ions. This screening effect is accounted for by the dielectric constant ". Finally, from the restoring force F c together with the inertia of the oscillating particles, i.e. the effective electron mass me , the oscillation eigenfrequency !PL , is obtained as  !PL D

ne 2 ""0 me

 12 :

(2.4)

The eigenfrequency !PL is referred to as plasmon frequency. It scales with the square root of the carrier concentration. The plasmon frequency, derived in this way, applies for oscillations with infinite wavelength, i.e. vanishing wavevector q. Finite q values result in a slight eigenfrequency enhancement (q 2 ) because a finite wavelength implies spatially periodic carrier concentration gradients, which result in a carrier-diffusion-induced enhancement of the restoring force. As a general rule, for semiconductors with doping levels in the range n D 1017 cm3 to n D 1020 cm3 , the plasmon frequency is in the far- or mid-infrared spectral range. For ZnO with doping concentrations n D 1019 cm3 and 1020 cm3 , (2.4) yields !PL D 830 cm1 and 2;600 cm1 , respectively. When comparing the plasmon with the phonons discussed previously, an essential difference is the purely longitudinal character of the plasmon. No transverse plasmon wave can exist because the electron gas has no shear stiffness. Therefore,

2

Crystal Structure, Chemical Binding, and Lattice Properties

33

no transverse restoring force occurs, and the transverse eigenfrequency is zero. This is in clear contrast to the phonon vibrations, which occur in the three-dimensionally bonded solid lattice with considerable shear stiffness reflected in the eigenfrequency !TO . Nevertheless, plasmons are described formally in the same way as phonons within the Lorentz oscillator model, albeit with zero transverse eigenfrequency [36].

2.5.2 Coupling to Polar Longitudinal Phonons A strong coupling between a plasmon and a polar LO phonon occurs through their electric fields. For this pair of coupled oscillators, the two individual oscillator eigenfrequencies !LO and !PL are replaced by a new pair of eigenfrequencies, which are called !  and ! C : Their values are derived in the following way: According to Maxwell’s equation div("  "0 E / D , together with the absence of net charge in the crystal, i.e.  D 0, longitudinal waves are restricted to those frequencies for which ".!/ D 0. Thus, the new longitudinal eigenmodes are the roots of the dielectric function ".!/. This function contains the superposition of the dielectric response of the valence electrons, the polar lattice ions and the free carriers. In the infrared spectral range, the dispersionless valence electron contribution yields a constant background contribution "b (in literature also referred to as "1 ). In ZnO, it amounts to 3.7 [1]. For a more general treatment, see e.g. [36]. Thus, the total dielectric response ".!/ is expressed as: ".!/ D "b C

!p2 2 !TO



!2

 i !

C

! 2

2 !PL ;  i !=

(2.5)

where !p 2 is the phonon oscillator strength, !TO the transverse phonon eigenfrequency,  the phonon damping, and the plasmon damping constant. In Fig. 2.12, for ZnO, the roots of ".!/ are plotted against the square root of the carrier concentration n. Plotted in this way, the pure plasmon eigenfrequency would show a linear dependence.

Fig. 2.12 Doping dependence of the ZnO plasmon–phonon eigenfrequencies (from [36, 79])

34

J. Geurts

Fig. 2.13 Infrared reflectance spectrum of n-doped ZnO:Ga with carrier concentration n D 1:8  1020 cm3 . Temperature T D 10 K (after [36])

The pure LO phonon frequency is independent of the free-carrier concentration in this density range. Obviously, the pure plasmon character is essentially preserved for the ! C mode for eigenfrequencies well above the phonon. In contrast, in the range of comparable phonon and plasmon frequency, the mixed longitudinal modes show a pronounced frequency split. Instead of crossing, between ! C and !  a gap of at least 400 cm1 is opened (avoided crossing or anti-crossing behaviour). For high doping levels, the lower branch !  bends toward a constant value !  D !TO . Here, the original LO phonon is replaced by a longitudinal phonon-like eigenmode at the TO frequency. This seemingly surprising fact is explained straightforwardly by regarding this mode as an LO phonon, the macroscopic electric field of which is screened by the free carriers. Thus, due to the lack of this additional restoring force contribution, its eigenfrequency is !TO . The experimental data points for a series of ZnO samples with different doping levels in the wide range from n < 1018 cm3 up to 1:8  1020 cm3 are in very good agreement with the calculated eigenvalues [36, 79]. Experimentally, the longitudinal phonon–plasmon mixed excitations may be studied either by Raman or by infrared spectroscopy. In Raman spectroscopy, they yield scattering peaks with Raman shift !˙ . In infrared spectroscopy, the charge carriers manifest themselves by screening the incident radiation, resulting in an enhanced reflectance. Figure 2.13 shows the far- and mid-infrared reflectance spectrum of doped ZnO with carrier concentration n D 1:8  1020 cm3 . A broad reflectance band occurs, covering all frequencies below ! C , except for a small dip at the !  frequency. The high reflectance marks the range of negative ". The response of the plasmon oscillation (transverse eigenfrequency is equal to zero), superimposed on the background "B yields ".!/ < 0 for ! < ! C . At the phonon resonance frequency !TO , the additional polar phonon oscillation induces a narrow interval of positive ", i.e. reduced reflectance. Assuming the low-damping limit for the free carriers would result in R D 1 for ! < ! C , and subsequently a step-like decrease. The smearing out of the experimental spectrum corresponds to a considerable damping, which is quite plausible for this extremely high carrier concentration.

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References 1. U. R¨ossler, D. Strauch, in Semiconductors II–VI and I–VII Compounds; Semimagnetic Compounds, ed. by U. R¨ossler. Landolt-B¨ornstein III/41B Revised and updated edition of Vols. III/17 and 22 (Springer, Heidelberg, 1999) ¨ ur, Y.I. Alivov, C. Liu, A. Teke, M.A. Reshchikov, S. Dogan, V. Avrutin, S.J. Cho, ¨ Ozg¨ 2. U. H. Morkoc¸, J. Appl. Phys. 98, 041301 (2005) 3. C. Klingshirn, Phys. Stat. Sol. B 244, 3027 (2007) 4. G.F. Koster, J.O. Dimmock, R.G. Wheeler, H. Statz, Properties of the Thirty-two Point Groups (M.I.T. Press, Cambridge, MA, 1963) 5. D. Hallwig, E. Mollwo, Verhandl., DPG(VI) 10 HL 37 (1975) 6. L. Pauling, The Nature of the Chemical Bond (Cornell University Press, Ithaca, NY, 1960) 7. J.C. Phillips, Bonds and Bands in Semiconductors (Academic Press, New York, 1973) 8. A.B.M.A. Ashrafi, A. Ueta, A. Avramescu, H. Kumano, I. Suemune, Y.-W. Ok, T.-Y. Seong, Appl. Phys. Lett. 76, 550 (2000) 9. S.-K. Kim, S.-Y. Jeong, C.-R. Cho, Appl. Phys. Lett. 82, 562 (2003) 10. J.E. Jaffe, A.C. Hess, Phys. Rev. B 48, 7903 (1993) 11. S. Desgreniers, Phys. Rev. B 58, 14102 (1998) 12. J.E. Jaffe, J.A. Snyder, Z. Lin, A.C. Hess, Phys. Rev. B 62, 1660 (2000) 13. J. Serrano, A.H. Romero, F.J. Manj´on, R. Lauck, M. Cardona, A. Rubio, Phys. Rev. B 69, 094306 (2004) 14. P. Lawaetz, Phys. Rev. B 5, 4039 (1972) 15. H. Ibach, Phys. Stat. Sol. 33, 257 (1969) 16. W.N. Lawless, T.K. Gupta, J. Appl. Phys. 60, 607 (1986) 17. R.A. Robie, H.T. Haselton Jr., B.S. Hemingway, J. Chem. Thermodynamics 21, 743 (1989) 18. P. Wagner, Ph.D. Thesis, University Erlangen-N¨urnberg (Germany), 1978 19. G.A. Slack, Phys. Rev. B 6, 3791 (1972) 20. M.W. Wolf, J.J. Martin, Phys. Stat. Sol. (a) 17, 215 (1973) 21. F. Bernardini, V. Fiorentini, D. Vanderbilt, Phys. Rev. B 56, R10024 (1997) 22. Y. Lu, Chapter 13 in Zinc Oxide Bulk, Thin Films and Nanostructures, ed. By Chennupati Jagadish, Stephen J. Pearton (Elsevier, Oxford (UK), 2006) 23. A. Dal Corso, M. Posternak, R. Resta, A. Baldereschi, Phys. Rev. B 50, 10715 (1994) 24. R. Loudon, Adv. Phys. 13, 423 (1964) 25. P. Br¨uesch, in Phonons: Theory and Experiments I , ed. by M. Cardona, P. Fulde, H.J. Queisser. Springer Series in Solid-State Sciences, vol 34 (Springer, Berlin, 1982), p. 117 26. R.J. Collins, D.A. Kleinman, J. Phys. Chem. Solids 11, 190 (1959) 27. M. Tsuboi, J. Chem. Phys. 40, 1326 (1964) 28. M. Tsuboi, A. Wada, J. Chem. Phys. 48, 2615 (1968) 29. K. Thoma, B. Dorner, G. Duesing, W. Wegener, Solid State Commun. 15, 1111 (1974) 30. J. Serrano, F.J. Manjon, A.H. Romero, F. Widulle, R. Lauck, M. Cardona, Phys. Rev. Lett. 90, 055510 (2003) 31. W. Hewat, Solid State Commun. 8, 187 (1970) 32. J. Birman, Phys. Rev. 115, 1493 (1959) 33. T.B. Bateman, J. Appl. Phys. 33, 3309 (1962) 34. G. Carlotti, D. Fioretto, G. Socino, E. Verona, J. Phys. Condens. Matter. 7, 9147 (1995) 35. R. Cusc´o, E. Alarc´on-Llad´o, J. Ib´an˜ ez, L. Art´us, J. Jim´enez, B. Wang, M.J. Callahan, Phys. Rev. B 75, 165202 (2007) 36. C.F. Klingshirn, Semiconductor Optics, 3rd edn. (Springer, Heidelberg, 2007) 37. W.A. Harrison, Electronic Structure and the Properties of Solids (Dover Publ. Inc., New York, 1989) 38. T.C. Damen, S.P.S. Porto, B. Tell, Phys. Rev. 142, 570 (1966) 39. C.A. Arguello, D.L. Rosseau, S.P.S. Porto, Phys. Rev. 181, 1351 (1969) 40. M. Schumm, PhD Thesis, University of W¨urzburg, 2008 41. R.H. Callender, S.S. Sussman, M. Selders, R.K. Chang, Phys. Rev. B 7, 3788 (1973)

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42. H. Siegle, G. Kaczmarczyk, L. Filippidis, A.P. Litvinchuk, A. Hoffmann, C. Thomsen, Phys. Rev. B 55, 7000 (1997) 43. J.M. Calleja, M. Cardona, Phys. Rev. B 16, 3753 (1977) 44. W. Richter, in Resonant Raman Scattering in Semiconductors, ed. by G. H¨ohler. Springer Tracts in Modern Physics, vol 78 (Springer, Berlin, 1976) 45. M. Cardona, in Light Scattering in Solids II, ed. by M. Cardona, G. G¨untherodt. Topics in Applied Physics, vol 50 (Springer, Berlin, 1982) 46. J.F. Scott, Phys. Rev. B 2, 1209 (1970) 47. J. Serrano, F. Widulle, A.H. Romero, M. Cardona, R. Lauck, A. Rubio, Phys. Stat. Sol. B 235, 260 (2003) 48. I.H. Lee, K.J. Yee, K.G. Lee, E. Oh, D.S. Kim, Y.S. Lim, J. Appl. Phys. 93, 4939 (2003) 49. Aku-Leh, J. Zhao, R. Merlin, J. Men´endez, M. Cardona, Phys. Rev. B 71, 205211 (2005) 50. X. Wang, S. Yang, J. Wang, M. Li, X. Jiang, G. Du, X. Liu, R.P.H. Chang, J. Cryst. Growth 222, 123 (2001) 51. A. Kaschner, U. Haboeck, M. Strassburg, G. Kaczmarczyk, A. Hoffmann, C. Thomsen, A. Zeuner, H.R. Alves, D.M. Hofmann, B.K. Meyer, Appl. Phys. Lett. 80, 1909 (2002) 52. A. Tsukazaki, A. Ohtomo, T. Onuma, M. Ohtani, T. Makino, M. Sumiya, K. Ohtani, S.F. Chichibu, S. Fuke, Y. Segawa, H. Ohno, H. Koinuma, M. Kawasaki, Nat. Mater. 4, 42 (2004) 53. F. Reuss, C. Kirchner, Th. Gruber, R. Kling, S. Maschek, W. Limmer, A. Waag, P. Ziemann, J. Appl. Phys. 95, 3385 (2004) 54. L. Artus, R. Cusco, E. Alarcon-Llado, G. Gonzalez-Diaz, I. Martil, J. Jimenez, B. Wang, M. Callahan, Appl. Phys. Lett. 90, 181911 (2007) 55. J. Yu, H. Xing, Q. Zhao, H. Mao, Y. Shen, J. Wang, Z. Lai, Z. Zhu, Sol. Stat. Commun. 138, 502 (2006) 56. F. Friedrich, N.H. Nickel, Appl. Phys. Lett. 91, 111903 (2007) 57. M. Tzolov, N. Tzenov, D. Dimova-Malinovska, M. Kalitzova, C. Pizzuto, G. Vitali, G. Zollo, I. Ivanov, Thin Solid Films 379, 28 (2000) 58. M. Tzolov, N. Tzenov, D. Dimova-Malinovska, M. Kalitzova, C. Pizzuto, G. Vitali, G. Zollo, I. Ivanov, Thin Solid Films 396, 274 (2001) 59. S. Choopun, N. Hongsith, E. Wongrat, T. Kamwanna, S. Singkarat, P. Mangkorntong, N. Mangkorntong, T. Chairuangsri, J. Am. Ceram. Soc. 91, 174 (2007) 60. C. Bundesmann, N. Ashkenov, M. Schubert, D. Spemann, T. Butz, E.M. Kaidashev, M. Lorenz, M. Grundmann, Appl. Phys. Lett. 83, 1974 (2003) 61. F.H. Manjon, B. Mari, J. Serrano, A.H. Romero, J. Appl. Phys. 97, 053516 (2005) 62. T. Dietl, H. Ohno, F. Matsukura, J. Cibert, D. Ferrand, Science 287, 1019 (2000) 63. K. Sato, H. Katayama-Yoshida, Japan. J. Appl. Phys. 40, L334 (2001) 64. C. Liu, F. Yun, H. Morkoc¸, J. Mat. Sci. Mater. Electron. 16, 555 (2005) 65. K. Ueda, H. Tabata, T. Kawai, Appl. Phys. Lett. 79, 988 (2001) 66. H. Zhou, Ch. Knies, D.M. Hofmann, J. Stehr, N. Volbers, B.K. Meyer, L. Chen, P. Klar, W. Heimbrodt, Phys. Stat. Sol. (a) 204, 112 (2006) 67. M. Schumm, M. Koerdel, S. M¨uller, H. Zutz, C. Ronning, J. Stehr, D.M. Hofmann, J. Geurts, New J. Phys. 10, 043004 (2008) 68. M. Schumm, M. Koerdel, S. M¨uller, C. Ronning, E. Dynowska, Z. Goacki, W. Szuszkiewicz, J. Geurts, Phys. Stat. Sol. B 247, 1469 (2010) 69. Z.L. Wang, J. Phys. Cond. Mat. 16, R82958 (2004) 70. W.J.E. Beek, M.M. Wienk, R.A.J. Janssen, Adv. Mater. 16, 1009 (2004) 71. B. Jusserand, M. Cardona, in Light Scattering on Solids V. Topics in Applied Physics, vol 66 (Springer, Berlin, 1989), p. 49 72. A. Dinger, M. G¨oppert, R. Becker, M. Gr¨un, S. Petillon, C. Klingshirn, J. Liang, V. Wagner, J. Geurts, Phys. Rev. B 64, 245310 (2001) 73. V. Wagner, J. Geurts, W. Kiefer, Raman Spectroscopy on II–VI Interfaces, Quantum Dots, and Quantum Wires, in Quantum Dots and Nanowires, Chapter 7, ed. by S. Bandyopadhyay, H.S. Nalwa. Nanotechnology Book Series (American Scientific Publishers, Stevenson Ranch, CA, 2003), pp. 241–302

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74. 75. 76. 77. 78. 79.

V.A. Fonoberov, A.A. Balandin, Phys. Rev. B 70, 233205 (2004) L. Bergman, X.-B. Chen, J. Huso, J.L. Morrison, H. Hoeck, J. Appl. Phys. 98, 093507 (2005) K.A. Alim, V.A. Fonoberov, A.A. Balandin, Appl. Phys. Lett. 86, 053103 (2005) K.A. Alim, V.A. Fonoberov, M. Shamsa, J. Appl. Phys. 97, 124313 (2005) B. Mar´ı, J. Cembrero, F.J. Manj´on, M. Mollar, R. G´omez, Phys. Stat. Sol. (a) 202, 1602 (2005) M. G¨oppert, F. Gehbauer, M. Hetterich, J. M¨unzel, D. Queck, C. Klingshirn, J. Lumin. 72–74, 430 (1997)

Chapter 3

Growth Andreas Waag

Abstract This chapter is devoted to the growth of ZnO. It starts with various techniques to grow bulk samples and presents in some detail the growth of epitaxial layers by metal organic chemical vapor deposition (MOCVD), molecular beam epitaxy (MBE), and pulsed laser deposition (PLD). The last section is devoted to the growth of nanorods. Some properties of the resulting samples are also presented. If a comparison between GaN and ZnO is made, very often the huge variety of different growth techniques available to fabricate ZnO is said to be an advantage of this material system. Indeed, growth techniques range from low cost wet chemical growth at almost room temperature to high quality MOCVD growth at temperatures above 1;000ıC. In most cases, there is a very strong tendency of c-axis oriented growth, with a much higher growth rate in c-direction as compared to other crystal directions. This often leads to columnar structures, even at relatively low temperatures. However, it is, in general, not straight forward to fabricate smooth ZnO thin films with flat surfaces. Another advantage of a potential ZnO technology is said to be the possibility to grow thin films homoepitaxially on ZnO substrates. ZnO substrates are mostly fabricated by vapor phase transport (VPT) or hydrothermal growth. These techniques are enabling high volume manufacturing at reasonable cost, at least in principle. The availability of homoepitaxial substrates should be beneficial to the development of ZnO technology and devices and is in contrast to the situation of GaN. However, even though a number of companies are developing ZnO substrates, only recently good quality substrates have been demonstrated. However, these substrates are not yet widely available. Still, the situation concerning ZnO substrates seems to be far from low-cost, high-volume production. The fabrication of dense, single crystal thin films is, in general, surprisingly difficult, even when ZnO is grown on a ZnO substrate. However, molecular beam epitaxy (MBE) delivers high quality ZnMgO–ZnO quantum well structures. Other thin film techniques such as PLD or MOCVD are also widely used. The main problem at

A. Waag Institut f¨ur Halbleitertechnik der Technischen Universit¨at, Braunschweig, Germany e-mail: [email protected]

39

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A. Waag

present is to consistently achieve reliable p-type doping. For this topic, see also Chap. 5. In the past years, there have been numerous publications on p-type doping of ZnO, as well as ZnO p–n junctions and light emitting diodes (LEDs). However, a lot of these reports are in one way or the other inconsistent or at least incomplete. It is quite clear from optical data that once a reliable hole injection can be achieved, high brightness ZnO LEDs should be possible. In contrast to that expectation, none of the LEDs reported so far shows efficient light emission, as would be expected from a reasonable quality ZnO-based LED. See also Chap. 13. As a matter of fact, there seems to be no generally accepted and reliable technique for p-type doping available at present. The reason for this is the unfavorable position of the band structure of ZnO relative to the vacuum level, with a very low lying valence band. See also Fig. 5.1. This makes the incorporation of electrically active acceptors difficult. Another difficulty is the huge defect density in ZnO. There are many indications that defects play a major role in transport and doping. In order to solve the doping problem, it is generally accepted that the quality of the ZnO material grown by the various techniques needs to be improved. Therefore, the optimization of ZnO epitaxy is thought to play a key role in the further development of this material system. Besides being used as an active material in optoelectronic devices, ZnO plays a major role as transparent contact material in thin film solar cells. Polycrystalline, heavily n-type doped ZnO is used for this, combining a high electrical conductivity with a good optical transparency. In this case, ZnO thin films are fabricated by large area growth techniques such as sputtering. For this and other applications, see also Chap. 13.

3.1 Bulk Growth The availability of high quality low cost ZnO substrates is believed to be one of the key features for further development of ZnO technology. In the case of sapphire, which is mostly used to date as a hetero substrate, it is not only the mismatch of lattice constants and thermal expansion coefficients that causes problems but also a pronounced diffusion of Al occurs into the ZnO, which makes conductivity control difficult. Diffusion can occur over many micrometers [1]. The most promising technique for fabricating ZnO wafers is supposed to be hydrothermal bulk growth. Large area wafers can be fabricated at low cost and with high throughput. Other techniques are e.g. vapor phase transport (VPT), chemical transport techniques, pressure-melt, and flux growth techniques.

3.1.1 Vapor Phase Transport VPT is a quite common growth technique not only for bulk ZnO [2] but also for ZnO nanorods [3] and thin films [4]. The source semiconductor, in this case zinc oxide as a binary or Zn metal, is evaporated and gets transported to the reaction

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41

chamber by an inert gas (e.g., argon or nitrogen). Later, oxygen gas is added. The reactor consists of an open quartz tube, which is placed in an oven. By controlling the temperature gradient, growth on the substrate is initiated. Often, the chemical process is enhanced by the additives such as carbon in ZnO mixtures for better evaporation, including possible catalytic effects, for example, the reduction of ZnO. Details on VPT can be found elsewhere [5–8]. References to older work going back to the 1960s may be found, e.g., in [5, 6, 9].

3.1.2 Solvothermal Growth Solvothermal growth techniques ([10] and for earlier references [11]) are quite attractive in terms of mass production. Growth occurs at relatively low temperature and often at normal pressure, and the material is close to thermodynamic equilibrium. The solutions consist of a solvent, in which the material of choice is dissolved. The solubility of the base material changes with temperature being the basis for crystal growth initiated by a temperature gradient. Ideally, the solvent should have a low melting point. Low vapor pressures help to keep the ratio of solvent and solute constant. In principle, a high crystal quality can be achieved, since the growth occurs very close to thermal equilibrium, where growth rate and dissolution rate are almost equal. Adding the solute species leads to super-saturation, and a suitable temperature gradient initiates crystal growth. Solvents used are, for example, water (hydrothermal) of alkaline-metal chlorides. The scalability of this technique has already been demonstrated, since it is used for the production of quartz by hydrothermal growth. As nonaqueous solution growth is concerned, various molten salts such as PbF2 , Zn3 P2 O8 , V2 O5 or MoO3 and B2 O3 and others have been used. The growth temperatures usually are above 800ı C due to the properties of the solvents. Sometimes, a seed is used, which is then pulled out of the solution at the growth speed of the crystal. Growth rates are in the range of 1 mm/h. A general problem of nonaqueous solution growth is the potential contamination by the solvent. For example, V contamination in the percent range has been determined in respective material [12]. Owing to the above-mentioned properties of the solvents, growth from nonaqueous solutions has not yet been applied for the fabrication of large area ZnO substrates with a high quality. For some examples of melt growth, see [13–16]. The hydrothermal growth of ZnO has been developed with better success. In hydrothermal growth, aqueous solvents in combination with mineralizers are used under elevated temperatures. Since the solubility of most solute species in water is very low, mineralizers have to be employed, which increase the solubility of the solute in the solvent. The technique is very popular for the high throughput fabrication of quartz [17]. The hydrothermal growth takes place in an autoclave at high pressure and temperature by using a seed crystal. The pressure–temperature situation leads to water in the supercritical state (super-critical water), with an enhanced acidity, reduced density, and reduced polarity as compared to water in its normal

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state. Mineralizers increase the solubility by forming compounds with ZnO, which then decompose at the growing crystal surface. Typical mineralizers are LiOH, NaOH, KOH, Li2 CO3 , and H2 O2 and mixtures thereof. In particular, a mixture of LiOH and KOH leads to interesting results in terms of crystal quality and growth rate [10]. Often, the full width at half maximum (FWHM) of the (0002) reflection of the high resolution X-ray diffraction (HRXRD) rocking curve is given as a measure of crystal quality. However, this particular reflection can be very sharp even when high dislocation densities are present [18]. Therefore, the defect density has to be checked also by other means. Values of 15 arcsec for the (0002) FWHM in an Omega-scan have been reported [9]. With 0.7% HCl etching, an etch pit density (EPD) as low as 300 cm2 could be obtained [10]. The impurity incorporation depends drastically on the growth face, and hence varies throughout the crystal, the basal sectors being the best ones. It is not surprising that both Li and Na are the most prominent impurities, with concentrations in the 0.1–1 ppm range. Since Li and Na can form deep acceptors (see Chaps. 5, 10 or [19,20]), these deep acceptors result in high resistivity material, which may be even difficult to dope n-type. Although large ZnO crystals with a diameter of 3 in. have been demonstrated by solvothermal processes, 2-in. technology is also said to be commercially available [10, 21, 22]. Alkaline-metal chloride solutions at temperatures below 650ıC have been used for that.

3.2 Epitaxial Growth Techniques Epitaxial growth techniques usually rely on the availability of suitable substrates. In the case of ZnO, the availability of large area ZnO substrates has often been cited to be a major advantage. Even though a number of companies worldwide are pursuing the growth of high quality substrates, the situation is still – up to this point – quite unsatisfactory. High quality substrates meanwhile have been demonstrated, but are not yet readily available, and still very expensive as mentioned already above. To judge the suitability of a ZnO substrate for the growth of high quality ZnO thin films, the substrates have to be analyzed before growth. For that, both HRXRD as well as the determination of the EPD can be employed, besides other techniques. In the case of compound semiconductors with polar faces, as is the case in ZnO, both faces cannot be treated with the same chemistry to reveal etch pits [23]. It was shown that zinc- and oxygen-terminated sides of ZnO bulk wafers reveal a different chemical reactivity concerning etching [24]. Etch rates of oxygen-face ZnO is usually much higher as compared to that of zinc-face ZnO. Etching of oxygen-face ZnO results in the formation of hillocks, whereas etch pits appear on the surface with opposite polarity. The number of these etch pits is normally used to define the density of threading dislocations on zinc-face ZnO. As an alternative to wet chemical etching, there is a possibility to employ thermal treatment of the surface [25, 26]. Xing Gu et al. showed in [25] the appearance of

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Growth

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atomic terraces after annealing in air for 3 h at 1;050ı C. S. Graubner et al. [26] state that annealing in oxygen environment causes the formation of atomic terraces only at temperatures higher than 1;100ı C. In 1971, the appearance of hexagonally shaped etch pits on oxygen face of ZnO bulk wafer after thermal treatment in helium atmosphere at 1;200ı C was also reported [27]. In order to get an idea on the quality of ZnO substrates achievable so far, Fig. 3.1 shows atomic force microscopy (AFM) images of as delivered substrates, from two different producers. Oxygen- and zinc-terminated surfaces of “Crystec” samples are depicted in Fig. 3.1a b, these surfaces are delivered without thermal treatment. Both surfaces have a similar roughness of 0.336 and 0.456 nm rms for oxygen and zinc faces. In contrast to that, “Tokyo Denpa” substrates are already thermally treated before delivery. Terraces are present on both oxygen- and zinc-polar sides of the substrates. Here, the roughness on oxygen-terminated face is 0.726 nm and on zincterminated 0.560 nm rms. [4.19 nm] 6.51 nm

a

3.50

2.00

2.00

[2.34 nm] 3.84 nm [nm ]

b

6.00

3.00

5.00 4.00

[μm]

[μm]

2.50 2.00

[nm]

3.00

1.50 2.00

0.50

0

[μm]

2.00

1.00

0

0

1.00

0

0

[μm]

[3.77 nm] 5.66 nm

10.0

d

2.00

2.00

[4.64 nm] 10.1 nm [nm ]

c

2.00

0

[nm] 5.00

8.00

[μm]

[μm]

4.00 6.00

3.00

4.00

2.00

1.00

0

0

2.00

0

0

0

[μm]

2.00

0

[μm]

2.00

Fig. 3.1 AFM images of as delivered ZnO substrates: (a) [O] – face of “Crystec” sample, (b) [Zn] – face of “Crystec” sample, (c) [O] – face of “TokyoDenpa” sample, (d) [Zn] – face of a “TokyoDenpa” sample. From [28]

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A. Waag

Fig. 3.2 AFM images of substrates etched in a 20% solution of HNO3 for 90 s at room temperature: (a) 50  50 m2 area of a “Crystec” sample [Zn] – face, (b) 2  2 m2 area of a “Crystec” sample [Zn] – face, (c) 50  50 m2 area of a “TokyoDenpa” sample [Zn] – face, (d) 2  2 m2 area of a “TokyoDenpa” sample [Zn] – face. From [28]

An AFM image of a zinc-face “Crystec” substrate etched with HNO3 acid is shown in Fig. 3.2a. One can obviously see black spots distributed all over the surface of the crystal. According to data reported in the literature [23, 24, 27], etch pits obtained by a standard wet chemical etching approach are hexagonally formed. The EPD calculated for this sample is about 2  105 cm2 . For comparison, an image of “Tokyo Denpa” substrate’s zinc face is depicted in Fig. 3.2c, d. The EPD in this case is about 2  105 cm2 and does not differ so much from the one obtained for the “Crystec” substrate. Thermal etching reveals well-defined hexagonally formed etch pits as it can be seen in Fig. 3.3a, b. Here the oxygen-terminated face of the “Crystec” substrate annealed at 1;050ıC for 4 h in air is shown, with EPD values of 5  105 cm2 , which corresponds to the results for the chemically etched zinc side. After a more intense annealing step (1;100ı C for more than 1 h), additional features appear on the surfaces. One such example is shown in Fig. 3.4a. These structures seem to be correlated with mechanical scratches on the surface. This

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Fig. 3.3 AFM images of “Crystec” substrate (which face) annealed at 1;050ı C for 4 h in air: (a) 50  50 m2 area, (b) 2  2 m2 area. From [28]

Fig. 3.4 AFM images of “Crystec” substrate annealed at 1;100ı C for 5 h in air: (a) 50  50 m2 area, (b) 2  2 m2 area. From [28]

indicates a pronounced etching of mechanically induced defects, e.g. scratches, and imperfections and inclusions. Moreover, a distortion of atomic terraces at 1;150ı C in air can be observed. This can be clearly seen in Fig. 3.5. These results demonstrate that an optimized surface treatment is necessary to use these substrates for the subsequent epitaxial growth of ZnO-based heterostructrures. The growth of ZnO epilayers on ZnO substrates initially resulted in very low quality material. Often, the ZnO epilayer even did not stick to the substrate. Some kind of surface contamination of the ZnO substrate is thought to be the reason for this behavior. Meanwhile, an efficient surface preparation technique has been developed, which is simply based on a high temperature annealing under oxygen flux. An alternative to ZnO homoepitaxial substrates are SCAM substrates (ScandiumAluminum-Magnesium-Oxide [29]). SCAM is also hexagonal and has a lattice mismatch of only 0.09% relative to ZnO, allowing for low defect densities. However,

46

A. Waag

Fig. 3.5 AFM images of “Crystec” substrate annealed at 1;150ı C for 4 h in air: (a) 10  10 m2 area, (b) 2  2 m2 area. From [28]

the growth and fabrication of SCAM is difficult, partly due to the brittleness of the material. Therefore, even though first exciting work has been published on SCAM substrates, it is not widely used up to now [30]. Because of this difficult substrate situation, very often sapphire substrates are still employed as a basis for material development (partly with a GaN buffer layer). However, it seems that the high dislocation density in ZnO grown on sapphire is drastically influencing the residual carrier concentration. In this situation, the success of systematic doping experiments is questionable. An improvement of structural quality as well as purity of the substrates is urgently needed. More details on that problem will be discussed in the “doping” Chap. 5.

3.2.1 Metal Organic Chemical Vapor Deposition Metal organic chemical vapor deposition (MOCVD) is the standard epitaxial technique for the growth of nitride and other III–V based LEDs and laser diodes. Equipment for and experience in mass production by MOCVD is available. Therefore, MOCVD would be the most suitable technique for ZnO, to enter, e.g., lighting application markets. In contrast to MOCVD, MBE will in general not be able to offer the high throughput necessary in applications for solid state lighting. However, especially for ZnO, there are also arguments in favor of MBE growth as outlined in Sect. 3.2.2. MOCVD is a very versatile technique, as long as suitable precursors are available, allowing to grow high quality material and heterostructures. For Zn and Cd precursors, diethyl-metal as well as dimethyl-metal components have been used [31, 32, 96]. For the Mg precursor, bis-cyclopentadienyl-Mg has been employed successfully [33].

3

Growth

47

The problem of MOCVD in general is to find precursor combinations so that the chemical reaction is only taking place at the substrate surface, but not in the gas phase. Since most oxygen precursors are quite reactive, the prereactions in the gas phase are a major problem in the case of ZnO MOCVD growth. This is particularly true when pure oxygen is used [34]. In this case, the reactor pressure has to be reduced drastically, making the growth of ZnO difficult. This is the reason why groups have also focused on alternative precursors for oxygen, with a reduced reactivity in the gas phase. Alternative oxygen precursors such as butanole [35], iso-propanole, or N2 O (nitrous oxide or laughing gas) have been investigated for their use in MOCVD. A comparison has been made in [36]. In Fig. 3.6 the growth rate of ZnO as a function of growth temperature is shown for t-Butanole, iso-propanole and nitrous oxide as oxygen precursors, and DEZn as a Zn precursor. At low temperatures, the growth rate is limited by the chemical reaction rates, which are temperature activated (kinetically limited regime). At higher temperatures, the growth rate decreases due to prereactions in the gas phase. In an intermediate temperature range, the growth rate is constant, being mass flow limited. In this case, at a constant flow rate, the growth rate will almost not at all depend on temperature, and all the chemical species transported toward the surface are reacting toward the end product. As can be seen from the figure, the three different precursors shown here are useful for different temperature regimes. The growth rate as a function of reactor pressure also increases, up to a point where reactions in the gas phase limit the growth rate. Growth rates up to 3 m=h can be achieved with the precursors shown here. Growth rates of some m per hour are a good compromise, being fast enough for the growth of buffer layers, and allowing a precise enough control for the growth of complicated heterostructures. The growth rate as a function of reactor pressure is shown in Fig. 3.7.

Growth Rate (μm/h)

2.4

(1)

(2)

(1) lsopropanol (2) tert-butanol (3) nitrous oxide

1.0

300

400

500 600 700 Temperature (°C)

(3) (4)

800

Fig. 3.6 Growth rate of ZnO grown by MOVPE, as a function of growth temperature. A kinetically limited regime and a mass flow limited regime can be distinguished. After [36, 37]

48

A. Waag

growth rate [μm/hr]

2.4 2.2 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6

iso-propanol tert-butanol nitrous oxide

0.4 50 100 150 200 250 300 350 400 450 500 550 reactor pressure [mbar]

Fig. 3.7 Growth rate during the MOCVD growth of ZnO as a function of reactor pressure. From [21]

Alternative metal precursors such as Zinc acetyl acetonate can also be used [38]. Bis-cyclo-pentadienyl-magnesium (Cp2 Mg) is an often used Mg precursor for the growth of ZnMgO. The ZnMgO thin films are frequently grown on ZnO/sapphire buffer layers, as shown in Fig. 3.8. Since Cp2 Mg is very reactive, reacting readily with oxygen in the gas phase, ZnMgO growth is not straight forward. The reactor pressure has to be reduced to prevent gas phase reactions, and therefore the growth rates are reduced substantially. The magnitude of the pressure reduction depends on the geometry of the MOCVD reactor. Even a quite high Mg/Zn flux ratio results in the incorporation of only a few percent of Mg into the ZnO matrix, as seen in Fig. 3.9. An Mg/Zn flux ratio of one leads to an incorporation of Mg of only 5%, indicating a substantial prereaction of Cp2 Mg in the gas phase. The width of the PL peaks from the ZnMgO increases with Mg incorporation, mostly because of line broadening by spatial fluctuations of the Mg concentration. Nevertheless, good quality ZnMgO–ZnO quantum well structures can be grown, one example of that is shown in Fig. 3.10. Here, the PL of the ZnO buffer, ZnMgO barrier as well as ZnO quantum well can well be distinguished. The principal setup of the ZnMgO/ZnOquantum well structure is shown in Fig. 3.11. Internal quantum efficiencies of 5% have been reported at room temperature, depending on confinement energy and well width. The two IIb –VI oxides CdO and ZnO are quite dissimilar materials in terms of their temperature stability. Similar to Indium in InGaN, Cd in ZnCdO can only be incorporated at relatively low growth temperatures. Again, a high DMCd/DEZ flux ratio has to be used to incorporate a few percent of Cd into the layers (see Fig. 3.12). A further analysis of the ZnCdO layers sometimes indicates a phase separation into two different ZnCdO regions with two distinctly different Cd concentrations [31]. This phase separation of Cd in MOCVD grown ZnCdO can directly be seen in cathodoluminescence (see Fig. 3.13), photoluminescence (Fig. 3.14) as well as

3

Growth

49

300 nm Zn1–xMgxO 800 nm ZnO buffer

GaN/AI2O3 template

Fig. 3.8 Basic setup of the thin film structure for the analysis of ZnMgO thin films grown by MOVPE Magnesium concentration 0.0

0.1

20

10 3.35

FWHM (meV)

Energy (eV)

3.55

0 0.0

1.5 Mg/Zn flux ratio

Fig. 3.9 Near band gap photoluminescence – position and corresponding line width – for ZnMgO layers grown by MOVPE, as a function of Mg/Zn flux ratio, indicating a very low incorporation coefficient for Mg (after [39]) Low temperature PL

Norm. intensity (a.u.)

I = 2 mW/cm2 T = 2.1 K ZnO layer

3 nm Zn0.9Mg0.1O/ZnO SQW Zn0.9Mg0.1O barrier

ZnO QW FWHM 8 meV

3.35

3.40

3.45

3.50

3.55

3.60

3.65

Energy (eV)

Fig. 3.10 Photoluminescence at 2.1 K of a ZnMgO/ZnO quantum well structure. The setup is shown in the next figure [40]

50

A. Waag ZnO quantum well, Lz

300nm Zn1–xMgxO

800 nm ZnO buffer

GaN/AI2O3 template

Fig. 3.11 Setup of a ZnMgO/ZnO quantum well structure

Cd concentration

0.03

0.0 0.0

1.0 2.0 3.0 4.0 DMCd / DEZn Flux Ratio

Fig. 3.12 Cd content of ZnCdO layers as a function of DMCd/DEZn flux ratios during MOVPE growth. After [31]

1μm bright areas dark areas

3.20 - 3.22 eV 2.90 - 3.05 eV

Fig. 3.13 Cathodoluminescence of a ZnCdO layer, with a color (gray) coding of the emission wavelength of maximum CL intensity. A clear separation into regions with higher and regions with lower Cd concentration can be seen. After [31]

Growth

51

Intensity (a.u.)

3

CdxZn1–xO c/c = 1.7e-3 c/c = 4.5e-3

ZnO buffer

GaN NL

34.0

34.8 2 theta (°)

Fig. 3.14 HRXRD of a ZnCdO thin film grown on a ZnO/GaN/sapphire template. Again, two distinctly separate Cd concentrations can be detected. After [31]

Fig. 3.15 Photoluminescence at 2.1 K for ZnCdO thin films with varying Cd content, indicating two distinctly different Cd concentrations in the same film. After [31]

X-ray diffraction (Fig. 3.15). This behavior has to be overcome for the development of devices based on ZnCdO active regions, grown by MOCVD. The band gap of ZnCdO decreases with Cd concentration. Considering the Cd concentrations from SIMS measurements, a bowing parameter can be derived from such a set of samples. The band gap decreases much faster than expected by a linear interpolation taking the band gaps from ZnO and CdO (Fig. 3.16). For examples of the luminescence of ZnCdO/ZnO quantum wells, of ZnCdO alloys, and for further data on the dependence of the band gap on the Cd concentration see Chaps. 4 and 6.

A. Waag PL Peak Position (eV)

52 3.4

2.9 0.0

0.05 Cadmium Concentration

Fig. 3.16 Near band gap PL emission of ZnCdO as a function of Cd content, indicating a deviation from the linear behavior. After [31]

During MOCVD growth at high temperatures, pronounced self-organization effects occur, resulting in the formation of ZnO nanorods. The properties of these nanorods will be discussed later in more detail in Sect. 3.3. It should be noted that the strong trend toward self-organization is one particularly interesting property of ZnO, even though it occurs in other materials as well. Nano rod research is now well established, with ZnO being one of the main enablers. For the MOCVD growth of doped layers, most of the group III metal precursors can be used for n-type doping. Trimethylgallium .TMG.CH3 /3 Ga/ or trimethylaluminum (TMAl.CH3 /3 Al) is well known from III–V technology. Very high doping levels beyond 1021 cm3 can be achieved in this way, in particular with aluminum doping. See for example [41] or Sect. 2.5. In contrast, p-type doping is still a substantial problem. Even though LEDs grown by MOCVD have been reported (see Chap. 13), these devices fail to demonstrate efficient electroluminescence, leading to a critical discussion concerning the underlying processes for carrier injection. Various materials have been used, such as, for example, NH3 for nitrogen and phosphine .PH3 / or arsine .AsH3 / for P or As incorporation, respectively. However, most of the results are not convincing until today. The situation concerning p-type doping of ZnO is in general complex, and will be discussed in more detail in a separate section of Chap. 5. A very attractive precursor for oxygen is molecular oxygen in itself. In this case, however, prereactions are much more pronounced as compared to e.g., N2 O growth. The prereactions can cause a white fog to occur in the reactor, containing ZnO nano particles in the gas phase. The importance of prereactions depends drastically on the geometry of the reactor. Reactors with a vertical design, including a small showerhead/substrate distance, seem to be most suited for avoiding prereactions. A suitable geometry allows using reasonable pressures and hence reasonable growth rates. Also, precautions have to be taken in order not to blow up the MOCVD reactor due to a chemical reaction of oxygen and hydrogen. Provided that a suitable MOCVD system for the use with oxygen is available, the ZnO MOCVD growth with oxygen as a precursor can give very good results. The higher effective oxygen/zinc ratio during growth obviously leads to a better

3

Growth

53

Fig. 3.17 SIMS profile of hydrogen, carbon, and oxygen for a ZnO thin film grown by MOCVD using t-Bu(OH) as an oxygen precursor, indicating a substantial hydrogen and carbon incorporation (after growth, before annealing). From [43]

two-dimensional growth. Very flat ZnO thin films have been grown on sapphire and GaN, with rms roughness values lower than 1 nm on a 2  2 m scale [42]. Finally, it should also be mentioned that hydrogen and carbon incorporation can pose a substantial problem during the MOCVD growth of ZnO grown at low temperatures. Figure 3.17 shows a SIMS profile of a structure with two ZnO layers grown on GaN/sapphire templates. The ZnO layers have been grown by using N2 O and t-BuOH, respectively. Clearly, a pronounced carbon contamination has been detected in the layers grown with t-BuOH as an oxygen precursor due to the much lower growth temperature. Obviously, the oxidation of hydrocarbon molecules is not efficient enough in this temperature regime and with this oxygen precursor. Substantial carbon incorporation can even be seen by naked eye, resulting in gray or even black “ZnO” layers. Throughout both N2 O-grown and t-BuOH-grown ZnO layers, a continuous hydrogen background can generally be detected in SIMS. The role of hydrogen in ZnO will be discussed later on in more detail (see section on doping in Chap. 5).

3.2.2 Molecular Beam Epitaxy One of the main advantages of molecular beam epitaxy (MBE) is the fact that the thin film surface can directly be analyzed during growth in situ by high energy electron diffraction (RHEED). Therefore, MBE is usually the fastest technique to explore a novel material system. Also, since active oxygen (including oxygen radicals, ions, and atoms) and Zn species are used, growth can take place far off

54

A. Waag

thermodynamic equilibrium. At low temperatures, the incorporation of, for example, dopants as well as magnetic ions can be enforced. Dealing with ultra high vacuum is one of the main technical disadvantages of the MBE technique. This is particularly true when high volume manufacturing is to take place. The problem is not the UHV itself, but the long time scales necessary to bring a system down to base pressure after maintenance openings. During maintenance, the MBE system is opened to air, and moisture and other adsorbents contaminate the inner surface of the reactor. The inner surfaces are extremely large, mostly consisting of nano-porous, amorphous semiconductor dust adsorbed at the inner walls during MBE growth. Therefore, an extensive annealing step at elevated temperatures is necessary to desorb any contaminants and get back down to reasonable base pressures being a prerequisite for a clean background environment. Water is in general the most problematic contaminant, since both oxygen and hydrogen have a detrimental effect on most semiconductors. This is particularly true for III–V semiconductors. Cooling the MBE system with liquid nitrogen is used to reduce the redesorption of contaminants, but again makes MBE more difficult and increases the operating cost. ZnO MBE is different from conventional III–V MBE in various aspects. Water is not necessarily a contaminant in the case of ZnO MBE. Water and hydrogen peroxide have even been shown to be reasonable oxygen precursors, and have been introduced into MBE systems on purpose. Desorption of water during growth is quite uncritical for the ZnO quality, but the possible incorporation of hydrogen should be kept in mind. In addition, metallic contaminants will be oxidized efficiently, as long as activated oxygen molecules or atoms are around. A metaloxide surface contamination again is uncritical, since vapor pressures are in general very low. This means that MBE of ZnO not necessarily suffers from the disadvantages in terms of high volume manufacturing, which are well known from III–V MBE, and could indeed be a serious candidate for high volume manufacturing of, e.g., ZnO-based LEDs. A sketch of a typical MBE system is shown in Fig. 3.18. An MBE system for the growth of ZnO-based materials usually uses metallic sources for Zn, Mg, Cd, etc., being evaporated from effusion cells usually equipped with PBN crucibles. Pyrolitic boron nitride (PBN) is a boron nitride ceramic, which is fabricated in a chemical vapor deposition process. This leads to an extremely clean and temperature-resistant material. Only when the evaporation temperatures are beyond 1; 000ıC, PBN starts to dissociate and other types of crucibles are to be used. The metals are available in very high purity, up to 7N. Figure 3.19 shows the vapor pressure of both Zn and Mg, evaporated from effusion cells with PBN crucibles, as a function of the cell temperature with the operating time in oxygen containing environment as parameter. While in the Zn case, no degradation of the vapor pressure as a function of operation time can be seen, the Mg flux is reduced relative to the original value during time. This behavior is obviously due to Mg oxidation during growth, even though special effusion cells were used in this case, as has been the case in Fig. 3.19.

3

Growth

55 UHV pump

CAR

Substrate heater Substrate RHEED

RHEED screen

e-gun

Quartz pipe

Zn

O

Mg

Effusion cells

RF-plasma

leak valve Valve

to primary pump

H2O2

stainless-steel vessel

Fig. 3.18 The most fundamental components of a ZnO MBE system including a UHV system, substrate manipulator, and RHEED for in-situ analysis. From [44]

new source after 4 weeks after 8 weeks

1

1 Mg beam flux (A/s)

Zn beam flux (A/s)

10

new source after 4 weeks after 8 weeks

0.1

0.1

260 280 300 320 340 360 380 400 420 440 lower zone Zn cell temperature (°C)

380 400 420 440 460 480 500 520 540 560 lower zone Mg cell temperature (°C)

Fig. 3.19 Zn and Mg beam fluxes for different consuming periods from double zone effusion cells vs. base temperatures. The tip temperature is 150ı C higher than the base temperature. Data measured with water-cooled quartz thickness monitor at the substrate position. From [44]

56

A. Waag

There exists a variety of possibilities concerning the oxygen source for MBE. Pure molecular oxygen does not work well, because the reaction rate with Zn is too small. This might be a surprise at first glance, since Zn obviously can easily be oxidized in air at higher temperatures. However, the very low oxygen pressure during MBE growth has to be kept in mind here, which can be as low as 106 mbar. Therefore, oxygen gas has to be activated to achieve higher growth rates, most often in a plasma cell. Using plasma cells in MBE has become popular in the early 1990s, where these cells have been used for nitrogen doping of ZnSe laser diodes. Therefore, the plasma cell technology has been available in many MBE laboratories, which made the “switching” from ZnSe to ZnO easy and straight forward from this point of view. Another possibility is the use of oxygen containing molecules such as water .H2 O/ or hydrogen peroxide .H2 O2 / [45, 46]. In this way, the original MBE technique is converted into a CBE growth technique (chemical beam epitaxy). However, this nomenclature is not really important, since still the pressure during growth is in the high vacuum range, below 103 mbar, leading to mean free paths of the atomic or molecular species much larger than the typical source–substrate distances. In general, chemical reactions in the gas phase can usually still be neglected. When working with liquid precursors such as water or H2 O2 , the vapor pressure above the liquid surfaces are high enough so that a direct valved feed through into the MBE chamber can be used, possibly in combination with heating the source reservoir. In the case of H2 O2 , one has to take into account the instability of this molecule. H2 O2 concentrations in the reservoir will change with time. Alternative precursors also include ozone .O3 /. When cooled down, ozone can be stored in the liquid state and used as a very efficient precursor. However, safety measures are to be taken into account, since this precursor then is explosive. Even though low cost fabrication techniques for ZnO substrates are available, most of the MBE epitaxial growth to date has been done on hetero substrates, in particular sapphire. The reason for that is that ZnO substrates have not been readily available before, are still expensive, and are not readily available in 2-in. sizes. Smaller substrate pieces are often used, but are not really well suitable for the development of a new technology. Lateral temperature gradients are higher, leading to a reduced control on growth. The temperature is a very sensitive parameter, for example, for the incorporation of dopants. Also, it is very difficult to develop the back end processing techniques like lithography, etching, and contacts, when the substrate area is too small. Sapphire substrates are readily available, relatively low cost and with reliable quality. The disadvantage, however, is the huge mismatch in lattice constant as well as thermal expansion coefficients. This in general leads to defect densities in the range of 108 –1010 cm2 . The first ZnO LED has been reported being grown by MBE on a very special substrate, Scandium Aluminum Magnesium Oxide .ScAlMgO4 ; SCAM/. SCAM is also hexagonal and has a lattice mismatch of only 0.09%, allowing for low defect densities [29, 47, 48]. However, the growth and fabrication of SCAM is difficult, mostly due to the brittleness of the material. Therefore, it is not used anymore. At present, more and more work is published on homo epitaxial growth of ZnO,

3

Growth

57

indicating that the availability of ZnO substrates as well as the insight into the necessity to reduce defect densities is increasing. See also the discussion concerning substrates at the beginning of Sect. 3.2. For the growth on sapphire, it is necessary to develop suitable buffer procedures to overcome this misfit problem. The general strategy is to first grow a buffer layer at low temperature for nucleation, (possibly using a special interface material first like GaN) then perform an annealing step for recrystallization, improving the surface quality, possibly repeat this procedure, and finally continue with the growth of ZnO at optimized temperatures. The crystallographic relationship between c-sapphire substrates and ZnO are usually assumed to be ZnO.0001/==Al2 O3 .0001/ and ZnO.10–10/==Al2 O3 .11–20/ [49, 50]. Mostly, the ZnO thin films have microcrystalline character. In high resolution X-ray diffractometry (HRXRD), both tilt and twist of these micro-crystallites can be analyzed. It is surprising that very narrow symmetrical reflections can be achieved, with full widths at half maximum FWHM below 20 arcsec. Figure 3.20 shows a mapping of a symmetric (0002) Omega-2 Theta-reflection across a 2-in. wafer with very narrow line widths and nice thickness fringes, indicating a very small tilt and a good interface between ZnO and sapphire. In contrast to that, the asymmetric reflections have a much larger width, in the range of 100s or 1000s arcsec, reflecting a pronounced twist, and hence microcrystallinity. So a very narrow symmetric reflection does not reflect a low defect density. Both values are practically uncorrelated. Similar observations have been made for other materials, like ErAs/GaSAs [52] and AlN/sapphire [53]. Such diffraction patterns can be explained by a combination of long range and short range order in the epitaxial system [18]. The sharp peak is a correlation peak, which has been attributed to dislocation networks [54, 55]. A cross-sectional TEM of a ZnO epitaxial layer grown by MBE on sapphire is shown in Fig. 3.21. The micrograph was taken with the electron beam parallel to

Fig. 3.20 HRXRD scan across a 2-in. ZnO/MgO/sapphire, with ZnO and MgO grown by MBE. XRD spots are varying from left to right on the 2-in. wafer. From [51]

58

A. Waag

Fig. 3.21 Cross section HRTEM of a ZnO thin film grown on sapphire by MBE, using a thin MgO buffer layer. From [45]

10

20

30

40 47

Fig. 3.22 Fourier-filtered image using the ZnO (1120) reflection and the (3030) for Sapphire. From [45]

the [10–10] axis. Extra planes of misfit dislocations at the interface are denoted by (T). All misfit dislocations are confined at the MgO/Sapphire interface: 40 planes of (1120) type in ZnO correspond to 47 planes of (3030) type in sapphire. Assuming a 100% release of the misfit between ZnO and sapphire, one extra plane is required for six planes, which is indeed observed. A Fourier-filtered image using the ZnO (1120) reflection and the (3030) for sapphire is shown in Fig. 3.22. Again, the Fourier-filtered image demonstrates that most of the misfit dislocations are confined at the interface region. In Fig. 3.21, a dislocation having the Burgers vector perpendicular to the basal planes is denoted by a circle in the ZnO far from the interface. Such dislocations often occur in ZnO thin films far from the interface. The growth of an optimized MgO buffer layer is very important for the growth of high quality ZnO on sapphire. A thorough analysis of the buffer layer by TEM reveals the formation of a spinel structure made of MgAl2 O4 with the following

3

Growth

59 MgO 26 nm

100 nm

Sapphire

Fig. 3.23 Morphology of a 26-nm thick MgO film deposited on sapphire at 700ı C. The BF micrograph reveals that the MgO film consists of individual grains in epitaxial relation with the substrate. A thourough analysis reveals reflections from the spinel compound MgOAl2 O3 . After [1]

a

AI2O3 <1-210>

b

MgO <110>

MgO <112>

c

ZnO <1-100>

ZnO <1-210>

d

ZnO <1-100>

ZnO <1-210>

e

ZnO <1-100>

ZnO <1-210>

AI2O3 <1-100>

Fig. 3.24 RHEED patterns depicting the surface morphology evolution during the ZnO growth stages. (a) Sapphire substrate after 20 min treatment in plasma at 700ı C. (b) 2D nucleation of MgO buffer layer at 700ı C. (c) Low temperature ZnO buffer layer growth at 300ı C. (d) Low temperature ZnO buffer layer after annealing at 700ı C for 5 min. (e) Main ZnO epitaxial layer growth at 500ı C. From [56]

relation of various directions: [1120] Al2 O3 ==Œ112MgA12 O4 ==Œ112MgO== Œ1010ZnO [1], a TEM figure of this MgO buffer is shown in Fig. 3.23. RHEED patterns during the different stages of ZnO growth are shown in Fig. 3.24. As can be seen, two-dimensional (i.e., streaky) RHEED patterns can be obtained

60

A. Waag

a

b

Ts = 475 °C, Fzn= 2.6 A/s Plsma @ 400 W

O-rich

0.84 3.2 sccm

Specular spot intensity (a. u.)

stoichiometric

2.8 sccm

2.4 sccm

2 sccm

Zn shutter open

1.6 sccm Zn shutter closed 1.2 sccm

0

20

40 60 80 Growth time (s)

100

ZnO Growth Rate A/S

0.78

0.72

Zn-rich

0.66

0.60 Fzn = 2.6 A/s Ts = 475 °C

0.54 0.7

1.4

2.1 2.8 O2flow sccm

3.5

˚ Fig. 3.25 RHEED intensity oscillations at rZn D 2:6 A=s; Ts D 475ı C; Prf D 450 W and differ˚ Ts D 475ı C; Prf D 450 W as a function ent oxygen flow (a). ZnO growth rate at rZn D 2:6 A=s; of oxygen flow (b). From [57]

even on sapphire, when suitable MgO buffer layers are used. Assuming that one RHEED period correlates with the growth of one monolayer of ZnO, the ZnO growth rate can be deduced (Fig. 3.25). As expected, the growth rate depends on Zn/Ox flux ratio. By varying e.g. the oxygen flux, the transition from Zn-rich growth to oxygen-rich growth can be identified. This is an important prerequisite to optimize ZnO MBE growth. A growth rate of 0.2 ML/s can still be reached at a temperature as high as 800ıC, indicating that the plasma sources used nowadays indeed deliver a reasonable amount of active oxygen species. Of course, these values depend on the exact situation in the growth machine (Fig. 3.26). A nearly constant growth rate is observed between 450ıC and 550ı C as shown in Fig. 3.26b. In this temperature region, the growth rate is assumed to be determined by the oxygen radicals. The kinks correspond to a change of the growth stoichiometry from O-rich (at high TS ) to Zn-rich (at low TS ), where the growth is governed by Zn and O incorporation, respectively (Fig. 3.27). From a comparison of absolute flux measurements by a piezo-monitor and the growth rates measured by RHEED, the Zn sticking coefficients can be derived. They change with temperature and Zn/Ox ratio, and reach values between 10 and 20% in the relevant temperature range between 500 and 700ı C (Fig. 3.28) [44]. The activation energies for both regions agree well with previously reported data [58]. The kink rZnO values are equal to the activated O-flux supplied by the RF plasma source. Absolute sticking coefficient values vs. TS , defined as

3

Growth

61

a Ts=700°C RHEED Specular Spot Intensity (a.u.)

Ts=600°C

b

Growth Rate (ML/S)

Ts=400°C

Growth Rate (ML/S)

0.6 Ts=500°C

0.5

0.4

0.3

Ts=200°C 0.2 0

10

20 30 40 50 Growth Time (s)

Fzn = 0.3 nm/S FO2 = 1.6 sccm Ppower = 400 W 200 300 400 500 600 700 800 Growth Temperature (°C)

60

Fig. 3.26 (a) RHEED specular spot intensity oscilllations on 00 rod on <11N 00> azimuth at rZn D ˚ 4:5 A=s; rO D 2:4 sccm; Prf D 400 W and different TS . (b) The temperature dependence of the growth rate in monolayer per second evaluated from the set of such RHEED oscillations. From [56]

a

700 600 500

400

300

Ts (°C)

200

2

Growth rate (A/s)

E AO2 = 0.033 eV

1 0.8 E Azn= 0.156 eV

0.6

0.4 1.0

1.2

1.4 1.6 1.8 1000/Ts (K–1)

2.0

2.2

˚ Fig. 3.27 ZnO growth rate as a function of the substrate temperature TS for rZn D 3 A=s; rO D 1:6 sccm, and Prf D 400 W. The horizontal shaded line shows the kink rZnO value. From [44]

˛Zn D rZnO .T/=rZnO.max/, where rZnO .max/ is recalculated from the Zn flux measured by a quartz monitor, using Zn/ZnO molar mass and density ratios, are shown in Fig. 3.28. Extrapolation of the dependence to lower TS gives ˛Zn .300ıC/  0:5, which fits reasonably well to the value determined in a ZnSe MBE (45) at this

62

A. Waag

Fig. 3.28 Absolute ˛Zn values Vs. TS , defined as ’Zn D rZnO .T/=rZnO .max/, where rZnO .max/ is recalculated from the Zn flux measured by a quartz monitor. From [44]

a

b

c

0.5mm

0.5μm

0.5mm 0 nm

10 nm

1.5 nm

15 nm

0 nm

0 nm

Fig. 3.29 AFM images of surfaces of ZnO layers grown at different temperatures: (a) 400ı C, (b) 500ı C, and (c) 700ı C. From [59]

particular temperature. This indicates that the desorption of impinging Zn atoms is mostly out of a physisorbed state. The surface morphology of ZnO layers drastically depends on O/Zn flux ratio. The flattest surface morphology of ZnO is obtained for values between 0.7 and 1.0. The growth under O-rich conditions leads to the formation of hexagonal pyramids. At higher O/Zn ratios, a 3D growth is observed, with the top layer formed by perfectly c-oriented columnar structures. However, even then the 2D growth can be recovered by switching to a Zn-rich growth condition. Better surface conditions can in general be achieved at higher growth temperatures. In the case of growth at 400ıC, AFM micrographs of the surface show islands with irregular and rough steps. A root mean square (rms) surface roughness of 5.0 nm was estimated (Fig. 3.29a). When the growth temperature was increased to 500ıC, the roughness decreased from 5.0 to 0.2 nm. A coalescence of the hexagonal islands is observed and the step edge becomes regular (Fig. 3.29b). When the growth temperature was further increased to 700ı C, the formation of hexagonal pits on an atomically flat surface with a rms roughness of 0.45 nm was observed.

3

Growth

63 2.00

[nm] 5 4 3

[μm]

2 1 0

0

2.00

[μm]

0

Fig. 3.30 AFM image (2 m  2 m) of the surface of 0.6- m thick ZnO epitaxial layer on sapphire substrate; evaluated roughness (rms) is 0.26 nm. From [56] Int. Signal

a.u.

FWHM

69.72 66.83 63.95 61.06 58.17 55.28 52.39 49.50 46.61 43.72 40.84

nm 14.3 14.2 14.1 14.1 14.0 13.9 13.8 13.8 13.7 13.6 13.5

T

Fig. 3.31 PL mapping of 2-in. ZnO layers grown on (0001) sapphire with HT-MgO buffer: (a) PL intensity mapping; (b) PL FWHM mapping. From [60]

As mentioned above, an optimized MgO buffer layer is a prerequisite to grow high quality ZnO thin films on sapphire. In Fig. 3.30, an AFM plot of a ZnO layer grown with MgO buffer is shown. Figure 3.31 shows a photoluminescence mapping of a 2-in. ZnO/MgO/sapphire quasi-substrate, indicating a good homogeneity concerning the integrated PL signal at room temperature, which could possibly be used as a quasi-substrate for a subsequent GaN growth. With the buffer procedures as a basis, ZnMgO–ZnO quantum well structures can be grown by MBE. For Mg concentrations below about 30% in the barrier, no problems due to the different lattice structures of MgO have been encountered. Figure 3.32 shows the increase of the band gap of the ZnMgO barrier layer as a function of Mg incorporation, whereas Fig. 3.33 shows the PL signature of ZnMgO–ZnO

64

A. Waag

a

b 13 K Peak Energy(eV)

3.7

x = 0.13

c

x = 0.1

c-lattice constant (A)

Intensity (arb. units)

x = 0.22

x = 0.07 0

DX ZnO

FX

x=0 3.2

3.3

3.4

3.5

3.6

3.7

3.8

3.6 3.5 3.4 3.3 5.208 5.200 5.192 5.184 5.176

3.9

0.00

Energy (eV)

0.05 0.10 0.15 Mg Content (x)

0.20

0.25

Fig. 3.32 (a) PL spectra of ZnO and Znx Mg1x O (x up to 0.22) measured at 13 K excited by the 325.0 nm line of a HeCd, (b) the band gap evaluated from PL measurements, and (c) c-lattice length constant evaluated from XRD measurements dependence on the Mg content. From [61] QW

K = 13 K

L w =1.1 nm

ZnO buffer barrier

PL Intensity [a.u]

L w =1.5 nm

L w =2.3 nm

L w =4.7 nm

3.1

3.2

3.3

3.4 Energy [eV]

3.5

3.6

3.7

Fig. 3.33 PL spectra of Zn0:85 Mg0:15 O=ZnOSQWs at 13 K with different well widths .LW / After [62]

3

Growth

65

Table 3.1 Calculated activation energy Ea from the fit to the temperature dependent intensity for SQWs in comparison with the FWHM of the SQWs PL peaks and the change of the exciton confinement energy caused by 1 ML fluctuation in well barrier. After [62] Well width (nm) 4:7 2:3 1:5 1:1 Ea .meV/ 13:6 14:7 16:9 19:4 FWHM (meV) 12 16:1 19:2 26:15 dE (1 ML) (meV) 10 17:5 21 29:5

quantum wells with varying ZnO quantum well thickness. As expected, the confinement energies increase with decreasing quantum well thickness. The broadening of the quantum well emission is due to the increasing importance of monolayer fluctuations with decreasing quantum well width (Table 3.1). For more optical spectra of alloys and quantum wells see Chaps. 4 and 6. In order to avoid the problems of ZnO hetero epitaxy on sapphire, ZnO substrates would be the preferable choice. Various publications appeared concerning the characterization of ZnO substrates [63]. Recently, 2–in. substrates became available, which obviously have a reliable quality. Before growth, an annealing procedure is necessary to desorb surface contamination and establish a high quality surface [64]. Also, surface etching is advantageous to clean the surface. Even then, a low temperature ZnO buffer layer has been reported to avoid 3D growth [64, 65]. Good growth conditions on Zn- and O-polar ZnO substrate surfaces are very different [66]. Impurities like Li can be reduced to a certain extent by annealing [65]. Annealing temperatures of 1;100ı C can produce ZnO surfaces with atomic steps [26]. Growth on ZnO substrates – if optimized – in general improves the quality of thin films and heterostructures as compared to growth on sapphire. An internal quantum efficiency of 9.6% has been reported for homo epitaxial ZnO films [67]. ZnMgO/ZnO as well as ZnO/ZnCdO quantum well structures with emission energies down to 2.5 eV could also be demonstrated [68].

3.2.3 Pulsed Laser Deposition Pulsed laser deposition (PLD) is a technique that has successfully been used for the growth of a large variety of oxides. An excimer laser pulse is guided onto a target made from the base materials, flash evaporating it and forming a plasma plume in the gas phase. In the case of ZnO, oxygen serves as a residual reactor gas. As a consequence of the plasma plume, reactive oxygen species are available. One advantage of PLD is the fact that neither hot effusion cells nor complicated metal-organic compounds need to be used. The excimer laser is outside of the vacuum and is guided into the chamber and onto the targets through a window at the reactor chamber. The reactive species formed in the plasma plume are impinging onto the substrate surface, which is heated up to a certain temperature. Like in MBE, RHEED surface analysis can be performed during growth. In contrast to MBE, however, high

66

A. Waag

energy particles occur in the plasma plume, possibly affecting the surface morphology and introducing defects. However, the substrate temperatures can substantially be lowered because of the presence of reactive oxygen, enhancing the incorporation of dopants. The PLD targets are made by sintering the compounds that are to be grown by PLD later, in this case ZnO, from ZnO powder. The target not necessarily evaporates stoichiometrically, and even if so, a stoichiometric growth condition is not guaranteed due to the different sticking and incorporation coefficients of both cations and anions. Therefore, an oxygen background pressure is usually used in the PLD of oxides to control the II/VI ratio during growth. The background pressures are small enough to still allow electron diffraction during growth. When the flash evaporation is nonstoichiometric, the composition of the target will change with growth time, making the control of composition in ternary compounds difficult. Another problem of PLD is in general thought to be the limitation to small area growth. However, large area PLD with good homogeneity should be possible by further improving the growth apparatus. In the case of ZnO, 2-in. PLD ZnO layers on sapphire substrates have already been demonstrated [69]. In this case, a thorough optimization of the target–substrate distance and geometry has been performed. Recently, ZnMgO– ZnO quantum well structures of good quality could also be demonstrated by PLD [70]. Also, the incorporation of dopants has been demonstrated, and even material indicating p-type character could be fabricated [71]. A recent overview on ZnO PLD can be found in [30] and references therein.

3.3 Growth of Self-Organized Nanostructures One of the very interesting but at the same time problematic features of ZnO growth is the occurrence of a pronounced trend towards self-organization. Since the surface properties of ZnO are very different for the different crystal orientations, chemical reactivity and growth rate vary drastically as a function of surface orientation. In combination with a large surface diffusion of Zn, this often leads to the formation of ZnO crystallites on the micro- or nano-scale. Under certain circumstances, ZnO nano pillars are formed, with very large aspect ratios. These structures are then called nano pillars, nano spirals, nano springs, etc., depending on their particular shape. High resolution scanning electron microscope images show beautiful ZnO structures at the nano scale. However, it should be mentioned that these pictures of single, isolated nanostructures often hide the fact that only a very limited control over the growth of these nanostructures is achieved, with a drastic inhomogeneity across the growth area. This is particularly true for simple physical vapour deposition systems, where the temperature varies with position in the reactor. After growth, one has to do a screening of the inhomogeneous substrate to search for nanostructures of the desired shape. If such self-organized nanostructures are to be used in some kind of technological process, however, control on relevant properties

3

Growth

67

needs to established, including size, composition, band gap engineering inside the nanostructures, doping, position, etc.

3.3.1 Growth Techniques for Nano Pillars ZnO has a strong tendency for self-organized growth. For the fabrication of ZnO nano pillars, there exists a large variety of different growth techniques. Originally, a vapour–liquid–solid approach (VLS) has been used [72] in a physical vapor transport growth reactor. Here, the Zn and oxygen vapor is guided over a substrate surface, which is covered with gold nano particles. At temperatures below the melting point of gold, Zn diffuses into the gold nano particles and reduces the melting temperature of the eutectic. It is supposed that in the liquid phase, oxygen and zinc diffuse to the semiconductor surface, where growth is initiated. This resembles a liquid phase epitaxy, where the liquid phase is localized due to the limited size of the gold nano particle. In this way, it should be possible to control the size and position of the ZnO nano pillars, since this is given by the size and position of the original gold nano particle. For example see [73, 74]. Gold has been shown to be kept on top of the nano rod during growth, but on the other side, often enough the original gold nano particle cannot be identified any more after growth. Also, some of the gold has been found to remain at the interface [75]. The growth mechanism seems to be more complicated than the simple model mentioned above. In the early work [72], a mixture of carbon and ZnO powder is used, which under hydrogen flow and at elevated temperatures decomposes into water, carbon oxides, and zinc vapor. It is this mixture in the gas phase, which has been used as a source for zinc and oxygen. A similar self-organized growth is also possible, when elemental Zn and oxygen gas are used [76]. However, the control on composition and doping, as well as the incorporation of ZnMgO/ZnO heterostructures is difficult, when this type of straight forward growth technique is used. For a few examples on the incorporation of radial or longitudinal quantum structures into nanorods and for doping, see below and [73, 77–80]. ZnO nanorods have also been fabricated by MOCVD [81], in this case with pure oxygen as a precursor. As a consequence, the reactor pressure has to be kept low to prevent gas phase reactions, for example, an oxidation of the metal-organic precursors. Yi et al. have demonstrated the growth of high quality ZnMgO–ZnO quantum well structures, embedded into ZnO nano pillars by MOCVD [82]. The typical growth temperatures were between 400 and 500ıC (Fig. 3.34).

3.3.2 Properties of Nanopillars The strong interest in these nano pillar systems stems from the fact that the structural quality of this material usually is very good. This is due to the small footprint

68

A. Waag

a

Ec

Ev

b

ZnO Lw ZnMgO

MQWs

ZnO

AI2O3(00.1)

Fig. 3.34 Multiple quantum wells embedded into ZnO nanorods, consisting of 10 ZnMgO.x D 0:2/=ZnO supperlattice periods. FE-SEM images of the MQW nanorods are shown on the right side. From [82]

on the substrate, in combination with a high aspect ratio. Defects such as dislocations, introduced at the substrate/ZnO interface can propagate toward the nano pillar sidewalls and disappear. This does not mean that all nano pillars are always defect free, but at optimized growth conditions and aspect ratios completely defect free regions can regularly be identified by TEM. The defect densities of ZnO thin films, which are grown on hetero substrates or even ZnO substrates, are much higher (in the 1010 cm2 range). Due to the influence of defects on the residual carrier concentrations in ZnO, and in view of the p-type doping problem, ZnO nano pillars are supposed to be interesting candidates to study p-type doping. The introduction of p-type and n-type doping as well as quantum wells into nano pillars (see above) could be very interesting for the development of novel devices for solid state lighting. The defect free nature of nano pillars in combination with an additional freedom in lateral strain engineering could lead to high efficiency light emitters in the UV spectral region, being the basis for white LEDs. Such concepts have first been developed in the ZnO field, but due to a lack of a reliable p-type doping technique, efficient LEDs could not be realized. These ideas, however, have now been transferred to the GaN world, and it has already been demonstrated that highly efficient GaN LEDs can be fabricated using this nano LED approach. Other interesting aspects are the optical wave guiding along the nano pillar axis, as well as an additional control on the electromagnetic modes by using the photonic crystal properties of the nano pillar arrangement. All these interesting aspects, however, have not yet been exploited in commercial devices for solid state lighting. In order to take advantage of the interesting properties of nano pillars, the aspect ratios need to be much larger than one, mostly in the range of 5–10 or even above. Since a conventional LED structure has a thickness of a few micrometers, the diameters of these nano pillars are expected to be in the 100 nm range. Having these

3

Growth

69

Fig. 3.35 Single ZnO nanopillars with e-beam lithographically patterned contacts, including the IV-characteristics between contacts a and e. After [83]

dimensions in mind, it is necessary to explore the influence of the nano pillar sidewall surface on the electrical and optical properties. In contrast to other materials, ZnO-based nano pillars have the advantage that surface oxidation is obviously not relevant, since we already deal with an oxide. This, however, does not mean that surface effects are irrelevant per se. Metal oxides in general and ZnO in particular have been shown to have a rich surface chemistry, and are hence often used in gas sensors. One of these reactions is the formation of hydroxile bonds (–OH) with water molecules in the gas phase. The response of ZnO nano pillars to different gas species in the environment resembles the behavior of polycrystalline thin films, like the ones being used in sensors. In nano pillars, however, one eventually has a better control on the surface-to-volume ratio relevant for sensor sensitivity. For more examples, data and references on these application oriented aspects see Chap. 13. The analysis of the electrical properties of single, isolated nanorods is not easy. For that, the nano pillars, well aligned in c-axis orientation, can be detached from their substrate and brought into suspension. This suspension is then brought onto an electrically isolating substrate (e.g., SiO2 =Si) by a spin-on process. Depending on concentration in the suspension, this leads to a more or less dense distribution of ZnO nano pillars across the wafer. In order to fabricate contacts on single nano pillars, the position of these pillars first has to be identified by high resolution scanning electron microscopy. In the next step, the patterning of electrical contacts and interconnects has to be realized by electron beam lithography, with a subsequent metallization and lift-off. After bonding of gold wires, the electrical characteristics of single nano pillars can finally be analysed. See Fig. 3.35 or for another example [84]. An alternative way to analyse the electrical properties of nano pillars is to contact the nano pillars directly by sharp nano needles. For that, a piezo-manipulation system with nanometer precision in combination with a microscopy tool has to be used to observe both contact needle and nano pillar at the same time. One elegant way to do that is using a BEEM system (ballistic electron emission microscopy, [85]). Here, the electron beam from a field emission tip as a point source is accelerated towards a screen, with the nano pillar on a semitransparent grid lying in between

70

A. Waag

Fig. 3.36 Scheme of the experimental setup. Electrons emitted from a field emission tip T scatter at a nano wire Z and generate a magnified projection image on a screen S. A manipulation tip M is used to contact the nano wire and to determine its conductivity. After [85]

emitter and screen. In this way, a shadow picture of both the nano pillar as well as the contact needle can be seen. The approaching needle can be controlled precisely. One contact is the needle; the other one is the point where the nano pillar touches the metallic grid. By moving the needle along the nano pillar, it has been possible to analyse 2-point resistance as a function of distance between both contacts, and in this way separate contact resistance from nano pillar resistance (Fig. 3.36). The resistance of the nano pillars obviously is expected to scale with diameter. Comparing the behavior of resistance vs. diameter with the expected theoretical behavior, a systematic deviation has been seen. At diameters below 100 nm, the resistance of the nano pillars is larger than expected, with differences exceeding one order of magnitude (Fig. 3.37). A core-shell model of the nano pillar conductivity can explain these observations. In this model, the outer regions of the nano pillar are expected to have a drastically reduced conductivity, caused by a Fermi level pinning at the surface of the nano rod. The necessary charges are then screened, leading to a depletion region from the surface toward the center of the nano pillar, similar to the situation in a p–n-diode or a metal-insulator transition. This depletion region then does not contribute to carrier conduction [83, 97]. The extension of the depletion region depends on doping level as well as built-in potential barrier. At high carrier concentrations, often measured in ZnO nanorods grown by a wet chemical approach, such a deviation of resistance has not yet been seen. As stated earlier, the resistance of ZnO nano pillars depends on moisture and other chemical residues in the gas phase. This can not only be measured using single nano pillars, but also ensembles of nano pillars. In order to make contact to an ensemble of nano pillars, a top metal contact has to be fabricated. One way to do that is to embed the nano pillar ensemble into an organic matrix (e.g., photo resist), with a subsequent metallization step. This approach has the disadvantage that the nano pillars are no longer open to the gas phase. Without organic matrix, however, there

3

Growth

71 10 experimental data 1/d2 fit

RL (MΩ/nm)

1 0.1 0.01 1E-3 1E-4

0

200

400 600 800 1000 1200 Wire diameter (nm)

Fig. 3.37 Plot of the wire resistance per unit length RL vs. the wire diameter for vapor phase grown ZnO nanowires, comparing experimental results with the expected scaling due to a reduced diameter. A clear deviation can be seen. After [85] 10 6

VPT grown Ref. [10-25]

Resistivity(Ωcm)

10 4 10 2 10 0 10 –2 10 –4

0

100

200 300 Diameter (nm)

400

500

Fig. 3.38 Resistivity values of single ZnO nanowires over their diameter. Data from measurements of VPT grown samples (stars). For literature references see [83], after [83]

is the risk of sidewall metallization, and hence of electrical shorts across the nano pillars. If the nano pillar density is high enough, however, the sidewall metallization can be avoided by metalizing under a shallow angle. In this case, only the top of the nano pillars will be metalized, since the shadowing effect of the neighbored nano pillars is avoiding side wall metallization. Such devices have been tested and show, for example, a certain sensibility on the humidity in air [86]. Similar experiments have been performed on single nano pillars [87]. In this case, however, the device fabrication technique is very complicated, as described earlier, which is a substantial disadvantage if this technique is considered for high volume production.

72

A. Waag d ~ 700 nm TES

PL Intensity [a.u.]

increasing power

3.20 3.25

D°X SX 3.30 3.35 3.40 Energy [eV]

d ~ 200 nm

M

PL Intensity [a.u.]

M

D°X

n=1

FXA

IX

decreasing power

SX 3.15

3.20

3.25 3.30 Energy [eV]

3.35

3.40

Fig. 3.39 SX line from excitons bound at surface related levels. Inset: PL spectra of another nanopillar sample with thicker rods obtained at 13 K under different excitation powers. After [92] NBE

PL Intensity [a.u]

ZnO nanorods/6H-SiC

IX 1LO-IX 3.2

3.1

inc

re

as

ing

te

m

pe

ra

tu

re

3.1

3.2

3.3

3.4

Energy [eV]

Fig. 3.40 PL spectra at various temperatures of ZnO nanorods grown on 6H-SiC. The spectra are plotted over each other for clarification. After [93]

It is this sensitivity on chemical surface passivation, which is supposed to be the reason for the pronounced scattering of transport data of ZnO nano pillars [83]. Figure 3.38 shows a comparison of literature data. No correlation of conductivity and growth technique used could be established. Surface states do not only influence the conductivity, but also the photoluminescence response of ZnO nano pillars. For long ZnO nano pillars, very narrow photoluminescence lines occur, which again indicates that the influence of strain is very much reduced in nano pillars as compared to thin films grown on heterosubstrates. Strain would shift the band gap and contribute to an inhomogeneous broadening of all photoluminescence lines. Also, an extra photoluminescence line

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73

appears in thin nano pillars, often indicated as SX in the literature [88–91]. This line is supposed to be correlated to surface related recombination. It is located at higher energies as compared to the mostly dominant D0 X transitions, and it is particularly pronounced in thin nano pillars, and less pronounced or not visible in nano pillars with larger diameters (Fig. 3.39). The room temperature photoluminescence spectra of ZnO nano pillars often exhibit an energy shift of about 80 meV to lower energy in comparison with that of bulk ZnO as well as ZnO epilayers. The emission band observed at 3.31 eV (IX in Fig. 3.40 at low temperature) dominates the photoluminescence at room temperature. High internal quantum efficiencies of about 33% have been obtained, and have been attributed either to excitons bound to surface defect states or to [e,A] transitions [93], see also Chap. 6. Overall, all these experiments indicate that there is a substantial influence of the sidewall surfaces on the electrical and optical properties of ZnO nano pillars. This has to be kept in mind when applications of these structures are discussed. For more data on the luminescence of nanorods see Chaps. 6 and 12. For more information see also e.g. [94, 95].

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26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56.

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57. A. Elshaer, Dissertation, TU Braunschweig (2008) 58. A. Ohtomo, R. Shirokil, I. Ohkubo, H. Koinuma, M. Kawasaki, Appl. Phys. Lett. 75, 4088 (1999) 59. A. Elshaer, A. Che Mofor, A. Bakin, M. Kreye, A. Waag, Superlattices Microstruct 38, 265 (2005) 60. A. Bakin, A. Elshaer, A. Che Mofor, M. Kreye, A. Waag, F. Bertram, J. Christen, M. Heuken, J. Stoimenos, J. Cryst. Growth 287, 7 (2006) 61. A. Elshaer, A. Bakin, M. Al-Suleiman, S. Ivanov, A. Che Mofor, A. Waag, Superlattices Microstruct 42, 129 (2007) 62. M. Al-Suleiman, A. El-Shaer, A. Bakin, H.-H. Wehmann, A. Waag, Appl. Phys. Lett., 91, 081911 (2007) 63. H. Wenisch, V. Kirchner, S.K. Hong, Y.F. Chen, H.J. Ko, T. Yao, J. Cryst. Growth, 227, 944 (2001) 64. M.W. Cho, C. Harada, H. Suzuki, T. Minegishia, T. Yao, H. Ko, K. Maeda, I. Nikura, Superlattices Microstruct 38, 349 (2005) 65. C. Neumann, S. Lautenschl¨ager, S. Graubner, J. Sann, N. Volbers, B.K. Meyer, J. Bl¨asing, A. Krost, F. Bertram, J. Christen, Physica Status Solidi (b) 244, 1451 (2007) 66. K. Huaizhe Xu, M. Ohtani, X. Yamao, H. Ohno, Appl. Phys. Lett. 89, 071918 (2006) 67. D. Takamizu, Y. Nishimoto, S. Akasaka, H. Yuji, K. Tamura, K. Nakahara, T. Onuma, T. Tanabe, H. Takasu, M. Kawasaki, S.F. Chichibu, J. Appl. Phys. 103, 063502 (2008) 68. S. Sadofev, P. Sch¨afer, Y.-H. Fan, S. Blumstengel, F. Henneberger, D. Schulz, D. Klimm, Appl. Phys. Lett. 91(29), 201923 (2007) 69. D.J. Rogers, D.C. Look, F. Hosseini T´eh´erani, K. Minder, M. Razeghi, A. Largeteau, G. Demazeau, Physica Status Solidi (c) 5, 3084 (2008) 70. S. Heitsch, G. Zimmermann, J. Lenzner, H. Hochmuth, G. Benndorf, M. Lorenz, M. Grundmann, AIP Conference Proceedings, Physics of Semiconductors, vol. 893–1, 2007, p. 409 71. B.Q. Cao, M. Lorenz, A. Rahm, H. von Wenckstern, C. Czekalla, J. Lenzner, G. Benndorf, M. Grundmann, Nanotechnology 18, 455707 (2007) 72. M.H. Huang, Y. Wu, H. Feick, N. Tran, E. Weber, P. Yang, Adv. Mater. 13, 113 (2001) 73. H. Zhou et al., Appl. Phys. Lett. 92, 132112 (2008) 74. H. Zhou et al., J. Korean Phys. Soc. 53, 2893 (2008) 75. R. Hauschild et al., Phys. Stat. Sol. (b) 243, 853 (2006) 76. A. Che Mofor, A. Bakin, A. Elshaer, D. Fuhrmann, F. Bertram, A. Hangleiter, J. Christen, A. Waag, Phys. Stat. Sol. (c) 3, 1046 (2006) 77. Chinkyo Kim, Won Il Park, Gyu-Chul Yi, Miyoung Kim, Appl. Phys. Lett. 89, 113106 (2006) 78. C. Czekalla, J. Guinard, C. Hanisch, B.Q. Cao, E.M. Kaidashev, N. Boukos, A. Travlos, J. Renard, B. Gayral, D. Le Si Dang, M. Lorenz, M. Grundmann, Nanotechnology 19, 115202 (2008) 79. Cao et al., Nanotechnology 20, 305701 (2009) 80. A. Bakin, A. Elshaer, A. Che Mofor, M. Al-Suleiman, E. Schlenker, A. Waag, Physica Status Solidi (c) 4, 158 (2007) 81. W.I. Park, D.H. Kim, S.-W. Jung, Gyu-Chul Yia, Appl. Phys. Lett. 80, 4232 (2002) 82. Won Il Park, Gyu-Chul Yi, Miyoung Kim, Stephen J. Pennycook, Adv. Mater. 15, 526 (2003) 83. E. Schlenker, A. Bakin, T. Weimann, P. Hinze, D.H. Weber, A. G¨olzh¨auser, H.-H. Wehmann, A. Waag, Nanotechnology 19, 365707 (2008) 84. D. Weissenberger et al., Appl. Phys. Lett. 94, 042107 (2009) 85. D.H. Weber, A. Beyer, B. V¨olkel, A. G¨olzh¨auser, E. Schlenker, A. Bakin, A. Waag, Appl. Phys. Lett. 91, 253126 (2007) 86. Jae Young Park, Dong Eon Song, Sang Sub Kim, Nanotechnology 19, 105503 (2008) 87. B.S. Kang, F. Ren, Y.W. Heo, L.C. Tien, D.P. Norton, S.J. Pearton, Appl. Phys. Lett. 86, 112105 (2005) 88. L. Wischmeier, T. Voss, I. R¨uckmann, J. Gutowski, Nanotechnology, 19, 135705 (2008) 89. J.-P. Richters, T. Voss, D.S. Kim, R. Scholz, M. Zacharias, Nanotechnology, 19, 305202 (2008)

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Chapter 4

Band Structure B.K. Meyer

Abstract This chapter deals with the ordering of the valence bands – a topic that has controversially been discussed for more than 40 years. The 7 , 9 , 7 ordering is discussed in the light of very recent ab initio band structure calculations, and the important role is emphasized, which the Zn 3d-band position plays to the sign of the spin–orbit splitting. This topic is touched again from a different point of view in Chap. 6 on free excitons. Then we summarize the experimental findings on the cationic and anionic substitutions in ZnO and random alloy formation essential for quantum hetero-structures. The chapter closes with the data on the valence and conduction band discontinuities in iso- and hetero-valent hetero-structures.

4.1 The Ordering of the Bands at the Valence Band Maximum in ZnO The ordering of the crystal-field (CF) and spin–orbit coupling ( so ) split levels of the p-type states at the valence-band maximum (VBM) in wurtzite (WZ) ZnO has been and still is a subject of controversy (see [1–18]). It has been under discussion for more than 45 years, and experimental studies have provided pros and cons without being fully accepted by the respective opponents. Additional input is now given by recent theoretical works, which provide strong evidence for a negative spin–orbit coupling within the p-states of the valence band. Why is that essential? The lowest conduction-band edge of ZnO is mainly s-like, whereas the states at the VBM are p-like located at the  point of the first Brillouin zone (BZ). At the VBM, spin–orbit coupling ( so / splits the atomic p level into two states, j D 3=2 fourfold and j D 1=2 doubly degenerate, respectively (see Fig. 4.1). In the absence of a CF splitting, i.e. in zinc-blende (ZB) ZnO the question whether the so is positive or negative can be answered straightforwardly by experiment. For a negative

B.K. Meyer Physikalisches Institut, der Justus Liebig Universit¨at Giessen, Giessen, Germany e-mail: [email protected]

77

78

B.K. Meyer

Fig. 4.1 Energy level diagram (schematic) of the valence band splitting under the action of crystalfield only, crystal-field and spin–orbit and spin–orbit interaction alone (from left to right, after [16])

so as shown in Fig. 4.1, the j D 1=2 state (twofold degenerate) is above j D 3=2 (fourfold degenerate) whereas the ordering is reversed for positive so . Uniaxial stress measurements would easily distinguish between j D 1=2 and j D 3=2, in the latter case a heavy hole light hole splitting would be observable as found in other II–VI ZB semiconductors such as ZnSe or ZnTe. Unfortunately, the cubic modification of ZnO is not stabilized by volume crystal growth techniques and evidence for ZB ZnO in thin film growth stabilized by cubic substrates is not convincing in the absence of detailed optical investigations (polarized reflectivity, etc.) [19, 20]. The complications in WZ ZnO arise from the simultaneous interaction of the WZ crystal-field and the spin–orbit interaction, where the j D 3=2 level is further split by the hexagonal CF into two doubly degenerate states. Neglecting spin–orbit coupling on the p-states at the VBM, the CF will split a threefold-degenerate p level into a nondegenerate state and a doubly degenerate one (group notation: 1 and 5 ). In the double group notation (including spin), the 1 state is denoted as 7 and so splits the nonrelativistic state 5 into 7 and 9 (for a detailed description see [6]). A schematic energy-level diagram of the band splitting under the action of CF and spin–orbit interactions in WZ crystal with a negative so is shown in Fig. 4.1. It presents the splitting induced only by the CF, the splitting induced only by the spin–orbit interaction and the combined case is shown in the middle. The three states arising are labeled from top to bottom A, B and C, the respective energy gaps are Eg .A/, Eg .B/, and Eg .C/. They enter in the calculations of the binding energies of A, B, and C excitons, respectively. From studies of the polarization dependence of reflectivity spectra, Thomas [1] and Hopfield [2] concluded that the energetic ordering at the VBM should be 7 , 9 , 7 . On the basis of absorption and reflection spectra, Park [3, 5, 6] claimed the 9 , 7 , 7 ordering, 9 being the state with the highest energy, though misinterpreting the dip between the A and B5 excitonic reflection features as a reabsorption dip caused by bound exciton complexes. See also Chap. 6. Reynolds also arrived more recently, from polarized reflectance and magnetophotoluminescence measurements, at the conclusion that the ordering should be 9 ,

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79

Fig. 4.2 Splitting between the A and B and B and C valence band states as a function of the Zn 3d-band position, the dashed lines give the experimental values (after [13])

7 , 7 [8]. This claim was supported by recent studies of Chichibu [9], Gil [14, 15], and Adachi [10]. Experimentson the magneto-optical properties of bound excitons [11, 12] in contrast provide evidence of 7 symmetry of the upper valence band. Moreover, the 9 , 7 , 7 assignments are questioned in the theoretical works by Lambrecht [13], and Laskowski et al. [16] based on the density functional theory (DFT), and it is argued that the original sequence proposed by Thomas [1] and Hopfield [2] is correct. The sequence 7 , 9 , 7 was attributed to a spin–orbit splitting parameter, which is negative as a result of hybridization with the Zn d states (see Fig. 4.2 and the discussion at the beginning of Chap. 6). Lambrecht et al. [13] claimed that the ordering proposed by Thomas [1] can be understood in terms of an effective negative spin–orbit splitting. The possibility of a negative spin–orbit splitting was first suggested by Cardona in a study of copper and silver halides [21]. The origin is the presence of lower-lying d bands. The VBM is an anti-bonding combination of anion p-likes state and cation d-like states, which results in a negative contribution of the atomic d orbitals to the effective spin–orbit splitting. Thus, one expects the possibility of a negative spin–orbit parameter if the d bands lie fairly close to the VBM and have a strong atomic spin–orbit parameter. The situation is very different in ZnO, because the 3d-bands here lie about 7 eV below the VBM (according to photoemission data [22]). In the following, we go along the arguments of Lambrecht [13] based on first principles linear muffin-tin orbital density functional band structure calculations. They derive an ordering 7 , 9 , 7 . They further conclude that the participation of Zn-3d bands results in a negative so , and the result is robust even when effects beyond the local density approximation on the Zn 3d-bands are included. The sign of the spin–orbit splitting was determined in two ways: First, for the case of ZB ZnO, where the VBM splits into a fourfold state of symmetry 8 and twofold state of symmetry 7 . From the degeneracy of the eigenvalues, Lambrecht [13] obtained that the 7 state lies above the 8 , indicating a negative spin–orbit parameter. Second, inspection of the wave

80

B.K. Meyer

80

Δi (meV)

60

Δ1 Δc

40 20 0

Δ3 Δ2

–20 –40 – 7.5

Δso – 7.0 – 6.5 – 6.0 – 5.5 Zn 3d band position (eV)

– 5.0

Fig. 4.3 Crystal-field ( 1 D cf / and spin–orbit splittings so as a function of the 3d-band position. 2 and 3 refer to the anisotropic spin–orbit parameters (for details see [13]). The dashed vertical line marks the position of the Zn 3d-band at 6:25 eV (after [13])

functions in the WZ case revealed that the highest valence band contains pz and s components, indicating 7 symmetry, while the second state had pure px; py (and some d admixture) but absolutely zero pz or s components, i.e., a negative spin– orbit splitting is obtained. One essential point is as mentioned already just above the energetic position of the Zn 3d-states, which according to photoemission studies is about 7 eV below the valence band maximum. Figure 4.2 shows the experimental A–B and B–C valence band splitting by the dashed lines. Good agreement with the experimentally deduced EA –EB and EB –Ec splitting is found for a d-band position of 6:25 eV. Lambrecht [13] furthermore calculated the dependence of the CF and spin–orbit energies as a function of the Zn 3d-band position (see Fig. 4.3). At 6:25 eV, the spin–orbit splitting at this d-band position is negative, and the overall dependence on the d-band position is linear. Around 6.9 eV the spin–orbit splitting passes through zero. However, for d-band positions where the spin–orbit splitting becomes positive, the CF splitting is strongly underestimated. Laskowski [16] presented ab initio calculations of the band-edge optical absorption in ZnO, and included the effects of the electron–hole correlations (i.e., excitonic effects) as accounted for by solving the Bethe–Salpeter equation. The band structure was determined in the framework of DFT, however, with a band gap, which has been corrected by means of a scissors operator. Three excitons indexed as A, B, and C have been identified. They could show that due to too high-lying Zn 3d states, standard DFT–GGA calculations result in spectra with the wrong A–B splitting and the C exciton located in the conduction band instead in the band gap region. These problems were solved by applying the LDACU scheme (for details see [16]). The LDACU calculations not only improved the calculated optical response but also resulted in a correct energy position of the Zn 3d peak. The calculated binding energies of the A, B, and C excitons (the C-exciton now being located in the band gap)

4

Band Structure

81

Table 4.1 The exciton transition energies into the n D 1, 2 and 3 states and the calculated series limit A nD1 nD2 nD3 n!1 3:3768 3:4227 3:4309 3.4371 (calculated) [23] 3:3768 3:4231 [9, 24] 3:3773 3:4221 3:4303 [6] 3:3768 3:4225 [1] B

C

nD1 3:3834 3:3830 .3:3895/ 3:3830

nD2 3:4276 3:4290 .3:4325/ 3:4275

nD3 3:4359

n!1 3.4425 (calculated)

nD1 3:4223 3:4214 3:4225

nD2 3:4664 3:4679 3:465

nD3 3:4747

n!1 3.4813 (calculated)

[23] [9, 24] [6] [1] [23] [9, 24] [6]

are almost identical and range from 67 to 68 meV. Laskowski [16] further calculated the polarisation properties of the A, B, and C excitons and derived the conclusion that the A exciton derives from the 7 valence band. The energy positions of the A, B, and C excitons have been determined with high precision by various authors [1, 6, 9, 23, 24] using reflection (transmission) or luminescence experiments (see Table 4.1 and some figures in Chap. 6). The data of Reynolds [6] on the B-exciton series are shown in brackets, since they are significantly different from the values of the other authors. See the comment above. From the energetic distance of n D 2 and n D 3 transitions to the series limit (n!1/, one can deduce the effective Rydberg Ryeff of the excitons. According to H¨ummer [23], polaron coupling effects should be less significant in the n D 2 and n D 3 states than for the n D 1 state (see later). Using E D 1=4 Ryeff – 1=9 Ryeff one obtains for the exciton binding energies Eex .A/ D 59 meV, Eex .B/ D 59:7 meV, and Eex .C/ D 59:7 meV, thus, within experimental error all three excitons have identical binding energy. In Lambrecht [13], the contributions to the binding energies of the A, B, and C excitons in the n D 1 and n D 2 states were calculated taking into account the anisotropy (masses, dielectric constants), inter sub-band coupling and polaron corrections. Anisotropy and inter sub-band coupling give small contributions compared with the effective Rydberg (see Table III in [13]) and the polaron correction. A major contribution to Ryeff of approximately 50 meV or 22% comes from the polaron coupling, and that implies that the exciton binding energies cannot be directly obtained from the experimental separation of the n D 1 and n D 2 states by the relation 4/3 of E12 . The treatment of the polaron effect on the binding energy was considered as a fairly rough estimate; nevertheless, more sophisticated polaron models will not change the order of the A, B, and C exciton ground state properties. Since the binding energy differences for the three excitons are small compared with

82

B.K. Meyer

Fig. 4.4 Photoluminescence spectra taken at T D 2 K in the energy range around the free A-exciton transition for different ZnO bulk crystals (after [25])

the valence band splittings, it is concluded that the lowest valence band exciton (A) is primarily derived from the state of the valence band maximum, a 7 state [13]. In 1999, Reynolds et al. [18] reported on the valence band ordering in bulk ZnO grown by seeded vapor transport. They determined the A–B valence band splitting of 9.5 meV, a value that is unusual compared with the splitting found in other bulk crystals. This is exemplified in the luminescence experiments shown in Fig. 4.4. It shows the bound exciton recombination lines I1 and I0 together with the longitudinal and transversal A-exciton transitions AT and AL from ZnO bulk crystals from different vendors and grown by different growth techniques [25]. For more spectra see Fig. 6.14 or 12.2a. One notes that the line positions are not constant but differ significantly; however, a polarity dependence Zn-face vs. O-face is not detectable. The results on the A–B and A–C splitting along with the longitudinal transversal splitting of the A and B excitons (see Table 4.2) demonstrate that obviously residual strain must be present, which influences the valence band splitting. However, the A–B splitting only ranges between 5.6 and 6.5 meV, and a value as high as 9.5 meV as found by Reynolds et al. [18] deserves further explanation (see also Chap. 6).

4

Band Structure

83

Table 4.2 Energy splitting between various longitudinal (L) and transversal (T) free exciton states for different ZnO volume crystals (after [25]) Splitting UW3 UW3 TD TD Crystek Cermet Cermet in meV Zn-face O-face Zn-face O-face O-face 1,496 1,468

A(LT) 1:800 1:840 2:070 1:960 1:850 1:960 2:030

B(LT) 9:750 8:360 10:200 9:370

(A(L)B(L)) 12:320 13:570 14:180 12:330 12:270 13:940 13:010

(A(T)B(T)) 6:500 5:930 5:700 5:670

(A(T)C(T)) 46:920 46:600 47:470 47:320 47:350 47:320 47:640

The question, therefore, arises whether as much strain will influence the A–B splitting. It can be answered for hetero-epitaxially grown ZnO films on c-plane sapphire. Gruber et al. determined the dependence of the A- and B-exciton transition energies as a function of biaxial tensile and compressive strain. While the line positions are clearly strain dependent (the contribution from the deformation potentials), the influence on the CF and spin–orbit energies is small. Figure 4.6 in [26] also clearly demonstrates that the A–B splitting is within experimental accuracy constant for strains from 4  103 to C4  103 and equals the value found in bulk crystals of 5–6 meV. A recent theoretical work [17] motivated by the fact that the valence band ordering is still under discussion has looked into the role of strain on the valence band structure and the possibility whether strain can change the valence band ordering. Schleife [17] computed the band structure and exciton parameters for biaxially strained ZnO in the WZ structure (for details of the calculation method see [17]). To account for biaxial strain, the a-lattice constant was fixed at several values, whereas the c-lattice constant and the internal cell parameters u were allowed to relax. The ˚ biaxial strain was defined as "b D "xx D "yy D .a  a0 /=a0 with a0 D 3:283A as the theoretical lattice constant for the unstrained case. The resulting strain in the c-axis direction is given by "zz D Rb "b with Rb D 2C13 =C33 . For the experimental values of C13 of 104.6 GPa and C33 D 210:6 GPa, one finds to a good estimate "zz D "b . The bands at the  point without and with spin–orbit interaction as a function of the biaxial strain are shown in Fig. 4.5. See also Chap. 2. The uppermost state possesses 7 symmetry resulting in a level ordering 7 , 9; 7 , at least for not too large tensile biaxial strains (see Fig. 4.5). The spin–orbit induced splitting between the 7 – and 9 – states is in first order not influenced by the biaxial strain or stress that is the energy distance between A and B remains almost uninfluenced. Figure 4.5 also shows that the strain values used in the calculation are an order of magnitude larger than that found in the hetero-epitaxial growth of ZnO on c-plane sapphire, and a reversal of ordering most likely does not occur. The computed exciton binding energies were in excellent agreement with the experimental values of about 60 meV [23]. The binding energies for the A, B, and C excitons are rather similar (59.3, 60.1, and 63.4 meV, respectively).

B.K. Meyer

Quasiparticle energy ε (eV)

84 3.24 3.22 with SOC 3.20 Γ7c

without SOC

Γ1c Γ1v

0.05 0.00

Γ7+v Γ9v

Γ5v

–0.05 –0.10 –0.15

Γ7-v –0.02

–0.01

0.00 0.01 Biaxial strain Œb

0.02

Fig. 4.5 Conduction and valence band states at the  point in ZnO without (dotted lines) and with spin–orbit interaction (solid lines) as a function of biaxial strain (after [17])

The topic of the VB ordering will be discussed again as mentioned earlier under slightly different aspects at the beginning of Chap. 6 as a basis for more detailed investigations of the optical properties of free A, B, and C excitons.

4.2 ZnO and Its Alloys For modern optoelectronic (light emitting diodes and lasers) and electronic (field effect transistors) devices, it is essential to realize quantum structures to confine charge carriers and photons. Concepts such as modulation doping to separate carriers from the scattering centers require band gap tuning that is the quantum well should be placed between barriers resulting from a material with higher band gap energy. In type I quantum structures, electron and holes have to be confined simultaneously in the same material, which requires corresponding conduction and valence band discontinuities between the barrier material and in most cases the binary quantum well material. For ZnO-based quantum structures, the band gap tuning is a critical issue. For many systems the band gap tuning and engineering is possible while maintaining the same crystallographic structure, e.g. zinc-blende as for AlGaAs/GaAs or WZ as for AlGaN/GaN and still have a direct optically allowed valence band to conduction band transition, whereas for the ZnO-related alloys this point is not obvious. The binary compounds that allow alloying with Zn are WZ BeO, MgO, and CdO, where the latter compounds crystallize in the cubic rock salt structure. Table 4.3 shows the values of the a-lattice constants and band gap energies of BeO, MgO, and CdO. In principle the barrier materials can range from band gap energies of 10.68 eV (BeO) down to 2.22 eV (CdO) that is from high in the UV

4

Band Structure

85

Table 4.3 Band gap energies at room temperature and a-lattice constants of the binary oxides forming an alloy system with ZnO ˚ Compound a (A) Eg (eV) ZnO 3.249 3.37 BeO 2.698 10.58 MgO 4.207 7.83 CdO 4.696 2.22 Mg0:4 Zn0:6 Oa 3.27 4.3 Cd0:32 Zn0:68 Ob 3.559 2.52 For the ternaries the highest compositions are given for which still wurtzite structure is achieved a After [27, 29] b After [28]

a

b

12

5,0 4,5

10 MgO

8 6 Mg0.4Zn0.6O

4 CdO

ZnO

2 2,5

Bandgap energy (eV)

Bandgap energy (eV)

BeO Mg0.4Zn0.6O

4,0 3,5 3,0

ZnO

2,5

Cd0.32Zn0.68O

Cd0.32Zn0.68O

3,0

3,5 4,0 lattice constant (A)

4,5

5,0

2,0 3,2

3,3 3,4 3,5 lattice constant (A)

3,6

Fig. 4.6 Band gap energies and a-lattice constants for possible ZnO-based alloy systems (a). In (b) the triangle spanned by MgZnO, ZnO and CdZnO for the respective compositions of the ternaries for which the wurtzite crystal structure is stabilized according to [27, 28]

into the orange-red visible spectral range (see Fig. 4.6a). However, barrier and well materials have to be stabilized in the same crystallographic structure for heterostructure systems such as MgZnO/ZnO/MgZnO or ZnO/CdZnO/ZnO. This will be possible only in a limited composition range before phase separation occurs (WZ vs. rock salt). The triangle that can be spanned by the MgCdZnO alloys is shown in Fig. 4.6b.

4.2.1 Cationic Substitution: Mg, Cd, Be in ZnO Depending on the deposition technique and substrate temperature WZ Mgx Zn1x O (x < 0:5) and cubic phase alloys (0:5 < x < 1) can be stabilized, but also MgO segregation occurs. The band gap energies in dependence on composition for the

86

B.K. Meyer MgxZn1–xO Room temp.

100

x=0.45 0.33

80

0.25 0.14

X=0 4.4

60

0.07 single phase

4.2

40

Bandgap (eV)

Transmittance (%)

0.36

20

0.03

4.0 3.8 3.6 MgO segregation

3.4 3.2 0.0

0 1.5

2.0

0.1 0.2 0.3 0.4 Mg Content (x)

0.5

2.5 3.0 3.5 Photon Energy (eV)

4.0

4.5

Fig. 4.7 Transmittance spectra of wurtzite Mgx Zn1x O films measured at room temperature. From [27]

WZ phase of MgZnO are: Eg .x/ D .3:36 C 1:54x/ eV from luminescence measurements at 4:2K; Eg .x/ D .3:24 C 2:08x/ eV, Eg .x/ D .3:3 C 2:75x/ eV, and Eg .x/ D .3:30 C 2:36x/ eV from transmission measurements at room temperature [27–30]. NB: In the evaluation of the composition dependence of ZnO related alloys systematically too low values for the band gap energy of ZnO are deduced (see Table 4.3) with the consequence that the values for x D 0 deviate in the above equations from the correct value by about 100 meV. In transmission experiments usually the spectrum of the absorption tail is evaluated considering neither the effect of excitonic contributions nor the role of the Urbach tail (see also the discussion of this point in Chap. 6). The results obtained are also very much dependent on the thin film growth technique (from 2D-growth to columnar and c-axis textured polycrystalline growth) (Fig. 4.7). Taking into account the Stokes shift between luminescence and absorption (see Fig. 4.8), all so far published data agree on a essentially linear dependence of the band gap on Mg composition (on average Eg .x/ D .3:3 C 2:75x/ eV, and the highest band gap composition with WZ structure achieved so far is limited around x D 0:5 (see Fig. 4.9). The lattice constants also vary linearly with Mg composition. Figure 4.10 summarizes the results on the a- and c-lattice constants as well as the cell volume on Mg compositions. The relatively small change in the a-lattice constant allows for the pseudomorphic growth of ZnO/MgZnO hetero-structures without relaxation and the formation of misfit dislocation and hence the realisation of efficient UV emitting devices and tuning of the band gap between 3.32 and 4.3 eV. In equilibrium growth techniques (e.g., melt growth), the solid solubilities of Mg and Cd are limited to compositions x < 0:04. Only deposition techniques working far from equilibrium may achieve higher solubilities. It is therefore not astonishing that molecular beam epitaxially grown CdZnO films reached compositions of 0.32

4

Band Structure

87 MgxZn1–xO 4.2K

x=0.19

Absorption (arb. units)

x=0.14

x=0.07

4.0

x=0.03

x=0

ex.

Peak Energy (eV)

Photoluminescence Intensity (arb. units)

x=0.33

3.8

3.6

3.4

3.2

3.2

3.4

3.6

0.0

0.1 0.2 0.3 Mg Content (x)

3.8

4.0

0.4

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Photon Energy (eV)

Fig. 4.8 Photoluminescence (solid lines) and absorption spectra of wurtzite Mgx Zn1x O films measured at 4.2 K. From [27]

Fig. 4.9 Dependence of the room temperature energy gap Eg on Mg content x for wurtzite (WZ) and rocksalt (RS) Mgx Zn1x O films (after [29], see references therein)

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Fig. 4.10 Mg content (x) dependences of the a- and c-lattice constants and the unit volumes for WZ and RS Mgx Zn1x O films (after [29] and references therein)

with still perfect crystallinity. Deposition temperatures were as low as 150ı C. The composition dependence of the band gap energy (see Fig. 4.11) shows a pronounced nonlinearity (bowing) [29, 31, 32] as shown by absorption measurements at room temperature (Eg .x/ D .3:29  4:40x C 5:93x 2 / eV for 0 < x < 0:07) and luminescence experiments at T D 2:1 K (Eg .x/ D .3:35  9:19x C 8:14x 2 / eV for 0 < x < 0:05). (The above comment on determination of the values of the gap applies also here or in Figs. 4.11, 4.13, and 4.14.) This bowing, i.e. the term in x 2 , is also reflected in the change of the a- and c-axis lattice constants, which do not ˚ are: a.x/ D 3:25 C 0:143x  0:147x 2 follow Vegards law: lattice parameter (in A) 2 and c.x/ D 5:204 C 0:956x  5:42x . Ternary Bex Zn1x O alloys may cover the UV spectral range due to the high band gap energy of BeO of 10.58 eV. BeO has the same hexagonal WZ structure as ZnO; however, its toxicity may be a severe problem. Growth of Bex Zn1x O thin films have been conducted but there is limited information on the structural, morphological, and optical properties of this alloy system. In the first report by Ryu et al. [33], data were presented on the compositions x D 0:11, and from x D 0:44 to 0.6 showing that the band gap increases in a nonlinear behavior accompanied by a nonlinear decrease of the c-axis lattice constant. In a second report [34], the same group presented evidence for a linear relation of the band gap energy on the c- and a-axis lattice constants; however, the composition x was not given. For amorphous

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89 2.0X105

3.4

1.5

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y =0

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Zn1–x Cdx O Room temp.

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y =0.0013

3.0 0.5

0.00

y =0.027 0.10 0.05 Cd Content (y)

y =0.043 y =0.073

0.0 2.0

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Photon energy (eV)

Fig. 4.11 Concentration dependence of absorption spectra of Zn1x Cdx O epilayers obtained at room temperature. After [28]

Bex Zn1x O films Khoshman et al. [35] claim a linear dependence of the band gap energy on compositions for x < 0:2, for x D 0:18 a band gap energy of 4.25 eV was found. Whether the Bex Zn1x O alloy system can compete with the superior quality of Mgx Zn1x O films and hetero-structures remains to be investigated (Fig. 4.12). A few more examples of the optical spectra of cation substituted alloys are given in Chap. 6, mainly under the aspect of excitonic properties.

4.2.2 Anionic Substitution: S, Se in ZnO Because of the large electronegativity and size differences between O and S (Se), one can expect that the bowing parameters of ZnO1x Sx and ZnO1x Sex are large. Transmission measurements of ZnO1x Sx films were taken at room temperature. From these spectra, the dependence of the band gap on the composition of the ZnO1x Sx layers was determined and is shown in Fig. 4.13. The energy gap of a ternary compound semiconductor as ZnO1x Sx is described by: EZnO1x Sx .x/ D xEZnS C .1  x/ EZnO  b.1  x/x; where EZnS and EZnO are the band gap energies at 300 K of the binary compounds, respectively, and b is the optical bowing parameter. The interpretation of the results presented in [36] gave a bowing parameter of approximately 3:0 eV (see Fig. 4.13, dotted line). In the sulphur dilute limit the slope is 22 meV/%, whereas for the oxygen dilute limit it is 32 meV/%. Thus, the bowing parameter in the ZnO1x Sx

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Fig. 4.12 Optical properties of ZnCdO epilayers grown by low-temperature MBE. (a) Transmission at room temperature for a Cd content of (i) 0.06, (ii) 0.13, (iii) 0.21, and (iv) 0.32. (b) Room temperature PL of the same epilayers as in (a) excited above the Mgx Zn1x O buffer band gap (after [31])

Fig. 4.13 Dependence of the band gap energy on sulphur content in ZnO1x Sx thin films measured at room temperature. The dotted line shows the calculated dependence, while the solid lines give the slopes in the oxygen and sulphur rich composition ranges (after [36])

system might be expressed by a constant value of 3 eV, i.e., it is independent of composition x. In Fig. 4.14 are the results obtained on ZnO1x Sex thin films prepared and analyzed in the same manner [37]. They could be synthesized only in a narrow

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Fig. 4.14 Band gap energy dependence in ZnO1x Sex thin films close to the binary endpoints ZnO and ZnSe, respectively. The solid lines give the slopes (after [37])

composition range close to the binary constituents ZnO and ZnSe. This finding could indicate a limited solubility of O in ZnSe. However, a sizeable down shift in energy is found and indicates an even larger bowing. In contrast to the ZnO1x Sx system the slopes are markedly different, i.e., it is 78 meV/% in the Se dilute limit and approximately half of it 42 meV/% in the oxygen dilute limit. This is an indication that the bowing parameter b itself is a function of composition as found for CdS1x Tex . However, due to the limited data a composition independent value of b was used and resulted in a bowing parameter around 7 eV.

4.3 Valence and Conduction Band Discontinuities This section is devoted to the band discontinuities, starting with iso-valent heterostructures and proceeding then to hetero-valent ones.

4.3.1 Iso-Valent Hetero-Structures The realisation of quantum hetero-structures is essential for optoelectronic applications and requires the confinement of electrons and holes in one kind of layer (type I hetero-structures). Typically an ultra-thin layer of a narrower band gap semiconductor B is sandwiched between two layers of a larger band gap semiconductor A, for example, MgZnO/ZnO/MgZnO or ZnO/CdZnO/ZnO. The band gap difference

Eg between the forbidden gaps Eg .A/ and Eg .B/ of the two semiconductors is distributed between the valence band discontinuity (or offset) EB and the conduction band discontinuity EC . The informations on the hetero-junction bandoffsets of CdZnO/ZnO and ZnO/MgZnO can be found in [38, 39]. In both cases, X-ray photoelectron spectroscopy was used. For Cd0:05 Zn0:95 O=ZnO, the offsets were

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EV D 0:17 eV and EC D 0:30 eV for a band gap of Cd0:05 Zn0:95 O of 2.9 eV [38], while for ZnO=Mg0:15 Zn0:85 O the values are EV D 0:13 eV and EC D 0:18 eV for the band gap energy of Mg0:15 Zn0:85 O of 3.68 eV [39]. The important information is that type-I quantum hetero-structures can be realized with sufficient offsets for electron and hole confinement. To summarize for CdZnO/ZnO, the ratio

EV = EC is around 0.56 and for ZnO/MgZnO around 0.7, respectively. For the ZnO1x Sx alloys a strong valence band offset bowing was reported in [40] based on ultraviolet photoelectron spectroscopy. The valence band offset between ZnO and ZnS is 1.0 eV placing the conduction band of ZnS  1:4 eV higher in energy compared to the conduction band edge of ZnO. Thus a type-II alignment results where in a quantum well structure, electrons from ZnO will recombine spatially indirect with holes in ZnS. The results presented by Persson [40] showed that the valence band offset EC .x/ increases strongly with x, whereas the conduction band edge EC .x/ increases only very slowly for small S incorporation (x < 0:3). This finding implies only weak confinement of the electrons for ZnO1x Sx alloys with x < 0:3. However, the main conclusion of the work of Person et al. [40] is that the nitrogen doping may be enhanced in the ZnO1x Sx alloys with small valence band offsets.

4.3.2 Hetero-Valent Hetero-Structures Among the possible hetero-valent hetero-structures, the system ZnO/GaN has attracted considerable interest based on the fact that device structures such as p-GaN/n-ZnO can be realized easily and that the lattice mismatch between ZnO and GaN (both have WZ symmetry) is modest with 1.9%. Electroluminescence devices were fabricated of the type p-GaN/i-ZnO/n-ZnO, which showed under forward bias UV emission at 3.08 eV explained by Mg-related emission in the p-GaN layer [40]. See also Chap. 13. Based on the Anderson model and using the values of the electron affinities of ZnO and GaN, valence and conduction band offsets were estimated of 0.12 and 0.1 5eV, respectively [41, 42]. These values are in sharp contrast to photoelectron spectroscopy (UPS, XPS) measurements on ZnO/GaN (0001) hetero-interfaces from which a valence offset between 0.8 and 1.0 eV was obtained [43]. It will place the conduction band of GaN by 0.8 eV higher in energy. The ZnO/GaN heterostructure is thus of type II. Capacitance voltage measurements confirmed this large conduction band discontinuity [44] by detecting a large build up of electron concentration (around 1018 cm3 / at the hetero-interface. Density functional calculations in [45] resulted also in a type II band alignment. The type-II alignment forces the electrons in the conduction band of n-ZnO to recombine spatially indirectly with holes in the valence band of p-GaN. However, the situation might be more complicated since the band offsets depend on the polarity of the constituent materials forming the junction (e.g., Ga-face GaN on O-face ZnO) and the resulting interface dipoles. The polarisation fields (spontaneous polarisation) – both GaN and ZnO are polar materials with comparable spontaneous polarisations – may change the band

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offsets significantly. For the system ZnO/AlN also a type II band alignment has been deduced from X-ray photoemission spectroscopy, with the valence band of ZnO 0:43 ˙ 0:17 eV below the one of AlN and consequently the AlN conduction band 3:29 ˙ 0:20 eV above the one of ZnO [46]. Another system of interest is ZnO/SiC since SiC can be doped p-type and thus the materials system ZnO/SiC provides an alternative to ZnO/GaN to test ZnObased p  n hetero-junctions. The polytype 4H-SiC existing in the same WZ crystal structure and with a reasonable lattice mismatch of around 5% has been tested in [47]. The band gap energies of 4H-SiC and ZnO are almost identical. Following the Anderson model, the authors predict an energetic barrier for electrons (holes) of 0.3 eV (0.4 eV) [47]. For a light emitting device, one would thus expect that electron injection from n-type ZnO to p-SiC is more pronounced than hole injection from p-SiC into n-ZnO that is the device will show mainly weak electroluminescence from the indirect semiconductor SiC. Data for the VB offset between p-type Si and n-type ZnO are found in [48].

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

13. 14. 15. 16. 17. 18. 19. 20. 21.

D.G. Thomas, J. Phys. Chem. Solids 15, 86 (1960) J.J. Hopfield, J. Phys. Chem. Solids 15, 97 (1960) Y.S. Park, C.W. Litton, T.C. Collins, D.C. Reynolds, Phys. Rev. 143, 512 (1966) B. Segall, Phys. Rev. 163, 769 (1967) W.Y. Liang, A.D. Yoffe, Phys. Rev. Lett. 20, 59 (1968) D.C. Reynolds, C.W. Litton, T.C. Collins, Phys. Rev. 140, A1726 (1965) D.C. Reynolds, T.C. Collins, Phys. Rev. 185, 1099 (1969) D.C. Reynolds, D.C. Look, B. Jagai, C.W. Litton, T.C. Collins, T. Harris, M.J. Callahan, J.S. Bailey, J. Appl. Phys. 86, 5598 (1999) S.F. Chichibu, A. Uedono, A. Tsukazaki, T. Onuma, M. Zamfirescu, A. Ohtomo, A. Kavokin, G. Cantwell, C.W. Litton, T. Sota, M Kawasaki, Semicond. Sci. Technol. 20, S67 (2005) S. Adachi, K. Hazu, T. Sota, S. ChiChibu, G. Cantwell, D.C. Reynolds, C.W. Litton, Phys. Status Solidi C 2, 890 (2005) A.V. Rodina, M. Strassburg, M. Dworzak, U. Haboeck, A. Hoffmann, A. Zeuner, H.R. Alves, D.M. Hofmann, B.K. Meyer, Phys. Rev. B 69, 125206 (2004) B.K. Meyer, H. Alves, D.M. Hofmann, W. Kriegseis, D. Foster, F. Bertram, J. Christen, A. Hoffmann, M. Strassburg, M. Dworzak, U. Haboeck, A.V. Rodina, Phys. Status Solidi B, 241, 231 (2004) W.R.L. Lambrecht, A.V. Rodina, S. Limpijumnong, B. Segall, B.K. Meyer, Phys. Rev. B 65, 075207 (2002) B. Gil, Phys. Rev. B 64, 201310 (2001) B. Gil, A. Lussov, V. Sallet, S.-A. Said-Hassani, R. Triboulet, P. Bigenwald, Jpn. J. Appl. Phys. Part 2, 40, L1089 (2001) R. Laskowski, N.E. Christensen, Phys. Rev. B 73, 045201 (2006) A. Schleife, C. R¨odl, F. Fuchs, J. Furthm¨uller, F. Bechstedt, Appl. Phys. Lett. 91, 241915 (2007) B.C. Reynolds, D.C. Look, B. Jogai, C.W. Litton, G. Cantwell, W.C. Harsch, Phys. Rev. B 60, 2340 (1999) A.B.M. Almamun Asdhrafi, A. Ueta, A. Avramescu, H. Kumano, I. Suemune, Y.-W. Ok, T.-Y. Seong, Appl. Phys. Lett. 76, 550 (2000) S.-K. Kim, S.-Y. Jeong, C.-R. Cho, Appl. Phys. Lett. 82, 562 (2003) M. Cardona, Phys. Rev. 129, 69 (1963)

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22. R.T. Girard, O. Tjernberg, G. Chiaia, S. S¨oderholm, U.O. Karsson, C. Wigren, H. Nylen, I. Lindau, Surf. Sci. 373, 409 (1997) 23. K. H¨ummer, Phys. Stat. Sol. 56, 249 (1973) 24. S.F. Chichibu, T. Sota, G. Cantwell, D.B. Eason, C.W. Litton, J. Appl. Phys. 93, 756 (2003) 25. A. Hoffmann, private communication 26. Th. Gruber, G.M. Prinz, C. Kirchner, R. Kling, F. Reuss, W. Limmer, A. Waag, J. Appl. Phys. 96, 289 (2004) 27. A. Ohtomo, M. Kawasaki, T. Koida, K. Masubuchi, H. Koinuma, Y. Sakurai, Y. Yoshida, T. Yasuda, Y. Segawa, Appl. Phys. Lett. 72, 2466 (2001) 28. T. Makino, Y. Segawa, M. Kawasaki, A. Ohtomo, R. Shiroki, K. Tamura, T. Yasuda, H. Koinuma, Appl. Phys. Lett. 78, 1237 (2001) 29. A. Ohtomo, A. Tsukazaki, Semicond. Sci. Technol. 20, S1 (2005) 30. S. Sadofev, S. Blumstengel, J. Cui, J. Puls, S. Rogaschweski, P. Sch¨afer, Yu.G. Sadofyev, F. Henneberger, Appl. Phys. Lett. 87, 091903 (2005) 31. S. Sadofev, J. Blumstengel, J. Cui, J. Puls, S. Rogaschweski, P. Sch¨afer, F. Henneberger: Appl. Phys. Lett. 89, 201907 (2006) 32. Th. Gruber, C. Kirchner, R. Kling, C. Reuss, A. Waag, F. Bertram, D. Forster, J. Christen, M. Schreck, Appl. Phys. Lett. 83, 3290 (2003) 33. Y.R. Ryu, T.S. Lee, J.A. Lubguban, A.B. Corman, H.W. White, J.H. Leem, M.S. Han, Y.S. Park, C.J. Youn, W.J. Kim, Appl. Phys. Lett. 88, 052103 (2006) 34. W.J. Kim, J.H. Leem, M.S. Han, I.-W. Park, Y.R. Ryu, T.S. Lee, J. Appl. Phys. 99, 096104 (2006) 35. J.M. Khoshman, D.C. Ingram, M.E. Kordesch, Appl. Phys. Lett. 92, 091902 (2008) 36. B.K. Meyer, A. Polity, B. Farangis, Y. He, D. Hasselkamp, Th. Kr¨amer, C. Wang, Appl. Phys. Lett. 85, 4929 (2004) 37. A. Polity, B.K. Meyer, Th. Kr¨amer, C. Wang, U. Haboeck, A. Hoffmann, Phys. Stat. Sol. A 203, 2867 (2006) 38. J.-J. Chen, F. Ren, Y. Li, D.P. Norton, S.J. Pearton, A. Osinsky, J.W. Dong, P.P. Chow, J.F. Weaver, Appl. Phys. Lett. 87, 192106 (2005) 39. S.C. Su, Y.M. Lu, Z.Z. Zhang, C.X. Shan, B.H. Li, D.Z. Shen, B. Yao, J.Y. Zhang, D.X. Zhao, X.W. Fan, Appl. Phys. Lett. 93, 082108 (2008) 40. C. Persson, C. Platzer-Bj¨orkmann, J. Malmstr¨om, T. T¨orndahl, M. Edoff, Phys. Rev. Lett. 97, 146403 (2006) 41. H.Y. Xu, Y.C. Liu, Y.X. Liu, C.S. Xu, C.L. Shao, R. Mu, Appl. Phys. B 80, 871 (2005) 42. D.-K. Hwang, S.-H. Kang, J.-H. Lim, E.-J. Yang, J.-Y. Oh, J.-H. Yang, S.-J. Park, Appl. Phys. Lett. 86, 222101 (2005) 43. S.-K. Hong, T. Hanada, Y. Chen, H.-J. Ko, A. Tanaka, H. Sasaki, S. Sato, Appl. Phys. Lett. 78, 3349 (2001) 44. D.C. Oh, T. Susuki, J.J. Kim, H. Makino, T. Hanada, T. Yao, H.J. Ko, Appl. Phys. Lett. 87, 162104 (2005) 45. M.N. Huda, Y. Yan, S.-H. Wei, M.M. Al-Jassim, Phys. Rev. B 78, 195204 (2008) 46. T.D. Veal, P.D.C. King, S.A. Hatfield, L.R. Bailey, C.F. McConville, B. Martel, J.C. Moreno, E. Frayssinet, F. Semond, J. Z´un˜ iga-P´erez, Appl. Phys. Lett. 93, 202108 (2008) 47. A. El-Shaer, A. Bakin, E. Schlenker, A.C. Mofor, G. Wagner, S.A. Reshanov, A. Waag, Superlattice. Microst. 42, 387 (2007) 48. H. Sun, Q.-F. Zhang, J.-L. Wi, Nanotechnology 17, 2271 (2006)

Chapter 5

Electrical Conductivity and Doping Andreas Waag

Abstract In this chapter, the electrical properties of ZnO are discussed, which essentially include doping, carrier mobility, contacts, and some other topics listed below. Nominally undoped ZnO is always n-type. This fact could be possibly due to intrinsic defects or due to hydrogen, which is a donor in ZnO and a rather ubiquitous element (also in most of the growth processes). Therefore, hydrogen in ZnO is treated first and then other donors for efficient n-type doping. The next section is devoted to p-type doping and the persistent difficulties to obtain reliable, stable, and high p-type conductivity. The chapter continues with information on the carrier mobility and the observation of the integer quantum Hall effect. The next electric properties concern the use of ZnO in varistors and high-field transport. The final aspect is photoconductivity.

5.1 Introduction As already mentioned above, the missing control on p-type doping of ZnO is considered to be the main obstacle toward high-quality ZnO-based LEDs. The p-type problem is not really surprising, since the compensation of dopants is correlated to the energetic positions of both conduction and valence bands relative to the vacuum level or to certain reference defect levels and, in general, increases with increasing band gap. In ZnO, the valence band is very low in energy, relative to the vacuum level, which can explain the pronounced general trend toward compensation of acceptors. A compilation of the band-edge positions for a variety of different semiconductors has been made by van de Walle and Neugebauer [1] see Fig. 5.1. Usually, the electronic transition level of interstitial hydrogen lies in the band gap, leading

A. Waag Institut f¨ur Halbleitertechnik der Technischen Universit¨at, Braunschweig, Germany e-mail: [email protected]

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–0

Cds

Cdse

CdTe

GaSb

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InN

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Si

Energy (eV)

H2O

ZnTe

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ZnSe

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AISb

GaAs

InP

AIP

GaN

Ge –5

AIN

ZnO

–10

Fig. 5.1 Band alignments of various semiconductors with the position of the electronic transition level of hydrogen interstitials. For further explanation, see text below. All energies are calculated values, band offsets agree with experimental data where available. After [1]

to an amphoteric behavior of hydrogen, depending on the Fermi-level position; it compensates both acceptors and donors. The authors point out that the situation is different in ZnO. Here, owing to the low-lying band edges of ZnO, the electronic transition level of interstitial hydrogen in ZnO lies in the conduction band. Hence, hydrogen plays a very special role in ZnO, in contrast to most other semiconductors. In ZnO, hydrogen always acts as a donor, independent of the p- or n-type character of the material. We will come back to this point later. In any case, it should be kept in mind that the band edges of ZnO are very low lying in energy, relative to the vacuum level and other semiconductors, including GaN. For a doping control in ZnO, knowledge on the native point defect situation is very important. These point defects control doping and diffusion and the minority carrier lifetime and optical efficiency. Native point defects like oxygen vacancies and Zn interstitials, as they are supposed to be common in an oxygen-deficient situation during ZnO growth or annealing, have been calculated and found to have high formation energies in n-type ZnO and are therefore quite unlikely to form, in contrast to the common assumption [2]. According to these first-principles calculation, the oxygen vacancy is a deep donor, 1 eV below the conduction band edge. Hence, it is assumed that it cannot serve as the origin of residual n-type doping, even though it may act as a compensating defect in acceptor-doped ZnO. The same group [3] has calculated Zn interstitials to be shallow donors and fast diffusers; they are therefore probably not stable. Their migration barriers are as low as 0.57 eV. Zn vacancies are found to be deep acceptors, and are supposed to be the

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compensating species in n-type ZnO [3]. On the contrary, oxygen vacancies, being deep donors, can be efficient compensating centers in acceptor-doped ZnO. As a result, it has been concluded [3] that native point defects can be sources of self-compensation, but they are unlikely to be the origin of the residual n-type doping levels in ZnO. The authors suggest that the incorporation of unintentional dopants is responsible for the n-type background in as-grown ZnO, hydrogen being the most likely candidate. On the other hand, a recent study pointed out that the interaction of intrinsic defects has been neglected so far, but has to be taken into account when their concentration gets high [4]. The shallow donor ZnI and the deep donor VOx are suggested to have a strong attraction due to exchange interaction between the respective orbitals, leading to a significant reduction in their formation energies [4], which could explain the high n-type carrier concentration in oxygen-deficient ZnO. Of course, a lot of other different residual impurities in ZnO can be imagined. One very common candidate is, for example, aluminum, which diffuses out of the sapphire substrates, which are often used during ZnO epitaxy. However, it seems that the role of hydrogen in ZnO has particularly been underestimated in the recent past. Therefore, a certain emphasis will be put on hydrogen as a residual impurity here.

5.2 Hydrogen in ZnO A comprehensive study of the role of hydrogen has been performed recently on the basis of the density functional theory in the local density approximation [1, 5]. The authors point out that the effect of defect passivation by hydrogen may be crucial to the performance of many optoelectronic and photovoltaic devices. In most semiconductors, hydrogen is amphoteric and counteracts thus the prevailing conductivity. In contrast to ZnO, interstitial hydrogen acts, for example, in GaN as a donor in p-type material and as an acceptor in n-type material. Since the energy level of the neutral hydrogen H0 is generally always above HC or H , only the charged states occur. The Fermi-level position at which the charge transfer from H to HC (or vice versa) occurs is called the electronic transition level of hydrogen. It is indicated in Fig. 5.1 for a variety of different semiconductors by the horizontal lines. As mentioned above, for most of the materials the electronic transition level of hydrogen lies in the band gap. Therefore, for n-type material, with the Fermi energy close to the conduction band edge, the hydrogen interstitial is negatively charged. For p-type material, the situation is reversed, resulting in the compensation of both n-type and p-type doping by hydrogen interstitials as stated above. In contrast to that, the electronic transition level of interstitial hydrogen lies well in the conduction band of ZnO, and hence always acts as a donor [1]. It is shown that hydrogen in ZnO can also substitute on an oxygen site (HO ) and form a multicenter, with bonds to the four nearest-neighbor Zn atoms [6]. This complex seems to be highly stable. This has also been supported experimentally by positron annihilation and optical transmission experiments [7]. Zn interstitials have been identified not to be the intrinsic donor in as-grown ZnO [7]. It has been

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suggested that annealing in oxygen ambient forms Zn vacancies and that this would facilitate the p-type doping with Ag or Cu. On the other hand, it is suggested that red-colored crystals, full of oxygen vacancies, would facilitate p-type doping with nitrogen, phosphorous, or arsenic. Experimental evidence by EPR and Hall measurements also demonstrated that hydrogen occurs in nominally undoped bulk ZnO [8]. A clean, oxygen-terminated ZnO surface has been shown to reconstruct into a (1  3) O–ZnO surface. This surface is unstable and very reactive for H2 O adsorption, being converted to a ZnO surface terminated by hydroxyl groups (OH–ZnO) [9, 10]. This hydroxyl-terminated surface is stable, with a (1  1) reconstruction. These experimental results have also been corroborated by DFT calculations [11]. The hydroxyl-terminated surface has been exposed to atomic hydrogen [12], and shallow donors could be formed. Subsequent annealing resulted in a reversible loading and depletion of near-surface hydrogen. The situation has been investigated by high-resolution electron energy loss spectroscopy [12]. These shallow donors had ionization energies of 25 meV. By comparing the results of thermal desorption and energy loss spectroscopy, two channels for the reduction of the near-surface hydrogen donor concentration during annealing could be identified. One of the corresponding activation energies agrees well with reported values for hydrogen diffusion in ZnO. Hydrogen donors obviously not only desorbed off the surface during annealing but partly also diffused into the bulk of the ZnO [12]. It is possible that this is one of the key mechanisms leading to high hydrogen concentrations in ZnO. In [13], the dehydrogenation of hydrogen in ZnO is described as a function of temperature. Only after annealing, the nitrogen acceptors in ZnO:N could be activated. The role of hydrogen for the operation of ZnO LEDs has also been pointed out [14]. In this case, it was assumed that residual hydrogen in SiN films lead to compensation in ZnO after annealing. For obtaining a reasonable LED characteristic, the SiN had to be removed before annealing. In contrast to that, SiO2 dielectrics had a lower concentration of residual hydrogen and did not have to be removed for activating the LED during an annealing step [14]. Hydrogen diffuses even at temperatures between 100 and 200ıC [15, 16], as has been evaluated in ZnO thin films deuterated throughout. It is argued that at low concentration, deuterium is likely to be in a positively charged atomic form, which can be influenced by an external electric field. At higher concentrations, the deuterium may be present mostly in electrically neutral D2 -states, which cannot be influenced by an external field [15]. In conclusion, hydrogen can obviously play an important role in the conductivity control of ZnO.

5.3 Donors in ZnO: Al, Ga, In Controlling n-type doping of ZnO is – in certain limits – quite straightforward. Degenerate doping is interesting for transparent conductive oxides and transparent electronics. Group III metals like, Al, Ga, or In, can be used for this, Ga probably

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being the best suited. This is partly due to the very similar bond lengths of both ˚ and Zn–O (1.97 A). ˚ Ga-doped ZnO has been widely studied in the Ga–O (1.92 A) past [17–23]. See also Sect. 2.5. A recent study on optical properties of heavily doped ZnO:Ga [24] shows that for carrier concentrations between 2  1018 cm3 and 2 1020 cm3 the dominating photoluminescence line changes from I1 (ionized donor-bound exciton) to IDA (donor–acceptor-pair transition) to I8 (neutral donorbound exciton transition) The IDA transition is believed to be due to the combination of a Ga donor and a VZn acceptors [24]. More details can be found in the chapter on optical properties. Aluminum is also an often-used donor in ZnO. Recently, for example, ZnO:Al has been optimized by atomic layer deposition and pulsed laser deposition and has been used as an efficient transparent contact for organic LEDs. Conductivities above 3,000 S/cm could be achieved [25] at growth temperatures of only 150ıC and below. Optical transparencies of 90% for wavelengths between 380 and 2,500 nm could be achieved [26]. Storing in air at elevated temperatures reduces the conductivities [26]. Unintentional Al, In, or Ga donors have been found to form a highly conductive surface layer in nearly all types of bulk ZnO samples [27]. In this case, no indication of a hydrogen donor could be found.

5.4 Acceptors in ZnO Reports on successful p-type doping some years ago have boosted a tremendous amount of global research efforts on ZnO. As already mentioned, these early reports were in one way or the other either too positively interpreted, hardly reproducible or even inconsistent. The vast number of publications on p-type ZnO published during the past years suggests at a first glance that the problem of fabricating p-type ZnO is finally solved; however, the real situation is far from that. There is little doubt that with a successful hole and electron injection into an active ZnO-based quantum well an efficient light-emitting diode should be possible, which has not yet been demonstrated up to now. Nitrogen, arsenic, phosphorous, and antimony on oxygen sites are supposed to be interesting candidates as acceptors in ZnO, and there are numerous reports on achieving p-type ZnO using these anionic dopants. With the exception of nitrogen, these atoms have larger ionic radii as compared to oxygen. Most of the experimental reports are on heteroepitaxial and hence high-defect density material – only a few of them report on p-type doping during homoepitaxy, for example, [28–31] – so defect densities are definitely high, which could complicate the situation substantially. To illustrate the present state of the art, we mention strong indications for p-type ZnO:P nanorods [32] contrasted by the observation of n-type conductivity in ZnO:P homoepitaxial thin films [33]. Another problem is the fact that often doping levels up to several % are claimed; however, such high doping levels frequently contradict solubility limitations, and in any case the formation of impurity bands would have to be taken into account at such high doping levels. In addition, the fact that the hole

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A. Waag

concentrations deduced from Hall measurements (neglecting all other implications of this technique discussed below) result in hole concentrations, which are several orders of magnitude smaller than the claimed incorporation concentrations, clearly demonstrate that our knowledge on the real situation is still limited. Note that the concentration of ZnO molecules is 4:2  1022 cm3 . Anionic dopants, like Li [34], Ag [35] and Cu [36, 37], on Zn sites and others have also been reported recently to have (at least partly in the form of complexes) acceptor character. Even a greenish-blue ZnO:Cu/ZnO:Al LED has been reported [38]. There will be no attempt made here to present a complete literature overview, or a classification of the large amount of papers reporting on p-type ZnO. Instead, the difficulties of rigorously measuring p-type conductivity in ZnO will be discussed. The analysis technique of choice in order to determine the type of conductivity of thin films is the Hall effect. This is often done in a van der Pauw configuration, when processing of the samples needs to be avoided. In order to apply the van der Pauw analysis, a homogenous distribution of the conductivity – both vertically and laterally – is an absolute prerequisite. Inhomogeneous thin films lead to experimental results which, analyzed in a conventional way and neglecting possible inhomogeneity, guides one to erroneous conclusions. A thin film with an inhomogeneous distribution of n-type conductivity can even lead to a Hall measurement indicating p-type conductivity. Such a situation has thoroughly been discussed in the past [39, 40, 111] for other material systems. A number of reasons for an inhomogeneous distribution of the conductivity have been identified in the case of ZnO thin films. This makes the direct interpretation of Hall data difficult. Some experimental facts are: 1. A photoluminescence (PL) line at 3.314 eV, often occurring in ZnO samples [40], has been shown to be an electron-acceptor transition, with an acceptor depth of 130 meV. Often interpreted in different ways in the literature, this acceptorrelated line has recently been attributed to a defect complex related to basal plane stacking faults, via a thorough comparison between PL and TEM data [40]. 2. A strong electrostatic potential has been detected around dislocations in ZnO by electron holography [41]. Enormous charge carrier concentrations between 5  1019 and 5  1020 cm3 in cylinders with radii up to 5 nm have been determined, and point defects in the vicinity of the dislocation core seem to be the reason for this. The electronic states associated with the dislocations are located in the lower half of the energy gap [41]. Both stacking faults and dislocations are omnipresent in hetero epitaxially grown ZnO. 3. After incorporation of arsenic and nitrogen during MOVPE growth of ZnO layers, an inhomogeneous distribution of p-type and n-type regions has been measured [42]. This could be demonstrated by scanning capacitance measurements, see Fig. 5.2 [42]. The maximum “p-type coverage” could be found with co-doping of nitrogen and arsenic. These results show that both extended and point defects will lead to an inhomogeneously distributed conductivity in ZnO thin films, which – at least in principle – can

5

Electrical Conductivity and Doping

101

Wavelength Image 377 T = 6K

375

374

Wavelength (nm)

376

373

372 10 µm

Fig. 5.2 CL image of the As-doped sample from Fig. 5.3 showing arsenic-related free-to-bound (e, A0 ) luminescence around 3.305 eV dominating in the growth pits (green dots). From [42]

lead to an erroneous interpretation of Hall measurements. In view of the facts described above, one should be very cautious in a straightforward interpretation of integral data from Hall effect or van der Pauw measurements. Indeed, it has recently been shown experimentally that van der Pauw measurements on n-type ZnO can lead to a p-type signal due to an inhomogeneity in the crystal [43], even though the ZnO crystal is entirely n-type throughout The situation is even more complicated, when a high carrier concentration at the substrate/film interface or the surface occurs [44]. An alternative way to determine the conductivity type is to measure the capacitance of a metal–semiconductor contact as a function of voltage. As shown before, spatially resolved capacitance-voltage data (CV) indicated an inhomogeneous doping behavior [42], and it is quite clear that under such circumstances an integral CV measurement cannot give reliable information. In view of all these uncertainties, an interpretation of doping results of homoepitaxial, low defect density ZnO seems to be most valuable. Tsukazaki et al. [28] reported on the growth of nitrogen-doped ZnO thin films on SCAM substrates (scandium aluminum magnesium oxide). These substrates are almost lattice matched to ZnO, and a high-quality growth could be achieved. See Chap. 3. Nitrogen has been incorporated using a temperature modulation technique. Low growth temperatures have been used for the incorporation of nitrogen, with a subsequent annealing step at higher temperatures in order to re-establish the structural quality. The method is very time-consuming, nevertheless first LED structures could be reported [28]. Recently, UV LEDs grown on ZnO substrates have been reported by the same group using MBE and nitrogen incorporation during normal growth temperatures [45]. In both

102

A. Waag

a

0

b

SCM

AFM

50µm 0

Δz = 300nm AFM

0

50µm

∂C/∂V = 20V SCM

50µm 0

Δz = 150nm

50µm

∂C/∂V = 20V

Fig. 5.3 AFM and SCM (scanning capacitance microscopy) images of a 5050 m2 area of nitrogen doped (a) and nitrogen and arsenic co-doped (b) ZnO samples. For the nitrogen-doped sample, a dominant n-type conductivity (blue color regions) is found and p-type conductivity (orange color) occurs only in regions with large defect concentrations. The co-doped sample is dominated by p-type conductivity and shows n-type conductivity only in defective regions. The SCM color bar goes from low p-type (light orange) to high p-type (black) then switches to n-type (black) and goes to low n-type (light blue). From [42]

cases, it has been pointed out that the structural quality of the ZnO thin films is of utmost importance (see also Chap. 13). An alternative for achieving low defect density ZnO is the fabrication of ZnO nanorods. Owing to their large aspect ratio, the dislocations are annihilated at the sidewalls, in most cases leading to defect-free ZnO (see also Chap. 3). Doping of these defect-free nanorods has also been studied. P-type ZnO nanorods have been reported, for example, by phosphorous doping during CVD [46] or pulsed laser deposition [47]. Nanorod LEDs could be demonstrated by arsenic ion implantation [48]. In nanorods, an analysis of the carrier type is even more difficult, since Hall

Electrical Conductivity and Doping

Fig. 5.4 Excitonic peaks of PL spectra at 10 K of n-type (green line), as-grown (red line), and annealed (blue line) ZnO:P NWs. After [46]

103

A2X PL Intensity (a.u.)

5

A1X

FXA

D1X D2X

FXB

D3X D4X 3.32

3.36 Energy (eV)

3.40

effect measurements cannot be performed. As an alternative, the optical spectra have to be analyzed (see Fig. 5.4 and [46]) or the electric field dependence for achieving depletion in single nanorod field-effect transistors needs to be interpreted [49]. Recently, p-type ZnMgO has also been reported [50]. Phosphorous doping during pulsed laser deposition has been employed for that. It turned out that the efficiency of P doping varies with Mg concentration, though without discussing systematic dependencies [50]. With 10% Mg, a higher p-type carrier concentration could be achieved; as compared to ZnMgO with only 5% Mg content. MOCVD- and sputter-grown ZnO thin films doped with nitrogen have been investigated by XPS and UPS [51], nitrogen monoxide (NO) has been used here as a source for both oxygen and nitrogen in the case of MOCVD. See also Chap. 3. By the analysis of core level spectra, it has been concluded that at least four different chemical environments for nitrogen in ZnO occur, including the NO acceptor, a double donor .N2 /O , and two carbon-nitrogen species in the MOCVD-grown films [51]. The carbon contamination is certainly due to a low growth temperature of only 400ı C. Even though high nitrogen concentrations of the order of 1021 cm3 could be realised, the concentration of nitrogen-related acceptors was some orders of magnitude lower, illustrating the above comment. Until today, it is difficult to finally comment on the degree of control on p-type doping achieved worldwide. Many more papers could be refenced here. Even though there are numerous reports on p-type ZnO, one would have to critically evaluate reported data in terms of the problems correlated to inhomogenous and compensated material. Often, the Hall effect, integral CV data, etc., are interpreted without taking this properly into account. Partly p-type doping or conductivity is claimed on the basis of luminescence features (like eA0 , A0 X, or DAP) only. As a consequence, this chapter did not attempt to give a comprehensive overview on all the literature on p-type doping available today. Instead, some of the problems, possible solutions, and scientific routes have been highlighted. Especially, the interplay of complex defects as well as self-compensation via interstitials and vacancies and the consequences

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A. Waag

for device operation and device characteristics (e.g., lifetime) are far from being understood.

5.5 Mobility Detailed investigations on the carrier mobility in n-type ZnO has been performed by various groups, partly for the whole temperature range from 4 K to room temperature. For some older and more recent references see, for example, [52–57]. Often, the reported room temperature mobilities of n-type ZnO thin films have been somewhat lower as compared to high-quality bulk material [58–60]. By a systematic optimization of the ZnO thin film quality, the mobilities recently reported are now even slightly higher than the ones from bulk material [61]. Values of even up to 5;000 cm2 /Vs for the maximum mobility at low temperature could be achieved [61] compared to 2;500 cm2 /Vs in bulk material [56]. Theoretical modeling of the electron transport in n-type ZnO [56, 62–64] has also been reported. In [56, 64], polar optical scattering, ioinized impurity scattering, acoustic phonon scattering and piezoelectric interactions have been considered. As can be seen from Fig. 5.5, polar optical scattering limits the mobility at room temperature and above. At lower temperature, down to 100 K, piezoelectric-phonon scattering is the limiting mechanism. In degenerately doped ZnO:Ga, the situation is different. Figure 5.6 shows the calculated mobilities for the different scattering mechanisms as a function of dopant

film

1000000

Polar scatt

–1 2

Bulk

Acoustic 100000 phonon

–1

µ (cm .V .s )

impurity

10000

piezo phonon

total 1000

100 5

6

7

8 9 100

2

3

4

T(K)

Fig. 5.5 Contributions to the total electron mobility as a function of temperature, calculated for a non-degnerate case, for a ZnO thin film and a ZnO bulk substrate for comparison, on the basis of a variational method. After [64]

5

Electrical Conductivity and Doping

105

a- ZnO

Acoustic phonon piezo phonon

10000

Polar scatt

1000

2

–1

–1

µ (cm .V .s )

300 K

total

100

ionized impurity

10 1E16

1E17

1E18

1E19

1E20

1E21

–3

ns (cm )

Fig. 5.6 Drift mobility calculations at 300 K as a function of carrier concentration, and a comparison to experimental Hall data (black dots). After [64]

concentration [64]. The mobilities of doped films are significantly smaller than for undoped films. At dopant concentrations above 5  1018 cm3 , ionized impurity scattering is the limiting scattering mechanism even at room temperature. In order to model the reduction of mobilities in the intermediate concentration range, plasmon scattering must probably be taken additionally into account [65, 66].

5.6 Ohmic and Schottky Contacts on ZnO In order to operate ZnO devices, ohmic contacts have to be fabricated. Ohmic contacts to wide band gap semiconductors are usually a problem since they often show a Schottky-type behavior. Surprisingly, in n-ZnO, it is more difficult to achieve a good Schottky behavior. The reliable fabrication of good Schottky diodes is a prerequisite for current–voltage and capacitance–voltage as well as deep-level transient spectroscopy. The electron affinity of (0001)-oriented ZnO has been found to be D 4:1 eV [67]. This would lead to Schottky barrier heights of 1 eV for Au, 1.02 eV for Pd, 1.05 eV for Ni and 0.16 eV for Ag, assuming the Schottky–Mott model being valid and taking the respective metal work functions into account [68] (Table 5.1). The published data substantially deviate from these numbers. For Au and Pd contacts, barrier heights of 0.66 eV and 0.60 eV, respectively, have been found in early reports [69]. In general, it turned out that the surface preparation is very important for the quality of the Schottky contacts, in situ preparation following an etch step being advantageous [67].

106

A. Waag

Table 5.1 Contact properties of Pd Schottky contacts on (0001)-oriented ZnO PLD films and single crystals, with different surface preparation: (a) acetone ultrasonic bath, (b) acetone C toluene C dimethylsulfoxide (c) hydrochloric acid, (d) surface treatment in N2 O. After [68] Method (a) (b) (c) (d) PLD thin films (0001)-oriented Effective barrier height (meV) 630 680 ... 600 Ideality factor 1.7 1.4 ... 1.95 Single crystals Effective barrier height (meV) Ideality factor

740 2.0

700 1.75

600 1.4

... ...

Table 5.2 Contact properties of different metals on ZnO PLD films and single crystals prepared by method (b) acetone C toluene C dimethylsulfoxide rinse in ultrasonic bath. After [68] Metal Ag Pd Au Ni PLD thin films (1120)-oriented Effective barrier height (meV) 590 680 ... ... if < I >B (meV) 760 790 Ideality factor 1.4 1.4 ... ... Single crystals Effective barrier height (meV) if < I >B (meV) Ideality factor

560 760 1.5

730 840 1.75

560 ... 2.0

620 ... 1.7

Pd, Ag, Au, and Ni contacts have been investigated by electron beam-induced current (EBIC) Table 5.2 and [68] in order to measure their homogeneity. Only for homogenous contacts, reliable results for the barrier height have been obtained. The dependence of the barrier heights on the ZnO surface polarity has also been pointed out for Pt and Pd diodes [70], but no significant effect on surface polarity was observed for Ag and Au diodes (see also Fig. 5.7). Highest Schottky barriers were achieved with Ag and Pd diodes, with barrier heights between 0.77 eV and 1.02 eV, respectively [68, 70]. The Schottky barrier heights are sensitive to hydrogen treatment [71]. The rectifying I–V characteristics of the Schottky diode showed a breakdown when subject to an H2 environment [72]. The recovery of this breakdown was shown to be thermally activated. This property can be used for hydrogen sensing [73]. Metal–ZnO contacts have recently been investigated by depth-resolved cathodoluminescence spectroscopy and by current–voltage measurements. It has been reported that native defects in the ZnO crystal as well as from the metallization procedure seem to influence the Schottky barrier heights as well as the ideality factors [74]. The correlation between deep-green luminescence and the ohmic/Schottky behavior of Au contacts to ZnO has been discussed in view of near-surface states, which can be influenced by a remote oxygen plasma [75]. The transition from ohmic to rectifying behavior has been reported by H2 O2 treatment for a Au/ZnO Schottky contact [76]. It is supposed that the rectifying behavior is due to the reduced conductivity close to the surface because of a reduction of surface OH termination and the formation of a vacancy type of defect [76].

5

Electrical Conductivity and Doping

107

1.00 Pt11

Effective barrier height φB(eV)

0.95

10

Pt

0.90 0.85

Ag5

Zn-Polar face O-Polar face non-Polar face Ag6

Pd7 Au4

0.80 0.75

Pd8

Ag4

0.70

Pd9

2

Ir12

Au

0.65

Au3

0.60 1.0

1.1

1.2 1.3 1.4 Ideality factor n

1.5

1.6

Fig. 5.7 Effective barrier height ˚B as a function of ideality factor for Schottky diodes reported in the literature. After [88], for references see also there

Schottky diodes have also been investigated on ZnO nanorods grown by MOCVD [77], using Au being evaporated on the tips of the nanorods and a contacting AFM tip for single nanorods current–voltage measurements. Pt Schottky diodes on single nanorods [78] show excellent ideality factors of 1.1. The current–voltage characteristic becomes ohmic under UV illumination, probably because of the large electron-hole concentrations. Schottky junctions have also been fabricated by using a conductive polymer, PEDOT:PSS (poly(3,4-ethylenedioxythiophene): poly(styrenesulfonate)) [79], with an ideality factor of 1.2. The quality of ohmic contacts to ZnO drastically depends on the doping level. Since n-type doping levels in ZnO can be very high, there is usually no problem in making good ohmic contacts to n-type ZnO, for example, Ti/Au ohmic contacts have been reported, with specific contact resistances in the 104  cm2 range after annealing at 300ı C in nitrogen atmosphere [80]. Non-alloyed Al/Pt contacts with contact resistances in the range of 104 ˝ cm2 on ZnO with carrier densities in the 1018 cm3 ranges are possible [81]. The dependence of contact resistance on the carrier concentration has also been reported for Ti/Al/Pt/Au contacts. For carrier concentrations varying in the range 7:5  1015 –1:5  1020 cm3 , as-deposited specific contact resistance in the range from 3  104 to 8  107  cm2 could be achieved [82]. Owing to the difficulties in obtaining p-type ZnO, work on ohmic contacts to p-ZnO is much more limited. Ohmic contacts to ZnO:Sb with contact resistances in the low 104 Ohm cm2 range have been reported by using Au/Ni contacts [83], which is quite surprising and raises questions on the underlying doping type and its

108

A. Waag

consistent measurement. Nevertheless, the use of Ni as a potential contact material could be explained by the fact that NiO is one of the few oxides which are intrinsically p-type in nature. Ohmic contacts on single nanorods have also been reported. These depend drastically on the background carrier concentration in the nanorods [84, 85].

5.7 Two-Dimensional Electron Gas and Quantum Hall Effect Two-dimensional electron gas systems (2DEG) formed by modulation doping or forming spontaneously by piezoelectric effects in a semiconductor heterostructure are well-suited vehicles to demonstrate the degree of control and quality achieved in the respective semiconductor system. In addition, such a 2DEG also serves as a basis for the fabrication of high electron mobility transistors (HEMTs) and other devices. In polar semiconductors (GaN and ZnO), a high carrier concentration in a 2D channel can not only originate from modulation doping, but is generally also obtained by strong polarization effects. ZnO has a slightly higher saturation velocity as compared to GaN, which is often claimed to be advantageous in HEMT devices. However, the process technology for high-quality ZnO HEMT structures has not yet been developed to a degree that commercial devices seem to be possible. The goal of a 2D channel is to separate ionized impurities from the 2D electron or hole channel and hence reduce the ionized impurity scattering and therefore increase the mobility, since ionized impurity scattering is the dominant scattering mechanism at room temperature for dopant concentrations above 1  1018 cm3 , see Fig. 5.6; whereas at lower dopant levels, the mobility at RT is mostly controlled by polar optical phonon scattering. Also, the structural quality of the ZnO under investigation plays an important role. In thin films, the structural properties depend, for example, on the growth of an efficient MgO buffer layer [86]. Recently, Hall mobilities of 5;000 cm2 /Vs at 100 K and 440 cm2 /Vs at RT have been reported for undoped ZnO grown by Laser-MBE [87]. This mobility is a factor of two higher as compared to relevant mobilities in bulk material grown by vapor-phase transport, with values of 230 cm2 /Vs at room temperature and 2;200 cm2 /Vs at low temperature [89, 90]. On 2-in. bulk substrates, a room temperature mobility of 200 cm2 /Vs has been reported [91]. A typical structure for the investigation of a 2DEG is shown in Fig. 5.8. The electron channel is formed at the bottom of the top ZnO layer because of the mismatch between ZnMgO and ZnO in electric polarization. The electron concentration in the 2DEG channel can be controlled by the Mg concentration and extrinsic doping in the barrier. Two configurations are possible for the fabrication of a 2DEG: oxygen-polar ZnO on ZnMgO, and Zn-polar ZnMgO on ZnO [92–96]. Therefore, the control of polarity during growth is obviously of importance. An Al2 O3 gate dielectric grown by atomic layer deposition has been used here to control the 2DEG by an external field [92]. Both a metal–insulator transition as well as the Shubnikov de Haas oscillations (SdH) could be obtained in a magnetic field [92]. The 2DEG

5

Electrical Conductivity and Doping

109

a

b Source Drain

Source

Gate-Electrode AI2O3 (40 nm) Zn0.88Mg0.12O

ZnO

Psp

Ppe

ZnO (100 nm) 2DEG

Zn1-xMgxO

Psp

Zn0.88Mg0.12O

Fig. 5.8 Typical 2DEG structures, including the conduction band alignment, for samples with and without a top gate in order to control the 2DEG. After [92]. Psp and Ppe is the spontaneous and piezoelectric polarization 100

3000

1012

0

Magnetic field (T) 2 4 6 8 10 12

2000 1000 1500

900 800 700 600

1011

500 10

1000

Mobility (cm2/Vs)

2500

Rxx(Ω)

Sheet carrier concentration (cm–2)

10

500 0

100 Temperature (K)

Fig. 5.9 Hall mobility as a function of temperature for a Zn-polar 2DEG. Note the low values for ZnO. After [96]. Also shown are Shubnikov de Haas oscillations

carrier concentration as derived from the SdH oscillations was in good agreement with Hall measurements (Fig. 5.9), indicating the consistency of the structure and the evaluation, with a highest mobility of 5;000 cm2 /Vs for oxygen-polar FETs. For structures grown on zinc polar ZnO, a mobility of up to 14;000 cm2 /Vs has been reported [94], the difference to laser-MBE being most likely due to a different growth technique (Laser-MBE vs. MBE). The quantum Hall effect could be observed in ZnMgO/ZnO high-mobility heterostructures, and the electron effective mass could be obtained from the temperature dependence of the SdH oscillations [97]. The carrier concentration in the 2D channel could be controlled by varying the Mg concentration in the barrier as well as the growth polarity. Well-defined quantum Hall plateaus, however, could not be observed.

110

A. Waag 400

mobility (cm2/Vs)

350 300 250 200 150 100 50 0 0

50

100

150

200

250

300

350

T (K)

Fig. 5.10 Temperature dependence of the mobility of a ZnO layer (bottom) and a modulationdoped ZnMnO/ZnO 2D electron gas. After [98]

The formation of a 2D electron gas has also been demonstrated in magnetic material, for example ZnMnO-ZnO heterostructures [98]. Only a slight increase of the maximum mobility at low temperature could be achieved in this case, even though the channel was in the binary ZnO. Obviously, a pronounced impurity or defect scattering or a scattering at interface roughness still limits the maximum achievable mobilities in these samples. All values remain significantly under those of good bulk samples. Figure 5.10 shows the temperature dependence of the mobility of a ZnO layer in comparison to a modulation-doped ZnMnO/ZnO 2D electron gas (from [98]). Both mobilities show a maximum at around 100 K. However, the mobility of the 2DEG at the ZnMnO–ZnO interface does not decrease because of ionized impurity scattering at lower temperatures, in contrast to the case of ZnO. The longitudinal magnetoresistance (Fig. 5.11) shows oscillations for magnetic fields above 3.7 T. In principle, an influence of the s–d interaction leading to giant g-factors should occur, but has not yet been seen in these experiments. In this case, a strong temperature dependance of the position of the integer filling factors should be observed. However, temperature-dependent measurements have obviously not been performed.

5.8 High-Field Transport and Varistors The high-field drift velocity in ZnO, for example, has been calculated theoretically by a Monte Carlo method, with a spherically symmetric and non-parabolic approximation of the relevant conduction bands [99]. In this publication, the conduction bands have been derived from a full potential, linearized muffin-tin orbital method in the local density approximation. Drift velocities were calculated for temperatures

5

Electrical Conductivity and Doping

111

1.12 1.85 K γ= 12

1.10

ρxx(B)/ρxx(0)

1.08

γ= 11

γ= 10

1.06 γ= 13

1.04 1.02 1.00

I = 2 µA

I = 20 µA

0.98

I = 100 µA

0.96 0

2

4 B (T)

Fig. 5.11 Longitudinal magnetoresistance at a temperature of 1.85 K for the ZnMnO/ZnO 2DEG of Fig. 5.6. After [98]

Drift Velocity (107 cm/s)

4

3

ZnO GaN

2

1

0 0

100

300 200 Electrical field (KV/cm)

400

Fig. 5.12 Comparison of theoretically calculated drift velocities as a function of electric field for both GaN and ZnO. After [99]

of 300 K, 450 K and 600 K. Drift velocities higher than 3  107 cm/s are reached at room temperature at fields near 250 kV/cm (see Fig. 5.12). At higher temperatures, the drift velocities are significantly lower, as shown in Fig. 5.13. Again, the drift mobilities are found to be limited by strong polar optical phonon scattering. The cusp in Fig. 5.12 is found to result from the non-parabolicity of the lowest conduction band in ZnO [99]. The high electric field properties are also used in ZnO-based variable resistors, called varistors. In normal mode, ZnO varistors have a very high resistance (more

112

A. Waag

Electron drift velocity (107 cm/s)

4

3

2

1

0 0

100 200 Electric field (KV/cm)

300

Fig. 5.13 Calculated electron drift velocities as a function of electric field for various temperatures. After [99]

(b)

a = 1 a = 2 a = ∞

–200

(a)

2

1

Current (mA)

Fig. 5.14 Typical current–voltage curve for a ZnO varistor, demonstrating the switching behavior from “ON” to “OFF”. For comparison, the I –V curves for different non-ohmic exponents are also shown [100]

–100 100

200

Voltage (V)

–1

–2

than 1010 Ohm cm) below a certain voltage threshold and switch to a very low resistance state above a certain voltage threshold. A typical current-voltage characteristic of ZnO varistors is nonlinear, and is shown in Figs. 5.14 and 5.15. The high-voltage switching behavior can be used to protect electronic circuitry against voltages peaks,

5

Electrical Conductivity and Doping

113

1000 Region I

II

III

VOLTAGE (V/mm)

500

Impulse

200 100

20°C

50

50°C

dc

1 20

1/2

75°C 100°C

8 10 10–10

10–8

10–6

10–4

10–2

CURRENT

(A/cm2)

1

20 10

t (µs) 2

104

Fig. 5.15 Varistor I –V characteristics on a logarithmic scale. For an explanation of the three regions, see text. From [100]

and for example in overvoltage surge arresters. The first varistors were developed as early as 1968 [100, 101]. Commercial products are available and are widely used. See also Chap. 13. The varistor behavior is not due to an intrinsic ZnO property, but is caused by the typical transport behavior across grain boundaries. Varistors are fabricated by sintering ZnO into a semiconducting ceramic, with a small amount (in the percent range) of additives like Bi2 O3 , MnO, CoO, and Sb2 O5 . The deviation of the I–V curve from a linear, ohmic behavior is expressed with a parameter ’, which is defined by modeling the current–voltage behavior by a simple empirical equation I D .U=C/’ For ’ D 1, the device is a simple ohmic resistor. The larger the value for ’, the larger is the deviation from the ideal ohmic behavior. Typical values for ’, which are found in ZnO varistors, are between 30 and 100 [100]. For varistors, three regions of operation are distinguished (Fig. 5.17). Below threshold, typically at current densities below 1 A=cm2 , the non-ohmic properties are not dominating. Between this threshold voltage and a voltage corresponding to a current of approximately 100 A=cm2 , the device is very much non-ohmic. This is region II. Above 100 A=cm2 , in region III, the non-ohmic behavior is less prominent. Varistors are characterized by the parameter ’ and their range, in which the most prominent non-ohmic behavior occurs (region II). The fundamental structure of the ZnO material used for varistors exists as single grains, which have a reasonably low resistance on their own. However, the overall electric transport behavior is governed by grain boundaries. The breakdown voltage

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between two electrodes is proportional to the number of grain boundaries between these electrodes. The breakdown voltage should hence be inversely proportional to the grain size. Typical grain sizes are between 5 and 20 m. By adding the additives, certain intergranular phases form during annealing and cool down, with complicated microstructures at the grain boundaries. The most important ingredient is the Bi2 O3 additive, resulting in pronounced non-ohmic properties. One of the goals of adding these materials is to suppress ZnO grain growth in order to get a high number of grains and hence a large threshold voltage. Various models have been proposed in order to describe the non-linear I–V characteristics of ZnO varistors, including space-charge-limited currents [102], tunneling through an interface barrier layer [103], tunneling through surface and interface states, and hole-induced breakdown [100, 104]. Also, bypass effects through a Bi2 O3 interface layer have been discussed [105]. Recent work focuses on the implementation of additional additives to further optimize the operation characteristics of ZnO varistors, in particular their voltage range, their stability as well as the clarification of the microscopic phenomena causing the non-linear behavior. ZnO varistors are ageing under sufficiently high DC current densities. The original I–V curves can be restored when the varistors are annealed at temperatures above 200ıC [106]. It has been pointed out that the excess oxygen at the grain boundary interfaces, as well as the strong oxygen ion conduction of Bi2 O3 at the grain boundaries, plays an important role for the functionality of the varistor [107].

5.9 Photoconductivity ZnO has a rich surface chemistry. Usually, it is assumed that a Fermi-level pinning, surface band bending and depletion layers at the surface influence the transport behavior of nanoparticles and nanorods. With illumination above the band gap, electrons and/or holes can diffuse to the surface and cause desorption of adsorbed species, or be the cause of additional surface chemistry in general. The surface depletion of ZnO nanorods has already been discussed in the chapter 3 – “Growth”. Owing to the electric field in the surface region, electrons and holes created by illuminating the nanorods with above band gap light will be separated. The general situation is schematically shown in Fig. 5.16. In this case, holes will diffuse to the surface and can initiate desorption of oxygen molecules. The change of surface termination then influences the band bending, the depletion zone and hence the conductivity of the nanorods (or nanoparticle). This effect is most pronounced for low carrier concentrations. A photoconductive response is common to all semiconductor systems, as long as the concentration of excited electrons and holes modifies the existing equilibrium carrier concentration in the material under investigation. This photoresponse, however, decays with the recombination of excited electron–hole pairs. In contrast to that, the photoresponse in ZnO nanorods, nano-particles, or polycrystalline

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O2

O2

O2

O2

O2

115

O2

EC

EC

EF

EF

EV

EV

O2

in the dark

O2

O2

under illumination

Fig. 5.16 Schematics of the band bending at a ZnO nanorod surface, including the desorption of adsorbed species (in this case oxygen molecules) because of illumination. From [108]

thin films has a much longer decay time; on the order of seconds, minutes, and hours. In addition, the photo-response decay rate (i.e., the inverse of the decay time) drastically depends on the environment. Oxygen (dry or wet), nitrogen, or air environments lead to different decay rates. One of the many results from literature is shown in Fig. 5.17, where the current through a nanocrystalline ZnO film at constant voltage is shown as a function of time. After illumination with above band gap light, the conductivity of the material changes by up to six orders of magnitude. On this time scale, the increase in conductivity after switching on the illumination is instantaneous. After switching off the illumination, the conductivity slowly returns to its original value, time scales being on the order of 1,000 s. The decay rate of the photoresponse depends on the gas environment. Both oxygen molecules as well as water vapor in the gas seem to be important ingredients leading to a faster decay rate relative to the behavior in gross vacuum (see Fig. 5.17). For more examples on the application of ZnO as sensor, see Chap. 13. Photoconductivity and the photo-Hall effect have also been measured in order to get information on the carrier concentrations in polycrystalline material [109]. However, in view of the non-homogenous character of the material under investigation, the reliability of the Hall data has to be discussed critically. See also the discussion above. Nevertheless, conductivity has been found to be surface-charge-controlled. Photoconductivity is thought to be due to the capture of holes at surface oxygen states, which produces an equal number of electrons in the conduction band [109].

116

A. Waag 1E-4 vacuum H2 N2 O2 air

UV @ 365 nm

1E-5 1E-6 Current (A)

1E-7 1E-8 1E-9 1E-10 1E-11 1E-12 1E-13 1E-14 0

200 400 600 800 1000 1200 1400 1600 1800 Time (s)

PO2 (a.u.)

Fig. 5.17 Temporal photoresponse of a sintered ZnO nano-particle thin film in various gas environments. Turn-on of illumination at 250 s, turn-off illumination at 700 s. From [108]

a

e

b c

d 1/2(Pzn) 200

400

600 T (K)

800

1000

1500

Fig. 5.18 O2 desorption after adsorption of oxygen at different temperatures (a) adsorption at 100 K (physisorbed) (b) adsorption at 300 K (chemisorbed) (c) desorption from roughened surface (edge and kink desorption) (d) sublimation of the crystal. After [110]

Oxygen bound to a ZnO surface at various temperatures has been analyzed by thermal desorption spectroscopy, shown in Fig. 5.18 [110]. This desorption then influences the band bending as well as the conductivity of the material. In general, the study in [110] shows that the surface concentration of intrinsic point defect deviates substantially from their bulk values, leading to strong accumulation layers with very high carrier concentrations, with a strong influence on catalytic properties [110].

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Chapter 6

Intrinsic Linear Optical Properties Close to the Fundamental Absorption Edge C. Klingshirn

Abstract In this chapter, we review the intrinsic linear optical properties of ZnO close to the fundamental absorption edge. This comprises band-to-band transitions and free excitons and polaritons in bulk samples and epitaxial layers; free and localized excitons and polaritons in quantum wells and wires, including nanorods; also localized excitons in alloys and in quantum dots (or nano crystals) and finally cavity polaritons. By the term “free excitons”, we mean the quanta of the intrinsic electronic excitation in semiconductors (and insulators), which can move freely through the sample and which are described by a plane wave factor exp.i Kr/ in d dimensions (d D 3, 2 or 1), where K is the wave vector of the centre of mass motion described by r, multiplied by the envelope function of the relative (hydrogen-like) motion of electron and hole around their common centre of gravity. By the terms “bound exciton complexes” or “bound excitons” [(BEC) and (BE), respectively], we understand excitons that are bound to some centres like neutral or ionized donors or neutral acceptors but also to more complex centres. They will be treated in Chap. 7. In contrast, by the term “localized excitons”, we mean electron–hole pairs, which are localized by disorder like intrinsic alloy disorder, for example, in Mg1x Znx O and/or fluctuations of well (or wire) width in quantum structures. These phenomena are inherent to alloys and to structures of reduced dimensionality and are therefore included in this chapter. The influence of external fields on both free and bound excitons is then covered in Chap. 8.

6.1 Free Excitons in Bulk Samples We show in Fig. 6.1a the schematically and simplified one-particle states of valence and conduction bands of a direct-gap semiconductor; in Fig. 6.1b the two-particle exciton states and in Fig. 6.1c the dispersion of exciton polaritons, resulting from the diagonalization of the Hamiltonian containing the photon field, the exciton and

C. Klingshirn Institut f¨ur Angewandte Physik, Karlsruher Institut f¨ur Technologie KIT, Karlsruhe, Germany e-mail: [email protected]

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Fig. 6.1 Schematic drawing of the conduction and valence band states of a direct-gap semiconductor as one-particle states (a), the dispersion of excitons with main quantum numbers nB D 1, 2 and 3 followed by the ionization continuum as two-particle states (b) and the close-up of the intersection region of exciton and photon dispersion for nB D 1(dotted lines), the resulting polariton branches and a possible longitudinal branch (solid lines) and a spin-triplet state (dashed line) (c). According to [1–3]

their interaction. The results of this procedure are quanta, which describe a mixed state of electromagnetic and excitonic polarization fields and which are known as exciton polaritons. For more details, see [1, 4–18] and references therein. There is a lower polariton branch (LPB) which starts with a linear (so-called photon-like) dispersion and then bends over to an exciton-like dispersion, followed towards higher energies by a finite transverse-longitudinal splitting LT , possibly a longitudinal exciton branch and then by an upper polariton branch (UPB), which becomes photon-like again. In addition, we show by the dashed line the dispersion of an exciton which does not couple to the electromagnetic field (e.g. a dipoleforbidden and/or spin-triplet state) and consequently does not form a polariton. The linear photon-like parts of the dispersion relation have slopes „c/ni , where ni is the square root of the static and of the background dielectric constants for LPB and UPB, respectively. The transition region between photon- and exciton-like dispersion is called “bottleneck”. We present in Chap. 8 data on the influence of (external) fields essentially of magnetic and strain fields on the excitonic complexes, while non-linear optics, high excitation effects and stimulated emission are treated in Chap. 11 and the dynamics in Chap. 12. Before we start with free excitons, we give a short rehearsal or extension of the topic “band structure” treated in more detail in Sect. 4.1 of Chap. 4 and also in Sect. 8.1.4 of Chap. 8.

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123

Fig. 6.2 The atomic ns2 and mp6 levels for ZnO for n D 4 and m D 2 (a), their splitting at the  point and the dipole selection rules without and with inclusion of spin for cubic zinc-blende-type structure (b), for the hexagonal wurtzite - type structure for the normal valence band ordering and

so  cr (c), for the inclusion of cr only and neglecting spin and so (d), for the situation j so j << cr and normal VB ordering (e) and finally for a significant influence of p–d coupling and again j so j << cr resulting in the inverted ordering (f). Strongly dipole-allowed transitions (i.e. those without spin-flip) are indicated by a solid vertical double arrow, ones involving a spinflip by a dashed one, w/o and w stand for without and with spin, respectively, and ? or jj in the transition arrows give finally the polarisation of E, where applicable. See also Fig. 4.1. According to [19–27]

We start in Fig. 6.2.a with the fact that the conduction band (CB) has close to the  -point s-symmetry because it arises from the empty 4s levels of ZnCC (stressing the ionic binding) or from the lowest antibonding sp3 hybrid states (stressing covalent binding). See also Chap. 2 on the aspect of chemical bonding. Both notations result in the same symmetries and selection rules. In the same sense, the valence band (VB) originates from the occupied 2p states of O-- or the energetically highest bonding sp3 states. We give for the various levels the correct i symmetries but for the case of argumentation also the values of the angular momentum (L) and the sum of angular and spin angular momentum J , noting that these quantities have to be used with great care in crystals [1] and are reasonable quantum numbers only up to L D 1 or J D 3=2 in cubic symmetry. In the uniaxial wurtzite-type structure, only their z-components can be related to the  ’s and only up to Lz D ˙1 or Jz D ˙3=2. For a short introduction to group theory and its application to semiconductor optics, see [1] and references therein. If we consider (Fig. 6.2b) cubic zinc-blende-type symmetry (point group Td ), we obtain from the compatibility relations without spin CB:1 and VB:5 . The transition is dipole-allowed independent of polarization E. Including spin and the

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spin–orbit splitting so , we obtain for the CB 6 and for the VB .8 C 7 /. Both transitions between VB and CB are again dipole-allowed for all orientations. If we go from there to the hexagonal wurtzite-type modification (point group C6v ) and introduce a hexagonal crystal field splitting cr comparable to so as realized, for example, in CdS or CdSe, we obtain CB: 7 , VB: 9 , 7 , 7 . See Fig. 6.2c. The transition 9 ! 7 is dipole-allowed only for E ? c (5 ), where E and c are the polarization of the electric field and the orientation of the polar, crystallographic c-axis (cjjz). The transitions 7 ! 7 are allowed from arguments of group theory for both polarizations E ? c and E jjc.1 /. In Fig. 6.2d, we show the situation for hexagonal crystal-field splitting cr only, which leads without spin in C6 (or 6mm) symmetry to CB: 1 and VB: 1 C 5 . One transition is dipole-allowed only for E ? c.VB 5 ! CB 1 /, the other only for E jjc.VB 1 ! CB 1 /. If we now allow for a small so << cr (Fig. 6.2e), this perturbation splits the 5 -VB into 9 C 7 but since it is assumed to be a weak perturbation the transitions from the two upper VB bands to the CB have still considerable oscillator strength only for E ? c (actually, the transition from the upper 7 VB to the 7 CB is dipole-allowed also for E jjc as mentioned above, but spin-flip forbidden), while the transition from the lower 7 VB has still substantial oscillator strength only for E jjc.1 / while the transition with E ?c.5 / is again dipole-allowed but spin-flip forbidden. With the term “spin-flip forbidden” we mean that the transition involves a spin-flip and has therefore very small oscillator strength, while a “spin-flip allowed” transition does not involve a spin-flip and has, if it is simultaneously also dipole-allowed, strong oscillator strength. Spin-flip forbidden transitions lead usually from the crystal ground state to a spin triplet (s D 1) electron–hole pair state while spin-flip allowed transitions go to a spin-singlet state (s D 0). In Fig. 6.2f, we show finally the influence of a strong p–d coupling in the VB (see below) resulting in the inverted valence-band ordering but keeping the selection rules as long as j so j cr holds. If we want to know how large the value of so in ZnO might be without the influence of the lower d states, we do not trust a theoretical Z ˛ dependence on the nuclear charge Z for atoms or ions, but we just consider the experimental data for various IIb –VI semiconductors, e.g. from [45]. The inspection of these data shows that so depends as expected with rather high accuracy only on the anion (i.e. it is, e.g. the same for all IIb -selenides) and it is also only marginally dependent on the crystal structure, i.e. zinc-blende- or wurtzite-type, which have both tetrahedral coordination. Therefore, we plot in Fig. 6.3 so as a function of the Z of the anion for group IIb -tellurides, IIb -selenides and IIb -sulphides. We find an empiric relation so  Z 2:2 , extrapolate it to the IIb -oxides (Z D 8) and obtain

oxides D .17 ˙ 2/ meV. This means that the 9 level should lie, according to so Fig. 6.2b, about 17 meV above the upper 7 level. Unfortunately, this quantity is not experimentally accessible, since ZnO does not occur in cubic form in good qualitity, where cr would be zero, nor can the influence of the d states be switched off. On the other hand, the band structure of CdO is not sufficiently well known to deduce from this material. the value of oxides so The point now is that in ZnO the atomic ZnCC 3d levels are closest to the mp anion (here, m D 2 for O-- ) levels for all Zn–VI compounds [1,28]. These 3d levels

6

Intrinsic Linear Optical Properties Close to the Fundamental Absorption Edge

125

Fig. 6.3 The values of the spin–orbit spitting of the VB of group IIb -tellurides, IIb -selenides and IIb -sulphides as a function of the anionic Z number, including the extrapolation to Z D 8, i.e. Oxygen. According to [2, 3]

split in an upper J D 5=2 and lower J D 3=2 state by spin–orbit coupling. This upper J D 5=2 state splits in C6 symmetry further in an upper 7 level followed to lower energies by 8 and 9 levels. The interaction, mixing and level repulsion between this upmost 7 d-VB and the upper 7 VB state of Fig. 6.2c may shift this latter state above the 9 level as sketched in Fig. 6.2f. If this shift is only of the order of 25 meV, it is sufficient to have in ZnO the upper 7 VB level about 5 meV above the 9 VB level, a value close to the experimentally determined A–B VB splitting of 4.5 meV. For older and recent theoretical considerations of this aspect, see Chap. 4 and, e.g. [26, 28, 29]. The term inverted valence band ordering is correct when comparing Fig 6.2e and 6.2f but the term “negative spin–orbit splitting” is misleading in so far as the spin–orbit splitting between the upper 7 and 9 VB states is always positive (Fig. 6.2c, e), but the interaction with the relatively close-lying VB originating from ZnCC d-levels causes the shift of 7 above 9 . After this short excursion to band structure, we proceed now to free excitons.

6.1.1 Free Excitons in Bulk Samples, Epitaxial Layers, and NanoRods Before we show optical spectra and dispersion curves of excitons or exciton polaritons, we present in Table 6.1 the exciton states with main (or Bohr) quantum number

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C. Klingshirn

Table 6.1 The A-, B- and C-exciton levels of ZnO for nB D 1. The occurrence of a spin-flip is indicated. According to [1, 19–25] Exciton state DipoleSpin-flip involved Oscillator strength A 1 Allowed for Ejjc Yes Small A 2 Forbidden Yes Very small A 5 Allowed for E?c No Large B 6 Forbidden Yes Very small B 5 Allowed for E?c No Large C 1 Allowed for Ejjc No Large C 2 Forbidden Yes Very small C 5 Allowed E?c Yes Small

nB D 1, which are formed from an electron in the CB and a hole in one of the three upmost VBs. The irreducible representations of the exciton states are given in general by the direct product of the irreducible representations of electron and hole wave functions (e , h ) and of the envelope function env , i.e. ex D e ˝ h ˝ env For the nB D 1 states env D 1 , resulting in ex D 7 ˝ .A7 C B9 C C7 / ˝ 1 D A1 C A2 C A5 C B6 C B5 C C1 C C2 C C5

(6.1)

This means that we can expect strong signals in absorption and reflection spectra for the A5 and B5 excitons for E ?c and for the C1 exciton in E jjc. See Fig. 6.4. For the luminescence, the situation may be more complicated because the thermal population probability, the excitation depth and the escape length enter in addition to the oscillator strength. The occupation is at low temperatures much higher for the lower lying spin-triplet states than for the higher singlet states and even higher for the bound excitons (if thermal equilibrium is established). Three further aspects should be mentioned concerning k-linear terms, close-lying resonances and birefringence: Group theory allows for the point group C6v (or 6mm) of ZnO for bands with 7 symmetry a k-linear term for the direction k?c. See, e.g. [1, 19–27, 30, 31]. This effect is shown schematically in Fig. 6.4 for the A7 VB. A similar term can be expected for the C7 VB [18]. The one for the 7 CB is expected to be negligible. The k-linear term in the A7 VB mixes the A5 and the A.1 C 2 / exciton states and gives the latter a small oscillator strength increasing with k?c. This small oscillator strength has the consequence that the LPB converges for the A-exciton polariton for E ?c and k?c to the A.1 C 2 / states which are practically degenerate at k D 0 and not to A5 T . Additionally, an intermediate A-polariton branch appears between A.1 C 2 / and A5 T as shown in Fig 6.5a. It should be noted that the graph Fig. 6.5a is valid only for E ?c and k?c. From the two 5 states in the x–y plane (normal to c), one forms the transverse exciton polariton and the other the

6

Intrinsic Linear Optical Properties Close to the Fundamental Absorption Edge

127

Fig. 6.4 Schematic drawing of the band structure of ZnO in the vicinity of the  point. The polarisations of the dominant transitions are indicated. Compare with Fig. 6.2f and Table 6.1. According [2, 3]

a

b 3.380

k x, E y

k

energy (eV)

3.379

hωl

long.

3.378

c

hω z

E z

hωo

3.377 3.376 3.375 (a)

3.374 0

k (106 cm–1)

2

k

Fig. 6.5 Real parts of the exciton-polariton dispersion (solid lines) of the exciton resonances with strong oscillator strength (see Table 6.1) for k?c and E ?c where the longitudinal exciton is indicated by a dotted line (a) schematic for the C1 exciton and k?c and E jjc where no longitudinal exciton exists, for simplicity with neglected exciton dispersion (b) and for an example of mixedmode polaritons, here the C 1 state. The angles between k and c are indicated (c). According to [27]

longitudinal exciton. For kjjc and E ?c, both 5 states are transverse and both the k-linear term and the longitudinal exciton branch are absent. We come back to this aspect in Fig. 6.14. Theory predicts approximately equal oscillator strengths for the A5 and B5 excitons [19–25, 34]. This would imply for well-separated resonances also roughly equal longitudinal–transverse splittings LT realized, e.g. in hexagonal CdS. In ZnO, the A5 and B5 exciton resonances are, however, not well separated but are very close in energy and interact with each other. The linear superposition of two

128

C. Klingshirn

Fig. 6.6 The dielectric function of two close-lying resonances separately (a,b) and their superposition (c). From [1]

close-lying resonances reduces the LT value of the lower one and increases that of the upper one as shown schematically in Fig. 6.6 where the real part of the dielectric function is shown independently for the A and B resonances in Fig. 6.6a, b and for the sum of both in Fig. 6.6c. For simplicity, both damping and the dependence of the exciton energy on k (the so-called spatial dispersion resulting from a non-local

6

Intrinsic Linear Optical Properties Close to the Fundamental Absorption Edge

129

response function ".!; k// are neglected. Therefore, the transverse eigen energies are simply given by the poles of ".!/ and the longitudinal ones by the zero transitions as usual. The background dielectric constant must be counted only once in Fig. 6.6c. The shifts of the longitudinal frequencies indicated by horizontal arrows are obvious, while the positions of the poles remain unchanged. For more details see [1, 35, 36]. In Fig. 6.5b, we show the situation for the C 1 exciton polariton for k?c and E jjc. Since the 1 oscillator state is only one-fold and oriented jj c, there exist for this orientation only one transverse lower and one UPB, but no longitudinal one. The splitting and possible coupling to the dipole or spin-flip forbidden C2 and C5 states are here neglected. For the orientation kjjc, the 1 state forms simply a longitudinal exciton branch. ZnO is, as stated already in Chap. 2, a uniaxial material with a polar hexagonal c axis (cjjz). Therefore, ZnO shows birefringence and dichroism. The ordinary beam has E polarized perpendicular to the main section. This is the plane defined by k and c. The extraordinary beam has E in the main section. Its dispersion depends on the angle ˛ between c and k. In the exciton resonance region, the extraordinary beam corresponds to the so-called mixed-mode polaritons [1, 27, 37–42] in the following sense: We consider for simplicity a 1 oscillator which has its elongation parallel to c, as already mentioned. If a light beam impinges on the sample with E in the main section (the plane defined by k and c) and at an arbitrary angle ˛ ¤ 0ı , 90ı between k and c, this E has components perpendicular (transverse) and parallel (longitudinal) to c, i.e. it is in a mixed mode. In other words, only the component of the incident electric field which is jjc couples to the 1 oscillator and consequently the oscillator strength f varies like f .˛/ D fo sin2 ˛:

(6.2)

This behaviour is shown in the polariton dispersion curves of Fig 6.5c. The dichroism, i.e. the dependence of the absorption spectrum on the polarization relative to the c-axis follows directly from the selection rules in Figs. 6.2 and 6.4 or Table 6.1 and is seen in Fig. 6.12.

6.1.2 Experimental Observations We start this part with reflection spectra. It should be noted that these spectra are rather sensitive to surface contaminations (especially for surfaces parallel to c) so that they should be measured only on fresh, high-quality as-grown, cleaved or etched surfaces. In Fig. 6.7, we show review spectra for the two polarizations, with the wellpronounced nB D 1 states of A-, B- and C-excitons in their respective polarizations (see Table 6.1) and, in addition, states with nB D 2, 3 followed by the smooth contributions from the ionization continuum. These types of spectra have been observed

130

C. Klingshirn

Fig. 6.7 Overview spectra of the excitonic reflection spectra of ZnO at T D 1:8 K for the two polarisations E ?c and E jjc. According to [27, 44]

by many authors already in the past [18–27, 41–50] and references therein but also more recently, e.g. in [51–53]. Spectra which look differently in the sense that, e.g. A- and B-excitons merge already at low temperature or that A-, B- and C-excitons are seen in the same polarization with similar signal strength [54] or show unusual signal heights for A- and B-excitons [55] are distorted, e.g. by strain [9], by surface defects or surface-charge layers [27, 41, 42, 44, 46, 56] or are due to misorientations of the sample. For (thermo-, photo- or wavelength-) modulation spectroscopy of the reflection spectra of partly isotopically pure samples, see e.g. [57–60]. The analysis of the states shows that the exciton series for A-, B- and C-excitons follow in ZnO with a good accuracy a hydrogen-like series: Ex .k D 0; nB / D Eg  Ry  =n2B ;

(6.3)

with an excitonic Rydberg energy Ry of (59 ˙ 1) meV. See [19–27, 45] and references therein. These data are confirmed by absorption measurements (see below). This is to some extend surprising because this value is close to the LO-phonon energy „! D 72 meV (see Chap. 2) and one finds frequently enhanced binding energies for the nB D 1 state for Ry „!LO :

(6.4)

With the effective masses of me D 0:28m0 and mh D 0:58m0 (see Chaps. 4, 7 or [45]), this value results in an effective dielectric constant © in   Ry D 13:6eV = m0 "2

(6.5)

6

Intrinsic Linear Optical Properties Close to the Fundamental Absorption Edge

131

Fig. 6.8 Experimental reflection spectra of the nB D 1 excitons in ZnO at 1.8 K together with theoretical models using different abc’s. According to [27]

of " D 6:56 and an excitonic Bohr radius aB D 1:8 nm where  is the reduced mass,  D 0:19 m0 . In [53], lower values of the exciton-binding energy Exb D Ry for the B and C excitons in the range of 50 meV are given. This discrepancy results from the unusual procedure applied there to count the binding energy from the excitonic reflection minima, i.e. from the longitudinal exciton states. Considering the data in [53] and counting as usual from the transverse (or from the very close-lying spin triplet) states results in the generally accepted value for all the three exciton series given above. In Fig 6.8, we show a close-up of the nB D 1 reflection spectra in their respective polarisations with theoretical fits. If the dielectric function involves a non-local response ©.t  t 0 ; r  r 0 / these dependences result in the Fourier transform in a dependence on the independent variables ! and k. See [16–25,27,35,36,41,42,44– 47, 61–63] and the references therein. ".t  t 0 ; r  r 0 /

FT ".!; k/: )

(6.6)

This, in turn, results in the effect of spatial dispersion, i.e. the existence of two (or more) propagating or evanescent modes for the same frequency, wave vector and polarization. The latter point makes the difference to birefringence as can be seen, e.g. by inspection of Fig. 6.1c. This situation is not covered by the two independent boundary conditions following from Maxwell’s equations that, e.g. the normal components of the electric displacement D and the tangential one of the electric field strength E are steady across the interface, but requires either so-called additional boundary conditions (abc’s) or more elaborate models cited, e.g. in [1]. One of the consequences of spatial dispersion is that the reflectivity does no longer reach unity in the stop band even for vanishing damping, because there is for

132

C. Klingshirn

every frequency at least one propagating mode. See Fig. 6.5a, c. In contrast, the k-dependence of ©.!; k/ has been neglected for simplicity in Fig. 6.5b resulting in a true stop band. We do not want to go into further details here, but refer the reader, e.g. to the above references. Furthermore, one observes in Fig. 6.8a clearly the different values of LT for the two resonances despite roughly equal oscillator strengths. Compare with Fig. 6.6. We have introduced the concept of mixed-mode polaritons with Fig. 6.5c for the C1 exciton, i.e. for an oscillator oriented parallel to c. In Fig. 6.9, we show measured reflection spectra (with theoretical fits) for the A- and B-exciton resonances which have been obtained under normal incidence to planes cut under various angles  relative to the c axis. The electric field E is linearly polarized in the main section. An angle  D 0ı corresponds to kjjc and E ?c and thus to the ordinary beam.

a 0.6

ordinary mode

Zn0 d = 30Å

0.4 0.2

e

0

b 0.6 θ = 45°

3.40

θ = 80°

BL

θ = 45°

d = 40Å

0.4

0

c 0.6

θ = 70° d = 30Å

0.4

d = 75Å

energy (eV)

reflectivity

0.2

θ = 0° BT AL AT

0.2

θ = <(k,c) E mainsection

0

d

3.36

0.6 θ = 80°

d = 85Å

0.4

0 2.106 real part of wave vector (cm–1)

4.106

0.2 0 3.37 AT AL BT

BL

3.40

energy (eV)

Fig. 6.9 Reflection spectra measured for normal incidence on surfaces cut perpendicular (a) or under oblique angles relatively to the c-axis (b–d) and the corresponding dispersion relations (e) of A- and B mixed-mode polaritons for various angles  between c and the surface normal for E in the main section. According to [27, 46, 47]

6

Intrinsic Linear Optical Properties Close to the Fundamental Absorption Edge

a 02

Zn0

E c

133

02

reflectivity

02

b 02

02

0.2

02

02

c 02 0.6

d

TL = 5K

77K

100K 02

02

02 3.44

3.40 3.36 photon energy (eV)

3.44

3.40

3.36

3.44

3.40

3.36

Fig. 6.10 Reflection spectra of the ZnO A and B 5 excitons with increasing temperature (from left to right) and excitation (from 0 to 8 MW=cm2 from bottom to top). According to [64]

Note that the two-fold degenerate A5 and B5 oscillators can be elongated only in the x–y plane normal to c. Therefore, no longitudinal branch exists for this orientation as already mentioned above. Finite angles  correspond in this configuration to mixed-mode polaritons. The k-linear term of the A exciton and damping have been neglected for simplicity in Fig. 6.9e. For increasing angle , one observes clearly the decrease of the oscillator strengths and of the reflection signals for A- and B-excitons in analogy to (6.1). Note that the longitudinal energy defined by ".!L / D 0

(6.7)

remains fixed, but the transverse one varies with the angle . The spectra shown so far have been obtained at low temperature, to elucidate finer details which would be obscured by increasing damping. The population of the phonon states increases with temperature resulting in an increasing damping, i.e. homogeneous broadening  . This effect is qualitatively obvious in Fig. 6.10 where we show reflection spectra of the nB D 1 A5 and B5 exciton resonances with increasing temperature in the lowest line. A similar effect occurs with increasing excitation density (from bottom to top) because of the scattering of excitons with other excitons or free carriers. This aspect follows qualitatively from a comparison of the left- and right-hands columns. We come back to this aspect in Chap. 11 and note here that the homogeneous width of the nB D 1 excitons in ZnO is in highquality samples and at low temperatures T  4 K in the order of or even below 1 meV and reaches 40 meV (FWHM) at 300 K. We shall also come back to this aspect in connection with Fig. 6.15 below.

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C. Klingshirn

Fig. 6.11 An early example of the RT absorption spectrum of ZnO. According to [66, 67]

Now, we turn to the observation of exciton(-polariton)s in transmission, i.e. absorption spectroscopy. In Fig. 6.11, we show – to the best of our knowledge – the oldest absorption spectrum of a thin ZnO film from 1944, produced by oxidizing a thin metallic Zn layer on quartz glass. The broadened peak at RT around 3.3 eV corresponds to the broadened, unresolved A and B5 exciton resonances and is possibly the first observation of an excitonic feature in a semiconductor at all, though this aspect was not known to the author of [66, 67] at that time. This absorption spectrum has been reproduced in the meantime many times, e.g. [43,68– 72], partly showing LO-phonon sidebands, but generally without knowing of or citing the earlier work [43, 66, 67]. As one can see, the absorption coefficient is in the band-to-band transition region above 105 cm1 . This means that samples with a thickness around 0:1 m are necessary to measure the absorption spectrum, even more so at lower temperatures where the absorption in the excitonic peaks may exceed 106 cm1 . We show in Fig. 6.12 data for E ?c and E jjc at low and room temperature, showing in the first case the exciton states up to nB D 3 together with some structures resulting from the interaction of excitons with LO-phonons, labelled LIJ . Compare this data to the reflection spectra of Figs. 6.7, 6.8 and 6.10. The shift of the exciton resonance with temperature, the increase of the damping and the Urbach tail behaviour [1] of the low-energy absorption tail below the exciton ground state are obvious. We come back to these topics below. We mentioned above, with Table 6.1, that some of the exciton states have small oscillator strength, because they are dipole-forbidden and/or involve a spin-flip. Nevertheless, these states can be observed as weak absorption signals in transmission. The nB D 1 A and B excitons are seen in E jjc as weak absorption dips in Fig. 6.13, where we show also the dependence on an external magnetic field B up to 20 T . For this aspect, see Chap. 8. The A1 CA2 spin-triplet states, which show within experimental resolution an accidental degeneracy at B D 0 split for B ¤ 0 because of the Zeeman effect. See for more details of this effect Sect. 8.1. The A5L ,

Intrinsic Linear Optical Properties Close to the Fundamental Absorption Edge Photon-Energy (eV) 3.6

3.5

3.4 C(n= 1)

3.3

A(n = 1)

B(n = 3) A(n = 3) B(n = 2) A(n = 2)

4

E//c (b) 4.2°K

4.2°K

1

3500

3600

Wavelenth (Å) (1a)

(a) 295°K

Ic2 A(n=1)

C(n= 1)

L1

?

C(n=1)

L1b L1a

A,B(n = 1) (a) 295°K

2

L3

L2

L2b L2a

3

L1

L1b L1a

3620

L2

3600

C(n= 3) ? C(n= 2)

(b) 4.2°K

L3

Absorption Coefficient (105 cm–1)

5

135

Photon-Energy (eV)

3.4 B(n = 1)

3.5

L2b L2a

6

3700

3400

3500

3600

3700

Wavelenth (Å) (1b)

Fig. 6.12 The absorption spectra of ZnO for the two polarisations and for 1.8 K and RT. According to [43]

is weakly seen as a mixed-mode polariton (see above) because of the finite angle of aperture of the light beam. Similar arguments may hold for B5 T (or B6 ). The narrow absorption peak labelled S is an isotropic point corresponding to the energy at which the dispersion relations for E jjc and E ?c cross between the nB D 1 Aand B-exciton states. Under this condition, energy can be exchanged between both polarisation states under energy and momentum conservation. For more details on the influence of magnetic fields, see Chap. 8. As a last aspect in this context, we show the manifestation of free exciton states in ZnO in luminescence and start with the zero-phonon line. To observe finer details low temperatures T  10 K are again obligatory. However, it should be mentioned, that the zero-phonon lines of the intrinsic A- and B-excitons are at low temperatures, much lower than the ones of bound excitons, since free exciton (polaritons) move through the sample until they are trapped at a defect without a chance of thermal re-excitation into free, i.e. delocalized states. In Fig. 6.14, we show the luminescence for various polarisations of E and orientations of k relative to c together with the corresponding polariton dispersion relations. For c?k?E ?c (the x, y plane is normal to cjjz), one has a k-linear term, which couples the spin-singlet A5 and -triplet A (1 C 2 ) states resulting in the intermediate polariton branch as detailed above. Furthermore, there is a longitudinal branch (in the orientation of Fig. 6.14a,b, the x-oriented component of

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C. Klingshirn

Fig. 6.13 The transmission spectrum of the nB D 1 A and B excitons, however, in the polarization E jjc, showing same dipole- and/or spin-flip forbidden transitions and their variation with a magnetic field. According to [73]

A5 /. These various branches, i.e. the LPB, the intermediate one and the UPB show up in the luminescence spectra in the given orientation, the longitudinal one may contribute because of the finite angle of aperture via mixed-mode polaritons. See above or for mixed-mode polaritons in luminescence [1, 27, 37–41]. For the orientation of Fig. 6.14c, d, both A5 oscillators are transverse; consequently, there is neither a longitudinal A5L branch nor a k-liner term (since kjjc see Sect. 6.1). Consequently, the luminescence arises simply from the bottleneck region of the LPB without any structure. Specifically, there is also no coupling between the spinsinglet and -triplet states and no intermediate polariton branch. The difference in the luminescence spectra is a strong argument in favour of the k-linear term in the A-valence band and in the A-exciton and consequently for the inverted VB ordering in ZnO. The fine structure in Fig. 6.14b has been observed by many authors but they frequently ignore it and its implications for the VB ordering or misinterpre it as separate contributions from A5 excitons and polaritons (e.g. [53, 74, 75]). For some more discussion of this aspect, see also [2, 3, 76] and references therein. We shall come back to it in connection with exciton dynamics in Chap. 12. In Fig. 6.14f, we show finally the luminescence in the 1 geometry, i.e. for E jjc. As already stated several times above, the A1 exciton is dipole-allowed for this orientation, its oscillator strength is, however, tiny because of the involved spin-flip resulting in a tiny polariton effect only, as shown schematically in Fig. 6.14e and a narrow emission feature (compare Fig. 6.14f with b and c). The small width of about 0.2 meV

6

Intrinsic Linear Optical Properties Close to the Fundamental Absorption Edge

a

137

b

3.380

k

x, E

k c, E c

y

z

energy (eV)

3.379 3.378

long.

3.377 3.376 3.375 3.374 0

k (106 cm–1)

2

c

llum (arb. u.)

d

3.380

k

c, E

y

k c, E c

z

energy (eV)

3.379 3.378 3.377 3.376 tr 3.375 3.374 0

e

2 k (106 cm–1)

f

3.380

llum (arb. u.)

k c, E

c

energy (eV)

3.379 3.378 3.377 3.376 3.375 3.374 0

2 k (106 cm–1)

llum (arb. u.)

Fig. 6.14 The zero-phonon luminescence of exciton polaritons in ZnO at 1.8 K for various geometries and the corresponding dispersion relations at. The dotted line in (a) stands for the longitudinal exciton and in (b) for a spin-flip forbidden one. According to [2, 3, 27, 32, 33]

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C. Klingshirn

implies additionally a homogeneous broadening   0:2 meV and a dephasing time T2 10 ps. A detailed analysis of the luminescence spectra revealed furthermore a splitting of 0.2 meV between A1 and A5 T . The analysis of the coupling between A1 and A5 via a k-linear term and a magnetic field results in a value of the k-linear term of the A VB for k?c of 2 107 meVcm [32, 33]. The luminescence of free excitons is at low temperatures relatively weak for two reasons: The escape depth of free exciton polaritons is rather small as a result of the large absorption coefficient; furthermore, the conservation law for the component kjj to the surface limits the fraction of polaritons in the bottleneck region, which can leave the crystal as luminescence quanta. Additionally, the thermalisation process favours, as mentioned above, the capture of free (exciton-like) polaritons by some defects forming energetically lower-lying BEC, which are treated below in Chap. 7. The strong absorption reduces also the intensity ratio of the zerophonon exciton–polariton luminescence and its LO-phonon replica. Consequently, it is incorrect to deduce a Huang–Rhys factor for free excitons from the intensity ratio of zero-phonon line and its first LO-phonon replica. To overcome these problems, we consider now a series of luminescence spectra for T 100 K since the BEC luminescence starts to disappear in ZnO at temperatures above 60–80 K because of the thermal dissociation of excitons from their centres. We show in Fig. 6.15a–c, a series of luminescence spectra for temperatures between 100 and 300 K. See also [2, 3, 65, 77, 78]. The zero-phonon emission around 3.37 eV is already at 110 K so strongly homogeneously broadened that the finer details discussed with Fig. 6.14 are no longer visible. The shoulder on the highenergy side arises from the B5 exciton, which becomes substantially populated at these temperatures, while only minor contributions remain from the BEC around 3.35 eV. With further increasing temperature (see, e.g. T D 200 K in Fig. 16.15b), the homogeneous broadening increases further because of the increasing population of phonons and the scattering between phonons and excitons. At RT (Fig. 16.15c), the zero-phonon line and its LO-phonon replica merge to an unstructured band. Note that owing to this composition of various contributions a fit of the luminescence band with a simple Gaussian or Lorentzian is physically not meaningful nor an identification of the emission maximum with the free exciton energy. In Fig. 6.15a–c, we show also a line shape fit which we describe shortly below. For more details, see [2, 3, 65] and references therein. For the zero-phonon line(s), we used a simple Lorentzian with a homogeneous broadening  .T /. This approach is applicable if  LT , i.e. for the A5 exciton for T 50 K. The LO-phonon satellites are given by the product of the square-root density of states of the excitonp like polaritons, the dependence of the matrix element on k  E kin ( k for the first LO-phonon replica and independent on k for the higher ones [65]) and the Boltzmann occupation probability, since the difference to Bose–Einstein statistics is marginal for the density and temperature ranges of Fig. 6.15a–c. The line shape calculated in this way [77] has then to be folded with a damping [65]. We used the same  .T / as for the zero-phonon line. The agreement between experiment and fit is excellent for T D 110 and 200 K in Fig. 6.15. At 290 K, there is a discrepancy on the high-energy side because of reabsorption since the absorption tail follows the

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a

139

b PL-spectrum model

T=110 K

PL-spectrum model

1

T=200 K

norm. PL-intensity

norm. PL-intensity

1

0 3.20

3.25

3.30

photon energy (eV)

c

3.20

d

3.25

3.30

3.35

3.40

photon energy (eV) 0

PL-spectrum model

T=290 K

norm. PL-intensity

transmission data PL data

50 band gap shift (meV)

1

0

3.40

3.35

numerical fit with α=0.5

–100 –150 –200 –250 –300 –350

0 3.20

3.25

3.30

3.35

3.40

e

0

100 200 300 400 500 600 700 800 900 temperature (K)

photon energy (eV)

Damping factor Γ (meV)-HWHM

25 Γ (eV) fit

20

Γ(Τ)=Γ0 + αΤ + β/exp[(hΩ/kθT)–1] Γ0=0.65 + – 0.60 meV

15

α=0.016 + – 0.013 meV/K β=47 + –12 meV hΩ=33.0 + –7.4 meV

10 5 0

0

50

100

150

200

250

300

Temperature (K)

Fig. 6.15 Luminescence spectra of ZnO for various temperatures (a–c), the resulting temperature dependence of the band gap (d) and of the homogeneous width of the exciton (HWHM). (e) According to [2, 3, 65]

Urbach rule [1] and extends with increasing temperature more and more to lower photon energies. It should be noted first that only the LO-phonons („!LO D 72 C 0:5 meV) appear as replica with substantial intensity (not the TO!) and second that the distance from the m-LO-phonon satellites to the free exciton energy has to be measured from the low-energy side of the LO-phonon replica (approximately the point of inflection) and not from the maximum. The latter procedure leads to erroneous results

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[79]. Furthermore, the maximum of the luminescence at RT does not coincide with the energy of the free exciton [65, 80] as mentioned above already. As has been shown already in [77], the ratio of the integrated intensities of the first and second LO-phonon replica depend on temperature. After the theoretically expected linear increase with T, there is a bend over when the first LO-replica becomes affected by reabsorption [77]. The fits to the luminescence line shape allow deducing two important quantities, namely, the temperature dependence of the band gap and the homogeneous broadening of the free exciton resonance. The shift of the exciton energy and thus also of the band gap is shown in Fig. 6.15d up to 800 K. The data up to RT are deduced from the luminescence spectra and above from absorption. These data coincide with those of other authors in the respective temperature ranges (see, e.g. [2, 3, 43, 76, 81–87] and references therein or Fig. 6.11 and 6.12). The shift from zero to RT is about 80 meV. The experimental data could be roughly fitted by the Varshni formula [88], but a better fit, shown in Fig. 6.15d, is obtained using a two-oscillator model following the ideas of [89]. The damping  of the free exciton resonances A5 and B5 starts with values around 1 meV at low temperatures in agreement with the fit of reflection data (see Fig. 6.8) and increases with temperature because of scattering with acoustic phonons (the term ’T in the formula in Fig. 6.15e) and an Einstein term averaging over all optical phonons with the parameters given in Fig. 6.15e. It should be noted that the half-width at half-maximum is at RT already slightly above 20 meV, i.e. comparable with the exciton-binding energy. In [90], the same approach has been used, however, with physically completely unlikely parameters resulting at RT in values  around 1 eV as detailed in [65]. In [91, 92], similar, though not identical, data have been obtained. One of the authors (CK) of [65] was not aware at the time of writing the reviews [2, 3] of these data and he apologizes for this shortcoming. We come back to these data in Sect. 12.1. The spectra of the refractive index of the birefringent material ZnO may be found in [81, 82, 93–97]. It should be noted that the luminescence yield even of high-quality bulk ZnO samples is (as in many other direct-gap semiconductors [1]) considerably below unity. We show in Fig. 6.16 the temperature dependence of the absolute external luminescence yield lum of a high-quality bulk sample [98]. The open circles correspond to the near-edge luminescence (NEL), which comprises the zero-phonon lines of free and bound excitons and their phonon replica. The open squares give the deep centre emission. The data have been obtained by placing the sample in an integrating sphere (Ulbricht sphere) fitted into a cryostat and calibrated with various (laser-) emission lines over the whole near-UV/VIS range. The NEL starts at low temperatures with values of lum around 0.1 or below (also for other samples) and decreases up to RT by roughly another order of magnitude. Similar numbers hold also for deep centre luminescence. The activation energies deduced from thermal and negative thermal quenching are in the range from 10 to 70 meV, i.e. they comprise the binding energy of excitons to defects, the exciton-binding energy itself and the LO-phonon energy.

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Fig. 6.16 The temperature dependence of the absolute external luminescence yield ˜lum of the near-edge (open circles) and of the deep centre luminescence (open squares) of a high-quality bulk sample. The activation energies deduced from the fit procedure for thermal quenching Ei and for negative thermal quenching Ei0 are given in the figure. According to [98]

As mentioned already, the optical spectra of good epilayers or of nanorods are identical to the ones of bulk samples. To demonstrate this fact, we collect a few examples in the following sequence of graphs, keeping in mind that the measurements of absorption and reflection spectra are hardly possible for nanorods while luminescence spectra and photoluminescence (PL) excitation spectra can be obtained for the latter, even for single nanorods. See, e.g. [99]. Furthermore, we note that epitaxial layers are usually grown on substrates with some lattice mismatch. See Chap. 3. This fact results generally in strain and/or dislocation networks occurring preferentially at the interface side of the epilayer. Frequently, the strain is inhomogeneous over the layer thickness with the consequence that reflection spectra look different when measured on the surface or at the interface to a transparent substrate, while absorption and luminescence spectra integrating over the whole layer thickness or parts of it can be inhomogeneously broadened. Another point, which has to be considered, is diffusion of atoms from the substrate into the growing layer. ZnO layers grown, e.g. on sapphire .Al2 O3 / generally have a substantial Al incorporation (see Chap. 3) and thus a high n-type doping close to the interface which may seriously influence, e.g. Hall measurements and also the PL spectra. A further aspect which has to be considered is the fact that even epitaxial layers consist generally not of one mono-crystalline layer but of many grains with grain sizes of tens to hundreds of nanometres. See Chap. 3. The grain boundaries may seriously influence the carrier mobility (see Chap. 5), the luminescence yield or the lifetime of excitons. Finally, it should be mentioned that surfaces

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Fig. 6.17 The comparison between the low-temperature reflection and luminescence spectra of a bulk sample (bottom) and an epitaxial layer grown by pulsed laser deposition on sapphire and subsequent annealing (top). According to [123, 124]

normal to c which are either O- or Zn-terminated may show different optical and other properties in agreement with the fact that c is a polar axis. For examples, see [100–105]. Since the number of relevant papers concerning the optical properties of ZnO layers and rods is too large to cite here, even a reasonable selection, we refer the reader to data collections like INSPEC, Web of Science or the reviews [2,3,18,106] the papers [107–122] or [153]. We select from these a few results first for epitaxial layers (not necessarily the best, but interesting ones) and then proceed to the lowtemperature data of nanorods. In Fig. 6.17, we show the comparison of reflection and luminescence spectra of a bulk sample and an epilayer, grown by PLD (see Chap. 3) on Al2 O3 and subsequently annealed at 500ı C for 15 min resulting in an average grain size of 80 nm [123, 124]. The bulk sample shows the well-known A- and B-reflection features (identified in the 50 K spectrum by the dips, i.e. by their longitudinal eigen energies) and narrow BEC emission in the PL spectrum together with some LO-phonon replica. The small peak at 3.326 eV could be a two-electron transition (TES) in a BEC (see Chap. 7) rather than the LO-phonon replica of the longitudinal B exciton. The epitaxial layer shows a broadened, but only marginally shifted BEC emission though a significantly different reflection spectrum. The peak around 3.25 eV is evidently a Fabry–Perot mode. The interpretation of the double feature around 3.37 eV is not unique.

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Fig. 6.18 Comparison of the 8 K luminescence spectra of a bulk ZnO sample (d) and of various epilayers grown on ScAlMgO4 . Excitation with a He–Cd laser at 325 nm (3.81 eV). According to [125, 126]

If this double feature is due to the A and B5 exciton states (the interpretation adopted in [123, 124]) there must be substantial strain (see Sect. 8.2 or [29]) which modifies strongly the oscillator strengths, the energetic distance and the broadening of the two resonances, but surprisingly hardly shifts here the BEC emission. Another problem with this interpretation comes from the calculations in [29], which show that the A–B VB splitting is hardly influenced by strain. Another, possibly more realistic, interpretation would thus be to ascribe the lower energy peak at 3.36 eV still to another Fabry–Perot mode and the smaller, high-energy reflection peak around 3.38 eV to a broadened and therefore unresolved superposition of the signals from the A and B5 exciton resonances. The decision between the two models could come from absorption measurements, which should be possible since the Al2 O3 substrate is transparent in the relevant spectral range. In Fig. 6.18, we show luminescence spectra from [125, 126] comparing a bulk sample and epilayers grown on almost lattice-matched ScAlMgO4 (SCAM) with an intermediate high-temperature-annealed buffer layer. This procedure reduces the point defects and results in luminescence spectra comparable to good bulk samples. The fine structure of the A5 exciton polariton is seen (compare to Fig. 6.14). The luminescence of the BECs is well resolved and their two-electron satellites (TES) are visible. The surprising aspect in [125, 126] is the absence of thermalisation between the free exciton levels in spectra (a) and (b), including the nB D 2 states, which can be expected and evidently occurs for bulk material. We show in Fig. 6.19 (a) the luminescence of a single ZnO nanorod at 10 and 50 K. The free A-exciton, various BEC and their LO-phonon replica can be seen together with the TES. As discussed above, the BEC luminescence dominates at 10 K together with its LO-phonon replica, while the free A-exciton is two orders of

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Fig. 6.19 The luminescence of a single ZnO nanorod at 10 and 50 K (a) and details of the BEC emission at 10 K (b). According to [127]

magnitude weaker than BEC, and its LO-phonon replica .#/ are hardly visible. This trend changes at 50 K. The free A5 exciton has increased by an order of magnitude relative to BEC, its fine structure is clearly visible (compare to Fig. 6.14) and its LO-phonon replica dominate over the ones of the BEC ."/. Time-of-flight (TOF) measurements have been carried out in bulk ZnO [128] using as a light source the luminescence from an electron–hole plasma (see Chap. 11) created in a thin layer by 300 fs pulses on one side of a 0.5 mm thick sample and detecting the temporally and spectrally resolved arrival of the luminescence on the other side. The delay increasing with „! allows reconstructing the polariton dispersion since the group velocity is proportional to the slope of the dispersion relation. The claim in [128] is that a polariton is involved which is formed by donorbound excitons Dı X at 3.36 eV. However, the polariton dispersion deduced from the data shows a transition from the photon-like to the exciton-like dispersion at an energy around 3.39 eV only and no resonance-like feature at 3.36 eV, though such BEC-based polariton structures can and have been seen, e.g. in CdS in reflection [64]. The value of 3.39 eV is neither compatible with the Dı X energy nor with the free .A C B/5 resonances, but could be explained with the C1 resonance occurring around 3:42 eV, see Fig. 6.7. However, for this interpretation, the light had to be polarized E jjc. For measurements of the dielectric function or of photoelectron emission spectra for photon energies exceeding the fundamental gap and revealing data on deeper VBs, e.g. using synchrotron radiation, see [129–135] and references therein.

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6.2 ZnO-Based Alloys In order to influence the band gap, ZnO has been alloyed with various other oxides like CdO, MgO and BeO forming Zn1x Xx O with X D Cd, Mg, Be. See also Chap. 4. While alloying with Cd reduces the band gap Eg , the other two compounds lead to an increase of Eg . Unfortunately, the first two compounds crystallize in the cubic rock salt (NaCl) structure, the latter one like ZnO in the hexagonal wurtzite structure but with a significant lattice mismatch to ZnO (BeO: a D b D 0:26967 nm, c D 0:43778 nm; ZnO: a D b D 0:3249 nm, c D 0:5206 nm). Consequently, the solubility or miscibility ranges of all three oxides with ZnO are limited, and the occurrence of secondary phases cannot be excluded, even if they are not yet visible in XRD [136–138]. For higher Mg concentrations, Zn1x Mgx O shows the rock salt structure. The transition occurs around x  0:6. The spectra show substantial localization effects resulting in inhomogeneous broadening due to alloy fluctuations [1]. Below, we discuss some optical spectra. Some more spectra and data deduced from them have been given already in Chap. 4. In Fig. 6.20, we show the luminescence of an epitaxial Bex Zn1x O layer with x D 0:2 ˙ 0:05. The inhomogeneous broadening is so large that the LO-phonon replica merge with the zero-phonon line. Furthermore, it should be noted that these broadened luminescence and absorption spectra contain also contributions from excitons bound (additionally, to localization by the alloy disorder) to some defects in the sense of BEC [1, 243].

Fig. 6.20 The luminescence of a Bex Zn1x O layer. The excitation is with the second harmonic of the green line of a cw ArC laser. The small peak labelled “ZnO” comes from a ZnO buffer layer. According to [139]

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Fig. 6.21 The onset of the absorption edge of Zn1x Mgx O layers at RT for 0  x  0:52. According to [140] Fig. 6.22 A 5 K absorption spectrum of a Cd1x Znx O layer with x D 0:99. From [141]

Figure 6.21 gives the onset of the absorption edge of PLD-grown Zn1x Mgx O layers. The blue-shift with increasing x is obvious. Similarly, a red-shift occurs with increasing Cd concentration [140]. In Fig. 6.22, we show a low-temperature absorption spectrum of a Cd0:01 Zn0:99 O layer grown by PLD. The exciton resonance seen in Fig. 6.22 is a superposition of the A and B excitons and is broadened and red-shifted to 3.34 eV compared to 3.375 eV for ZnO. The peak on the high-energy side labelled X C LO is presumably an exciton–phonon bound state. See for this, term [1] and Fig. 6.12. In Fig. 6.23, we show RT luminescence spectra in the middle for pure ZnO and on top and bottom for Zn:95 Mg:05 O and Zn:95 Cd:05 O, respectively. The ZnO spectrum is comparable to the one in Fig. 6.15 concerning position and half-width. The other two are blue- and red-shifted, respectively. The low-energy shoulder in the upper spectrum indicates possibly ZnO inclusions in ZnMgO.

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Fig. 6.23 Room temperature luminescence spectra for Zn0:95 Mg0:05 O, ZnO and Cd0:05 Zn0:95 O layers. According to [142]

Alloys tend to show already at low temperatures a (frequently exponential) absorption tail of localized states below the free exciton energy caused just by the disorder introduced by alloying which is frequently also called an Urbach tail, followed towards higher energy by the Tauc regime. See below or [1] and references therein. The luminescence of alloys is therefore, especially at low temperatures, frequently Stokes, i.e. red-shifted with respect to the excitonic absorption peak,

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Fig. 6.24 A summary of the composition dependence of (from top to bottom) the band gap Eg , of the sub-band splittings and of the excitonic binding energy of Zn1x Mgx O. According to [143]

because electron—hole pairs relax into the deeper localized states before recombination. Since these pairs tend to be excited thermally at increasing temperatures to higher states from where they can subsequently relax into even deeper localized states one observes in this temperature range a pronounced red shift of the emission. With still further increasing temperature also extended states above the mobility edge are reached, with a significantly higher density of states. Therefore, one observes frequently with increasing temperature first a red-shift of the emission maximum „!max due to thermally activated hopping into deeper localized states, then a blue-shift due to thermal excitation into extended states and finally again a red-shift, following then essentially the temperature dependence of the band gap. This non-monotonous behaviour of „!max .T / is frequently called S-shaped behaviour (though it is actually an N-shaped one) and must be kept in mind together with the Stokes shift, when deducing the band gaps of alloys from luminescence. Figure 6.24 from [143] finally summarizes the data for Zn1x Mgx O for the whole range 0  x  1. The data have been obtained from ellipsometry. The ranges of wurtzite and rock salt structures are indicated. The data show from top to bottom the variation of the band gap Eg , of the sub-band splitting AB and AC for the wurtzite-type structure and the spin–orbit splitting parameter so for the cubic modification. The lowest part gives finally the dependence of the exciton-binding energy Exb on x. It should be noted that the values of this quantity around 200 meV for pure MgO can be also found in literature [144] in contrast to the value of 85 meV in Fig. 6.24. Some more information on ZnO-based alloys may be found in Chap. 4 or in [145–149] and references therein.

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Before we proceed to surface exciton polaritons, a comment on the determination of the band gap from absorption spectra. ZnO has, as stated already several times, a relatively large exciton-binding energy of 60 meV. Consequently, the band gap Eg is situated 60 meV above the intrinsic excitonic absorption peek. In the band-to-band transition region, the absorption coefficient ’ is of the order of ’ D 2  105 cm1 and in the exciton region even higher. These, in principle, trivial statements can be easily verified by inspection of Figs. 6.11 and 6.12. With increasing temperature, the exciton resonance gets broader and an exponential Urbach tail of ’.„!/ develops on the low energy side of the exciton resonance, which gets flatter with increasing temperature T , i.e. it extends more to lower photon energies, and which results from interaction with phonons. In disordered semiconductors like alloys or amorphous samples, an additional, essentially temperature-independent contribution occurs to this tail already at low temperatures, which is caused, e.g. by alloy fluctuations as discussed above. See [1]. What one had to do for the determination of Eg from optical spectra is in principle obvious, namely measure the absorption spectrum ’.„!; T / around the exciton resonance and determine Eg to be situated by the exciton-binding energy above the exciton resonance. Since ’.„!; T / is in the relevant region 105 cm1 as stated above, this requires samples with thicknesses around 0:1 m, in order to measure the transmitted light with a reasonable signal to noise ratio since one obtains for a sample of only 1 m thickness already for ’.„!/ D 105 cm1 exp.1 m105cm/ D exp.10/  4:5  105

(6.8)

Such samples are not easily available. Therefore, only the onset of the absorption edge can be measured frequently. Several authors (See, e.g. [142, 150–156]) use a procedure to deduce from this onset alone a value of the gap, which systematically underestimates Eg . They plot .„!/2 ln T D f .„!/

(6.9a)

.„!/2 ˛ 2 .„!/ D f .„!/

(6.9b)

or similar expressions like

over the photon energy „!, where T is the transmission, extrapolate a (generally relative limited) linear part of the experimental data to lnT D 0 or to ’.„!/ D 0 and claim the result to be the band gap, sometimes also called an “optical band gap”. Generally, the transmission is at the thus-determined photon energy still in the 10% region, which is a first argument that the result of this procedure has nothing to do with the true value of Eg . A second argument that the thus-determined value is wrong, is the fact that it systematically underestimates the correct value of Eg namely .3:439 ˙ 0:002/ eV at 4 K and .3:365 ˙ 0:005/ eV at RT [45]. Frequently, the authors give these correct data in the introduction of their papers and much lower values in the main part, often without mentioning or noticing the discrepancy. See also the comments to Figs. 4.9 to 4.11, 4.13 and 4.14.

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The other point of concern is the assumption with which the above procedure is derived. The starting point is generally either a simple square-root dependence of the absorption starting at Eg [1], i.e. ˛.„!/ D ˛0 .„!  Eg /1=2 for „! Eg and zero below Eg

(6.10a)

Such a simple square-root absorption spectrum starting at Eg follows from theory only for simple parabolic bands and neglecting all electron–hole correlations (i.e. excitonic effects) and all other broadening effects. The simple relation (6.10a) is never observed in reality; also, for ZnO the above preconditions are not fulfilled. The other approach leading to   .„!/2 ˛ 2 .„!/ D const „!  Egopt

(6.10b)

is a result for disordered semiconductors (the so-called Tauc-regime) and is valid only for the range of strong absorption beyond the above-mentioned Urbach tail. opt It defines the optical (or mobility) gap Eg . Again, the use of (6.10b) is not justified for the applications mentioned above, especially not for crystalline layers of ZnO, which are frequently claimed to be of good quality. Since „! is varied in these applications, generally only over a small interval of typically 100–200 meV, the approaches [(6.10a) and (6.10b)] are in this sense even equivalent. What the authors find in this type of fitting procedure is at best an onset of the absorption edge, which must not be confused with Eg . But also in this understanding a fit with an exponential Urbach tail is physically much more reasonable. The approach according to (6.10a) and (6.10b) is especially inadequate, when applied to highly n-type doped ZnO layers (see, e.g. [150–154]) since the shape of the absorption edge is determined in the presence of a degenerate electron gas mainly by the Fermi function. See, e.g. [155, 156]. The position of the onset of absorption is, in this case, the result of a delicate interplay between the red-shift of the gap due to many-particle effects (mainly exchange and correlation) and the blueshift caused by the filling of the conduction band states, the so-called Burstein–Moss shift.

6.3 Surface Exciton Polaritons For many bulk modes of collective excitations of solids, there exists also a so-called surface of interface mode. These are collective excitations, which propagate along a surface or interface only and the amplitude of which decays exponentially on both sides, with a decay length which is typically of the order of the wavelength. Examples are bulk and surface phonons or plasmons. These surfaces modes are characterized by a dispersion relation „!.kjj / where kjj is the wave vector along the surface or interface. The exponential decay normal to the surface or interface

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can be described by an imaginary k? . Note that the decay length can be different on both sides. In this section, we concentrate on surfaces (i.e. an interface between ZnO and vacuum (or air) which is described by a refractive index nQ  1) and on surfaceexciton polaritons. It is noteable that the term “surface exciton” is used in the literature also for excitons bound to defects at or close to the surface. These are spatially localized states which have nothing in common with the intrinsic surface exciton polaritons treated here. For a general discussion of this topic, see, e.g. [1,6,7] and of the series [157] the volumes 1 and 9 [158, 159], and references given therein. We show in Fig. 6.25c the calculated dispersion relations of the nB D 1C1 exciton polariton state with (LPBs and UPBs) and of the surface exciton polariton. The dispersion relation of the latter is comprised between the transverse and the longitudinal eigen frequencies because in this frequency interval there are no propagating modes in ZnO, and consequently the surface polariton cannot decay into the bulk of the sample, and it is situated on the r.h.s. of the dispersion relation of photons in vacuum (no D 1 in Fig. 6.25c) because then a decay into the vacuum side (i.e. luminescence) is excluded because of the conservation of kjj . These facts have, however, also the consequence that it is not possible to couple from outside to the surface exciton polaritons, i.e. to see them in transmission, reflection or luminescence spectroscopy directly. There are, however, some tricks to overcome this restriction. One is the so-called attenuated total reflection (ATR). See Fig. 6.25a. One sends a monochromatic light beam with photon energy „! into a transparent (quartz ) prism in a way that total internal reflection occurs at the prism base. Under this condition, an evanescent wave propagates along the prism base on the vacuum side with kjj determined by the refractive index of the prism, by the wavelength of the light beam in vacuum and by the angle of incidence. This later aspect is the most important one in this context. The electric field amplitude of the evanescent wave decays over a distance of the order of  normal to the prism base. The frequency „! can be tuned trivially and kjj for a fixed „! by changing the angle under which the incident beam hits the prism base, as long as one remains in the regime of total reflection. If a ZnO sample is now brought close enough to the prism base, the evanescent wave can couple to the surface exciton polaritons if both kjj and „! coincide with a point on their dispersion curve. If this is the case, energy can be transferred from the evanescent wave to this surface mode and the reflectivity drops. This effect is called ATR. A signal is shown in Fig. 6.25b and the data points on the dispersion relation of Fig. 6.25c result from this independent variation of „! and kjj . Similar signals have also been reported for the surface exciton polariton connected with the bulk A and B5 exciton states [161,162]. A simultaneous investigation of the excitonic reflection spectra and of ATR gives a detailed picture of the optical surface properties of ZnO as demonstrated in [56]. Another method to couple to surface polaritons is to create a grating on the surface with grating constant g, e.g. by etching parallel groves into the surface. As a consequence of this new periodicity, kjj is conserved only modulo integer multiples of this new reciprocal lattice vector h with

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Fig. 6.25 Schematics of the set-up to measure the dispersion of surface polaritons by ATR (a), measured and calculated ATR spectra for the nB D 1 C1 exciton resonance (b) and the calculated dispersion curves of bulk and surface exciton polaritons together with experimental data points from ATR (c). According to [160]

h D m2=g.m D ˙1; ˙2 : : : :/:

(6.11)

If g and m are properly chosen, coupling to the surface polariton mode becomes also possible as shown for ZnO, e.g. in [1, 163–167]. A random surface roughness also relaxes the conservation of kjj (but not in a well defined way) and allows coupling to surface-polariton states.

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6.4 Excitons in Structures of Reduced Dimensionality In this part, we proceed from quasi two-dimensional (multiple) quantum wells (M)QW or superlattices (SL) over quasi one-dimensional structures (essentially nanowires) to ZnO powders, nanocrystallites or quantum dots (QD).

6.4.1 Excitons in Quantum Wells and Superlattices As discussed in Sect. 4.4 with the band alignment, QWs and SLs of type I can be produced either with Zn1x Cdx O wells and ZnO barriers or with ZnO wells and Zn1x Mgx O or Zn1x Bex O barriers. The latter choice is more frequently used. Owing to the so-called common-anion rule (which has however only limited validity), the band offset is usually in the oxygen-based VB smaller than in the cation-based CB. Zn1x Cdx O alloys as wells, which reduce the gap significantly to produce a substantial confinement, have generally rather poor crystal quality and luminescence yield and exhibit in addition alloy disorder or even Cd-rich precipitates in the well. Therefore, more work is devoted to binary ZnO wells and ternary barriers. This choice has the additional advantage to shift the emission to shorter wave lengths, a feature which is highly desired, e.g. to improve the data storage density on discs. However, recently, good progress has also been made in the field of Zn1x Cdx O quantum wells [168–170] with the hope to obtain semiconductor laser diodes for the green spectral range. In the following, we present some examples. Figure 6.26 shows low-temperature luminescence and absorption spectra of a bulk-like 50-nm- thick ZnO layer (bottom) and of ZnO=Mg:12 Zn:88 O QWs of different well widths lz D LW . The overall blue-shift with decreasing lz is obvious. The bulk-like sample shows the A and B excitons in absorption and above signatures of exciton-phonon bound states. See above and [1]. The luminescence is dominated by BEC in the bottom spectrum. With decreasing well width, there is an increasing Stokes shift between absorption and luminescence peaks caused partly by localization effects resulting from wellwidth fluctuations and partly (not mentioned in [171, 172]) by excitons bound to defects. It would be unrealistic to assume that the centres binding excitons in bulk samples like Dı or Aı would be absent in QW. However, the binding energy depends also on the well width and additionally on the position of the centre in the well. See [1] and reference therein. Therefore, the BEC result no longer in sharp absorption or emission features. Figure 6.27 shows explicitly the CB and VB offsets and the observed blue-shifts with decreasing lz . More experimental data can be found, e.g. in Chap. 4 or in [144, 173–196]. The model calculation in [171, 172] uses with 1.8 m0 an unusually high value for the hole mass mh . For ZnO, a value around 0.59 m0 is more adequate (see Chap. 4 or [45]) and a higher value caused by the admixture of MgO hole wave function should lead to an lz dependence of mh .

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Fig. 6.26 Absorption and luminescence features of a bulk-like ZnO film and of quantum wells of different thicknesses LW at 5 K. According to [171, 172]

Figure 6.28 gives the dependence of the exciton-binding energy Ebx on lz for different compositions. One observes first the typical increase of Ebx with decreasing lz reaching here a maximum close to twice the value in bulk ZnO followed for even smaller lz by a decrease, which is due to the increasing penetration of the electron and hole wave functions into the barrier ([1] and references therein) and converging for lz ) 0 to the Ebx value of the barrier material. The lower calculated curve tends to fall below the value of ZnO of 60 meV for lz ) 0 in agreement with Fig. 6.24. As a last example, we show in Fig. 6.29 luminescence spectra of the abovementioned system Zn1x Cdx O=ZnO. If there is some lattice mismatch, one has usually to deal with strain in QWs. In crystals without a centre of inversion and (partly) ionic binding, this strain results in piezoelectric fields depending on the orientation. See Sect. 2.3. These fields are well known both in zinc-blende- and wurtzite-type structures; see [1] and references therein. There is a tendency that this effect is more pronounced in the latter case. The piezo-electric fields tilt the bands resulting with increasing well width in a redshift of the transition energies, in a spatial separation of electrons and holes and consequently in a decrease of the overlap of their wave functions and of the excitonic oscillator strength. See Fig. 6.29b. Since these piezo-fields can be screened by an

6

Intrinsic Linear Optical Properties Close to the Fundamental Absorption Edge

155

Fig. 6.27 Band alignments of ZnO=Mg:18 Zn:88 O QWs and the dependence of the exciton resonance energy on the well width deduced from photoluminescence (PL) and absorption spectra. According to [171, 172]

increasing number of electron–hole pairs, these effects are strongly dependent on the sheet density of carriers in the wells. All these effects have been calculated and observed, e.g. in ZnO=Mg1x Znx O QW and also in other ZnO-based QW systems by various groups, e.g. [171, 172, 176–178] and for Cd1x Znx O=ZnO QW in [175]. We come back to this aspect in Chap. 12. More data on ZnO based QWs can be found, e.g. in [179–196, 242] and references therein including even QW incorporated into nanorods.

6.4.2 Quantum Wires Most of the work on quasi one-dimensional ZnO-based structures refers to nanorods. As we have shown above, the nanorods exhibit essentially bulk properties concerning

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Fig. 6.28 Dependence of the exciton-binding energy on the well width of ZnO=Mg1x Znx O QWs with two different Mg concentrations. From [171, 172, 174]

excitons or exciton-like polaritons. Their diameters are with typical values of 30–100 nm, too large to result in observable confinement energies. They form, however, very good one-dimensional wave guides for light or more precisely for photon-like polaritons since the step of the real part of the refractive index from ZnO to vacuum is with a value around 1.5, extremely large compared, e.g. to the one between core and cladding of fibre optics. We address the waveguide aspect first, which will become important again in the stimulation emission of (single) nanorods (see Chap. 11), and then present few data of quasi one-dimensional quantum wires based on ZnO where confinement effects are important. The index step from ZnO to air (vacuum) is sufficiently large to produce guided modes for typical rod diameters. Such a step occurs not only at the perimeter of a ZnO nanorod but also at its end face and possibly also at its foot point. In Fig. 6.30a, we show the calculated longitudinal mode patterns of a standing wave in two ZnO nanorods for the fundamental transverse mode (see insert (b) in Fig. 6.30a). One is assumed to have been grown directly on GaN. Since the index step between ZnO and GaN is small in the near-UV, a lot of light leaks into the substrate (Fig. 6.30a l.h.s.). Sometimes, a gold layer (more precisely, a layer of Au particles) remains at the interface between substrate and rod in the VLS growth mode (see insert (c) and Chap. 3). This layer enhances the reflectivity and the confinement of light in the quasi one-dimensional cavity (see Fig. 6.30a r.h.s.). Higher lateral modes have been also calculated in [197–199] and a selection is shown in Fig. 6.30b. See also [200, 201]. Furthermore, whispering gallery modes have been calculated in nanorods propagating in their hexagonal cross section for thicker rods. They have been observed, e.g. in the green deep centre emission and in the exciton-polariton regime [202,203, 242].

6

Intrinsic Linear Optical Properties Close to the Fundamental Absorption Edge

157

a PL intensity (arb. units)

Zn.89Cd.11O SQWs T = 5K

d = 1.5 nm

(X 2) d = 4.3 nm 1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

photon energy (eV)

b Zn.89Cd.11O SQWs T = 5K

PL peak position (eV)

3.2 3.0 2.8 2.6

Ee

eFd

2.4 Eh

2.2 2.0

0

1

2

3 d (nm)

4

5

6

c Zn1–xCdxO SQWs T = 5K

PL peak position (eV)

3.4 3.2 3.0 2.8 2.6 2.4

d = 3.35 nm d = 2.20 nm

2.2 0.00

0.05

0.10

0.15

0.20

0.25

X

Fig. 6.29 Luminescence of two Zn1x Cdx O=ZnO QWs (a), the dependence of the emission maximum as a function of the well width lz D d (b) and as a function of the Cd concentration x for two different values of d (c). According to [175]

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Fig. 6.30 The longitudinal (a) and transverse (b) mode pattern of ZnO nanorods. According to [197–199]

In [204], a report is given on nanorods with radii of .1 ˙0:1/ nm (i.e. comparable to the value of the excitonic Bohr radius aB D 1:8 nm) and lengths of a few 10 nm. The absorption spectrum of a solution of these rods shows at RT a clear blue-shift compared to bulk samples, epilayers or thicker rods as shown in Fig. 6.31. The arrow is placed at 3.53 eV. The peak maximum might be slightly lower but it is definitely above the value for excitons of bulk-like ZnO at 3.3 eV (compare to Fig. 6.11 and 6.12). The feature around 4.59 eV is attributed to the first excited state. In the inset, a luminescence spectrum is shown, which is decomposed into various Gaussians, partly involving deep centres. The interpretation of the green band at 2.57 eV via free holes might, however, be open for discussion bearing in mind the well-known difficulty with p-type doping of ZnO. See also Chaps. 5 and 9. In [205], in contrast a blue-shift of the luminescence of ZnO rods has been described which cannot be explained by the rod diameters ranging from 50 to 180 nm, but is tentatively attributed to a surface resonance. In [206], surface excitons have been observed in luminescence also in thick wires embedded in polymer; however, without any blue-shift. Another approach uses the growth of Mg0:2 Zn0:8 O=ZnO=Mg0:2 Zn0:8 O multishell layers on a ZnO core nanorod. These radial QW shows a blue-shift of about 100 meV of their luminescence with decreasing thickness in the range from 4.5 to 0.8 nm, while the emission of the ZnO core is hardly affected [207]. Furthermore single and multiple QW have been grown in or on nanorods with their plane normal to the rod axis [208–211], showing blue-shifts comparable to the ones of usual QWs described above.

6.4.3 Quantum Dots ZnO-based quantum dots are prepared by a rich variety of techniques (see [212], or [4, 106] and references therein) ranging from commercial ZnO powders with almost spherical- to needle-like crystallites ranging from several tens to hundreds

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Intrinsic Linear Optical Properties Close to the Fundamental Absorption Edge

159

28 3.

4.59eV

3.53eV

3.

54

eV

3.

05

eV

eV

57 2.

Intensity (arb. units)

Absorbance (arb. units)

eV

RT

2.0

2.5 3.0 Energy (eV)

3.5

ZnO rods O = 2.2nm

1

2

3 4 Energy (eV)

5

Fig. 6.31 Room temperature absorption and luminescence spectra of nanorods with 1.1 nm radius. According to [204]

of nanometres [213] down to crystallites in the range of a few nanometres grown, e.g. in the voids of opal-like structures or of zeolithes, in sol–gel processes or in a Volmer–Weber-like growth mode on CaF2 and other substrates. The larger crystallites show again no excitonic confinement effects similar to the case of nanorods in Sects. 6.1.1 and 6.4.2. The near edge luminescence (NEL) consists of free excitons and at low temperature of BECs, including those bound to surface states. We show an example in Figure 6.32. One observes very weakly at 3.375 eV, partly only as a shoulder, the free exciton emission followed to lower energies by BEC and LOphonon replica. The peak at 3.31 eV labelled SX has been attributed in [213] to an exciton bound to a defect at or close to the surface. Its emission persists up to RT. The insert shows the ratio of the SX and BEC emissions. It increases linearly with the inverse particle diameter, i.e. with the surface-to-volume ratio giving some support to this interpretation. However, alternative interpretations of this and similar emission bands have been put forward in, e.g. [214,215] in terms of a free-to-bound transition, namely of a free electron recombining with the hole bound to an acceptor e C Aı ! Aı C „!;

(6.12)

where the acceptor is considered to be a stacking fault. Strong arguments have also been given in favour of recombination at basal plane stacking faults [214, 215]. In Fig. 6.33, we show the temperature dependence of the absolute external luminescence yield ˜lum of the near-edge emission of a ZnO powder similarly as for bulk samples (see Fig. 6.16). The overall feature is a decrease of the luminescence of free

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Fig. 6.32 Low-temperature luminescence spectra of various commercial ZnO powders compared to a bulk sample. According to [213]

and bound excitons and their phonon replica by more than an order of magnitude from 10 to 300 K. The absolute values are again considerably below unity with the same conclusions as given with Fig. 6.16. When the nanocrystals or QD come in the diameter range below 10 nm, quantum confinement effects become visible, i.e. a blue-shift of the absorption and nearedge emission features with decreasing size, typically accompanied by a significant inhomogeneous broadening for ensemble measurements and a Stokes shift between emission and absorption peaks as typical for QD independent of the growth type [1]. A few examples are given below in Figs. 6.34 and 6.35. In Fig. 6.34, the RT absorption spectra are shown as ˛ 2 over „! for colloidal nanocrystallites with the time elapsed after their preparation as parameter. Evidently, there is a slow growth or ripening process manifesting itself in a red-shift of the prominent spectral features with time. In Fig. 6.35, we show the comparison of RT absorption and luminescence spectra of QDs prepared in a Volmer–Weber growth mode on Si or on Al2 O3 substrates. Both the quantum confinement and the Stokes shift are again obvious. In both cases, again a so-called “optical gap” has been determined from the plot and indicated by arrows. Again, the positions of these arrows have hardly anything to do with the real gap which occurs on the high-energy side of the (broadened)

6

Intrinsic Linear Optical Properties Close to the Fundamental Absorption Edge

161

Fig. 6.33 The absolute external quantum yield ˜lum of a selected ZnO powder sample as a function of temperature. According to [98]

V = 3.

(1)

E

E

g

g

75 e

59 e = 3.

= 3.

(3)

g

E

10 ²E²g = 3.44eV

α2 (arb. units)

(2)

48 e

V

V

20

0 3.0

22

4

1

time (days)

α = const(hν-Eg)1/2

3.5 4.0 Photon energy (eV)

4.5

Fig. 6.34 The absorption edge at RT of colloidal nanocrystallites measured various days after their preparations. According to [151]

exciton peak only. As explained above already with (6.9) and (6.10), the assumption of a square-root absorption edge is not justified and this statement remains true for QDs. For a small selection of further references, in addition to the ones given already above, see [217–228].

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Fig. 6.35 Absorption and luminescence spectra of ZnO QDs prepared on Si or Al2 O3 substrates. According to [216]

6.4.4 Cavity Polaritons We now treat the so-called cavity polaritons. These are simultaneously eigen states of structures of reduced dimensionality and exciton polaritons in the following sense. A cavity or Fabry–Perot resonator forms a quasi two-dimensional system for photons. Cavity modes occur in the simplest case of two plane-parallel mirrors, if an integer number of half-waves fit into the resonator. In the plane of the resonator, these cavity modes show a hyperbolic dispersion relation [1]. If one brings now a thin ZnO layer (e.g. a quantum well) into the cavity in a way that the exciton states of this semiconductor layer and a cavity mode are almost degenerate in energy, and if the decay time of the cavity mode and the dephasing time of the exciton resonance are sufficiently long to be in the strong coupling limit [1], a mixed state of the cavity mode and the exciton is formed – the cavity polariton. Similarly, as for the exciton polaritons in bulk samples treated in Sect. 6.1, the dispersion relation of the cavity polaritons results from the ones of cavity modes and excitons and the non-crossing rule but now only over a two-dimensional k-space in the plane of the cavity [1]. Cavity modes have been predicted for ZnO, e.g. in [229], though their Bose– Einstein condensation at RT might be more difficult to realize [2,3] than to calculate it in view of the large homogeneous broadening of the exciton resonance at this temperature. See Fig. 6.15. Nevertheless, cavity polaritons have been observed recently even in nanowire cavities [230–236]. We show here an example from [230]. The cavity has been formed from MgO=ZrO2 Bragg mirrors with a thin ZnO layer forming the cavity. On the l.h.s., RT luminescence spectra are shown for various angles of

6

Intrinsic Linear Optical Properties Close to the Fundamental Absorption Edge

163

Fig. 6.36 The RT luminescence of a cavity containing a thin ZnO layer for various angles of observation (a) and the dispersion of the cavity modes BB1 and BB2, of the A exciton XA and of the resulting lower (L) and upper (U) cavity polaritons together with experimental data points (b). According to [230]

observation (Fig. 6.36). The variation of the angle relative to the plane of the cavity serves to vary the in plane wave vector kjj , where ˚ D 0 corresponds to kjj D 0. The emission peaks are cavity-mode-like (corresponding to photon-like in bulk samples) and exciton-like. On the r.h.s., the calculated dispersion relations are shown for the cavity modes, the A-exciton resonance and finally for the cavity polaritons showing good agreement with the experimental data points. At lower temperatures and for higher Q-values of the cavity rather complex dispersion relations can be expected when considering the already non-trivial bulk dispersion relations in Fig. 6.14. Very recently, the whispering gallery cavity polaritons in micro rods and their quasi one-dimensional dispersion have been investigated experimentally and theoretically in [237–239]. Some comments concerning the validity of the concept of strong and weak coupling between exciton resonance and cavity mode, which has been developed for quasi two-dimensional micro cavities containing one or few QW, has been put forward in [240]. For colloidal ZnO quantum dots in pillar microcavities see [241].

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238. 239. 240. 241. 242. 243.

Chapter 7

Bound Exciton Complexes B.K. Meyer

Abstract In the preceding chapter, we concentrated on the properties of free excitons. These free excitons may move through the sample and hit a trap, a nonradiative or a radiative recombination center. At low temperatures, the latter case gives rise to either deep center luminescence, mentioned in Sect. 7.1 and discussed in detail in Chap. 9, or to the luminescence of bound exciton complexes (BE or BEC). The chapter continues with the most prominent of these BECs, namely A-excitons bound to neutral donors. The next aspects are the more weakly BEs at ionized donors. The Sect. 7.4 treats the binding or localization energies of BEC from a theoretical point of view, while Sect. 7.5 is dedicated to excited states of BECs, which contain either holes from deeper valence bands or an envelope function with higher quantum numbers. The last section is devoted to donor–acceptor pair transitions. There is no section devoted specifically to excitons bound to neutral acceptors, because this topic is still partly controversially discussed. Instead, information on these A0 X complexes is scattered over the whole chapter, however, with some special emphasis seen in Sects. 7.1, 7.4, and 7.5.

7.1 ZnO Luminescence: An Overview Before we start the discussion on the bound exciton (BE) recombination, we give an overview on the typical luminescence appearing in ZnO bulk volume crystals, thin epitaxial films, or nano rods. It extends from the free A exciton recombination at 3.375 eV at 5 K (see Fig. 6.14) well into the orange and red spectral ranges. For a color picture of the various emission bands, see, for example, [1, 2]. For a better discussion, we have separated the whole spectrum into four parts (see Fig. 7.1a–d). Figure 7.1a shows the whole range with the prominent deep center

B.K. Meyer Physikalisches Institut, der Justus Liebig Universit¨at Giessen, Giessen, Germany e-mail: [email protected]

169

170

B.K. Meyer

PL Intensity (arb. units)

visible emission

BE

DA-region

Cu/ V0

BE-2LO

BE-3LO

72 mev

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.15

PL Intensity (arb. units) 3.32

3.25

3.30

3.35

3.40

Energy (eV)

BE

bandedge

72 mev

72 mev

3.20

Energy (eV)

BE-1LO

bound excitons

free excitons

Y

FT FL

3.33

3.34

3.35

3.36

Energy (eV)

3.37

3.38

3.360

3.365

3.370

3.375

3.380

Energy (eV)

Fig. 7.1 Luminescence spectra of an epitaxial ZnO film grown on ZnO substrate at 4 K: (a) overview spectrum from the band edge at 3.4–2.0 eV. The shaded energy range is enlarged in (b), where mainly the longitudinal optical (LO) phonon replica of energy of 72 meV of the bound excitons (BE) are observable. The shaded part of (b) is enlarged in (c) and the part shaded there is again enlarged in (d) showing the free A5 and BE luminescence, labeled here as FT and FL . Compare with Fig. 6.14. From [3]

transition peaking around 2.45 eV. See also [4]. In most cases, there are different defects contributing in this spectral range. They only differ in the peak positions of otherwise broad Gaussian bands indicating strong electron–phonon coupling. There is one exception; the Cu green luminescence shows a well resolved rich phonon structure. This partially resolved phonon structure can be seen in Fig. 7.1a, resulting in a value of the Huang–Rhys factor S, which is around 6.5 [5]. For a more detailed discussion on deep center luminescence, see Chap. 9. In Fig. 7.1b, the range from 3.4 to 3.1 eV is shown on an enlarged scale. Here one observes the phonon-assisted transitions of the BEs. It is in this energy range in which we also expect to find shallow donor to shallow acceptor type transitions (see later). Between 3.6 and 3.2 eV, a prominent transition occurs at 3.333 eV labeled Y in Fig. 7.1c. It is tentatively assigned to excitonic recombination at structural defects. Figure 7.1d displays the range where the free A exciton-polariton (FT : transversal, FL : longitudinal) and the BE transitions occur.

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The complexity of excitonic recombination processes in ZnO has been documented already 40 years ago [6–25]. More than 12 individual (bound) excitonic transitions have been reported. From the luminescence experiments, the localization energies (or binding energies) EL are determined as the difference between the recombination energy of the respective BE lines and the free transversal exciton line (see Fig. 7.1d). In many semiconductors, the localization energies EL of excitons bound to ionized donors .DC /, neutral shallow donors .D0 /, and neutral acceptors .A0 / follow a certain ordering, i.e., EL .DC X/ < EL .D0 X/ < EL .A0 X/ as found in CdS [26] or EL .D0 X/ < EL .DC X/ < EL .A0 X/ as found in ZnSe [27] and proposed for GaN [28]. This sequence can be understood as a result of the electron to hole mass ratio  D me =mh , which has a characteristic value for each semiconductor. From this mass ratio, one can theoretically predict the localization energies of the BEs as a function of the binding energies of the shallow donors ED and acceptors EA . In addition, it also answers the question on the stability of the ionized donor BE complexes. A schematic drawing is shown in Fig. 7.2 indicating the spectral ranges where excitons bound to ionized donors DC X, neutral donors D0 X, and neutral acceptors A0 X will occur, a point we substantiate below. Around 3.32 eV, the two-electron satellite lines of the neutral donor BEs are detected [23, 24]. An example is also given below in Fig. 7.3. During the recombination of an exciton bound to a neutral donor, the donor final state can be the 1s state (normal D0 X line) or the 2s, 2p state (TES-line). The energetic distance between the D0 X and its TES is consequently the difference between the donor energies in the 1s and 2p states, which is 3=4 of the donor binding energy .ED / in the simple hydrogen-like effective-mass-approach (EMA).

–,+ –> FX 3.3758 eV

D0X 2S/2P TES

3.32

3.33

I9 A0X

3.34

3.35 Energy (eV)

I8

I5/6

I4

D0X

3.36

I2.3 D+X

3.37

3.38

Fig. 7.2 A schematic drawing of the energy ranges (shaded and in color) where the various bound exciton transitions may be positioned together with the level scheme for the two-electrontransitions of the neutral donor bound exciton with the neutral donor in the 1S ground and 2S/2P excited states

3.3636 eV

3.3220 eV

3.3664 eV

3.3189 eV 3.3137 eV

x 30

n=2

n=3

3.3058 eV

Intensity 3.3007

3.3614 eV

B.K. Meyer

3.3570 eV

172

3.3200

3.3573

3.3766

Energy (eV)

Fig. 7.3 Two-electron transitions at 3.322 and 3.3298 eV associated with the neutral donor bound exciton lines (after [24])

Therefore, by determining the position of the TES, the related donor binding energy can be measured with high precision.

7.2 Neutral Donor Bound Excitons (A-Valence Band) and Their Two Electron Satellites Since the BE recombination lines could not be assigned to a specific donor or acceptor, they were numbered I0 to I11 in the early work of Reynolds et al. [20]. The prominent lines in bulk ZnO are the BE transitions positioned at 3.3628, 3.3608, 3.3598, and 3.357 eV (labeled I4 , I6 , I8 , I9 /. For the donors that are responsible for the I4 to I10 recombination lines, we can deduce the 1s to 2p transition energy from the location of the two-electron-satellites (see Figs. 7.4 and 7.5 for a collection of the different TES lines and assignments used in the following). Transitions to higher excited states, e.g., n D 3; n D 4 : : : : have not been observed. In a simple hydrogen-like EMA, the energy separation between n D 1 and n D 2 states would be equal to the 3=4 of the donor binding energy R . A short range chemical potential of the impurity would affect only the states of the S-symmetry, thus leading to the chemical shift of the real donor binding energy ED from the effective mass

7

Bound Exciton Complexes

173

TES(I10) TES(I9) TES(I6-8)

I10

I8 I6/6a I4

I9

I2

ZnO:Na

PL Intensity (a.u.)

x50

ZnO:Li

x50

3.28

3.30

3.32

3.355 Energy (eV)

3.360

3.365

Fig. 7.4 Photoluminescence spectra of sodium and lithium-doped ZnO. The right side shows the excitonic range, the left side in magnification the two-electron-satellite range, T D 4:2 K, HeCd laser excitation. After [22]

PL Intensity (a.u.)

TES (I4) TES (I6/6a) 2p 2s

TES (I9) TES (I10) 2p 2s

2p

2s

TES (I8) 2p 2s

c)

3.29

a)

b)

3.30

3.31 Energy (eV)

3.32

3.33

Fig. 7.5 The two-electron-satellite transitions of the different donor bound excitons. The splitting of the excited states into the 2s and 2p states are indicated. After [22]

174

B.K. Meyer

value R and to the chemical shift of the 2S state. In this case, the donor energy ED can be estimated as .E2p –E1s / C 14 R . However, the 2S and 2P states in polar hexagonal semiconductors are additionally split because of the effects of anisotropy (into 2S, 2Pz , and 2Px;y states, where the hexagonal axis c is directed along z) and the polar interaction with optical phonons. The latter is different for states of S and P symmetries, and may also modify the chemical shift corrections on all states. The effects of the anisotropy on the ground and excited states donor energies (without taking into account the polaron effects) were described by second-order perturbation theory [29–31]. Thus, the binding energy of the donor is ch ; ED D E1S D R .1 C 0:72 2 / C E1s

(7.1)

ch is the chemical shift correction where the polaron self energy is omitted, and E1s to the 1S state. The polaron effective Rydberg R is calculated as

R D Ry: D

me 1 ; m0 "20

"? 0 ==

"0

;

3 2  D ? C == ;  me me me 3 1  D ?  == ; me me me

q "0 D

? "== 0 "0 ;

==

where Ry D 13:59 eV; m0 is free electron mass, "0 and "? 0 are the parallel and per== pendicular values of the static dielectric constant, me and m? are the parallel e and perpendicular values of the electron polaron mass, and  is the small parameter describing the anisotropy. The further polaron corrections / ˛ˇ=.1 C ˛=6/ where ˇ D R=ELO are negligible for the 1S state. Here ELO D 72 meV is the optical phonon energy, ˛ is the constant of the electron–optical phonon interaction assumed to be isotropic, and R D R =.1 C ˛=6/ is the electron Rydberg. The energies of the n D 2 can be now written as   R 37 ˛ˇ 2 ch 1 C 1:125 C  E2s E 2S D  ; (7.2) 4 480 1 C ˛=6   ˛ˇ R 7 1 C 0:8 C 1:15 2 C ; (7.3) E 2Pz D  4 160 1 C ˛=6   ˛ˇ R 7 E 2Px;yz D  1  0:4 C 0:5 2 C ; (7.4) 4 160 1 C ˛=6 ch ch where E2s D B E1s is the chemical shift correction to the 2S state. For the eval? uation of the data, the bare conduction band electron masses m== e D me D 0:21m0 were used. With an isotropic constant of the electron–optical phonon interaction, we get the isotropic polaron masses m== D me ? D 0:242m0 , me D 0:252m0, e  R D 50:1 meV,  D 0:038; and ˇ D 0:6. With these parameters, we obtain the binding energy of the effective mass (EMA) donor–polaron to be 50.15 meV. For

7

Bound Exciton Complexes

175

ch n D 2 states, we get E2S D 13:01 meV  B E1s ; E 2Pz D 13:19 meV, and E2Px;y D 12:61 meV: One can see that for all donors except for those with binding energies less than 48 meV, the largest energy separation is between 2Px;y and 1S states (see Fig. 7.6a). Therefore, the binding energies of the I5 to I8 donors can be determined as ED D .E2 Px;y E1S /C12:61 meV. This results in 51.55 meV for I6 donor close to the EMA donor, 53.0 meV for I6a , and 54.6 meV for I8 . The resulting energy separations of TES lines and the TES splittings are shown in Figs. 7.6a, b. One can see that due to the negative chemical shift, the 2S states become the deepest states of shallow I4 donor. Its binding energy can be then estimated as 46.1 meV, and the splitting of 2S and 2Pz states has a negative sign (see Fig. 7.6b), while for the other TES recombination lines, one expects a positive splitting of 2Px;y and 2S states. The donor binding energies ED show a linear relation to the BE localization energies Eloc D .EFX  ED0 X / Eloc D .EFX  ED0 X / known as Haynes rule Eloc D ˛ED [32]. Eloc is given by more generally by

Eloc D A0 C B 0 ED

(7.5)

and the quantities A0 and B0 must be determined form the experiment. The localization energies are given in Table 7.1. The fitting of the data in Fig. 7.6c gives A0 D 3:8 meV; B 0 D 0:365 (for comparison, we draw the solid line with A0 D 0; B 0 D 0:3). Magnetic resonance (ESR or EPR) showed that one of the shallow donors of the I4 line is hydrogen. On the basis of electron nuclear double resonance (ENDOR) experiments, the hyperfine interaction with a single H-nucleus was resolved [33]. Experiments showed that I4 annealed out completely at temperatures between 650 and 800ıC, depending on the annealing time. EPR showed a distinct reduction in the signal amplitude of the neutral donor resonance together with a disappearance of the hydrogen-related ENDOR signal. I4 and the hydrogen donor are typical for ZnO bulk crystals grown by the hydrothermal and seeded vapor transport methods. However, it is absent in crystals grown from the vapor phase. As to I6=6a , we can refer to the implantation studies of Schilling et al. [34]. They showed that upon implantation of Al and successive annealing, the I6=6a line gained in intensity and was the strongest for Al concentrations above 9  1016 cm3 . As already outlined by Gonzales et al. [35], Aluminum seems to be an omnipresent impurity in vapor grown ZnO. In Ga-doped epitaxial films, the prominent excitonic recombination line is I8 . There is a recent report on Ga-doped ZnO by the Sendai group [36]. In agreement with the findings in [22, 37, 38], they showed that the recombination of an exciton bound to a neutral Ga-donor occurs at 3.359 eV. I8 is always dominating in epitaxial films on GaN templates. SIMS experiments showed a severe interdiffusion of Ga from the GaN-template into the ZnO epitaxial film. The I9 emission line could be identified with the donor Indium based on diffusion [22] and implantation experiments [39]. M¨uller et al. [39] implanted radioactive 111 In into Zn bulk single crystals, and In occupies substitutional Zn lattice sites

176

B.K. Meyer

a

70

TES separation (meV)

65

2S - 1S 2Pz - 1S 2Px,y - 1S

60 55

I10 I9

50 45

I6

40

I6a

I8

I4

35 30

EMA donor (50.15 meV)

25 40

TES splitting (meV)

b

8 7 6 5 4 3 2 1 0 –1 –2 –3

Exciton localization energy (meV)

50

55

60

65

70

75

80

55

60

65

70

75

80

50 55 60 65 70 Donor binding energy ED (meV)

75

80

2Pz - 2S 2Px,y - 2S 2Px,y - 2Pz

40

c

45

45

50

26

Haynes rule: Eloc = 0.3 * ED linear fit: Eloc = 0.365 * ED – 3.8 meV

24 22 20 18 16 14 12 10 8

40

45

Fig. 7.6 The energetic distance of the two-electron-satellite transitions and the corresponding excited states from the respective bound exciton lines (a), the energetic splitting of the excited states (b), and the exciton localization energy, i.e., the binding energy of the exciton to the defect (c) as a function of the donor binding energy. After [22]

7

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177

Table 7.1 Free and bound exciton recombination lines and related properties Line Wavelength Energy Localisation Two-electron-satellite Donor binding Chemical (nm) (eV) energy (meV) separation .2Pxy  1S/ energy (meV) identity in (meV) AaL 367.12 3.3772 AaT 367.26 3.3759 I0 367.63 3.3725 3:4 I1 367.71 3.3718 4:1 I1a 368.13 3.3679 8:0 Ib2 368.19 3.3674 8:5 Ib3 368.29 3.3665 9:4 I3a 368.34 3.3660 9:9 I4 368.34 3.3628 13:1 34.1 46:1 I5 368.86 3.3614 14:5 I6 368.92 3.3608 15:1 38.8 51:55 I6a 368.96 3.3604 15:5 40.4 53 I7 369.01 3.3600 15:9 I8 369.03 3.3598 16:1 42.1 54:6 I8a 369.08 3.3593 16:6 I9 369.37 3.3567 19:2 50.6 63:2 I10 369.76 3.3531 22:8 60.2 72:6 I11 370.28 3.3484 27:5 a AL and AT are the longitudinal and transversal free A-exciton states. AT is the reference determination of the bound exciton localisation energy b I2 and I3 are assigned to ionised donor bound exciton recombination lines

H Al

Ga In

for the

after annealing at 700ıC. They monitored the photoluminescence while the donor In decayed into the stable and isoelectronic Cd [39]; the decay of the I9 line is shown in Fig. 7.7.

7.3 Ionized Donor Bound Excitons (A-Valence Band) Figure 7.8 shows the photoluminescence spectra of a homoepitaxial sample with prominent I6a (Al-donor) and I8 (Ga-donor) neutral donor BE recombination [40]. The I9 (In-donor) recombination is rather weak. They are accompanied by high energy transitions at 3.3726 and 3.3718 eV labeled I0 and I1 , respectively. These two lines have the same intensity ratio as I8 and I6a . Moreover, in samples with prominent I8 recombination as found for the samples grown on GaN-templates (interdiffusion of Ga into the ZnO layer), the I8 and I1 lines show up almost exclusively. For samples grown on sapphire substrates .Al2 O3 /, Al is the dominant impurity in the ZnO films, and I6a and I0 are observed as correlated pairs. Summarizing, it appears that I0 is related to I6a , and I1 to I8 . These findings are in agreement with data published by Bertram et al. [41] and Wagner and Hoffmann [42]. Another correlated pair of lines exists for I2 and I9 . In Na-doped ZnO crystals, the neutral donor BE recombination I9 related to Indium has the highest luminescence

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normalized Intensity [a.u.]

I9

(a) 31 h

(b) 95 h

(c) 243 h

I5 I6

3.352

3.356

3.360

3.364

Energy [eV]

Fig. 7.7 Photoluminescence spectra of the excitonic recombination luminescence of radioactive 111 In implanted ZnO (a) 31 h, (b) 95 h, and (c) 243 h after the implantation and annealing process. After [39]

I8 I6a

3.35

I1 I0

I2

Intensity (arb. units)

I9

I4 AT

3.36

3.37

AL

3.38

Energy (eV)

Fig. 7.8 Photoluminescence spectrum of a homo epitaxial ZnO thin film taken at T D 4:2 K showing the neutral donor bound exciton recombination lines I6a , I8 , and I9 and the corresponding ionized donor bound exciton lines I0 , I1 , and I2 . AT and AL are the transversal and longitudinal free A-exciton recombination bands. After [40]

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179 I9

I10

I8 I6/6a

I*

I2

PL Intensity (arb. units)

a

b

3.350

3.355

3.360

3.365

Energy (eV)

Fig. 7.9 Photoluminescence spectra taken at T D 4:2 K of ZnO bulk crystals grown from the vapor phase and doped with (a) Na and (b) Li. A correlation between I9 and I2 can be derived, as well as a tentative correlation between I10 and I . This Figure is a part of Fig. 7.4. After [40]

intensity due to compensation (see Fig. 7.9a) followed by I2 . The I6a and I8 recombination lines are much lower in intensity than the I10 line. A similar intensity ratio of I9 to I2 is found in a Li-doped sample; here the I10 recombination is more pronounced (see Fig. 7.9b). Figure 7.10 serves as a good compilation on what can be taken as established on the side of the donor BE recombination. In the sample with low dose implantation of 115 In, the incorporation of In as a donor is hardly detectable. The impurities present in the bulk before implantation and annealing are the main contributors to the BE recombination. These are the transitions I7 and I6 .D0 X/ and I1 and I0 .DC X/. The line I6B that is 4.5 meV above the I6 recombination is caused by excitons originating from the B-valence band (see later). Increasing the implantation dose by a factor of 100 causes the appearance of the I9 line (already attributed to the neutral In donor) and the I2 line (exciton bound to the ionized In donor) while the other transition are more or less uninfluenced. Magneto-optical experiments confirmed the nature of the I0 to I2 recombination [40] (for I2 =I3 see the published data in [20, 22, 43]). In Fig. 7.11, we show the localization energies of the ionized and neutral donor bound excitons as a function of the donor binding energy. Two aspects are remarkable: The localization energy EL has a linear dependence on the donor binding energy ED for both neutral and ionized BEs, although with a different slope, and for donor binding energies of ED < 47; meV excitons will not be bound to the ionized donors.

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B.K. Meyer I7I6

PL-Intensity (arb. units)

I9

B

I6

I2

I1I0

(a)

(b)

3.350

3.355

3.360

3.365

3.370

3.375

3.380

Energy (eV)

Fig. 7.10 Photoluminescence spectra at T D 4:2 K of 115 In implanted and subsequently annealed (700ı C) ZnO single crystals for two different implantation doses (a) 1012 ions=cm2 and (b) 1010 ions=cm2 . After [3]

Exciton localization energy (meV)

30 25 20

D°X

15 10 D+X

5 0 30

40

50 ED (meV)

60

70

Fig. 7.11 Localization energies of neutral D0 and ionized DC bound excitons in ZnO as a function of the donor binding energies ED . After [40]

7.4 A Comparison of the Localization Energies with Theoretical Predictions (the Haynes Rule) In the following, we want to put the experimental data in the context of theoretical estimates. Table 7.2 summarizes the theoretical results of EL as a function of  the ratio of EL to EB and the values EB , the impurity binding energies (ED or EA for

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181

Table 7.2 Theoretical predictions for the exciton localization energies EL , the impurity binding energies EB and the ratio of EL to EB as a function of the electron to hole mass ratio  Exciton bound to EL (meV)  D m EB (meV) Reference e =mh EL =EB values used in values used in the calculations the calculations Ionized donor DC X

13.4 9.4 3.3 Neutral donor D0 X – – Neutral acceptor A0 X – – a Based on the values of m D 0:24 m e h

0.2 0.3 44 0.46 0.15 59:4 0.275 0.06 55 0.3: : : 0.4a 0.3 55 0:3: : :0:4a 0.3 – 0.3: : : 0.4a 0.11: : : 0.13 – 0:3: : :0:4a 0.10: : : 0.15 – D 0:59 and m D 0:78 respectively h

donors or acceptors, respectively). For ZnO, the mass ratio  ranges between 0.3 and 0.4, depending on the hole mass used. We use for the electron mass a value of me D 0:24. For the hole mass, two values are available: mh D 0:59 from the calculation of the free exciton binding energy [44–46] and mh D 0:78 from the calculation of the excitonic transitions in ZnO/ZnMgO quantum well heterostructures [47]. We start with the neutral impurity BEs. They will be stable for all mass ratios. In the theoretical calculations of Hopfield [48] and Herbert [49] for D0 X, a ratio of EL =ED of 0.3 for 0:3 <  < 0:4 was obtained in perfect agreement with the experimental findings (see Table 7.2). Hopfield [48] used a donor binding energy of 55 meV, which resulted in localization energy of 16.5 meV. From experiments on the group-III donors (Al, Ga, In), the Ga-related I8 recombination comes closest with EL D 16:1 meV and ED D 54:6 meV. The ratio EL =ED is only weakly dependent on  for 0.3 <  < 0:4 as can be seen in Fig. 7.1 of Herbert [49]. In the case of the ionized donor BEs, two theoretical calculation are available (see Table 7.2). Skettrup et al. [50] used a mass ratio of 0.2 and EL D 13:4 meV and obtained EL =ED D 0:3 for ED D 44 meV. Smith et al. [51] calculated for  D 0:46 a value of 9.4 meV for EL (with ED D 59:4 meV). Changing the hole mass to 0.87 with the same electron mass, Smith et al. [51] achieved for EL a value of 3.3 meV for ED D 55 meV. D 0:275/. Both results were obtained by using a Pollmann–B¨uttner potential [52]. See Table 7.3. Experimentally, one finds for I0 and I1 localization energies of 3.4 and 4.1 meV, respectively, and for I2 an energy of 8.5 meV. The localization energies of I0 and I1 are in good agreement with the work of Smith et al. [51], which would be in favor of the parameters me D 0:24 and mh D 0:78 . D 0:3/. But with the same set of parameters, we cannot explain the localization energy of 8.5 meV of I2 . The theoretical results presented in Table 7.2 are based on the EMA. Central cell effects were not considered in the calculations of Smith et al. [51]. The localization energies of neutral donor BEs are less sensitive to central cell effects (see Table 7.2), while the ionized donor BEs are very sensitive (Table 7.2). In the calculations of the EMA donor binding energy ED , a value of 51 meV was obtained. The I9 recombination, which is correlated to I2 , is connected to a donor with a binding energy ED of

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Table 7.3 Experimental data on the exciton localization energies EL , the impurity binding energies EB , and the resulting ratio EL =EB Exciton bound to EL (meV) EL =EB EB (meV) Ionized donor DC X 3.4 .I0 / 0.064 53.0 (Al) 4.1 .I1 / 0.075 54.6 (Ga) 8.5 .I2 / 0.134 63.2 (In) 13.1 .I / 0.180 72.6 (X) Neutral donor D0 X 15.5 .I6a / 0.292 53 16.1 .I8 / 0.294 54.6 19.2 .I9 / 0.303 63.2 22.8 .I10 / 0.314 72.6 Neutral acceptor A0 X 16.5 – 24.7a 0.1: : :0.15b 165b a According to the estimates by Pan et al. [53] and Atzm¨uller et al. [54] b Binding energy of the nitrogen acceptor. After Zeuner et al. [55]

63 meV. This difference in donor binding energies (51 vs. 63 meV) is significant and indicates the remarkable influence of the core of the impurity donor on the binding energy that is the central cell shift. Therefore, it is not astonishing that the I2 localization energy deviates significantly from the calculated one using a value of 0.275 for . The influence of the central cell shift on the localization energies of ionized donor BEs compared with the neutral donor bound ones has already been outlined in the publication of Merz et al. [22]. Another interesting point is the I10 recombination, which is explainable from the localization energy as a D0 X recombination, according to Haynes’ rule in ZnO [22]. It is included in Fig. 7.10, and it is assumed that the line at 3.3630 eV (I in Fig. 7.9b) may be the corresponding ionized donor BE line. Indeed, this assignment fits into the general trend. Next, the case of the neutral acceptor bound excitons is considered. Theory predicts [53, 54] binding for 0:3 <  < 0:4 with ratios of EL =EA between 0.10 and 0.15 (see Table 7.2). Assuming an acceptor binding energy of 165 meV (as found for the nitrogen acceptor in ZnO [55]), localization energies between 16 and 25 meV will result (see Table 7.3). One can conclude that the localization energies of neutral donor and acceptor BEs in ZnO will be very close in energy, and an assignment of transition lines to donors and/or acceptors will not be straight forward. Localization energies between 60 and 70 meV are frequently reported for nitrogen, phosphorous, lithium, silver, and arsenic-doped ZnO [55–63], and attributed to A0 X recombination (in the spectral range from 3.31 to 3.32 eV). For a ratio of EL =EA between 0.10 and 0.15, acceptor binding energies between 400 and 600 meV would result, which are inconsistent with shallow acceptor formation and effective p-type doping. BE emission lines at the positions of I9 and I10 (see Figs. 7.4 and 7.9) have been attributed to A0 X recombination in [4] based on doping experiments. In the meantime, it has been shown that substitutional Li and Na on zinc sites form deep acceptors rather than shallow ones [64, 65]. However, recently, it has been shown that Li may form complexes, which act as shallow acceptors [66], adding to the complexity of the interpretations of the luminescence in the spectral region from 3.357 to 3.31 eV.

7

Bound Exciton Complexes

183

7.5 Excited State Properties of the Bound Excitons Blattner et al. [18] and Gutowski et al. [17] reported photoluminescence excitation spectra (PLE) of various BEs. Groups of resonances were observed and explained by rotational or vibrational excited states of the bound excitons and bound excitons where the B-valence band is involved. For a compilation of older data including excitation spectra in the presence of magnetic field, see Fig. 7.5 and 7.7 in [18]. Blattner et al. [18] found for I9 and I10 excited states, which are two times the A–B valence band splitting (i.e., 2  4:5 meV) above the ground state and have therefore been assigned to A0 X states consistent with temperature-dependent spectroscopy in magnetic fields, while emission lines that are generally assigned to D0 X did not show this excitation level. Gutowski et al. [17] performed intensity-dependent high resolution excitation spectroscopy and assigned most of the observed emission bands to A0 X states. In the following, we will show that in high quality bulk crystals temperaturedependent measurements under steady-state excitation, avoiding density effects by a pulsed excitation as in [17] is sufficient to resolve most of the spectral details of the excited states of the BEs. Bulk crystals from Cermet grown by the pressurized melt growth technique were employed, which apart from showing numerous line transitions had luminescence line width of the order of 140 eV. This allowed to clearly distinguish individual lines and to follow their behavior as a function of temperature. A typical spectrum is shown in Fig. 7.12 recorded at 10 K. The lines are labeled from 0 to 12 (as in Table 7.1) with an additional index (a to e), for an assignment see Table 7.4. At T D 4:2 K less lines are observed (apart from I0 to I12 only the lines I4a , I3c and I3b / – an indication that excited states are involved. Detailed temperature-dependent measurements showed that the recombination lines can be divided into two groups: lines that increase first in intensity upon a temperature increase and then at elevated temperatures start to loose in intensity and recombination lines that from the lowest measurement temperature loose intensity immediately upon raising the temperature. The latter is shown in Fig. 7.13

Table 7.4 Energy positions of free, bound excitons and bound exciton excited states and their assignments. From [3] Energy (eV) Recombination type Energy (eV) Recombination type 3.3774 3.3756 3.3733 3.3728 3.3720 3.3669 3.3652 3.3645 3.3642 3.3640

FXL FXT C I 0 .D X; I5a / C I .D X; I6 / 0 I0a .DC X; I7 / IB4 .I2a / IB6 .I3a / IB7 .I3b / IR2 4 .I3c / IR1 4 .I3d /

3.3636 3.3628 3.3625 3.3621 3.3614 3.3611 3.3608 3.3600 3.3567 3.3463

IR2 4b .I3e / I4 IR2 6 .I4a / I4b IR1 7 .I5 / I5a =IB9 I6 I7 I9 I12

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B.K. Meyer * ** I9 I7 I6 I5a I4b I4a I4I3eI3dI3cI3bI3aI2aI0a I0 I0 FXTFXL

PL Intensity (arb. units)

I12

3.345

3.350

3.355

3.360 3.365 Energy (eV)

3.370

3.375

Fig. 7.12 Photoluminescence spectrum of a ZnO single crystal recorded at 10 K, for the line assignments see Table 7.4. After [3]

I9

PL Intensity (arb. units)

I0a

E1 = 2.3 meV

0

5

100

150

0 50 1000/T (1/K)

E1 = 17,8 meV E2 = 3,6 meV 100

150

200

Fig. 7.13 Arrhenius plots of the recombination lines I0a and I9 ; squares: experimental data, solid drawn line fit to the data with the resulting activation energies. After [3]

7

Bound Exciton Complexes I7

I6

I5a I4b

I4a

I4

I3e I3d I3c I3b I3a I2a I0a

I*0

I0**

PL Intensity (arb. units)

I9

185

3.355

3.360

3.365 Energy (eV)

3.370

3.375

Fig. 7.14 Photoluminescence spectrum of a ZnO single crystal recorded at 10 K, the solid lines mark the transitions of the neutral and ionized donor bound excitons, respectively. After [3]

exemplified for the two transitions I9 and I0a , which we already have identified as D0 X and DC X recombination. They show a thermally activated decrease, and the activation energies E1 obtained by fitting to the experimental data are a measure of the respective localisation energies. All the transitions marked by the solid lines in Fig. 7.14 belong to these two classes of BE recombination lines, which always show the thermally activated decrease in the luminescence intensity. This is in contrast to the recombination lines shown in Fig. 7.15, and marked by the vertical solid lines (e.g., lines I3a : : : I3e /. Their behavior on a temperature increase can be understood with the help of Fig. 7.16. An increase in temperature from 4.2 K to  20 K leads to an increase in the luminescence intensity (i.e., a negative thermal quenching) expressed by the activation energy Ea . With a further increase in temperature, the intensity decreases again thermally activated with activation energies E1 (see Fig. 7.16). The activation energies E1 range between 15 and 20 meV and are indicative of the thermal decay of neutral donor BEs, since E1 scales with the localisation energies. The activation energies Ea range between 2 and 4 meV and indicate that excited states of the exciton are involved. Several scenarios are possible for the configurations of excited states of the exciton bound to a neutral donor leaving the donor in the ground state (excited states of the donor leaving the exciton in the ground state are known as the TES transitions, see Fig. 7.2 on this topic).

186

B.K. Meyer I7

I6

I5a

I4b I4a

I4

I3e I3d I3c I3b I3a I2a

I0a

I*0 I** 0

PL Intensität (willk. Einheiten)

I9

3.355

3.360

3.365 Energie (eV)

3.370

3.375

Fig. 7.15 Photoluminescence spectrum of a ZnO single crystal recorded at 10 K, the solid lines mark the transitions of excited states of donor bound excitons. After [3]

I3a

PL Intensity (arb. units)

I3d

E1 = 17.4 meV Ea = 2.7 meV 0

40

80

120

E1 = 19.2 meV Ea = 2.8 meV

160 0 40 1000/T (1/K)

80

120

160

Fig. 7.16 Arrhenius plots of the recombination lines I3a and I3d ; squares: experimental data, solid drawn line fit to the data with the resulting activation energies. After [3]

7

Bound Exciton Complexes

187

PL Intensity (arb. units)

I9

I7

B

I6 I9

I4

B

I7

B

B

I6

I4

4,5 meV 4,5 meV 4,5 meV 4,1 meV

3.356

3.358

3.360

3.362

3.364

3.366

3.368

Energy (eV)

Fig. 7.17 Photoluminescence spectrum of a ZnO single crystal recorded at 10 K showing the recombination lines of neutral donor bound excitons with A- and B-valence band derived excitons. After [3]

1. Excitons, which involve a hole from the B- instead of the A-valence band 2. Vibrational-rotational excited states of the excitons 3. Electronic excited states of the excitons Recombination lines that belong to class (1) can be identified on the basis of their line separations from the respective D0 XA transitions, which should be in close agreement with the energetic distance between the A- and B-valence bands. As demonstrated in Fig. 7.17, I9 , I7 , and I6 have matching lines, which are placed 4.5 meV higher in energy (the spacing between the A- and B-valence bands is 4.7 meV). For I4 , the distance is slightly smaller, but the high energy line tentatively identified with I4B is significantly broader compared with I6B or I7B . (another possibility is that I4B corresponds to I9 plus 2 AB , which would fit to an A0 X in the PLE spectra in [18]). The activation energy Ea obtained from experiment of 3–4 meV is still in fair agreement with the A-B splitting. The remaining lines .I3c to I3e and I4a / are attributed to process (2) – vibrational– rotational excited states of the excitons. With respect to [22], the calculations performed in [3] were more detailed and derived with the following results: An estimate of the vibration and rotation energies of the BEs can be obtained if the analogy to molecular vibrations is considered. Using a Kratzer potential   V .r/ D 2D a=r  a2 =2r 2

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B.K. Meyer

leads to E.; J / D   

.2ma2 =„/D 2 r   2    1 1 2 2ma2 C2 C J C 2 C „2 D

(7.6)

where  and J are the vibrational and rotational quantum numbers, respectively. D is the binding (or localization) energy of the BE, m is the relevant band mass, and a is the distance electron (hole)-impurity. The donor BEs are described in analogy to the “pseudo-donor model” for acceptor BEs. In the “pseudo-donor model,” the hole of the exciton is tightly bound to the neutral acceptor, and the electron is in a large orbit around the positive core. In such a case, the band mass for electrons would enter into (7.6) as well as a distance of 1.8 nm (Bohr radius). We assume for the donor BEs that the electron is tightly bound and the hole will be in a large orbit. With a band mass of 0:7mo , which is calculated from the acceptor ionization energy of 165 meV using the simple EMT-approach, a distance of 0.8 nm results. The excited state levels are calculated for  D 0; 1; 2 and J D 0; 1; 2 for all neutral donor BEs from I9 to I4 , and there is remarkable agreement between the calculated and the experimental results with this rather simple model. It is not possible on the basis of the experimental results to distinguish between rotational and vibrational states, since they are very close in energy and partially overlapping. The sum of all excited states results into two energy intervals, which are separated by only 0.2–0.3 meV. The possibility that lines belong to electronic excited states (3) of the BEs has been tested by using the formalism presented by Puls et al. [67] for donor-exciton complexes in CdS. Without going into detail, the first excited state of I6 (3.360 eV) (with the orbital quantum number n D 1 and the angular momentum quantum number l D 0) is placed at 3.3723 eV, very close to the FXT transition of the free A-exciton. In the experiments, one finds the line I0 at 3.3728 eV. The evidence to assign this line to an electronic excited state (apart from the agreement with the calculated value) comes from the fact that the thermal decay of I0 has an activation energy around 20 meV, despite the fact that the energetic distance to FXT is only 3 meV. For the D0 X recombination lines I9 to I12 , the excited exciton states will be 6–10 meV below FXT , and they may be good candidates to detect and study these transitions if samples have low impurity content, have extremely narrow line width, and if only one type of D0 X centers (e.g., I9 ) is present. The experimental findings on the neutral and ionized donor BEs involving the A- and B-valence band states are summarized in Fig. 7.18. The behavior of D0 XB compared with D0 XA is a consequence of the identical binding energies (and thus identical hole masses) of the A- and B-valence band derived free excitons. The trend for DC XB (dashed line in Fig. 7.18) is based on this assumption. The open triangles for D0 XA belong to transitions, which are most likely donor related (support comes from magneto-optical experiments) since they follow Haynes rule. A decisive and unambiguous assignment to a specific impurity cannot be made at present, but there is evidence that group VII elements are involved.

7

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189

3,378 FXA

3,376 3,374

PL Energy (eV)

3,372

D+XB

3,370 3,368

+

D XA

3,366 3,364 3,362

I4

3,360

I6

3,358

D0XB I7

3,356 3,354

D0XA

I9 46

48

50

52 54 56 58 60 Donor binding energy (meV)

62

64

Fig. 7.18 Energy position as a function of donor binding energy for neutral and ionized donor bound excitons involving A- and B-valence bands (open triangles are tentative assignments). After [3]

7.6 Donor–Acceptor Pair Transitions In wide-band gap semiconductors, bipolar doping has been a challenge of research for many years. ZnO can easily be doped n-type into concentrations where it shows metallic conduction, but reports on successful, reproducible, stable, and homogeneous p-type doping are very rare. See for example [68–75] and Chap. 5. In the late 1950s, Lithium and Sodium doping into ZnO was tested, but the group-I-elements act as self-compensating centers – Li (Na) at interstitial sites is a donor and when incorporated substitutionally on Zn sites, it behaves as a deep acceptor [4,64,65]. On the basis of magnetic resonance experiments, it could be demonstrated that Na and Li on Zn sites form in contrast to other II–VI semiconductors deep (600–800 meV) acceptors [64, 65, 76]. There are many theoretical reports on the properties of N in ZnO revealing a complex behavior by the interaction with intrinsic defects, passivation by hydrogen and formation of nitrogen molecules [77–79]. Nitrogen on oxygen site can be considered to be the best candidate as demonstrated by its success in p-type doping in ZnSe [80] and ZnS [81]. Experiments used ion implantation [22, 38, 82], doping during growth [55, 68, 70, 74], and diffusion [83]. There are only a few reports as to the optical properties of the materials in terms of donor acceptor pair (DAP) recombination involving a shallow nitrogen acceptor level [55, 70, 82–85].

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Fig. 7.19 Photoluminescence spectra of undoped (a) and nitrogen doped (b) ZnO films recorded at T D 4:2 K. After [55]

Figure 7.19 shows the luminescence spectrum of an epitaxial ZnO film doped with N during growth using NH3 as a nitrogen source. The same donor acceptor pair band was also found in samples where nitrogen was introduced by implantation and diffusion from the gas phase. Temperature-dependent measurements could be performed up to 150 K before the signal disappears in the noise (see Fig. 7.20). The transition energy is not very much temperature-dependent. The band gap energy decreases as a function of temperature .E.T / D E.T D 0/ – .5:05  104 T 2 /=.900  T //, which amounts to 16 meV for 150 K. See also Fig. 7.15. With increasing temperature, a line emerges at higher energies and takes over in intensity, which is typical for a change to a conduction band to acceptor transition (eA0 / when the donors start to become ionized. Correcting for the shift of band gap on temperature, the band-acceptor transitions shift to higher energies with approximately 12 kB T . The acceptor binding energy can be estimated from the peak position of the zero phonon line (ZPL) of the DAP transition at 3.23 eV i h    1=3 ; EA D Eg  ED  E D0 ; A0  ˛ND

(7.7)

with ED the shallow donor binding energy, ND its concentration and ˛ D 3  105 meV cm. In [55], time resolved luminescence was used to determine ND and – correcting for the Coulomb interaction term ˛ND1=3 – the acceptor binding energy EA of 165 ˙ 40 meV. Similar conclusions on EA have been derived by Reuss et al. [38] on nitrogen implanted ZnO.

7

Bound Exciton Complexes

191

Fig. 7.20 Temperature-dependent photoluminescence spectra of the donor–acceptor pair transition in ZnO/N. The dashed line shows the emergence of a band-acceptor transition and its respective shift to higher energies in comparison with the position of the DAP line. After [55]

The zero phonon line at 3.23 eV is repeated by longitudinal optical phonon replicas with an energy of 73 meV. The intensity of the ZPL with respect to 1LO, 2LO . . . replicas is described by a Poisson distribution (weak-coupling regime) In D I0 N n =nŠ;

(7.8)

with In the intensity of the nth phonon replica; n D 0; 1; 2; : : : I and N is the mean number of created phonons (or Huang–Rhys factor). N is 0.85 in ZnO/N, compared with 0.8 in ZnSe/N, indicating the close similarity between ZnO and ZnSe. A weak coupling to the lattice is indeed what we expect for a shallow acceptor. Note that the nitrogen acceptor binding energy in ZnSe is 110 meV for a band gap of 2.82 eV. Yamauchi et al. [84] showed in ZnO layers, grown by plasma-assisted epitaxy in mixed oxygen–nitrogen gas plasma, a donor–acceptor pair emission at 3.27 eV with practically identical phonon coupling (Fig. 7.21). They derived an acceptor binding energy of 135 eV assuming a shallow donor binding energy of 40 meV. Wang et al. [86] determined the ionization energy of nitrogen acceptors in bulk ZnO in as-grown, thermally annealed and N2 added samples. They assigned a DAP line at 3.216 eV to the nitrogen acceptor, and estimated a binding energy of 209 meV. Tamura et al. [85] reported on the optical properties of a DAP band in ZnO. The films were doped in situ by activated N species using a radio frequency plasma. The dependence of the DAD band on nitrogen concentration is shown in Fig. 7.22. They

192

B.K. Meyer

Fig. 7.21 PL spectrum at 20 K of nitrogen-doped ZnO layer grown in O2 C N2 mixed gas plasma with 0.1% N2 gas content. After [84]

observed a band with only partially resolved phonon structure, which was centered on 3.16 eV for nitrogen concentrations of 2  1018 cm3 . At elevated temperatures, they observed the appearance of the band to acceptor transition and determined from its analysis a binding energy of 266 meV for the acceptor. While the results of [38, 55] give an acceptor binding energy of .165 ˙ 40 meV/, the results of Tamura et al [85] are far off. This might indicate a different acceptor type or as Tamura et al. [85] stated the formation of unknown donor states by nitrogen doping. However, Tamura et al. [85] observed the band to acceptor transition at 3.178 eV (40 K) compared with the DAP line at 3.16 eV; hence, the acceptor must be different. The neutral donor BE line at 3.36 eV is independent of the doping level still dominating the spectra, and this can be taken as evidence that the films are still of n-type character. One of the first reports on p-type ZnO by homo epitaxial MBE growth was presented by Look et al. [70]. The films grown on Eagle–Picher ZnO substrates were doped by adding N2 into the O2 gas flow in the rf plasma. The low temperature PL results are shown in Fig. 7.23 as a comparison between the bulk ZnO substrate and the doped film grown on the substrate. The properties of an undoped film homo epitaxially grown on the substrate are unfortunately not available to be compared with. In the doped film, the band edge luminescence has merged into a broad band; individual transitions cannot be resolved. The spectrum is dominated by a broad transition centered at 3.315 eV assigned to a neutral acceptor bound exciton recombination. The transition at 3.238 eV could possibly be caused by the 1LO replica of the 3.315 eV line or be an independent donor acceptor pair recombination. Data in support of one or the other interpretation were not given. The A0 X assignment of the 3.315 eV line is in conflict with the localization energies estimated for A0 X

7

Bound Exciton Complexes

193

Fig. 7.22 Photoluminescence spectra in nitrogen-doped ZnO films grown on a SCAM .ScAlMgO4 / substrate as a function of growth temperature of 550–650ı C. These spectra were obtained at 10 K. Growth temperatures Tg and nominal nitrogen concentrations N are given in the Figure. After [85]

recombination lines (see above). A quite different interpretation is given in [87] and will be summarized in line with the experiments of As- and P-doped ZnO below. In the context of search toward p-type conductivity in ZnO, As- and P-doped ZnO films were investigated [88–92], and based on Hall-effect, measurements claimed to show p-type conduction. See again also Chap. 5. A typical result of MBE growth [82] obtained by fixing the temperature of the Zn effusion cell and varying the

194

B.K. Meyer 1600 0 A X

PL Intensity (arb. units)

N-doped MBE undoped bulk

0 D X

TES

1200 x1300 800

x16

x1

0

A X - 1 LO, and D0A0

400

0 3.20

3.25

3.30 E (eV)

3.35

Fig. 7.23 Photoluminescence spectra recorded at T D 2 K for two ZnO samples, an undoped bulk sample and an N-doped MBE-grown epitaxial layer. After [70]

temperature of a GaP effusion cell and vice versa is shown in Fig. 7.24. Sample (a) has n-type conductivity, (b) is ambiguous, (c) is p-type, samples (d), (e), and (f) ambiguous or n-type, and (d) is p-type. Two p-type samples had carrier concentrations at RT of 1:2  1018 and 6:0  1018 cm3 , respectively. For the sample with the lower carrier concentration, the phosphorus concentration in the films was 2  1018cm3 as measured by SIMS. The acceptor binding energy was estimated by Xiu et al. [91] to range between 127 and 180 meV. The astonishing point is that the carrier concentration is nearly identical to the doping concentration! According to the authors [91], the sample with the lower hole concentration has a D0 X transition at 3.364 eV and an A0 X line at 3.315 eV, while for the higher hole concentration, only the A0 X line at 3.317 eV is present. A donor–acceptor pair transition is hardly detectable (see Fig. 7.24g). The characteristic emission band at 3.31 eV observed in a variety of ZnO samples has been ascribed to various recombination types most often as conduction band to acceptor transition. From its energetic location, acceptors with binding energies of 130 ˙ 20 meV were determined irrespective of the chemical nature of the dopant, As, P, Sb or N. A recent experimental work [87] combining transmission electron microscopy, photoluminescence, and cathodoluminescence shed light into the nature of this transition. Figure 7.25 shows the temperature-dependent measurements where apart from the band acceptor transition also the donor acceptor pair transition appears. From its spectral position, the acceptor concentration NA < 4  1018 cm3 [see (7.7)] for a binding energy of EA of 130 meV was deduced. Schirra et al. [87] gained the information on the local appearance and structural origin of the band acceptor transition by correlating cathode-luminescence images with scanning and transmission electron microscope images. The main conclusion is that the acceptors are located in

7

Bound Exciton Complexes

195

Fig. 7.24 Photoluminescence spectra recorded at T D 8:5 K for two sets of phosphorous-doped ZnO films. After [91]

196

B.K. Meyer

Fig. 7.25 Photoluminescence spectra of an epitaxial ZnO film grown on a-plane sapphire substrate as a function of temperature showing the stacking fault related band acceptor transition at 3.31 eV. After [87]

basal plane stacking faults. Thus, the observation of the 3.31 eV transition is according to Schirra et al. [87], no implication that successful p-doping by substitutional acceptors has been achieved. With respect to BE recombination lines, an important aspect is still unsettled: the acceptor bound exciton transitions with the various possible acceptors. As outlined in Sect. 7.4, the localisation energies for neutral donor and acceptor BEs can be very similar. In the doped films, the line width of the BE lines increased significantly, and individual lines can hardly be distinguished. However, in recent luminescence excitation experiments on ZnO:N, a well resolved fine structure (compared with the PL) could be detected and may be helpful in the search for acceptor BEs [93].

7

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197

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39. S. M¨uller, D. Stichtenoth, M. Uhrmacher, H. Hofs¨ass, C. Ronning, J. R¨oder, Appl. Phys. Lett. 90, 012107 (2007) 40. B.K. Meyer, J. Sann, S. Lautenschlaeger, M.R. Wagner, A. Hoffmann, Phys. Rev. B 76, 184120 (2007) 41. F. Bertram, J. Christen, A. Dadgar, A. Krost, Appl. Phys. Lett. 90, 041917 (2007) 42. M.R. Wagner, A. Hoffmann (unpublished) 43. A.V. Rodina, M. Strassburg, M. Dworzak, U. Haboeck, A. Hoffmann, A. Zeuner, H.R. Alves, D.M. Hofmann, B.K. Meyer, Phys. Rev. B 69, 125206 (2004) 44. K. H¨ummer, Phys. Stat. Sol. B 66, 249 (1973) 45. R. Helbig, Habilitation Thesis, Erlangen (1976) 46. W.R. Lamprecht, A.V. Rodina, S. Limpijumnong, B. Segall, B.K. Meyer, Phys. Rev. B 65, 0725207 (2002) 47. G. Coli, K.K. Bajaj, Appl. Phys. Lett. 78, 2861 (2001) 48. J.J. Hopfield, Proceedings of the Seventh International Conference Physics of Semiconductors, Paris (Dunod, Paris, 1964), p. 725 49. D.C. Herbert, J. Phys. C 10, 3327 (1977) 50. T. Skettrup, M. Suffczynski, W. Gorzkowski, Phys. Rev. B 4, 512 (1971) 51. V.H. Smith Jr., P. Petelenz, Phys. Rev. B 17, 3253 (1978) 52. J. Pollmann, H. B¨uttner, Phys. Rev. B 16, 4480 (1977) 53. D.S. Pan, D.L. Smith, T.C. McGill, Solid State Commun. 18, 1557 (1976) 54. H. Atzm¨uller, F. Fr¨oschl, U. Schr¨oder, Phys. Rev. B 19 3118 (1979) 55. A. Zeuner, H. Alves, D.M. Hofmann, B.K. Meyer, A. Hoffmann, U. Haboeck, M. Strassburg, M. Dworzak, Phys. Stat. Sol. B 234, R 7 (2002) 56. H.S. Kang, B.D. Ahn, J.H. Kim, G.H. Kim, S.H. Lim, H.W. Chang, Y. Lee, Appl. Phys. Lett. 88, 202108 (2006) 57. D.C. Look, D.C. Reynolds, C.W. Litton, R.L. Jones, D.B. Eason, G. Cantwell, Appl. Phys. Lett. 81, 1830 (2002) 58. E. Prze´zdziecka, E. Kami´nska, K.P. Korona, E. Dynowska, W. Dobrowolski, R. Jakieła, Ł. Kłopotowski, J. Kossut, Semicond. Sci. Technol. 22, 10 (2007) 59. H.S. Kang, G.H. Kim, D.L. Kim, H.W. Chang, B.D. Ahn, S.Y. Lee, Appl. Phys. Lett. 89, 181103 (2006) 60. Y.R. Ryu, S. Zhu, D.C. Look, J.M. Wrobel, H.M. Jeong, H.W. White, J Crystal Growth 216, 330 (2000) 61. F.X. Xiu, Z. Yang, L.J. Mandalapu, J.L. Liu, W.P. Beyermann, Appl. Phys. Lett. 88, 052106 (2006) 62. X.D. Yang, Z.Y. Xu, Z. Sun, B.Q. Sun, L. Ding, F.Z. Wang, Z.Z. Ye, J. Appl. Phys. 99, 046101 (2006) 63. F.X. Xiu, Z. Yang, L.J. Mandalapu, J.L. Liu, Appl. Phys. Lett. 88, 152116 (2006) 64. D. Zwingel, J. Lumin. 5, 385 (1972) 65. D. Zwingel, F. G¨artner, Solid State Commun. 14, 45 (1974) 66. Y.-J. Zeng, Z.-Z. Ye, W.-Z. Xu, L.-L. Chen, D.-Y. Li, L.-P. Zhu, B.-H. Zhao, Y.-L. Hu, J. Crystal Growth 283, 180 (2005) 67. J. Puls, F. Henneberger, J. Voigt, Phys. Stat. Sol. B 119, 291 (1983) 68. K. Minegishi, Y. Koiwai, Y. Kikuchi, K. Yano, M. Kasuga, A. Shimizu, Jpn. J. Appl. Phys. 36, L1453 (1997) 69. M. Joseph, H. Tabata, T. Kawai, Jpn. J. Appl. Phys. 38, L1205 (1999) 70. D.C. Look, D.C. Reynolds, C.W. Litton, R.L. Jones, D.B. Eason, G. Gantwell, Appl. Phys. Lett. 81, 1830 (2002) 71. Y.R. Ryu, S. Zhu, D.C. Look, J.M. Wrobel, H.M. Jeong, H.W. White, J. Crystal Growth 216, 330 (2000) 72. Y.R. Ryu, W.J. Kim, H.W. White, J. Crystal Growth 219, 419 (2000) 73. Y.R. Ryu, T.S. Lee, H.W. White, Appl. Phys. Lett. 83(1), 87 (2003) 74. A. Tsukazaki, A. Ohtomo, T. Onuma, M. Oktami, T. Makino, M. Sumiya, K. Oktami, S.F. Chichibu, S. Fuke, Y. Segawa, H. Ohno, H. Koinuma, M. Kawasaki, Nat. Mater. 4, 42 (2005)

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82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93.

199

Chapter 8

Influence of External Fields M.R. Wagner and A. Hoffmann

Abstract The application of external fields provides a powerful tool to investigate a large variety of properties of excitons and exciton related processes. Within this chapter, we focus on the fundamental effects of static magnetic and strain fields on the optical properties of excitons in ZnO. The description is complemented by relevant examples. A general review of this topic can be found for constant fields in [Cho, Excitons, Topics in Current Physics, vol. 14 (Springer, Heidelberg, 1979)] and H¨onerlage et al. [Phys. Rep. 124:161, 1985] and for modulation techniques in [Cardona, Modulation Spectroscopy (Academic, New York, 1969); Seraphin, Modulation Spectroscopy (North Holland, Amsterdam, 1973); Goldsmith, NATO Science Series II, Frontiers of Optical Spectroscopy, vol. 168 (Springer Netherlands, 2005)]. Not much has been published on the influence of static electric fields on excitons. A few references are given at the end of Sect. 8.2.

8.1 Excitons in Magnetic Fields The investigation of optical transitions of free and bound excitons in magnetic fields enables the determination of binding energies, electron/hole g-values, impurity type (donor or acceptor), and charge state of excitons and defect centers as well as the symmetry ordering of the valence bands. Exposed to a magnetic field B electrons and holes perform a cyclotron motion which leads to a cyclotron energy Ec D „!c D „.eB=/;

(8.1)

where !c is the cyclotron frequency and  is the reduced mass of the exciton. Depending on the binding energy of the free exciton and the strength of the magnetic A. Hoffmann Institut f¨ur Festk¨orperphysik der Technischen Universit¨at, Berlin, Germany e-mail: [email protected] M.R. Wagner Institut f¨ur Festk¨orperphysik der Technischen Universit¨at, 10623 Berlin, Germany e-mail: [email protected] 201

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M.R. Wagner and A. Hoffmann

field, two cases are distinguished. For cyclotron energies larger than the binding b energy of the free exciton Ec  Eex , the appearance of Landau levels can be observed. The formation of Landau levels results from the quantization of the carrier motion in the plane perpendicular to the direction of the magnetic field. The required field strengths for ZnO are typically only available in pulsed magnetic fields. A general discussion of strong field effects and Landau levels is given in [1–3]. For static magnetic fields, the cyclotron energy is usually small compared to the binding b D 60 meV [4]. Thus, the magnetic field can be energy of the free exciton with Eex treated as perturbation of the excitonic system. This low field approximation is valid up to   0:4 with 1 e„B : (8.2) D 2 Ebex For ZnO,  D 0:4 corresponds to a magnetic field of around 80 T [5]. In this regime, the exciton energy states are influenced by two major effects of the magnetic field – the diamagnetic shift EDia and the Zeeman splitting EZ . The diamagnetic shift

EDia is a quadratic effect that leads to a blue shift of the exciton energy level by

EDia D

1 2 2 2 c aB B =; 2

(8.3)

where aB is the exciton Bohr radius. For ground state excitons n D 1 with a Bohr ˚ in ZnO, the diamagnetic shift is negligible compared to the radius of aB D 18 A energy shift by the linear Zeeman splitting. However, it should be noted that the diamagnetic shift increases for excited states n 2 as the Bohr radius of the exciton increases approximately by a factor of 4 from the n D 1 to n D 2 state [5].

8.1.1 Zeeman Effect The splitting of exciton lines in a magnetic field is caused by the interaction of the external magnetic field with unpaired electron and hole spins which contribute to a resulting magnetic moment. The size of the Zeeman splitting EZ is determined by the effective g-factor of the exciton gexc and depends linearly on the strength of the magnetic field (8.4)

EZ D gexc B B; where B is the Bohr magnetron. The effective exciton g-factor depends on the electron and hole g-factors ge and gh . In a general expression, gexc is given by gexc D jge ˙ gh j :

(8.5)

The effective exciton g-value gexc is not isotropic, which is mainly caused by the large anisotropy of the hole g-factor gh . In addition, there is an angular dependence of the electron g-factor ge with typical values for shallow donors of around 1.957 [6, 7]. However, due to the small difference in the electron effective g-values k ( ge D ge?  ge Š 0:001) which is usually not resolved in magneto-optical PL

8

Influence of External Fields

203

or absorption spectra but rather by EPR or ODMR, the electron anisotropy can be neglected in the following discussion of the Zeeman splitting. For an overview of g-factors determined by magnetic resonance techniques see Table 9.2 in Chap. 9 and references within. For gh , the absolute value of the hole anisotropic g-factor is given by q gh D

k

jgh j2 cos2  C jgh? j2 sin2 

(8.6)

where  is the angle between the c-axis and the direction of the magnetic field B [8]. Apparently, (8.6) delivers gh? for B?c and ghjj for B k c. The magnetic anisotropy can be explained in the quasi-cubic approximation considering the expectation values of the orbital angular momentum Lx , Ly , and Lz . For a 7 valence state having px , py like character, Lz and Lx;y are nonzero, so that gh ¤ 0 for any angle between B and c. In the case of a 9 valence band, Lx and Ly are zero and Lz ¤ 0. Hence, (8.6) can be simplified for a 9 hole state with gh? D 0. The effective hole g-value gh for a valence state with 9 symmetry is then given by: jj

gh D gh cos:

(8.7)

8.1.2 Free and Bound Excitons The Zeeman splitting of the exciton energy levels and hence the energy of optical transitions between the split excited and ground states depends on the type of exciton. Free excitons and excitons bound to ionized impurities can be distinguished from those bound to neutral impurities by a nonlinear splitting of energy levels in the magnetic field perpendicular to the c-axis, whereas excitons bound to neutral impurities exhibit a linear splitting behavior for B ? c. The different mechanisms suggest a separate discussion of free excitons, neutral donor, and acceptor bound excitons and ionized donor bound excitons.

8.1.2.1 Zeeman Splitting of Neutral Donor and Acceptor Bound Excitons A neutral donor or acceptor bound exciton consists of an electron–hole pair bound to a defect center which provides either one electron (donor) or one hole (acceptor) to the bound exciton complex. The neutral impurities as well as the bound exciton complexes represent doublet states (S D 1=2) since the two like particles form pairs with anti parallel spins. This fact leaves an unpaired electron in the case of an acceptor bound exciton, or an unpaired hole in the case of a donor bound exciton complex (Fig. 8.1). By contrast, a parallel spin orientation of the two electrons (donor) or two holes (acceptor) would result in an unstable configuration due to the exchange interaction. Considering exciton ground states (n D 1) without orbital angular momentum, the energy states of a neutral impurity in an external magnetic field will split according to the g-value of the unpaired particle in the exciton complex. For an acceptor

204 Fig. 8.1 Zeeman splitting of neutral bound exciton complexes involving 7 electron and hole states in a constant external magnetic field. The g-values in the ground and excited states depend on the spin of the unpaired particles

M.R. Wagner and A. Hoffmann

e– D+

e–

h–

(D0,X(Γ7)) B c –1/2 gh < ge

X

D0 B c gh

+1/2

σ–

σ+

e– +1/2

D+

ge

ge

–1/2

h+ A–

e–

h+

A0 B c

+1/2

ge

X

h+ A–

(A0,X(Γ7)) B c

ge

–1/2

σ+

σ– –1/2

gh < ge

gh

+1/2

bound exciton, the splitting of the excited state is determined by the electron g-factor ge whereas the splitting in the case of a neutral donor bound exciton is caused by the hole g-factor gh . By contrast, the ground state splitting is determined by the other particle as in the excited state, i.e. an electron in case of a neutral donor and a hole in case of a neutral acceptor. This four level system gives rise to two pairs of transition lines with energy separation controlled by jge  gh j and jge C gh j. Figure 8.2 shows the photoluminescence spectra of the I6a , I7 , and I8 bound excitons in magnetic fields up to 5 T. The graphs are displayed in Faraday and Voigt configuration for increasing magnetic field strength and for arbitrary angles at B D 5 T. The observed excitons exhibit narrow emission lines with   80 eV (see also Chap. 7 and [9–14]), which allows a clear separation of the I6a Zeeman components already at low magnetic fields of B D 1 T. In the case of the I7 and I8 bound excitons, the close proximity and similar intensity of the emission lines complicate the identification of the individual Zeeman components due to the overlapping of adjacent lines. Nevertheless, the very narrow line width and the examination of peak intensities enable doubtless attribution of all transition lines to the specific bound exciton complexes. The energies of the exciton lines as function of the magnetic field and angle  are displayed in Fig. 8.3. Since the three exciton complexes show an equal Zeeman splitting in all configurations, only the energetic positions of the I6a lines are shown for clarity. The linear Zeeman splitting in the Voigt geometry confirms the neutral charge states of the I6a , I7 , and I8 impurity bound exciton complexes. With increasing magnetic field strength, an additional splitting in B ? c geometry is visible [9]. This splitting is caused by a non-zero hole effective g-value gh? (Fig. 8.1). The reduction of the angle  from  D 90ı towards  D 0ı at a constant magnetic

8

Influence of External Fields

205

Fig. 8.2 Photoluminescence spectra of the I6a , I7 , and I8 bound exciton lines at 1.6 K for different magnetic fields, orientations, and angles. (a) Faraday configuration (B k c k k), (b) angles  D 0ı , 15ı , 30ı , 45ı , 60ı , 75ı , 90ı , between B and c with B D 5 T, (c) Voigt configuration (B?c k k). The black and gray lines indicate the spectra measured for right  C and left   polarized light, respectively [9]

Fig. 8.3 Zeeman splitting of the I6a bound exciton line at 1.6 K. (a) Faraday configuration (B k c k k), (b) arbitrary angles  between B and c with B D 5 T, (c) Voigt configuration (B?c k k). Solid and hollow triangles indicate the peak position for  C and   polarized light, respectively. Black dots mark the peak energies in the unpolarized measurements. Solid and dashed lines indicate theoretical fits for allowed and forbidden transitions, respectively [9]

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field leads to an increased splitting of the outer Zeeman components and a decrease of the effective splitting of the inner transition lines (Fig. 8.3b). This behavior is caused by the anisotropy of the hole effective g-value gh ./. The size of the splitting is derived from (8.6). For smaller angles , the intensity of the outer Zeeman split transitions is reduced. In Faraday geometry ( D 0), these lines are not observed as the transitions are forbidden by selection rules in the E ? c configuration, but active in E k c geometry. The size of the effective Zeeman splitting in Faraday configuration is smaller compared to those in Voigt geometry due to the contribution of a negative hole g-value (8.5). Polarization dependent spectra in B k c enable the spectral separation of the Zeeman split recombination lines already at low magnetic fields since either the right ( C ) or left (  ) circular polarized transitions can be suppressed (Fig. 8.2a). The high energy Zeeman component is  C polarized, while the low energy component is active in the   orientation in agreement with the model in Fig. 8.1.

8.1.2.2 Identification of Neutral Donor or Acceptor Bound Excitons Excitons bound to neutral acceptors (A0 X) can be distinguished from neutral donor bound excitons (D0 X) by the thermalization of the Zeeman split luminescence and absorption lines in external magnetic fields. The thermalization behavior of the PL components depends on the splitting of the complex excited state (A0 X) or (D0 X) while the thermalization in absorption is caused by the splitting of the ground state .A0 / or .D0 / of the respective bound exciton complex. The determination of acceptor or donor bound exciton complexes is facilitated in the Voigt configuration since gh? is small for a 7 hole and zero for a 9 hole. Therefore, the thermalization only depends on the splitting caused by the electron g-factor ge . According to Fig. 8.1, the splitting of the excited state of a donor bound exciton and the ground state of an acceptor bound exciton is given by gh? . Thus, equal intensities of the Zeeman split transition lines of donor bound excitons in luminescence and acceptor bound excitons in absorption are expected, which are independent of the temperature. By contrast, the splitting of the excited state for an acceptor bound exciton complex is given by the electron effective g-factor ge (Fig. 8.1). As a consequence, the intensity of the high-energy component of the .A0 X/ ! A0 transition at low temperatures should be smaller than the low energy component, but is expected to increase with rising temperature. This is explained by an increased occupation of the higher energy Zeeman level by thermal activation. In the case of donor bound excitons in absorption, the lower energy transition is weaker at low temperatures and increases for elevated temperatures. Similar considerations apply for the magnetic thermalization, where the increase of the magnetic field results in a larger splitting of the ground or excited state and may thereby lead to a stronger occupation of the lower energy Zeeman level. Based on the presented model, several publications report on the identification of donor and acceptor bound exciton complexes [9–11, 14–19]. Although several bound excitons were attributed to acceptor impurities in earlier works [11, 15] more

8

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recent publications could show that the I0 to I8 bound exciton are all donor related [14, 17–19]. This assignment also applies for the indium related donor bound exciton I9 [14, 17–20]. Nevertheless, theoretical considerations for shallow acceptors such as nitrogen with related localization energies of 16-25 meV (see Table 7.3) and the presence of excited states for the I9 and I10 with an energy spacing of twice the A-B splitting [10], also suggest the possible presence of acceptor bound excitons in the spectral region of I9 and below. For details please refer to the discussion in Chap. 7. One reason for the misinterpretation of donor bound excitons as acceptor related is given by the possibility of self-absorption which can result in a misleading thermalization behavior in luminescence. This is demonstrated by Rodina et al., who observed an increased intensity of the high energy PL line with increasing temperature for the I4 and I9 bound exciton lines in B ? c [17]. Following the previous discussion, such a behavior indicates an acceptor complex, although the PL data in B k c and absorption studies in the same work could prove that these lines originate from donor bound excitons in agreement with previous publications [21–23]. Consequently, absorption data are often required to confirm the thermalization results in the emission spectra.

8.1.2.3 Zeeman Splitting of Ionized Bound Excitons Excitons bound to ionized impurities exhibit a nonlinear splitting of transition lines in a magnetic field perpendicular to the crystal c-axis [8, 24]. The ground state consists of an impurity with no unpaired spin carrying particles and does not split in an applied magnetic field (1 symmetry). In the excited state of an ionized bound exciton, electron and hole spin of the exciton are unpaired. Hence, the Zeeman splitting of an ionized bound exciton line is solely determined by the splitting of the excited state. The energy level scheme for B?c and B k c is displayed in Fig. 8.4. In the absence of a magnetic field, only the 5 to 1 transition is allowed for E ? c. While the 5 exciton corresponds to a state with mainly anti parallel electron

(D+,X(Γ7)) B c D+/A–

e–

X h–

σ+

σ–

D+ / (A–,X(Γ7))

A– B c

B=0 g = ge+gh

Γ5

Γ5

g = ge–gh

Γ1,Γ2

Γ1,Γ2

E c

E c

E c

D+/A– Γ1

E c

E c E c Γ1

Fig. 8.4 Exciton level scheme of ionized bound excitons in zero field and constant magnetic field for hole states with 7 symmetry

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Fig. 8.5 Zeeman splitting of the ionized bound exciton I2 =I3 at 4.2 K. (a) Faraday configuration, (b) arbitrary angles  at B D 5 T, (c) Voigt configuration. Triangles and dots mark the energetic positions of the circular and linear polarized luminescence lines. Solid and dashed lines represent theoretical calculations for holes originating from valence bands with 7 and 9 symmetry, respectively (see Sect. 8.1.4) [17]

and hole spins, the 1 and 2 exciton states are constructed from products of the same band states but with the electron states interchanged. The dominant components of these states have parallel electron and hole spins. They are Kramers degenerate if the interaction with the crystal-field split-off band is neglected. As the zero-field exchange splitting between the 1 and 2 exciton states is known to be small, only the degenerated 1;2 level is displayed in Fig. 8.4 [25]. In the E k c polarization, the 1 exciton is dipole allowed but exhibits only small oscillator strength due to the involved spin flip process (for details see Chap. 6). The presence of a magnetic field in the B ? c orientation mixes the exchange split 5 exciton state (anti parallel spins) with the 1;2 states (parallel spins). As a result, the 1;2 , 1 transition is allowed in E ? c and E k c polarization, whereas the 5 , 1 transition is only allowed in the E ? c polarization for B ? c (Fig. 8.4). The two emission lines of the ionized bound exciton recombination in this configuration remain unsplit. Their energy dependency as function of the magnetic field is mainly determined by the zero-field splitting, which results from the spin– spin exchange interaction of the 5 and the 1;2 state (Fig. 8.5c). For the B k c configuration, a linear splitting of the 5 and 1;2 states into four excited states appears. This is demonstrated by the plot of peak positions of the ionized bound exciton lines I2 =I3 in Fig. 8.5a. The I2 transitions are circularly polarized with the upper energy component of the I2 line being active for the right-circular polarized light  C and the lower energy component for the left-circular polarized light   . By contrast, the I3 lines are only allowed in the E k c configuration in agreement with the model in Fig. 8.4. In the Voigt geometry

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(Fig. 8.5c), the transition from the zero-field allowed 5 exciton states and the 1;2 states, allowed by spin–spin interaction, are visible. The extrapolation of peak positions to B D 0 T reveals the presence of the zero-field splitting energy of 0.98 meV [17]. Such an interaction cannot occur in transition lines originating from excitons bound to neutral impurities, for the spin of the two like particles are anti parallel. Consequently, the I2 =I3 transitions have to originate from ionized bound excitons [12, 15, 17]. Similar results of magneto-optical photoluminescence measurements show that the I0 and the I1 related transitions also originate from excitons bound to ionized impurities with a zero-field splitting energy of 0.92 meV [14].

8.1.2.4 Zeeman Splitting of Free Excitons The Zeeman splitting of free excitons is similar to the splitting of ionized bound excitons, as the symmetry of the group representations of ionized bound exciton and free exciton states are equal [8.5]. Therefore, the energy level scheme for the ionized bound excitons in Fig. 8.4 is also valid for free excitons. The group representations of the free excitons are either 5 and 1;2 for an exciton involving a hole from a 7 valence band or 5 and 6 for a 9 valence state. In the latter case, the lower excited state of a free or ionized bound exciton in Fig. 8.4 is of 6 symmetry instead of 1;2 symmetry [12,17]. Again, the two exciton states are split by exchange interaction in zero-field. For an external magnetic field in the B ? c configuration no additional Zeeman splitting occurs. The energies of the Zeeman components of the 1;2 exciton and the 5 exciton for a non-zero component of B k c involving 7 hole states (7c , 7v transition) are given by: ˇ 1 ˇˇ jj ˇ E˙1;2 D E1;2 ˙ B ˇge  gh ˇ Bcos; 2  1  ˙ E5 D E5 ˙ B ge C ghjj Bcos: 2

(8.8) (8.9)

In the case of a 7c , 9v transition with 5 and 6 exciton states, the Zeeman split free exciton energies in a magnetic field are given by: ˇ 1 ˇˇ jj ˇ E˙6 D E6 ˙ B ˇgh C ge ˇ Bcos 2  1  E˙5 D E5 ˙ B ghjj  ge Bcos 2

(8.10) (8.11)

The Zeeman splitting of the A(5 ) and A(1;2 ) excitons together with the donor bound excitons I5 and I6 are shown in Fig. 8.6. Here, the magnetic field dependent peak positions between 0 and 7 T are displayed for angles  of 20ı (a) and 80ı (c) respectively. Consequently, the Zeeman splitting of the 1;2 exciton state in Fig. 8.6c is observed in contrast to the perpendicular orientation in Fig. 8.5c. The direct comparison between the splitting of free and bound excitons for small angles

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M.R. Wagner and A. Hoffmann

Fig. 8.6 Magnetic field and angular dependence of the free A excitons 5 and 1;2 , and the donor bound exciton I5 and I6 [26]

 in Fig. 8.6a illustrates the large effective g-value of the 1;2 exciton states due to a negative hole g-factor ghjj (8.8). Figure 8.7, which is identical to Fig. 6.13, shows transmission spectra in the region of the A and B free excitons with E k c polarization. Magnetic field spectra were recorded in the Faraday configuration with B k c. At zero field, the A(1;2 ) and A(5 ) exciton as well as the B(5 ) exciton states are visible. While all but the A(1 ) exciton represent forbidden transitions (see also Chap. 6), finite wave-vector effects, crystal strain, and magnetic fields can lower the symmetry sufficiently to produce absorption lines in E k c. With increasing magnetic field, ˇ a large splitting ˇ ˇ jj ˇ of the A(1;2 ) state with an effective g-value of gexc D ˇge  gh ˇ and a small splitˇ ˇ ˇ jj ˇ ting of the A(5 ) state with gexc D ˇge C gh ˇ are observed (Fig. 8.4). However, these effective g-values are only valid for hole states with 7 symmetry. For the B(5 ) exciton with a hole from the 9 valence band, the effective g-factor is given by gexc D ghjj  ge [17]. In addition to the Zeeman components of the free exciton states, a narrow absorption line S is visible in the presence of a magnetic field. The energy of this line corresponds to an isotropic point where the exciton polariton dispersion curves for E ? c and E k c coincide. Since the magnetic field leads to mixing of states with different polarizations, energy can be transferred from the E k c to the E ? c polarization, thus increasing the oscillator strength of the isotropic point. For B D 0 T the absorption at S is too weak to be detected. Doping of ZnO with transition metals may also affect the Zeeman splitting of the free excitons and can lead to new effects. In Zn1x Cox O, the transition metal ions of Co can substitute the cations and form a diluted magnetic semiconductor (DMS) (see also Chap. 10). Strong exchange interactions between sp carriers of ZnO and localized d electrons of the transition metal ion cause spin-dependent optical and

Influence of External Fields

Fig. 8.7 Transmission spectra in the region of the A and B free exciton for different magnetic field strengths between 0 and 20 T. Spectra are shown for E k c, B k c, k ? c at 1.8 K [5]

211 ZnO

1.8 K

E c, B c k c

20T Tranmission intensity (orb. units)

8

12.5T BΓ6 7.5 T S

T

0T

BΓ5 AΓ1,2 3.370

3.375

AΓ5L 3.380 (eV)

3.385

electrical properties [27]. In Fig. 8.8, a comparison of the reflectivity of ZnO and Zn1x Cox O is shown in the range of the free excitons under the influence of an external magnetic field. The first graph (a) displays the reflectivity spectra of ZnO at B D 0 T and at B D 6 T in  C and   circular polarizations. The spectra clearly exhibit the dominant reflection features of the A(5 ) and B(5 ) excitons. Under the influence of a magnetic field, the excitonic states show a small splitting into a  C and   polarized transition (b). In the case of Co doping, an increase in the effective g-value of the free excitons as a function of the Co concentration is observed. Reflectivity spectra of Zn0:996 O at B D 6 T in  C and   polarization reveal an energy splitting of 1.8 meV for the A exciton and 1.6 meV for the B exciton. The reversed energetic order of the  C and   polarized transition lines of the A and B band excitons in Fig. 8.8d originates from the different valence band symmetry of the A and B band (7 =9 ). With increasing cobalt concentration, a strong broadening of the exciton lines appears. This broadening is accompanied by a decrease of the reflection intensity which is most pronounced for the B and C excitons, hence leading to reduced intensity ratio of the B to A exciton with higher Co doping (Fig. 8.8c). For Co concentrations above 2%, the disappearance of free excitons prevents direct observation of the Zeeman splitting [28]. For a detailed discussion of transition metals in ZnO and related effects please refer to Chap. 9.

212

M.R. Wagner and A. Hoffmann 3381 ZnO

0.6

B

σ–

3379 3377

0.4 σ+

0.3 A

0.2 0.1 0

a

σ–

B

3375 T=1.6K A

fit B = 6T σ – B = 0T B = 6T σ +

σ+

b Zn1–xCoxO

0.5

σ–

B

3373 3371

σ+

3385

σ–

3383

σ – x = 0.4%

0.4 B=0

0.3

3381

A σ+

0.2

3379

B

0.1

c

0 3360

fit B = 6T σ – B = 0T B = 6T σ +

A T=1.7K

d

Energy [meV]

Reflectivity

0.5

Reflectivity

σ+

Energy [meV]

0.7

σ–

3377 σ+

3380 3400 0 1 2 3 4 5 6 Photon Energy [meV] B [ T]

3375

Fig. 8.8 Polarization dependent reflectivity spectra and Zeeman splitting of free A and B excitons in undoped ZnO (a, b) and Zn0:996 Co0:004 O (c, d) at low temperature [28]

8.1.3 Selection Rules for Zeeman Splitting of Exciton States in Magnetic Fields In order to determine whether a certain energy state in a crystal splits in an applied magnetic field, group theory considerations are beneficial. Thereto, the Kronecker product of the group representation of the magnetic field (B ) and the respective state (i ) must be calculated. A magnetic field leads to a splitting of a particular state, if the group representation of the state or the magnetic field is contained in the Kronecker product of the two: gexc ¤ 0 , B _ i 2 i ˝ B :

(8.12)

The group representation of a magnetic field perpendicular to the c-axis (B? ) is 5 , a magnetic field parallel to the c-axis (Bk ) transforms like 2 . Thus, certain symmetries lead to zero or non-zero g-values in dependence of the directions of

8

Influence of External Fields

213

the magnetic field and consequently result in the presence or absence of a Zeeman splitting. For a hole state with 7 symmetry, (8.12) leads for example to 7 ˝ 5 D 7 C 9 , g ? ¤ 0

(8.13)

7 ˝ 2 D 7 , g jj ¤ 0:

(8.14)

Therefore, the respective hole is expected to show a Zeeman splitting in both B ? c and B k c. Considering relevant symmetry states in ZnO, non-zero g-values gk for B k c are derived for 1 , 2 , 5 , 6 , 7 , and 9 states. For g ? , only 7 states show non-zero g-value which explains the missing splitting of the free and ionized bound exciton states in B ? c (Fig. 8.4).

8.1.4 Symmetry of Exciton Hole States Magneto-optical studies not only allow the determination of g-values, the differentiation between donor and acceptors, as well as the investigation of the charge state of the impurity, but also reveal information about the symmetry of the hole state involved in the exciton complex. This is of particular interest due to the long standing discussion of the valence band ordering in ZnO, i.e. if the A valence band in ZnO has 7 symmetry [1, 4, 5, 9–11, 15, 17, 25–27, 29–35] or 9 symmetry [12, 36–42] (see also the discussion of this topic in Chaps. 4 and 6). From the peak position of the I9 donor bound exciton complex in Fig. 8.9, it is evident that

Fig. 8.9 Zeeman splitting of neutral donor bound exciton I9 at 4.2 K. (a) Faraday configuration, (b) arbitrary angles, (c) Voigt configuration. Symbols indicate the energetic positions of luminescence lines, solid and dashed lines represent theoretical calculations for 7 and 9 hole states, respectively [17]

214

M.R. Wagner and A. Hoffmann

a

b (D0,X(Γ7)) gh⊥≅0

D0,X(Γ7v)

(D0,X(Γ9))

D0 ⎥gh⎥⎥⎥
⎥gh⎥⎥⎥>ge

σ–

σ+

σ+

D0

gh⊥=0

D0,X(Γ9v)

σ–

0

0

D

B=0

ge

B≠0 B^c

ge

ge

Bconst ≠ 0 cos(q)

B const ≠0 B

c

D

ge

cos(q)

B ≠0

B=0

B^c

Fig. 8.10 Energy level diagram of donor bound excitons as a function of magnetic field and angle  for exciton involving hole states from the 7 (a) and 9 (b) valence band [9]

the observed Zeeman splitting for B k c is smaller than the splitting in B?c configuration. In addition, the upper Zeeman component in Fig. 8.9 is found to be active for  C polarization, while the lower energy component is active for   polarization. Following the reasoning of Lambrecht et al. [25] and Rodina et al. [17], these k facts ˇ ? ˇcan be explained for the top valence band having 7 symmetry with gh < 0 and ˇg ˇ < ge . In agreement with previous reports [9–11, 15, 17, 25] the hole effective h g-factor gh? in B?c is considered to be small. Therefore, the Zeeman splitting in Voigt configuration is primarily determined by ge , while the influence of gh? on the splitting size can be neglected. Hence, the smaller splitting in Faraday configuration requires a negative hole effective g-value ghk for a 7 ! 7 transition (Fig. 8.1). Furthermore, the absolute value of the hole effective g-factor must be smaller than the electron effective g-value to ensure the  C polarized transition to be of higher energy than the   one. However this is not necessarily true if the top valence band is assumed to have 9 symmetry. To address this issue, the angular dependent PL data are of great use. According to theoretical calculations [17], the topmost valence band having 9 symmetry leads to a crossing of the peak positions of the two inner Zeeman components at an angle  between B and c of around 40ı , which is not observed in the spectra. The schematic level splitting of a donor bound exciton like I9 as a function of the magnetic field and angle  for hole states with 7 and 9 symmetry is shown in Fig. 8.10. Evidently, the anisotropy of the hole gvalue for a given effective exciton g-factor gexc has to be larger for a bound exciton involving a 9 hole (Fig. 8.10b) compared to a 7 hole state (Fig. 8.10a). This is demonstrated by the size of the splitting for a constant magnetic field as a function of cos (). Therefore, the crossing in the angular dependent data for an exciton with 9 hole symmetry follows from the larger hole g-value ghk compared to the electron g-factor ge [9].

8

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In conclusion, we have discussed in this chapter the influence of external magnetic fields on free and bound excitons in ZnO including symmetry considerations for selection rules and the valence band ordering. The different splitting mechanisms are explained to distinguish between ionized and neutral as well as donor and acceptor bound excitons in ZnO.

8.2 Excitons in Strain Fields Following the discussion of the influence of magnetic fields on exciton states, we now consider stress-induced effects. The lattice mismatch of ZnO epilayers grown by hetero-epitaxy on different substrates causes biaxial stress leading to pseudomorphic strained epilayers. Different thermal expansion coefficients of substrate and layer result in additional biaxial strain due to large temperature variations during device operation, growth, and low temperature optical measurements. In order to model the strain behavior of, e.g. heterostructures, the knowledge of the elastic constants and strain deformation potentials is required. These values can be studied under the influence of external hydrostatic or uniaxial stress which induces energy shifts or splittings of the optical recombination lines. In general, strain and stress are expressed by the symmetric second-rank tensors "O and O . The strain tensor "O describes the strain induced in the crystal by atomic displacements, whereas the stress tensor O defines the force per unit area applied to an elementary cube within the solid. In linear elasticity theory, the strain induced in a medium is proportional to the applied stress. The constants of proportionality O The can be expressed by the fourth-rank compliance tensor SO and stiffness tensor C. relation between strain and stress is given by: "ij D

X

Sijkl kl ;

(8.15)

Cijkl "kl :

(8.16)

k;l

ij D

X k;l

Since the strain and stress tensors are symmetric tensors, each can be described by six matrix elements rather than nine. In the contracted Voigt notation for symmetric tensors, the fourth-rank compliance and stiffness tensors can be denoted by 6  6 matrices [43]. For wurtzite structures with C6v symmetry, SO and CO posses five independent components. The matrix of the elastic stiffness coefficients is expressed by: 1 0 xx C11 B C BC B yy C B 12 C B B B zz C B C13 CDB B B yz C B 0 C B B @ xz A @ 0 xy 0 0

C12 C11 C13 0 0 0

C13 C13 C33 0 0 0

0 0 0 C44 0 0

10 1 0 0 "xx CB" C 0 0 C B yy C CB C 0 0 C B "zz C CB C; C B "yz C 0 0 CB C A @ "xz A 0 C44 "xy 0 .C11  C12 /=2

(8.17)

216

M.R. Wagner and A. Hoffmann

where the six elements of the strain tensor ©O are defined in the Voigt notation by .e1 ; e2 ; e3 ; e4 ; e5 ; e6 / D ."xx ; "yy ; "zz ; 2"yz ; 2"xz; 2"xy /:

(8.18)

The elastic stiffness constants C11 and C33 correspond to longitudinal modes along the [1000] and [0001] directions, whereas the constants C44 and C66 D .C11 C12 /=2 determine transverse modes propagating along the [0001] and [1000] directions, respectively. C13 in combination with the other four moduli describes the velocity of modes in less symmetrical directions such as [0011]. The values of the elastic constants can be determined using ultrasonic measurements [44– 47] and Brillouin scattering [48, 49] or be theoretically derived by first-principles calculations [50–52]. For a review of relevant publication see, e.g. [53] and Chap. 2. The influence of the atomic displacement, expressed by the variation of lattice constants and volume on the electronic band structure is determined by the deformation potentials. They describe the shifts and splittings of the band-structure eigenvalues as a function of the strain. Since the periodic deformation of the arrangement of atoms (phonons) influences electrons due to the resulting modulation of electronic bands, the strain deformation potentials describe the interaction of electrons and phonons. The variation of an energy level En;k in the contracted Voigt notation (8.18) is given by: ıEn;k D

6 X

j ej ;

(8.19)

j D1

where j are the deformation potentials and ej are the components of the strain tensor. For a hydrostatic or uniaxial deformation of the crystal, the (volume) deformation potentials are  D V .ıE=ıV / ;  D a.ıE=ıa/

(8.20) (8.21)

where •V and •a are deformation induced variations of the volume V and the lattice constant a, respectively. The particular deformation potential is determined by the evaluation of exciton energies during the application of hydrostatic or uniaxial pressure. It should be noted that only variations of the energy differences between two bands can be identified by optical measurements. Consequently, only relative deformation potentials are derived since the sum of the deformation potentials of conduction band and valence band affects the strain induced shift of the exciton transition energies (see Sect. 8.2.2). Following the general introduction, we now discuss the specific effects of external uniaxial and hydrostatic pressure and in-plane biaxial strain in ZnO and provide several relevant examples. For details on strain and deformation potentials see, e.g. [54, 55].

8

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217

8.2.1 Uniaxial Pressure Uniaxial pressure leads to a deformation of the lattice with variations of the lattice constants that are determined by the deformation potentials (8.21). Depending on the direction of the applied stress, not only the eigenenergies of the exciton states are changed but degenerate states can split if the symmetry of the crystal is reduced. In a wurtzite semiconductor with the point group C6v , a reduction of symmetry is given for any uniaxial pressure non-parallel to the c-axis. For pressure parallel to the c-axis P k c), only a shift of the exciton energy levels occurs as the symmetry C6v in this configuration is unchanged. The stress tensor O for uniaxial pressure parallel to c is given by: 0 1 000 O D @ 0 0 0 A ; (8.22) 001 where is the absolute value of the uniaxial stress and c k z. The components of the strain tensors are determined from the matrix of the compliance coefficients in (8.17). In the case of applied stress perpendicular to the c-axis, the crystal symmetry is reduced from C6v to C2v by the uniaxial distortion of the lattice. Early investigations of the influence of uniaxial stress on excitons in ZnO revealed a shift of the exciton energy levels [112] and were interpreted in terms of deformation potential theory based on one-electron energy bands [56]. However, the splitting of exciton lines in wurtzite crystals under uniaxial pressure perpendicular to the c-axis observed by Koda and Langer [57, 58] required a revision of this model, since all orbital degeneracies of the valence band are removed by the crystal field and spin-orbit interaction and therefore no splitting was expected. A theoretical interpretation for the splitting of the exciton states was provided by Akimoto and Hasegawa [59]. It was found that the combined effects of stress and the electron-hole exchange interaction in a quasi-cubic model were able to predict the splitting as well as observed polarization patterns of the free excitons (Fig. 8.11). The reflection spectra of ZnO in the range of the free excitons are displayed in Fig. 8.11. At P D 0 Bar, the A(5 ) and B(5 ) exciton states are observed. Uniaxial compression perpendicular to the c-axis (P ? c) with the k-vector of the incident light parallel to the c-axis (k k c) leads to a splitting of both exciton lines into two linearly polarized components. It should be noted that the displayed reflection spectra in Fig. 8.11 exhibit the characteristics of mixed mode polaritons as described in Chap. 6 (see Fig. 6.9). Therefore, a deviation from the k k c orientation due to tilting of the c-axis, variations of the crystal orientation or beam alignment issues are likely, although this is not explicitly stated in [57, 58]. For the A exciton, the higher energy line is polarized with E k P, whereas the B exciton shows reversed polarization of the split lines with E k P polarization of the lower energy component. For the P ? c; k ? c configuration (see [58]), only a shift of the E k P lines can be observed even though the crystal symmetry is also reduced. This is explained by the suppression of the E ? P components, due to the strong polarization of the A and B lines with E ? c.

218 ZnO #0714–1

1.8° K 0 kb

A

B

REFLECTANCE (ARB. UNIT)

Fig. 8.11 Reflection spectra of the A(5 ) and B(5 ) excitons as a function of uniaxial pressure between 0 and 4.24 kbar with P?c and k k c at T D 1:8 K. Solid and dashed lines represent components with E k P and E ?P polarization, respectively [57]

M.R. Wagner and A. Hoffmann

0.85

1.70

2.55

3.39

4.24

3680

3670

3660

3650

3640

3630

WAVE LENGTH (Å)

Using two-photon excitation spectroscopy (2P-ES) and three-photon difference frequency generation (3P-DFG), Wrzesinski and Fr¨ohlich were able to determine the deformation potentials of ZnO from measurements of the exciton–polariton resonances under the influence of uniaxial stress [60]. The six deformation potentials 1 to 6 are deduced from simultaneous least-squares fits of the observed shifting behavior of the resonances in four different orientations of the applied force and the k-vector of the incident light. Figure 8.12 displays the shift and splitting of the exciton polariton resonances as a function of the applied stress. R1, R2, R3, and R5 correspond to resonances of the A(5 ) exciton–polariton branches, R6 and R7 are related to the B(5 ) polariton, and R4, R8, R9, and R10 represent resonances on the C(1 ) polariton dispersion curve [60]. In order to reach the k-values of the lower polariton branches of the A(5 ) (R1, R2, R3) exciton–polariton and the C(1 ) (R4) three-photon difference frequency generation is applied. Thereby, a tunable dye laser and an anti-parallel oriented Nd-YAG laser beam are focused on the same sample position. The three available energies of the Nd-YAG laser (the fundamental wavelength at 1,064 nm and the Raman shifted energies in methane and hydrogen) result in an almost equidistant energy distribution of the resonances on the polariton branches at zero pressure (see Fig. 8.12). The splitting of the polariton resonances

8

Influence of External Fields

219

I

II

III

III

IV

3.44

R10

3.42

τ

[0001]

τ

[1010]

τ

[1010]

τ 45° to [0001]

K

[1120]

K

[1120]

K

[0001]

K

R9

AY AX BY CZ

3.40 Energy (eV)

[1120]

R8 R7 R5,R6 R4

3.38

R3 3.36 R2 3.34

R1 0

200

400

0

200

400 0 200 Stress (MPa)

400

0

200

400

Fig. 8.12 Stress induced shift and splitting of exciton–polariton resonances for different directions of stress and k-vector, measured by non-linear two and three photon spectroscopy. Dots denote experimental results; solid lines represent least-squares fits [60] Table 8.1 Deformation potentials 1 to 6 of ZnO Deformation Wrzesinski et al. potential [60] 1 3:90 2 4:13 3 1:15 4 1:22 5 1:53 6 2:88

Langer et al. [58] 3:8 3:8 0:8 1:4 1:2 2:8

R1, R2, and R3 for ?c and k k c (III) correlates to the splitting of the A exciton in Fig. 8.11. The symmetry of the crystal lattice in the four different configurations in Fig. 8.12 is unchanged for configuration I (C6v ), and reduced for the configurations II, III (C2v ), and IV (Cs ). Similar measurements using reflection spectroscopy and emission spectroscopy under uniaxial pressure were also performed by Langer et al. [58] and Solbrig et al. [61]. The calculated deformation potentials according to these works are listed in Table 8.1.

8.2.2 Hydrostatic Pressure The application of hydrostatic pressure leads to a simultaneous decrease in the lattice constants a and c, and thus the volume V . Since no symmetry of the unstrained

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M.R. Wagner and A. Hoffmann

crystal is reduced, the symmetry of wurtzite ZnO under pressure is still described by the point group C6v . The hydrostatic pressure P is specified by the diagonal stress tensor 0 1 xx 0 0 O D @ 0 yy 0 A ; (8.23) 0 0 zz whereby the components of the stress tensor are equal with ¢xx D ¢yy D ¢zz D P . Tensile stresses are positive while compressive stresses are negative by sign convention. With (8.17), the strain along the c-axis is given by "zz D RH "xx , where RH D

C11 C C12  2C13 C33  C13

(8.24)

is the hydrostatic relaxation coefficient expressed in terms of the elastic stiffness constants Cij . A uniform dilatation or compression by •V around the equilibrium volume V0 shifts the energies of the conduction band minimum Ec and valence band maximum Ev by amounts of Ec and Ev , respectively. In the regime of linear elasticity, these shifts of individual band edges as a function of the volume change under hydrostatic stress •V =V0 are determined by the absolute deformation potentials for the valence band v D V .•Ev =•V / and for the conduction band c D V .•Ec =•V /. The change in the band-gap energy Eg D Ec  Ev can therefore be expressed by the band-gap deformation potential g D c  v . While shifts of bands relative to each other can be extracted from, e.g. optical experiments, the absolute deformation potentials are difficult to obtain due to the lack of precise reference for the potential energy in a homogeneously deformed crystal, but can be derived from theoretical calculations. For details on the calculation of absolute deformation potentials using first principle methods see, e.g. [62]. Figure 8.13 displays the energy shift of the free A, B, and C excitons as a function of hydrostatic pressure. For all observed transitions, a linear dependence of the exciton energy on the hydrostatic pressure is observed. The pressure dependences of the exciton binding energies and bandgap energies are determined by the energy difference between 2P and 1S exciton states in a hydrogen like model with E.n/ D Eg  EFX =n2 , where EFX are the binding energies of the free excitons. The pressure coefficients of the bandgap for the A, B, and C valence band are determined to values of 24.7–26.8 meV/GPa [63]. In terms of the relative bandgap deformation potential g , the band-gap energy shift can be approximated with

E D g .V  V0 /=V:

(8.25)

The relative volume change caused by the applied pressure is expressed by the Murnaghan equation of state [64] 0

P D .B=B 0 /Œ.V0 =V /B  1;

(8.26)

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221

Fig. 8.13 1S and 2P exciton energies of the A, B, and C free excitons as a function of hydrostatic pressure [63]

C 2P

3.65 ZnO T=6K

3.60

B 2P A 2P B 1S

Energy (eV)

3.55 A 1S

3.50

3.45

3.40

0

1

2

3 4 5 Pressure (GPa)

6

7

Table 8.2 Exciton/bandgap pressure coefficients and hydrostatic deformation potentials determined by experimental measurements and theoretical calculations ˛ (meV/GPa) g (eV) v (eV) c (eV) B (GPa) B0 Reference 29.2 3:92 ˙ 0:15 2:13 6:05 ˙ 0:15 142.6 [65] 3.6 [66]a 23.6 ˙ 0.4 3:47 ˙ 0.04 142.6 [65] 3.6 [67]b 27:1 ˙ 1:3 4:55 ˙ 0:15 142.6 [65] 3.6 [67]c 24:5 ˙ 2:0 3:5 ˙ 0:4 142.6 [65] 3.6 [68]d 40:0 ˙ 3:0 8:1 ˙ 0:5 202.5 [65] 3.54 [68]e 23.6–26.5 3.51–3.81 142.0 [45] [63]f 1:7 0:6 2:3 [62]g 2:9 0:2 3:1 [62]h a ZnO nanowires b ZnO nanocrystallites c Mg0:15 Zn0:85 O d Wurtzite ZnO (bulk/thin films) e Rocksalt ZnO (bulk/thin films) f ZnO single crystals g LDA calculations h LDA+U calculations

where B D 142:6 GPa is the bulk modulus of wurtzite ZnO and B 0 D 3:6 is its pressure derivative (dB=d P) [65]. Values for the relative hydrostatic deformation, potential are listed in Table 8.2. The variation of the band-edge and deep luminescence energy in nanowires as a function of hydrostatic pressure is shown in Fig. 8.14. The solid lines in Fig. 8.14

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M.R. Wagner and A. Hoffmann

Fig. 8.14 Peak positions of the near band edge emission and broad green emission of nanowires as a function of hydrostatic pressure. Dots and squares are experimental values; solid lines represent least squares fits. Triangles represent peak positions in the pressure range of the structural wurtzite to rocksalt phase transition (B4 to B1) [66]

represent the least squares fit using the quadratic function E.P / D E0 C ˛P C ˇP 2 with the linear pressure coefficient ˛ D 29:2 meV=GPa and the small quadratic term ˇ D 0:38 meV=GPa for the near band edge luminescence [66]. By contrast, the green emission shows a weaker pressure dependence with a linear slope of 15.9 meV/GPa and a quadratic term ˇ D 0:71 meV=GPa. This difference in the pressure coefficients of the green emission compared to the excitonic one is consistent with deeply localized defect states such as oxygen vacancies which are less sensitive to the applied pressure compared to the conduction band edge at the  point. The pressure coefficients of excitons and the deformation potentials of nanostructures and bulk material are listed in Table 8.2 together with the bulk moduli used to derive the deformation potentials. In the pressure range between 12 and 15 GPa, the non-linear pressure dependence of the near bandgap luminescence (triangles) indicates the onset of the phase transition from the wurtzite to the rocksalt structure which is discussed in the next section. For further information on the influence of hydrostatic pressure on optical transitions see, e.g. [63, 67–71]. Similar to other II–VI semiconductors, ZnO undergoes a phase transition from the fourfold wurtzite (B4) structure to the sixfold correlated rocksalt (B1) structure upon the application of hydrostatic pressure (see also Chap. 2). It is explained by the pressure induced reduction of the lattice dimensions, which causes the inter-ionic Coulomb interaction to favor the ionicity over the covalent nature. This correlates with the instability of the wurtzite structure against shearing deformations [47, 51]. Energy-dispersive X-ray diffraction delivers a critical pressure of 8.7–9.1 GPa for the phase transition at room temperature [65, 72]. The transition to the rocksalt

8

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223

260

Elastic constants C u (GPa)

240

220 C11 C33

200

C66 C44

44 43 42 41 40 39 38

0

2

4

6

8

Pressure (GPa)

Fig. 8.15 Elastic stiffness constants of ZnO as a function of hydrostatic pressure at ambient temperature [47]

structure is accompanied by a large decrease of the unit cell volume of about 17% [65, 73]. Upon decompression, a strong phase hysteresis is present, which leads to a reversion to the wurtzite phase at pressures of 1.9–2.0 GPa [65, 72]. For nanostructures, the phase transition occurs at higher pressures between 12 and 15 GPa [66, 74]. Figure 8.15 displays the elastic stiffness constants as a function of hydrostatic pressure. The elastic moduli are determined by the conversion of acoustic travel times in ultrasonic measurements at low temperature [47]. With increasing pressure, a linear dependence of all elastic moduli up to P D 7:5 GPa is observed. For higher hydrostatic pressures, the B4 to B1 phase transition begins to occur. As seen in Fig. 8.15, the slope of the longitudinal modes C11 and C33 as a function of the hydrostatic pressure is positive with pressure derivatives of .dC11 =dP D 5:32 and dC33 =dP D 3:78). By contrast, the elastic shear moduli C44 and C66 reveal a negative pressure dependence with values of dC44 =dP D 0:35 and dC44 =dP D 0:30 [47]. Thus, ZnO becomes softer against shear-type acoustic distortions under pressure. The elastic shear softening observed at room temperature is enhanced at elevated temperature and leads to an onset of the B4 to B1 transition at about 6 GPa at 600ıC [47]. The influence of hydrostatic pressure on the phonon frequencies can be studied by Raman spectroscopy (see also Chap. 2). Group theory predicts the existence of the optical modes A1 ; 2B1 ; E1 ; 2E2 at the  point. B1 (low) and B1 (high) are silent modes, whereas A1 ; E1 ; E2 (low), and E2 (high) are Raman active. In addition, A1 and E1 are polar, infrared active modes and consequently split into longitudinal

224

M.R. Wagner and A. Hoffmann

Fig. 8.16 Top: Pressure dependence of the observed optical phonons. Open (full) symbols: propagation of light perpendicular (parallel) to c. Bottom: (LO – TO ) E1 phonon mode splitting vs. pressure. Solid lines are linear least-squares fits to the experimental points [77]

and transverse optical components (LO and TO) [75, 76]. The shift of the phonon frequencies under the influence of hydrostatic pressure is shown in Fig. 8.16. The disappearance of all Raman peaks at 8.7 GPa is caused by the phase transition to the rocksalt structure. In the harmonic approximation, the phonon frequencies exhibit linear dependence on strain and hence also on the lattice parameters. The pressure dependence of the lattice parameters is given by Murnaghan equation of state (8.26). For most semiconductors, (8.26) is expanded to the second order to describe the pressure dependence of the phonon frequencies. However, the shifting behavior of the optical Raman modes as a function of the applied hydrostatic pressure in Fig. 8.16 can be well described by the first order term of the expanded Murnaghan equation since the second order term is negligible small.

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225

The E2 (low) is the only mode which exhibits a decreasing Raman shift, whereas the frequency shift of the E2 (high), A1 (TO), E1 (TO), and E1 (LO) increases with pressure. The longitudinal-transverse splitting of the E1 (LO) mode (Fig. 8.16 bottom), shows weak pressure dependence which is attributed to a small variation of the chemical bond iconicity of wurtzite ZnO with pressure [77]. However, a recent study of a-plane ZnO revealed a negative slope of the LO-TO splitting as function of hydrostatic pressure in agreement with the tendency in other heteropolar semiconductors [113]. For details on the structural and vibrational properties under hydrostatic pressure including pressure coefficients, Gr¨uneisen parameters, and Raman line widths dependence see, e.g. Chap. 2 and [77–82].

8.2.3 Biaxial In-Plane Strain So far, we have discussed the influence of external uniaxial and hydrostatic pressure on mechanical and optical properties of ZnO. We now consider biaxial strain which can be treated as superposition of uniaxial and hydrostatic strain tensors and plays a significant role in hetero-epitaxial grown layers. If not explicitly stated otherwise, biaxial strain in this chapter refers to isotropic biaxial (bisotropic) in-plain strain. Bisotropic strain results in deformations which conserve the C6v point group symmetry since the uniaxial strain component is parallel to the principal c-axis (Sect. 8.2.1). Consequently, the strain tensor " is diagonal with the components "xx D "yy D .a  a0 /=a0 ;

(8.27)

"zz D .c  c0 /=c0 :

(8.28)

The corresponding diagonal stress tensor is given by Hooke’s law (8.17) for small variation from the equilibrium with xx D yy D .C11 C C12 /"xx C C13 "zz ;

(8.29)

zz D 2C13 "xx C C33 "zz :

(8.30)

A homogeneous biaxial stress in the plane perpendicular to the c-axis is expressed by constant forces in the plane xx D yy and vanishing forces along the c-axis with zz D 0. With (8.29), the relationship between the biaxial in-plane strain "xx and the uniaxial out of plane strain "zz is given by the biaxial relaxation coefficient RB with "zz D RB "xx , where RB is defined as RB D

2C13 : C33

(8.31)

The in-plane stress is related to the in-plane strain by the biaxial modulus Y with xx D Y "xx with 2 2C13 Y D C11 C C12  : (8.32) C33

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M.R. Wagner and A. Hoffmann

For uniaxial stress, the external forces vanish in the plane perpendicular to the stress direction which leads to an elastic relaxation of the lattice in this plane. The ratio of the resulting in-plane strain to the deformation along the stress direction is expressed by the Poisson ratio . For uniaxial stress zz parallel to the c-axis with xx D yy D 0, (8.29) gives the relation "xx D v"zz with the Poisson ration D

C13 : C11 C C12

(8.33)

For a detailed theoretical treatment of strained wurtzite crystals including first principles studies see, e.g. [83–87]. Heteroepitaxial layers are subject to biaxial in-plane strain due to the lattice mismatch between the substrate and the deposited layer as well as the difference in the thermal expansion coefficients of substrate and layer. The incorporation of impurities and defects leads to a local distortion of the lattice parameters due to their different ionic radii, which produces additional strain in the vicinity of the defects. The influence of the in-plane strain on the optical properties can be extensive and affect both the intrinsic and extrinsic transitions in the crystal. Photoluminescence and absorption spectra of free and bound exciton lines clearly exhibit shifted peak positions for samples with residual strain compared to those of completely relaxed samples. For highly strained systems, the strain may relax partially by the growth of islands or quantum dots. Smaller lattice mismatches result in the growth of pseudomorphic strained layers up to a critical thickness at which dislocations lead to partial relaxation of the epilayer. ZnO can be grown on a large variety of substrates with different lattice parameters. Reports of epitaxial grown ZnO layers exist for the substrates ZnO, GaN, AlN, Al2 O3 , 6H-SiC, Si, CsAlMgO4 , and GaAs. An overview of lattice parameters, lattice mismatch, and coefficients of thermal expansions is given, e.g. in [53]. For details on the influence of biaxial strain on the epilayers using various substrates see, e.g. for ZnO [88–92], GaN [93, 94], AlN [95, 96], Al2 O3 [97–100], 6H-SiC [101, 102], Si [103], ScAlMgO4 [104], GaAs [105]. In the case of hetero-epitaxial growth of ZnO on, e.g. c-Al2 O3 , the mismatch of the lattice parameter a and the difference in the coefficient of thermal expansion ˛ is given by aAl2 O3  aZnO =aAl2 O3 D 18:3% and ˛Al2 O3  ˛ZnO =˛Al2 O3 D 34%, respectively [98]. These large deviations result in the formation of serious residual strain which often leads to significant deterioration in terms of surface morphology, optical, and structural properties. The strain distribution can be investigated by the evolution of the lattice parameters as a function of the ZnO layer thickness. Figure 8.17a shows the a- and c-lattice constants of ZnO layers with a thickness between 40 nm and 2 m on c-Al2 O3 substrate. The a-lattice constant increases rapidly up to a thickness of about 500 nm and then decreases slightly whereas the c-lattice constant shows an opposite behavior. This characteristic can be explained by the contribution of compressive biaxial strain due to the lattice misfit and tensile biaxial strain caused by difference in the coefficient of thermal expansion. The horizontal line in the Fig. 8.17a indicates the lattice parameters of a strain free ZnO

Influence of External Fields c-axis lattice constant a-axis lattice constant

5.211 Vertical lattice constant (Å)

227

3.252 5.208 3.250 5.205

ZnO bulk (ref) 3.248

5.202

Horizontal lattice constant (Å)

8

3.246

XRD FWHM (arcsec)

5.199

10

FWHM of XRC (0002) ω –2θ (30-30) ω –2θ (0002) ω (30-30) ω –2θ

4

103

102

0

500 1000 1500 Layer thickness (nm)

2000

Fig. 8.17 (a) a- and c-lattice constants of ZnO films measured by !- 2 scans using (0002) and (10-11) reflections. (b) FWHM values of (0002) and (30-30) reflections for ZnO films. All data are displayed as a function of the layer thickness. ZnO films were grown by molecular beam epitaxy (MBE) on c-Al2 O3 [98]

bulk crystal as reference. For a thin ZnO layer, the c-lattice constant is larger as in the bulk sample. This proves the presence of biaxial compressive strain due to lattice misfit which relaxes towards a film thickness of 200 nm where compressive strain and tensile strain (due to the difference in coefficients of thermal expansion) are equal. At a film thickness of around 500 nm, the relaxation of misfit strain is estimated to be complete [98]. The presence of residual lattice strain in thicker films is attributed to the large difference of growth temperature and measurement temperature resulting in a residual biaxial tensile strain. The FWHM of the XRD rocking curve in Fig. 8.17b shows a strong decrease in the ! and !-2 half width up to a film thickness of 500 nm which is attributed to the crystal size effect. For thicker films, a slight increase of the FWHM is observed. The latter effect is attributed to lattice deformation by the mismatch of the coefficients of thermal expansions [98].

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M.R. Wagner and A. Hoffmann

Fig. 8.18 Reflectivity spectra of biaxial strained ZnO layers in the E ?c configuration at T D 10 K. Solid lines are measurements, dashed lines are theoretical calculations [93]

The influence of the in-plane biaxial strain on the free exciton energies is shown by optical reflection spectroscopy. Figure 8.18 displays reflectivity measurements of several ZnO layers with different tensile biaxial strain. The A(5 ) and B(5 ) excitons are observed for E ?c polarization. With increasing tensile strain, shift of the free exciton lines to lower energies occurs. This shift is accompanied by an increased exciton line-width in the reflection spectra. The calculation of the exciton energy shift by the evaluation of the strain-dependent Hamiltonian reveals the large contribution of the deformation potentials to the shift of the exciton energies, whereas the influence of the crystal field and spin–orbit parameters is small [93]. The energies of the A(5 ), B(5 ) and C(1 ) exciton as a function of biaxial stress are displayed in Fig. 8.19. For the A exciton a pressure coefficient of 0.34 meV/kbar is found when the biaxial compressive strain increases. By contrast, the center of gravity of lines B and C shows a 3.5 times stronger pressure dependence with a pressure coefficient of 1.15 meV/kbar [106]. This is explained by the strong influence of the deformation of the lattice due to the biaxial stress on the size of the crystal field splitting, whereas the A exciton only shows smaller hydrostatic pressure-like shift. In addition, the oscillator strengths of the A, B, and C exciton are altered by the presence of biaxial stress [39]. Based on the different stress dependences of the free excitons, it is shown that the band structure is very sensitive to strain in the epilayers, which may lead to reversal of the fundamental valence band structure for highly strained crystals. Ab initio studies of the strain influence on the valence band

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229

Fig. 8.19 Evolution of the 2 K free excitonic transitions in ZnO under (0001) biaxial stress. Solid lines are the calculated dependency; dots represent experimental data from different publications [106]

ordering further suggest that for strong tensile strains, the C exciton may have the smallest pair excitation energy. For details see, e.g. [107]. In conclusion, we first recalled basic relations of strain and stress in wurtzite crystals. Next, the influence of external uniaxial and hydrostatic stress on lattice parameters and crystal symmetry was discussed. The deformation potentials, which relate the mechanical lattice deformation to the electronic properties, were introduced and several examples of the effect of applied stress on the excitonic properties were provided. In addition, the influence of in-plane biaxial strain in epitaxial growth was discussed and possible effects on the valence band symmetry were considered. Not much is known about the influence of electro(-static) fields on the optical properties of free and bound excitons. A few references on the Pockels effect can be found in [108–111] and the references given therein.

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Chapter 9

Deep Centres in ZnO A. Hoffmann, E. Malguth, and B.K. Meyer

Abstract In ZnO, deep centres such as the transition metal ions Cu, Fe, Co, etc., deep acceptors such as Li and Na as well as intrinsic defects such as the cation and anion vacancies are the origin of light emissions in various regions of the visible and infrared spectral range. Several examples of deep centre related emissions are given, which are often found in bulk and epitaxially grown ZnO or in nano rods. The presentation of optical properties of various deep centres is complemented by data from electron paramagnetic resonance (EPR). It proceeds from the green and yellow emission bands and their interpretation to transition metals. From the intrinsic defects, the oxygen vacancy is discussed since many years as one of the origins of a broad emission band in the green spectral range. Other intrinsic defects are frequently discussed in recent literature, but the discussion is still rather controversial and the experimental findings on which the various assignments are based are frequently much less elaborate compared, for example, to transition metals. Therefore, no individual section is devoted to these complexes but some information is given, for example, at the end of Sect 5.1.

9.1 The Green and Yellow Emission Bands The band at 2.45 eV is very common in ZnO bulk crystals, thin films, powders and nanostructures. Various recombination models with the participation of intrinsic and extrinsic defects and defects complexes have been proposed. Only a small number A. Hoffmann Institut f¨ur Festk¨orperphysik der Technischen Universit¨at Berlin, Germany e-mail: [email protected] E. Malguth Institut f¨ur Silizium Photovoltaik, Helmholtz-Zentrum Berlin f¨ur Materialien und Energie, 12489 Berlin, Germany e-mail: [email protected] B.K. Meyer Physikalisches Institut der Justus Liebig Universit¨at Giessen, Germany e-mail: [email protected]

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of studies, luminescence/optical spectroscopy were combined with other techniques that would allow for an unambiguous identification of the involved defects (Fig. 9.1). Figure 9.1a shows the emission observed in a hydrothermally grown bulk ZnO substrate. The emission maximum is at 2.45 eV, and the band has a full width at half maximum (H1=2 or FWHM) of 460 meV. Annealing the substrate in a streaming oxygen gas flow for 1 h at 1;100ıC (see Fig. 9.1b) leads to the appearance of another band at 2.2 eV with a half width H1=2 of 390 meV, which is related to the deep Na acceptor (see later). After subsequent growth of an epitaxial film on this annealed specimen, the band is replaced by two other features (Fig. 9.1c): one with a resolved phonon structure related to the Cu acceptor (emission maximum at 2.5 eV, see below), and one peaking at 2.0 eV of unknown origin. Since Cu is a major trace impurity in the Zn metal used for CVD growth, the observation of the Cu related emission finds a plausible explanation. Na and Li are known to be present in ZnO substrates grown by the hydrothermal method in concentrations in the mid 1018 cm3 or 100 ppm range, and they may diffuse from the substrates into the films at the given growth conditions (substrate temperature around 600ıC for at least 4 h). Leiter et al. [2, 3] and Carlos et al. [4] investigated undoped ZnO single crystals from Eagle-Picher by using photo-luminescence (PL) and optically detected magnetic resonance (ODMR) spectroscopy. The low temperature emission was found to be dominated by the donor bound exciton (D0 X) at 3.366 eV. The broad, unstructured ‘green’ emission was located at 2.45 eV with a H1=2 of 320 meV (see Fig. 9.2 and Table 9.1). The Huang Rhys factor S and the mean phonon energy „! were

1,0

c)

PL-Intensity(arb. units)

0,8

a)

0,6

0,4

b) 0,2

0,0 1,8

2,0

2,2

2,4 2,6 Energy (eV)

2,8

3,0

Fig. 9.1 Deep centre luminescence of ZnO bulk ZnO samples (a) in the as received state and (b) after annealing in oxygen at 1;100ı C. Spectrum (c) represents the luminescence of an epitaxial film, which was grown using the annealed bulk sample as a substrate (after [1])

Deep Centres in ZnO

Fig. 9.2 Emission spectrum of undoped ZnO excited with the 325 nm (3.81 eV) line of an HeCd laser (5 K). The inset shows a recombination model for the ‘green’ emission located at 2.45 eV (after [2])

235 S=0

D°X S=1

Intensity (a.u.)

9

D°X 2.45eV

2.1

Table 9.1 Properties of the deep centre recombination in ZnO Luminescence Halfwidth Phonon energy maximum (eV) H1=2 (eV) „! (meV) 2:45 ˙ 0:02 0.32 38 ˙ 4 2:10 ˙ 0:02 0.44 50 ˙ 5 2:17 ˙ 0:02 0.40 45 ˙ 4

2.4 2.7 2.0 Energy (eV)

factor S factor S 13 ˙ 1 13 ˙ 1 16 ˙ 1

2.3

assignment assignment VO LiZn NaZn

obtained from the temperature dependence of the H1=2 , according to the following relation: (9.1) H1=2 D 2:36S „! .coth .„!=2kT//1=2 : A best fit to the experimental data was achieved for the values S D 12 and „! D 39 meV. This phonon energy does not correspond to any of the ZnO lattice phonons of the host material but is a local mode. The relaxation energy S „! is approximately 470 meV. The peak position was found to blue-shift with rising temperature, a typical behaviour of an intra-defect-transition, whereas the excitonic recombination features shift to lower energies as expected. Two types of ODMR signals were found for the ‘green’ band: (a) two resonant signals originating from a total spin S D 1 defect enhance the luminescence intensity; and (b) one signal associated with a shallow donor decreases the emission intensity. It could be proven that the S D 1 triplet resonances are detectable only in the energy range of the green emission band. The shallow donor resonance was also detectable in the excitonic range. In ZnO, shallow donors are characterized by a single line for a magnetic field strength corresponding to a g-value of g  1:96. In ZnO single crystals, the resonance is slightly anisotropic due to the wurtzite symmetry. In most cases, the EPR line width of shallow donors varies between 1 and 10 Gauss. A hyperfine interaction is rarely resolved, thus direct information on the chemical nature of the donors cannot be given. The reason is that the donor electron with a Bohr radius of about 1.5 nm is distributed over many lattice sites. Consequently, the electron density on the nucleus of the donor atom is low. Two cases where the hyperfine interaction was large enough to be resolved were reported. In the case of the In-donors, a 10 line spectrum was observed reflecting the I D 9=2 nuclear spin of the 115 In isotope (95% abundance) [5, 6], and Ga-donors appeared in the form of

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a four line spectrum due to the nuclear spin I D 3=2 [5, 7]. For the third common group III donor in ZnO, namely, Al, the enhanced resolution of the electron nuclear double resonance had to be used to resolve the interaction [8]. Similar experiments identified Hydrogen as a shallow donor. See [9] and Sect. 5.1. Discussing the origin of the triplet emission, Leiter et al. [10] pointed out similarities to the anion vacancies (F-centres) in CaO and MgO. The ground state of the neutral oxygen vacancy (F-centre) is a singlet state with two spin paired electrons. Excitation leads to an excited singlet state, from which the electrons can relax into the triplet state (S D 1) in which the ODMR is detected. The optical cycle is closed by radiative recombination back to the S D 0 ground state (see inset in Fig. 9.2). Zwingel and G¨artner [11], Meyer et al. [12], and Leiter [2] studied the deep recombination bands peaking at 2.18 eV in Na-doped ZnO and at 2.1 eV in Li-doped ZnO. These authors established the similarity between the deep LiZn and NaZn (Fig. 9.3) acceptors, both acting as deep acceptors in a donor–acceptortype recombination. The group-I elements Li and Na were the first to be tested in order to achieve p-type conduction. Lander [14] reported on the donor and acceptor properties of Li and gave first indications on the potential nature of the defects. He suggested an interaction between interstitial Lii donors and substitutional LiZn acceptors. In 1963, Schneider et al [15] reported on the first observation of the Li acceptor by electron paramagnetic resonance (EPR). In the EPR investigations reported by Schirmer in 1968 [16], the g-anisotropy and the hyperfine interactions of the LiZn acceptor were analysed. The interpretation of the hyperfine data showed that the hole was primarily located on one neighbouring oxygen atom along the c-axis inducing substantial distortion. The Na acceptor [17] behaves in a similar way.

Fig. 9.3 Magnetic resonance spectra of the deep Li and Na acceptors present in hydrothermally grown bulk ZnO substrates (after [13])

9

Deep Centres in ZnO

237

Both defects are responsible for the broad, strong phonon coupled luminescence bands in the visible spectral range. Temperature-dependent measurements in ZnO/Na revealed a Huang-Rhys-factor S D 16 ˙ 1:5 and participation of local phonons with „! D .45 ˙ 5/ meV. This leads to a (hypothetical) zero phonon transition at 2.87 eV (peak position plus S „!), that is, 580 meV below the band gap energy. The corresponding values for the Li acceptor are as follows: peak energy of 2.1 eV, a Huang-Rhys-factor S of about 13 ˙ 1 and participation of local phonons of „! D .50 ˙ 5/ meV, zero phonon transition at 2.7 eV (peak position plus S „!), that is, 700 meV below the band gap energy. The deep acceptors show up as the final states of DAP recombination starting at the shallow donors as was demonstrated by ODMR experiments [18]. Reshchikov et al. [19] investigated the visible luminescence bands in undoped and N-doped ZnO layers grown on sapphire by MBE. At low temperatures the broad Gaussian band has its maximum at 2.1 eV, and was attributed to transitions from a shallow donor to a deep acceptor having an ionization energy of about 0.4 eV. The deep acceptor was tentatively assigned to a VZn -related complex. First information on the Zn vacancies was already obtained in the 1970s by means of room temperature electron and neutron irradiation [20–22]. More recently, the work of Vlasenko et al. [23] investigated the creation of VZn and their annealing behaviour by low temperature electron irradiation. Frenkel pairs of the Zn vacancy with the Zn interstitial were observed, and the annealing stages below 170 K were related to the migration of the Zn interstitials. In correlating these ODMR results to the photoluminescence bands present in the material, the authors provide evidence that the Zn vacancy levels are at least 350 meV above the valence band [23]. However, there is still an ongoing discussion about the role of intrinsic and extrinsic defects with respect to ‘green’ light emission. A work commonly cited is the correlation study of Vanheusden et al. [24] using EPR, optical absorption and photoluminescence spectroscopy. They attributed the g D 1:96 EPR line to the singly ionized oxygen vacancy – an assignment that is not supported by experiments (see Table 9.2). Obviously, they correlated the number of neutral shallow donors with the intensity of the green band. It is well established that the oxygen vacancy is a deep defect and does not contribute to the n-type conductivity of ZnO [26, 36]. Whether other intrinsic defects such as zinc interstitial or zinc antisite as proposed in [37] contribute to ntype conductivity remains to be investigated. See also the comments in Chap. 5 on intrinsic defects. The future of ZnO as material for electronic and optoelectronic devices depends on its ability to dope it reliably p-type, and to find an efficient shallow acceptor. See Chap. 5. Nitrogen on oxygen site has the potential to be such an acceptor. A nitrogen acceptor centre was detected in EPR, originally in single crystals, later also in nitrogen-treated ZnO powders [4, 38]; however, the found g-values do not correspond with a shallow effective-mass-type acceptor (see Table 9.2). Also the anisotropy in the hyperfine interaction constants (nitrogen has I D 1 nuclear spin) rules against a shallow centre. According to Carlos et al. [4], the large anisotropy in the hyperfine interaction suggests the involvement of a p-orbital (p-hole). Atomic orbital analysis reveals that the centre has 96% p and 4% s character, and has 4%

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Table 9.2 Magnetic resonance parameter of shallow donors, deep donor and deep acceptors in ZnO Spin g-values Hyperfine Fine structure Defect Reference interaction assignment S D 1=2 gk D 1:957

A.115 In/ D 36:6 G

Shallow In donor

[5, 6]

g? D 1:956 S D 1=2 gk D 1:957

A.69 Ga/ D 4:2 G

Shallow Ga donor Shallow donor Shallow donor Shallow Al donor Shallow H donor

[5]

g? D 1:956

A.69 Ga;72 Ga/ D 6:7 G

S D 1=2 g D 1:9595

A.27 Al/ D 1:45 MHz

S D 1=2 gk D 1:9569

A.1 H/ D 1:4 MHz

g? D 1:9552 S D 1=2 gk D 1:9605 g? D 1:9595 S D 1=2 gk D 1:9945 Ak D 57:34 MHz g? D 1:9960 A? D 42:3 MHz axial centre Axx D 76:6 MHz, Ayy D 75:9 MHz, Azz D 94:8 MHz non-axial centre S D 1=2 gzz D 2:0038 gyy D 2:018

gxx D 2:0191 gk D 2:0149 g? D 2:0134 axial at room temperature S D 1=2 gzz D 2:0038

S D1

gyy D 2:018 gxx D 2:0217 gzz D 2:0095 gyy D 2:0141 gzz D 2:019

Shallow Zn interstitial

Ga [7] Ga [25] [8] [9]

[26]

Oxygen vacancy, [27] FCa [28, 29] [30, 31]

P-centre in [21] [20] Zinc-vacancy [20] related di-or trivacancy centresa [22] [30, 31]

Zinc-vacancy relateda

[20]

jDjD1;465 MHz Zinc-vacancy relateda jEj D 58 MHz

[20] [22] [30, 31] (continued)

9

Deep Centres in ZnO

Table 9.2 (Continued) Spin g-values S D 1=2 S D 1=2 S D1

gk D 1:9953 g? D 1:9633 gk D 2:0036 g? D 1:9935 gk D 1:971 g? D 2:0224

S D 1=2

gk D 1:984 g? D 2:025 gk D 2:020 g? D 2:006 gzz D 2:0033

S D1

gyy D 2:0188 gxx D 2:0175 gzz D 1:9815

S D 1=2

239

Hyperfine interaction Ak D 81:3 MHz A? D 9:5 MHz Ak D 9:8 MHz A? D 20:1 MHz

gyy D 1:9893 gxx D 1:9888 S D 1=2 gzz D 1:9811 gyy D 1:9892 gxx D 1:9885 a (after e or no irradiation)

Fine structure

Defect assignment Deep nitrogen acceptor N2  acceptor

D D 0:763 GHz DD 260  104 cm1

None Oxygen vacancy; F-centre

 .ZnC i –N0 /

Reference [4] [7, 32] [32, 33] [4] [2]

[34]

Zinc vacancy a

[26]

Zinc vacancyinterstitial zinc paira

[26]

LU 4a

[35]

localisation at the nitrogen atom. All these findings indicate a deep rather than a shallow acceptor, similar to the deep states of As and Pin ZnSe – a p-orbital on the impurity atom, which is Jahn–Teller distorted. Besides this deep N acceptor, also molecular nitrogen (N 2 ) acceptors were found [32, 33].

9.2 Transition Metal Ions With the prediction of room temperature ferromagnetism in ZnO doped with magnetic ions, the properties of the 3d shell impurities have found renewed interest. We will shortly outline the essential features of the magnetic transition metal ions (3d1 to 3d9 ) found in a tetrahedrally coordinated crystal field as is the case at the cation site, that is Zn2C in the case of ZnO. Table 9.3 gives a compilation of the electronic configurations of different charge states of the free ions with respect to high or low spin ground states. The charge state of a TM ion is referred to with respect to the cation it is replacing, for example Mn2C is the neutral state in ZnO, whereas Mn3C is the ionized donor and MnC the ionized acceptor charge state. Ionized donor and acceptor

Table 9.3 Ground states of transition metal (TM) ions 3d1 to 3d9 in tetrahedral symmetry and their charge states corresponding to the lattice site in II–IV–V2 and III–V compounds d1 d2 d3 d4 d5 d6 d7 d8 d9 II IV III (Zn2C ) (Ge4C ) (Ga3C ) 6C 6C 6C 6C 6C 4C 2C Mn Fe Co Ni Cu – – – – A B C3C 5C 5C 5C 5C 5C 5C C C Cr Mn Fe Co Ni Cu – – – A B C2C V4C Cr4C Mn4C Fe4C Co4C Ni4C Cu4C – – A2C B0 CC 3C 3C 3C 3C 3C 3C 3C 3C C  Ti V Cr Mn Fe Co Ni Cu – A B C0 2C 2C 2C 2C 2C 2C 2C 2C 2C 0 2 Sc Ti V Cr Mn Fe Co Ni Cu A B C – ScC TiC VC CrC MnC FeC CoC NiC A B C2 – – Sc0 Ti0 V0 Cr0 Mn0 Fe0 Co0 A2 B4 C3       3 5 – – – Sc Ti V Cr Mn Fe A B C4 2 0 2 2 2 4 6 – – – – Sc Ti V Cr Mn A B C5 3 4 5 6 5 4 3 2 2 D F F D S D F F D Free ion terms de2 dt1 de2 dt2 5 T2 de2 dt3 de3 dt3 5E de4 dt3 de4 dt4 3 Ta1 dte4 dt5 High-spin de2 Dte1 a 3 6 4 2 2 E A2 4T1 A1 A2 T2 de4 dt1 dte4 dt2 Low-spin de4 de3 2 1 2 3 E A1 T2 T1 a4 T1 and 3 T1 are not pure de2 dt1 and de1 dt4 states, but contain also contribution of dt2 de1 and de3 dt5 ; respectively

240 A. Hoffmann et al.

9

Deep Centres in ZnO

241

Fig. 9.4 Approximate positions of transition metals levels relative to the conduction and valence band edges of II–VI compounds. By triangles the dN =dN 1 donor and by squares the dN =dN C1 acceptor states are denoted (from [39])

charge states are only possible if the respective recharging levels Mn3C =Mn2C or Mn2C =MnC are located within the forbidden energy gap. The positions of the TMrelated donor and/or acceptor levels in II–VI compound semiconductors are shown in Fig. 9.4. This figure predicts, for example, in ZnO/Mn, that the neutral charge state, that is, Mn2C is the only stable charge state regardless of the position of the Fermi level, since neither the donor nor the acceptor level is found within the band gap. The ground state properties are well established by means of electron paramagnetic resonance, since most of the 3d ions are common residual impurities in bulk ZnO crystals (see Table 9.4). As a typical example, we present the EPR measurements obtained on a bulk substrate grown by the hydrothermal method. Without illumination we find the resonances of Co2C , Mn2C , Ni3C as well as those of a shallow donor (sd) caused by either Ga or In (see Fig. 9.5). The magnetic resonance parameters of the 3d ions are collected in Table 9.4. For Sc, Ti and Cr there are no reports. For V, Fe, Co, Ni and Cu, the internal transitions within crystal field split states have been detected either in absorption and/or in luminescence experiments. For ZnO/Mn, the radiative transition 4 T1 (G) to 6 A1 (S) of Mn2C has not been observed.

9.2.1 ZnO/V Magnetic resonance experiments detected Vanadium in the charge states V2C (3d3 ) and V3C (3d2 ) thus V induces a deep donor state in ZnO [40–43]. The optical

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Table 9.4 Magnetic resonance parameter of various 3d-ions, Pb and Mo in ZnO Spin g-values Hyperfine Fine structure Defect interaction assignment S D1 gk D 1:945 jAjk D jDj D V3C 66:6  104 cm1 748  104 cm1 g? D 1:932 jA? j D 74:1 S D 3=2 gk D 1:951

Reference [40] [41] [42] [41–43]

jAjk D jDj D 2; 606 V2C 4 1 42:9  10 cm g? D 1:923 jAC j D 46:4 S D 5=2 g D 2:0016 A D D D 216:9  Mn2C [44] 76  104 cm1 104 cm1 D D 594  Fe3C [45] S D 5=2 g D 2:0060 jAj D 4 1 4 1 10 cm 9:02  10 cm D D 5:5 cm1 Co2C [46] S D 1=2 gk D 2:2500 Ak D 15:3  104 cm1 g? D 4:5536 A? D 2;82  104 cm1 S D 1=2 gk D 2:243 Ak D [47, 48] 16:1  104 cm1 g? D 4:551 A? D 30  104 cm1 S D 1=2 gk D 2:143 Ni3C [49] g? D 4:318 S D 1=2 gk D 0:74 jAj D Cu2C [50] 195  104 cm1 g? D 1:531 S D 1=2 gk D 2:0133 Ak D 0:8107 cm1 Pb3C [51–54] 1 g? D 2:0135 A? D 0:8102 cm S D 3=2 gk D 1:963 Ak D 132 MHz Mo3C [55] g? D 3:933 A? D 165 MHz To understand the EPR parameters presented in Tables 9.2 and 9.4, we give a short outline of how they are defined. The magnetic resonance spectra were analysed in the framework of a SpinHamiltonian formalism: H D B  S  gQ  H C S  AQ  I For centres with a single unpaired spin (S D 1=2) in axial symmetry the Hamiltonian is: H D B Œgk Sz Hz C g? .Sx Hx C Sy Hy / C Ak Sz Iz C A? .Sx Ix C Sy Iy /

For S > 1=2 an additional fine structure interaction has to be taken into consideration: Q S H DS D which in the principal axis system leads to

 1 H D D Sz2  S.S C 1/ C ESx2  Sy2 3 The symbols have the following meaning: S ; I electron spin, nuclear spin, respectively, and their components Sx , Sy , Sz , Ix , Iy , Iz ; AQ hyperfine interaction tensor and its components Ak , A? , Axx , Q fine structure tensor and its Ayy , Azz ; gQ g-tensor and its components gk , g? , gxx , gyy , gzz ; D components D (axially symmetric part) and E (asymmetry parameter); H : magnetic field

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243

Fig. 9.5 Magnetic resonance spectrum of the 3d ions Co, Ni and Mn and shallow donors (sd) as found in hydrothermally grown bulk ZnO substrates (after [13])

properties of V3C in ZnO have remained undiscovered for a long time, in part because zero phonon luminescence line of the 3 T2 .F/–3A2 .F/ transition of isolated substitutional vanadium was observed at T D 1:8 K at 0.85342 eV and mistakenly correlated with Cu. The entire luminescence band detected at T D 1:8 K is shown in Fig. 9.6. The inset shows the zero phonon lines N1 at 0.85342 eV and N3 at 0.85390 eV for different temperatures. The line N3 is thermalized at T D 1:8 K and becomes stronger with increasing temperature. Therefore, the energy distance between N1 and N3 of 480 eV represents a splitting of the excited term. In order to identify the luminescence centre, magnetic field dependent measurements were carried out with varying polarisation and temperature. The results can be understood in the framework of a threefold split ground state and a twofold split excited state. Figure 9.7 shows the extracted threefold splitting of the ground term with an isotropic g-factor, g D 1:93˙0:02, and a zero field splitting as observed without magnetic field for the lines N1;2 , see inset Fig. 9.7. The zero field splitting corresponds to a splitting of the threefold ground state term in an energetic lower singlet and an upper doublet state. The behaviour of the ground state in a magnetic field is the finger print of an electronic d2 configuration with a 3A2 .F/ ground term. The observed g-value and the value of the zero field splitting in good agreement with those determined by Hausmann [40] in ESR-experiments for isolated V3C in ZnO. Therefore, the authors concluded that the luminescence of Fig. 9.6 is due to an electronic transition within the 3d-shell of isolated substitutional V3C with a 3A2 .F/-ground state term. Figure 9.8 shows the term scheme and the observed electronic transitions with their polarization properties.

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ZnO T = 1.8K Intensity (arb.unit)

480 μeV

T = 8K

N1

N3 T = 1.8K

0.8530

0.77

0.8540

0.8535

0.81 Energy (eV)

÷3

0.85

Fig. 9.6 Low temperature luminescence spectrum of ZnO. The inset shows the zero phonon region at T D 1:8 K and T D 8 K (after [56])

(97 ± 3) μeV

1

ZnO T = 1.8 K

B = OT

EIIc N1

N2 E⊥c

ΔE (meV)

Fig. 9.7 Splitting of the V3C (3 A2 (F))-ground state in a magnetic field. The shifts of the central components have been set to zero. The inset shows the zero filed splitting of the lines N1;2 (after [56])

0.8533

0 g

11

0.8535 energy (eV)

= 1.93 ± 0.02

g = 1.93 ± 0.02

–1 BIIc 10

5

B⊥c

0 5 Magnetic field (T)

10

In recent optically detected magnetic resonance experiments [43], the V2C resonance was detected on the N1 zero phonon line of V3C ; however, the internal luminescence of V2C did not show up. For V2C (3d3 ), the internal radiative transition should be of the type 4 A2 .F/–4 T2 .F/ as found in ZnS, ZnSe, CdSe and CdTe [57].

9.2.2 ZnO/Fe Iron is a very common impurity in ZnO and is found in most ZnO crystals and films. Only recent progress in the production of high quality material allows avoiding detectable Fe contamination. Fe-doped ZnO has recently gained interest as a promising material for carrier mediated spin-coupling for spintronics applications [58]. The Fe centre in ZnO has been studied as an unintentional impurity as well as a deliberately introduced defect centre. To date, the charge states 3C and 2C have

9

Deep Centres in ZnO

Fig. 9.8 Term scheme of the d2 -configuration containing the lowest energetic triplet terms. Ho : Coulomb interaction and Td -crystal field, H 0 : spin–orbit interaction and Jahn–Teller coupling, HC3v : C3v -crystal-field (after [56])

245 3

T2 (F) 3,1

5

4

3,2 2

3

2

3

N 1 N 2 N 3 E1 E1 3

A2(F)

5

3

1

0

C3 v

been observed. In contrast to some other II–VI and III–V semiconductors, in ZnO, Fe1C or a shallow level formed by the Fe centre have not been observed before [59]. Fe in ZnO forms an energy level deep within the band gap. The exact position of the Fe3C=2C donor level is still unknown. It can be narrowed down though to 1.8– 2.9 eV above the valence band, based on optically observed intracentre transitions of Fe3C and Fe2C that are presented below. A comparison with other II–VI semiconductors lets expect a position 2.5 eV above the VB (see also Fig. 9.4), based on the internal reference rule [59–61]. Thus, in the thermodynamic equilibrium, Fe will be present in the 2C charge state in ZnO that usually is n-type due to residual shallow donors. This assumption is confirmed by EPR experiments that detect Fe3C only at temperatures above 77 K [62]. The charge transfer process from Fe2C into Fe3C by exciting an electron into the CB has a small oscillator strength due its s–d character and can therefore not be observed in optical experiments, which is why the position of the Fe3C=2C donor level has not been determined unambiguously [63]. Further gap states are formed by the electronic structure of Fe ions. The respective term schemes are the result of a multiple splitting of the highly degenerate 3d orbitals of the free ion by symmetry reduction (e.g., Fig. 9.9). The Stark effect of the crystal field of the ZnO host lattice has the strongest impact. Further perturbations are spin– orbit coupling and electron–phonon interaction. The resulting electronic structures of Fe3C and Fe2C follow the pattern established for other II–VI and III–V semiconductors. Fe3C and Fe2C in ZnO have been studied by means of optical and magnetic spectroscopy. The results are presented in the following sections.

9.2.3 ZnO/Fe3C The Fe3C centre has been established thoroughly by optical and EPR investigations [45, 62, 63]. The most striking characteristic of Fe3C in ZnO is the intense luminescence line at 693 nm (1.788 eV) with a full width half maximum (FWHM) of 48 eV displayed in Fig. 9.10. It originates from the internal ‘spin–flip’ transition staring at the 4 T1 .G/ first excited state into the 6 A1 .S/ ground state of Fe3C with its

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Fig. 9.9 Qualitative term scheme of the Fe3C centre in the trigonal crystal field .C3V / of ZnO. The Hamiltonian of the isolated ion (Hfreeion ) is given at the bottom along with perturbation terms for the tetrahedral crystal field (HTd ), spin–orbit interaction, Jahn–Teller effect and the axial distortion along the c-axis in a hexagonal lattice (HC3v )). The energetic differences are not to scale. The spin– orbit splitting is not quenched as drastically by Jahn–Teller coupling as in Td symmetry. Because of the axial distortion, an additional splitting occurs into states of 4 , 5 and 6 symmetry

13

Intensity (arb. units)

ZnO

A

T = 1.8K 12 19

E||c 26

24

E⊥c

1.66

9 7

16

22

4 6

20

15

11 10

1.70

/5 2

3 3

1.74

5

/5

1.78

Energy (eV)

Fig. 9.10 Polarized photo luminescence spectra of the Fe3C 4 T1 .G/–6 A1 .S/ transition in ZnO at T D 1:8 K excited by the 488-nm line of an ArC ion laser. The ZPL at 1.787 eV has a FWHM of 48 eV and a lifetime of 25.2 ms. On its low-energy side, a vibronic side band is observed (taken from [63])

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Deep Centres in ZnO

247

3d5 configuration [63]. The emission decays with a time constant of 25.2 ms [63]. This relatively long lifetime is a result of the 4 T1 .G/–6 A1 .S/ transition being forbidden by symmetry and spin selection rules. The electric dipole transition becomes allowed mainly by the admixture of odd-parity states of the ligands to the d-like TM states by the covalent bonding or the spin–orbit interaction with the ligands [64]. In Fig. 9.10, the pronounced sideband on the low energy side of the zero phonon line (ZPL) at 1.787 eV represents vibrational replica mainly involving LO and TO phonons at the centre of the Brillouin zone as well as defect-specific vibrational modes. Particularly, a strong coupling on E2 modes is observed. High resolution photoluminescence PL spectra reveal an isotope shift of the position of the 4 T1 .G/–6 A1 .S/ transition [63]. A shift of C39 eV/nucleon occurs due to the natural abundance of Fe isotopes. Also the replacement of one of the 16 O ions 18 of the tetrahedral Fe3C O2 O causes a shift of 365 or 222 eV depend4 cluster by ing on the position within the tetrahedron. The isotope effect can be explained sufficiently by the contribution of mass-dependent local vibrational modes to the total energy of the involved states. In this context, also the Jahn–Teller coupling on such modes as well as the distortion of the Fe3C O2 4 cluster in the hexagonal lattice need to be taken into account [63]. The fine structure of the Fe3C .6 A1 .S// ground state was established by means of Zeeman measurements of the 4 T1 .G/–6 A1 .S/ luminescence and by EPR experiments. Zeeman spectra of the 4 T1 .G/–6 A1 .S/ luminescence show a sixfold splitting that, with increasing magnetic field, is linear for Bkc and nonlinear for B?c. In both cases, the centre of gravity shifts towards lower energies [63]. This behaviour is attributed to the 6 A1 .S/ state splitting into six levels with SZ D ˙1=2, ˙3=2 and ˙5=2. The same splitting was observed in form of five resonances in EPR spectra representing transitions between the six levels. The following spin-Hamiltonian describes the behaviour of the 6 A1 .S/ state of a 5 d system (S D 5=2) in a magnetic field [45]:   707 a 4 4 4 S C S C S  H D gˇ H S C 6 16     7F 35 95 2 81 2 4 C D SZ  C SZ  SZ C : 12 36 14 16

(9.2)

The axial symmetry component of the C3V crystal field of ZnO, given by the terms proportional to D and F , lies within the z-axis, the c-axis of a hexagonal lattice. This axis corresponds to a [111] axis in the cubic system given by ,  and , in which the cubic part of the crystal field is defined by the fine structure constant a. On the basis of EPR measurements, the following values were established for the parameters in the equation above: D D 7:38 eV, ˛ D 0:51 eV, a  F D 0:46 eV, g D 2:0062 [45, 62]. Thus, at zero magnetic field, and in the hexagonal crystal field of ZnO (C3V symmetry), the axial distortion of the crystal field causes a split into three Kramers doublets with the SZ D ˙3=2 and SZ D ˙1=2 states a few tens of eV above the SZ D ˙5=2 ground state. This splitting is represented by the parameters D and F of the spin-Hamiltonian.

248

2.5

T = 25K E

10 Intensity (arb. units

Fig. 9.11 Polarized temperature-dependent luminescence spectra of the Fe3C 4 T1 .G/–6 A1 .S/ transition in ZnO excited at 2.71 eV. With increasing temperature, higher 4 T1 .G/ sub-levels are populated resulting in additional ZPL’s on the high-energy side of the main peak (after [63])

A. Hoffmann et al.

D

T = 12K B 25

C T = 5K

A

ZnO

T = 2K

25 E||c E⊥c 1.787

Table 9.5 Assignment of ‘hot lines’ observed for the internal 4 T1 .G/–6 A1 .S/ transition of Fe3C in ZnO (after [63])

1.789 1.791 Energy (eV)

Emission line (eV) 1.78743 1.78863 1.78877 1.79005 1.79187

1.793

Involved 4 T1 .G/ sub-level 4 .6 / 5;6 .8 / 4 .8 / 4 .7 / 4;5;6 .8 /

Temperature-dependent PL spectra of the 4 T1 .G/–6 A1 .S/ emission are shown in Fig. 9.11. With rising temperature, four additional ZPLs appear on the high energy side of the line at 1.787 eV. These lines represent transitions starting at higher 4 T1 .G/ sub-levels. A detailed interpretation of the ZPLs based on their polarization and temperature behaviour is given in Table 9.5 representing the fine structure of the 4 T1 .G/ state. According to static crystal field theory, the excited Fe3C .4 T1 .G// state is predicted to suffer a fourfold splitting by spin–orbit interaction of roughly 10 meV. In cubic II–VI and III–V semiconductors, the four sub-levels 6 , 8 , 7 , 8 of the 4 T1 .G/ state are found to be reduced to a doublet or triplet with a splitting of only about 2 meV [59] by a strong dynamic Jahn–Teller coupling to E-type phonon modes drastically reducing the orbital momentum. In the case of the trigonal symmetry of hexagonal ZnO, the lower defect symmetry stabilizes the Fe3C centre against the Jahn–Teller coupling [63]. As a result,

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Deep Centres in ZnO

249

an only intermediate dynamic Jahn–Teller effect reduces the spin–orbit splitting to about 4 meV. Additionally in C3V symmetry, the four 4 T1 .G/ states are split into states of 4 , 5 , 6 symmetry as given in Table 9.5 (Fig. 9.9). A similar effect is known from Fe3C in GaN [65]. Only little is known about the magnetic behaviour of the Fe3C .4 T1 .G// state in ZnO. Merely a shift and twofold Zeeman splitting has been observed for the lowest sub-level with an anisotropic g factor: gk D 2:71, g? D 0:27. As mentioned earlier, at low temperatures, only the isoelectronic charge state Fe2C is present in n-type ZnO. As a consequence, no internal excitation processes of Fe3C have been observed that would allow for the investigation of the higher excited Fe3C states, 4 E.G/ and 4 T2 .G/, which are well established for GaN [63,65]. So far, only the capture of free holes by Fe2C is known as an excitation process for Fe3C : Fe2C C hB ! Fe3C .4 T1 /: These free holes can be generated by optical excitation. The excitation spectrum of the 4 T1 .G/–6 A1 .S/ emission demonstrates the generation of free holes via band gap excitation in the UV spectral region. Since the recombination of excitons represents a competing recombination channel for holes, local minima are found at the positions of the A, B and C exciton. In the visible region, the excitation spectrum shows a broad band staring at 2.25 eV. This band represents the generation of free holes via gap states that are still unidentified. Such an energy transfer from another defect to the Fe2C centre is known from ZnS and GaN. In ZnS, free holes were shown to be generated via a charge transfer process in which Cu2C impurities are recharged into Cu1C [66]. In GaN, free holes are generated in a two step process involving native double donors [67].

9.2.4 ZnO/Fe2C The Fe2C ion (3d6 , L D 2, S D 2) has a 5 D ground state, which is split by the impact of a tetrahedral crystal field into a 5 E ground and a 5 T2 excited state. According to group theory, spin–orbit interaction causes the former to split into five equidistant levels and the latter into six states. The just outlined splitting of the Fe2C states has been observed in other III–V and II–VI semiconductors with the strength of a dynamic Jahn–Teller coupling varying depending on the host material [59]. In hexagonal crystals, the trigonal symmetry C3V causes yet an additional splitting [68]. Fe2C is difficult to detect by ESR because 3d6 is a non-Kramers configuration. Therefore, the 2C charge state of Fe was investigated by means of Fourier transform infrared spectroscopy (FTIR). The studied Fe-doped ZnO samples were prepared by depositing Fe from the vapour phase onto three ZnO specimens. Each sample was annealed under a different atmosphere: vacuum, oxygen, Zn-vapour. A fourth

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specimen was not Fe coated but annealed in vacuum atmosphere as a reference. The best results were obtained for Zn atmosphere. Figure 9.12 displays the FTIR absorption spectra for different temperatures. At 1.8 K, an intense zero phonon line (ZPL) is observed at 395.7 meV. It is assigned to the allowed .5 E–5 T2 / transition of Fe2C on Zn site on the basis of two key arguments: Firstly, the lines in question only appear upon Fe doping. Secondly, these lines are found in the same spectral region as the Fe2C .5 E–5 T2 / transition in other host materials that is between 340 and 410 meV [59]. The relative independence of the crystal field splitting from the host material is the result of the small degree of covalency. The value of 395.7 meV even fits into the pattern that the energy of the .5 E–5 T2 / transition rises for an increasing degree of ionicity and small lattice constants of the host crystal [59]. The numerous other lines observed in Fig. 9.12 at T D 1:8 K are attributed to (a) Fe2C -related defect complexes in which a nearby defect changes the crystal field felt by the Fe2C centre and (b) vibrational replica of the ZPL at 395.7 meV. The involved vibrational modes may be ZnO lattice modes or defect-specific local vibrational modes (LVM).

Fig. 9.12 Temperature resolved FTIR absorption spectra of ZnO/Fe annealed in Zn atmosphere. A tentative assignment is given for the lines present at 60 K. The numbers refer to the involved 5 E and 5 T2 sub-levels with the numbering starting at the lowest energy. The first and second numbers denote the starting and initial state, respectively (after [59])

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251

Table 9.6 A tentative identification of the lines found in Fig. 9.12 at T D 1:8 K on the basis of their polarization, temperature dependence and the effect of the annealing atmosphere. The last two columns state other impurity centres in ZnO for which the same local vibration modes LVM) have been found. The references [6, 15–17] in the table correspond to [63, 69–71], respectively. (After [59]) Energy (meV)

Polarization

Assignment

380.9 394.5 395.7 400.3 404.2 409.7 415.0 418.3

k ?

Fe2C -complex Fe2C -complex Fe2C .5 E 5 T2 / Fe2C -complex LVM E2 (low) Fe2C -complex LVM

22.6

? ? ? ?

Mode energy (meV)

Reference

Fe3C , Cu2C , Co2C Cu2C Cu2C Fe3C , Cu2C , Co2C , Ni3C Fe3C , Cu3C , othersa

[6, 15, 17]

8.5 13.9

420 422.8 425.8

? ?

LVM LVM LVM

24.3 27.1 30.0

429.9

k

LVM

34.1

433.5 440.3

?

LVM LVM

37.8 2  22:6

a

Same mode for

[15] [15] [6, 15, 17]

[6, 16, 17]

A Raman peak at 34.3 meV was found for ZnO films doped with Fe, Sb, Al, Ga or N

A tentative association of the numerous absorption lines observed at 1.8 K to the just outlined phenomena is presented in Table 9.6. The interpretation is based on the temperature behaviour (Fig. 9.12), polarization and dependence of the lines on the annealing atmosphere. Only lines originating from Fe2C centres of axial crystal field symmetry may be polarized with respect to the c-axis. The formation of certain defects is supported or prevented by particular annealing atmospheres. Hence, an according dependence hints towards Fe2C involved in a complex with another point defect that may also show polarization. Phonon and LVM replica may be broadened and should exhibit the same temperature dependence as the ZPL. While the dominating ZPL at 395.7 meV is assigned to Fe2C on isolated Zn site of the hexagonal ZnO lattice, the lines on its low energy side are attributed to Fe2C -defect complexes of axial symmetry along the c-axis. This sort of symmetry is derived from the observed polarization of these lines. The line at 394.5 meV might be interpreted as a transition starting at an excited 5 E sub-level. However, in that case, it would be expected to increase with rising temperature, which it does not. The intense ZPL at 395.7 meV shows a replica at 13.8 eV. This energy is in the range of the E2 (low) phonon mode of bulk ZnO [72]. See also Chap. 2.

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Lines at 400.3 and 415.0 meV show a strong dependence on the annealing atmosphere. Therefore, they are assigned to Fe2C centres involved in defect-complexes. A tentative identification of the involved defects is that the lines at 400.3 and 415.0 meV originate from an Fe2C –VZn complex. Here, VZn is a zinc vacancy. The low-energy lines at 380.9 and 394.5 meV do not show a preference for a particular annealing atmosphere. Lines at 8.6, 22.6, 24.3, 27.1, 30.1, 34.1, 37.8 and 45.2 meV above the 395.7 meV line are attributed to the vibronic coupling between the Fe2C centre and its surrounding. As for most energies only one replica is observed, LVMs and vibronic 5 T2 sub-levels affected by a Jahn–Teller coupling cannot be distinguished. Resonances with energies similar to the ones found here are also observed for different transition metal centres in ZnO (Table 9.6) suggesting that they in fact represent local vibrational modes. See also Chap. 2 for this topic. Besides this, the temperature-dependent spectra cannot be interpreted straightforward as the same spectra of Fe2C in other III–V and II–VI compound semiconductors [59], where additional lines show up on the low-energy side of the low temperature ZPL representing transitions starting at excited 5 E states that become successively populated with rising temperature. In Fig. 9.12, with rising temperature, only one additional line emerges on the low-energy side at 392.7 meV. However, new lines show up on the high-energy side at 397.2, 398.6 and 401.1 meV. None of them shows a particular polarization with respect to the c-axis. Also these additional lines are found at the very same position in both the Zn- and the vacuum-annealed sample. At 250 and 300 K, only two broad peaks are present that shift to higher energies with rising temperature. Apart from broadening, the many high-energy lines stay unchanged at 60 K and are almost completely gone at 250 K. A tentative assignment of the new lines found at 60 K is given in Fig. 9.12 based on their temperature dependence. The numbers refer to the involved 5 E and 5 T2 sub-levels with the numbering starting at the lowest energy. The first and second numbers denote the starting and initial state, respectively. This assignment assumes that the (1–1) transition is the only one allowed from the bottom 5 E level into one of the four lowest 5 T2 levels as well as the only one allowed starting from one of the lowest three 5 E levels and terminating at the 5 T2 bottom level. This condition can be fulfilled according to selection rules if, in C3V symmetry, both the 5 E and 5 T2 bottom states are 2 states and the ones above 1 and 3 states. The inconsistency of this interpretation with the absence of polarization is discussed later. As the nature of the involved sub-levels is unknown, no conclusions regarding the oscillator strength of the observed transitions can be made. As a consequence, the energy differences between the involved sub-levels cannot be calculated from the temperature dependence. In the following, three possible explanations are given for the absence of phenomena expected for a Fe2C centre in C3V symmetry (a high number of polarized absorption lines on both sides of the 395.7-meV line). One reason could be a strong dynamic Jahn–Teller effect. If the impact of the Jahn–Teller coupling on the electronic structure exceeds that of the axial distortion (i.e. HJT HCF .C3v //, then this distortion may become negligible. Hence, the 5 E and 5 T2 sub-levels would be a result mainly of the spin–orbit coupling and the Jahn–Teller effect. Transitions

9

Deep Centres in ZnO

253

between these sub-levels have different oscillator strengths than those between spin– orbit levels unaffected by Jahn–Teller coupling [73, 74], which would explain the unequal intensities of the ZPLs at 60 K. Without knowing the oscillator strengths of the observed transitions, no quantitative conclusions can be drawn from the temperature-dependent intensities regarding the fine structure of the 5 E and 5 T2 states. As in other materials, the transition between the respective 5 E and 5 T2 ground states seems to have the highest oscillator strength [73, 74]. However, such a dominance of the Jahn–Teller effect on the electronic structure of Fe2C has not been observed before. The opposite was found for GaN where the C3V symmetry stabilizes the Fe2C centre against the Jahn–Teller effect. Very few studies of the Jahn–Teller effect on Fe2C in hexagonal configuration exist [75]. In [75] a coupling to only one TA phonon mode is considered and ZnO is not covered at all. Though following the trend found in [73], a coupling to optical modes should also become important for ZnO and a rather strong Jahn–Teller effect would be expected. The effect of nearby defects on the Fe2C centre is discussed above, and some of the lines found in the absorption spectra were attributed to such Fe2C -defect complexes. The presence of defects could also affect the symmetry of the Fe2C centre behind the 395.7-meV line and its hot lines. A high concentration of defects can affect the local symmetry in two ways: by distorting the lattice and by the admixture of additional wave functions. Both mechanisms could modify the C3V symmetry in a way that the c-axis is no longer a distinct direction. A high concentration of defects in the investigated samples is quite likely due to the applied production methods. The ratio of the c- to a-axes of wurtzite ZnO is known to vary depending on the growth technique and the correlated formation of crystal defects [76]. If the Fe impurity causes a local c/a-ratio that coincides with that of a zincblende structure, the Fe centre would experience a crystal field of tetrahedral symmetry. As a consequence, no polarization or complex splitting would be expected. This kind of symmetry would also enable a strong Jahn–Teller coupling that is discussed earlier and that would explain the intensity distribution at high temperatures.

9.2.5 ZnO/Co Co2C in ZnO has a d7 configuration and is detected only in the 2C charge state in absorption and luminescence experiments [70, 77]. Koidl [77] presented a detailed work on polarized-optical absorption measurement resolving and analyzing the crystal-field transitions from the 4 A2 ground state to the 4 T2 .F/, 4 T1 .F/ and 2 E.G/ multiplets. As an example the low-energy onset of the 4 T2 band is shown in Fig. 9.13, which consists of two line doublets. The smaller splitting is in line with the EPR results (see Table 9.6) and hence represents the ground state splitting. The centres of gravity of transitions starting at the 4 A2 ground state and terminating at the 4 T2 .F/, 4 T1 .F/, 2 E.G/, and 4 T1 .P/ multiplets are found at 4,070, 6,800, 15,180 and 16; 460 cm1 , respectively.

254

A. Hoffmann et al. photon energy [eV]

3617.3 3611.6

3635.9 cm–1 3630.8

(ARBITRARY UNITS)

0.49

b)

a)

π

Unpolarized

σ

OPTICAL DENSITY

E1/2

2.5

0.44

π σ σ

18.9 cm–1

E3/2

E1/2 E3/2

σ π E3/2 E1/2

2.6

5.4 cm–1

2.7 WAVELENGTH (μm)

2.8

Fig. 9.13 Long-wavelength part of the 4 A2 ground state to the 4 T2 .F/ excited state absorption of ZnO=Co2C taken at 4.2 K with (a) unpolarized and (b) polarized light (after [77])

The properties of the ZnO/Co emission shown in Figs. 9.14 and 9.15 demonstrate unambiguously that the transitions inverse to the 4 T2 .F/ absorption of Co2C have been detected [70].

9.2.6 ZnO/Ni The optical absorption of transition metal ions have generally been interpreted on the basis of rigid lattice models. It can usually explain the energy of the crystal field terms, their fine structure, caused by spin–orbit interaction and by weaker crystal field components; however, it can be profoundly influenced by electron–phonon coupling that is a dynamic Jahn–Teller effect (JTE). The absorption measurements of Ni2C in ZnO can only be explained considering a dynamic JTE corresponding to moderately strong electron–phonon coupling [78]. In tetrahedral symmetry, the 3 F ground state of a free Ni2C (3d8 ) ion splits into a 3 T1 , 3 T2 and a 3 A2 state, in order of increasing energy. Spin–orbit interaction leads

9

Deep Centres in ZnO

Spectral radiant flux φv (%)

100

255

wavelength λ (nm) 2850

80

ZnO :

2800

2750

2(F)

Γ1

No.1015

Γ4 Γ5,Γ6

T = 4.2 K 60

4T

2

(F)

4A

2

(F)

E||c 4A

40

2(F)

Td

20

2760

Γ3

4T

Co2+ (d7)

2780

E⊥c

Γ2 C3v

Γ5,Γ6 Γ4 C3v

0 3500

3550

3600

3620 3600 wave number v (cm–1) photon energy [eV]

3650

0.44

0.45

Fig. 9.14 Emission spectrum of a ZnO/Co crystal at T D 4:2 K. The spectrum originates from the transition 4 T2 .F/ !4 A2 .F/ of the Co2C .d7 / ion. The main peak in the survey scan (left-hand part) is plotted with higher resolution in the right-hand part. Inset: Splitting scheme of the relevant energy levels of a d7 configuration and interpretation of the zero-phonon doublet (after [70]) wavelength λ (nm) 680

670

660

662

658

660

100

80

95 tr

60

90

em

40 ZnO :

Co2+ (d7)

85

transmission t (%)

Spectral radiant flux φ v (%)

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No.1015

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20

4T

1

(F)

4A

2(F)

0 14600 1.80

1.82

14800 1.84

15000 1.86

15200 15100 1.88

15150 15200 wave number v (cm–1) photon energy [eV]

Fig. 9.15 Emission spectrum of a ZnO/Co crystal at T D 4:2 K in the range of the 4 T1 .P/, 2 T1 .G/, 2 E.G/ !4 A2 .F/ transitions of Co2C .d7 /. Excitation through the 27,488 and 28; 482 cm1 lines of an argon laser. The zero-phonon line in the survey scan (left-hand part) is resolved into a doublet (right-hand part) and compared with the transmission spectrum in the same region (after [70])

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0.6

T2

T1

4219

4250

4327

4736

4410

4797

4736

4797

4219

4244

4348

σ

4490

4348 4327

π

4410

Optical density (relative units)

A2(A2) E(E) E A E1 A2 1

Unpolarized

2.0

2.1

2.2 λ (mm)

2.3

2.4

Fig. 9.16 Near infrared absorption of Ni2C in ZnO at 6 K for unpolarized and polarized light. Polarized and unpolarized spectra were taken with different crystals. A portion of the unpolarized spectrum is shown with increased gain (after [78])

to a further splitting of each of the 3 T1 states into four levels. The ground state of the ion then has A1 spin–orbit symmetry and is separated from the first excited spin–orbit state by 160 cm1 in ZnO. Thus at low temperatures only the ground state is populated. Kaufmann et al. [78] presented optical transmission spectra (see Figs. 9.16 and 9.17) of ZnO=Ni2C in which all the expected transitions terminating at the spin orbit levels of the 3 T2 state were identified. These findings provide the opportunity to test the validity of a static crystal field model. The experimental data could only be explained if electron–phonon interaction is taken into account. Luminescence of Ni2C has not been reported. In Ni-doped ZnO crystals a luminescence band occurs at 0.76 eV, which has been tentatively attributed [70] to Ni3C (see Figs. 9.18 and 9.19). Ni3C is isoelectronic to Co2C , so the level scheme shown in Fig. 9.14 can be used for the description of the transitions. The assignment of the 0.76 eV emission to Ni3C was achieved by

9

Deep Centres in ZnO

257 wavelength λ (nm) 2375

Fig. 9.17 Transmission spectrum of a ZnO/Ni crystal at T D 2 K, featuring the principal structures of the 3 T2 .F/ 3 T1 .F/ transition of the Ni2C .d8 / ion (after [70])

2325

1%

E⊥c

transmission

unpol.

E||c

ZnO : Ni2+ (d8) No.1010

T = 2K 3T 2

4200 0.52

(F)

3T

1

(F)

4300 wave number v (cm–1) 0.53

photon energy [eV]

investigating ZnO crystals doped with different enriched Ni isotopes, and employing temperature-dependent magneto-optical spectroscopy [79]. The ZnO crystals were doped with 58=60 Ni and the enriched nickel isotopes 62 Ni and 64 Ni in the ppm range. The crystals show the well-known Ni2C absorption spectra. The zero phonon line (ZPL) region of the emission is shown in Fig. 9.19. Applying high resolution spectroscopy for crystals, which were enriched with different Ni isotopes, an isotope splitting for the ZPL in the order of 13:5 eV/nucleon is resolved (see insert of Fig. 9.19). The isotope splitting is positive that is the ZPL of the heavier isotope has a greater ZPL energy. This experiment [79] directly proves that nickel ions participate in the 0.76 eV luminescence. The emission originates from the Ni3C internal 4 T2 –4 A2 .F/ transitions as proven by Zeeman experiments (see Fig. 9.20). The ground state g-values of the 4 A2 .F/ state were in excellent agreement with the EPR experiments.

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100

wavelength λ (nm) 1.85 1.80 1.75

1.70

1.65

1.645

1.640

Spectral radiant flux φv (%)

ZnO : Ni3+ (d7) No.1008

80

T = 4.2K 4T

60

2

(F)

4A 2

(F)

40 20

0

E||c

5400 0.68

5600 0.70

5800 0.72

E⊥c

6080 6100 wave number v (cm–1) photon energy [eV]

6000 0.74

Fig. 9.18 Emission spectrum of a ZnO/Ni crystal. The main peak in the survey scan at T D 4:2 K (left-hand part) is resolved into a doublet in the right-hand part, taken at T D 2 K. The spectrum is assigned to the transition 4 T2 .F/ !4 A2 .F/ of the Ni3C .d7 / ion (after [70]) 58

ZnO : 62Ni E || c INTENSITY (arb. units)

Fig. 9.19 Polarized ZPL region of the Ni3C centre for T D 2 K and T D 10 K for ZnO=62 Ni and the corresponding fine-structure of the 4 T2 and 4 A2 states. The inset shows the isotope splitting of emission line A for ZnO:58=60 Ni, 62 Ni and 64 Ni doped crystals (after [79])

T2 ABCD

4

A2

62

64

Ni

Ni

Γ4 Γ5,6

4

E⊥c

Ni

Γ5,6 Γ4 755.1

755.3

2K 0 ×3

A

B, C

D 10 K

0 755

756 PHOTON ENERGY (meV)

757

9.2.7 ZnO/Cu Like Li and Na also copper was often used to suppress the high conductivity of n-type ZnO crystals. Cu2C (3d9 ) was identified by magnetic resonance experiments [50]. See also the discussion of the green emission band in ZnO in Sect. 9.1. An example of temperature-dependent EPR measurements [80] is shown in Fig. 9.21.

Deep Centres in ZnO

259 H || c B4

B3

H⊥ c D4

D4

D3

D1

B4

757 B3

D2

1640

C1

A3 B2

B1 755 A2

D1

1645

B2

A4

B1

A3 A2

753

A1

PHOTON ENERGY (meV)

Fig. 9.20 Zeeman pattern of the ZPL region for H k c and H ?c for ZnO=64 Ni. The fourfold splitting of the 4 A2 .F/ ground state is indicated by the emission lines (B2 , B1 , A3 , A1 ) (H kc) and (B3 , B1 , A3 , A1 ) (H ?c) (after [79])

WAVELENGTH (nm)

9

1650 A1 ZnO : 64Ni 12

Fig. 9.21 Magnetic resonance spectra of copper-doped ZnO single crystals at different temperatures (after [80])

9

751

T= 2.0 K T= 4.2 K

6 3 0 3 6 9 MAGNETIC FIELD (T)

12

18 °K 16 °K 14 °K ZnO HE 4a 9.299GHz H⊥c

10 °K 1 40

3.0

4.0 5.0 magnetic field strength [KOe]

With decreasing temperature, the four line spectrum caused by Cu2C increases in intensity accompanied by a significant line width narrowing. At 10 K, the identification of Cu is no longer ambiguous, showing the 2  4 line spectrum of the two Cu isotopes each with nuclear spin of I D 3=2. The intensities comply with the respective abundance of the isotopes. The ratio of the isotropic hyperfine splitting for both isotopes is in excellent agreement with the ratio of the corresponding nuclear moments [81]. A very elegant way to dope ZnO with Cu was presented in the work of Broser et al. [80]. They used radiochemical doping according to the nuclear reaction 30

Zn64 .n;  / !30 Zn65 .245 d/ !29Cu65

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1 100

t = 22 d

239 d

1 100

344 d

1 100

2.5

ZnO Fr 5x 4.2°K 9,299 GHz H⊥c

3.0

3.5 4.0 4.5 magnetic field strength [KOe]

5.0

5.5

Fig. 9.22 Magnetic resonance spectra of a neutron radiated radioactive ZnO single crystal. The four resonances between 3.5 and 5.0 kOe represent Cu2C (after [80]) Fig. 9.23 A schematic diagram of various transitions in ZnO/Cu in the hole presentation (after [86])

ZnO : Cu CB 2

T2

4

hv1r

Cu2+ 2E

5,6 4

hvgr α β γ

+

(Cu,h)

4 4 4

VB

by irradiating undoped ZnO crystals with thermal neutrons. The EPR investigations are collected in Fig. 9.22. The first spectrum was taken 22 days after irradiation with thermal neutrons, the second at the 239th day and the third at the 349th day. The increase in the Cu concentration was also detected in the appearance and increase of infrared absorption and in the luminescence yield of the green emission band caused by Cu2C (see below, and Figs. 9.24 and 9.25). According to Fig. 9.4, Cu may induce a donor and an acceptor level in the band gap of ZnO. Indeed the IR luminescence with the zero phonon line at 6;887 cm1 (associated above with V3C ) has been assigned erroneously to the Cu3C internal transitions, so there is no evidence for a donor charge state. The compensation of shallow donors by Cu doping implies that Cu acts as an acceptor. Electrical measurement in ZnO bulk crystals codoped with In and Cu allowed the determination of the 0=– .Cu2C =CuC / level at 190 meV below conduction band [84]. Such a high lying acceptor level naturally inhibits p-type conduction in ZnO/Cu.

Deep Centres in ZnO

ARBITRARY EMISSION INTENSITY

9

261

2LO

2.8590 ev LO

4000 3.0

4500

5000 2.5

Å

5500

6000

6500

2.0 photon energy [eV]

Fig. 9.24 Green band emission of ZnO caused by copper impurities measured at T D 1:6 K. The enlarged portion illustrates the involvement of phonons near the zero phonon lines (after [82])

Fig. 9.25 Part of the green luminescence caused by copper in ZnO. Luminescence spectrum (left) and luminescence excitation (right) spectrum were recorded in the region of the zero phonon lines and one-phonon-assisted transitions (after [83])

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Copper is a prominent luminescence activator in ZnO, which gives rise to luminescence and absorption bands in the visible and near-infrared spectral regions [50, 82, 83, 85, 86]. In ZnO, there are two transitions starting at the Cu2C ground state – the intra centre transition Cu2C .2 T2 –2 E/ and the Cu2C –.CuC , h) chargetransfer transition (see Fig. 9.23). The three Cu2C levels in ZnO have binding energies of 1.233 eV, 1.2 eV and 3.25 eV, respectively. See [86] and references therein. At the onset of the Cu2C charge transfer band, sharp resonances (usually called ˛-, ˇ- and  -ZPL (zero-phonon lines)) are observed and interpreted as (CuC , h) states, where h stands for a hydrogen-like hole state (see Figs. 9.24 and 9.25). The three zero-phonon lines, ˛-, ˇ- and  found in the PLE spectrum of the green luminescence of copper in ZnO [82, 83, 85, 86] used to be unclear for a long time. From an experimental point of view, it was quite clear that the ˛-, ˇ- and  -lines appear due to transitions between the ground Cu2C .2 T2 / and excited (CuC ; h) states of the impurity. The three ZPLs are found within an energy interval of 14 meV with a hole binding energy of about 380 meV. Therefore, it was impossible to identify these as hydrogen-like hole states of a Coulomb potential. Magneto-optical measurements showed that these ZPLs are Kramers doublets with different and anisotropic gfactors. It was shown that the ˛-, ˇ- and  -ZPLs were associated with excitons intermediately bound to copper impurities, [CuC .d9 Ce), h]. The degree of localization of the tenth electron in copper and the binding energy and symmetry properties of the hole are considerably influenced by the symmetry of the crystalline environment of the impurity (the C3v group). They are responsible for a significant change in the complex excitation spectrum and other properties. The suggestion that the ˛-, ˇ- and  -ZPLs represents the excitation of the intermediately bound excitons is supported also by additional experimental data on the isotope shifts of these ZPLs [85] and on their relaxation behaviour. The relaxation behaviour of the excited (CuC ; h) and Cu2C .2 E/ states was studied by means of time-resolved spectroscopy allowing the determination of the radiative part of the relaxation process as well as by calorimetric absorption spectroscopy (CAS) allowing the determination of the non-radiative part of the process. Using these data, calculations of the quantum efficiency for each transition were carried out. It was shown that the recombination of the excited (CuC .d9 C e/, h) states into the Cu2C .2 T2 / ground state are solely radiative. The model of intermediately bound excitons explains this observation. Hence, the intermediately bound exciton (CuC .d9 C e/, h) states in ZnO are well distinguished from the shallow CuC (d10 , h) states in ZnS, where a hole is weakly bound to the ionized Cu acceptor. Isotope shifts were measured [85] for the so-called photoluminescence ˛ and ˇ zero-phonon lines (see Fig. 9.25) associated with excitations of bound excitons, and of the zero-phonon line associated with the intra-centre Cu2C .2 T2 –2 E/ transition (see Fig. 9.26). These shifts appeared to be negative and nearly equal. A theoretical model explaining these results was proposed, which incorporated the mode softening mechanism and the covalent swelling of the impurity d electron wave functions, and the mechanism works both for the excited and ground states. Using reasonable values of the parameters of the system, the authors were able to explain both

9

Deep Centres in ZnO

263

He 19b

ZnO : CU Eexcit = 3.41eV

INTENSITY

2K 63

65

150μeV 2.8586

2.8590

2.8588

2.8594

63

INTENSITY

65

2.8592

E⊥c T = 1.8K

ZnO : CU (2T2 - 2E) 122μeV 0.7164

0.7166 0.7168 0.7170 ENERGY (eV)

0.7172

Fig. 9.26 High resolution excitation spectrum of the green Cu luminescence in ZnO showing the isotope shift of the ˛ line (upper part) and highly resolved transmission spectrum with isotope shift measured on the low energy zero phonon line of the 2 T2 –2 E transition (lower part) (after [85])

the sign and value of the isotope shifts. In an extension of the work [85] Broser et al. [87] demonstrated for copper in ZnO that the isotope effect depends not only on the mass of the copper impurity but also on the mass of the oxygen ligands. The local vibrational properties of copper in ZnO were investigated by means of resonant Raman spectroscopy and analysed in a cluster calculation in the valence force model of Kane, using the scaling factor approximation. The fit of the experimental data together with the calculations gave insight into the local binding properties around the impurity, the localization and the symmetry of the local vibrational modes. The copper incorporation results in a local bond softening in the ZnO lattice. The copper and the oxygen mass dependences of the local vibrational modes of the CuO4 -cluster were calculated. The mass dependence is mainly determined by the localization of the local vibrational modes. The anisotropic vibration of the

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CuO4 -tetrahedron explains the ligand-induced zero phonon line isotope shift, which was observed for the intra-centre Cu2C .2 T2 –2 E/ transition.

9.3 Outlook Deep centres in ZnO are not limited to 3d-ions, or deep extrinsic and intrinsic acceptors. As in other II–VI compound semiconductors, we can expect that impurities of group IV elements may act as deep double donors. So far, only Pb3C (see Table 9.6) has been detected by EPR, but not much is known about the electrical and optical properties of ZnO/Pb [88]. Mo in ZnO was unintentionally incorporated into ZnO when a sample was attached to a heated Mo holder during growth, though nothing more is known about the 4d-ions. The exceptional role played by the rare-earthions would require an extra chapter without contributing to the understanding and behaviour of deep level defects in ZnO.

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Chapter 10

Magnetic Properties Andreas Waag

Abstract The investigation of the magnetic properties of ZnO doped with “magnetic” ions such as Mn, Co, Fe, or Ni is still very controversially discussed. Therefore, we give here, after a general introduction, a short overview of the present situation only.

10.1 General Overview of the Topic The electron is an elementary particle, having charge as well as spin property. In electronic and optoelectronic devices today, only the “charge”-property of the electron is used up to now. An interesting concept is to also utilize the “spin”-property of the electron. “Spin” stands here not only for the angular momentum of the electron but also for its magnetic moment. Each electron has a magnetic moment equal to one Bohr magneton e„ B D 2m with e being the elementary charge, „ is Planck’s constant divided by 2, and m is the mass of the electron. Each electron is an elementary magnet with a magnetic moment of one Bohr magneton. According to quantum mechanical rules, the magnetic moment is subject to quantization. Therefore, for the z-component of the magnetic and angular momentum, only two values are possible: “spin-up” and “spin-down.” (This purely “spin-based” discussion is only possible if there is no angular momentum contributing to the total angular momentum of the electronic state of the electron. This is often the case for conduction band electrons in conventional semiconductors such as silicon, GaAs, or GaN). The use of spin property or the magnetic moment of electrons in electronic devices is a very interesting new field of semiconductor research, which comes under the name “spintronics.”

A. Waag Institut f¨ur Halbleitertechnik der Technischen Universit¨at, Braunschweig, Germany e-mail: [email protected]

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Various potential applications of spin polarized currents have been suggested, one of them being a spin analog of the electro-optic modulator, often called a spin-transistor [1]. The so-called Datta-transistor is a nice demonstrator for spin electronic concepts, but seems to be of limited use concerning high speed switching. In any case, a substantial prerequisite of spin-electronic devices is the creation of a spin-polarized current. In other words, all the electrons (or holes) contributing to current flow should ideally be polarized in only one of the two possible spin directions. One realization of a spin polarized current was believed to suggest itself, namely the utilization of a ferromagnetic metal contact. In ferromagnets, the spin polarization at the Fermi level reaches values of about 30%. It was believed that this degree of spin polarization could be injected into a semiconductor, when a ferromagnetic contact is used. However, this approach turned out to be unsuccessful. The reason for it became clear after the first successful realization of electric spin injection had been reported in 1999 [2], by using a semiconducting spin-polarizer instead of a ferromagnetic metal. The degree of spin injection from a (ohmic) ferromagnetic metal contact suffers from the conductivity mismatch between semiconductor and metal contact. A simple consideration of the parallel current paths of spin-up and spin-down electrons through the nonpolarized semiconductor directly leads to the conclusion that the degree of spin-polarized current depends on the conductivity ratio between metal contact and semiconductor. This ratio needs to be close to unity in order to result in relevant spin-polarization [3]. Later, it has been pointed out that efficient spin injection can also be realized by nondiffusive transport schemes [4,5], using ferromagnetic metal contacts. The first electrical spin injection into semiconductors has been realized by using contacts made of semimagnetic semiconductors also known as diluted magnetic semiconductors (DMS), in particular BeZnMnSe [2], being one example out of a whole family of semimagnetic semiconductors such as CdMnTe, HgMnSe, and others. Magnetic ions (often manganese, Mn) in a matrix of II–VI semiconductors are in most cases incorporated iso-electronically. Therefore, magnetic and electronic properties can be tuned separately. At low Mn concentration, the semimagnetic semiconductors are usually paramagnetic systems. The exchange coupling between neighbored Mn ions, which becomes increasingly important at higher Mn concentrations, is antiferromagnetic and leads to antiferromagnetically coupled Mn–Mn pairs at higher Mn concentrations. Since semimagnetic semiconductors with isolated Mn ions are paramagnetic systems, a relevant magnetization at reasonably low external magnetic fields can only be achieved at low temperature. In an external magnetic field, the Mn system is magnetized, leading to an exchange coupling between the conduction and valence band states and the d-levels of the magnetic ion. This exchange coupling makes the band edge states “magnetic,” in a sense that a giant Zeeman splitting occurs. The electronics states at the band edges “feel” the magnetization in the Mn system due to exchange coupling, which leads to a giant Zeeman splitting. The giant Zeeman splitting can be described by

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effective g-factors, which often reach values of 100 and above. As a consequence, the conduction band states are split into spin-up and spin-down levels, and this Zeeman splitting is large enough to give a 100% spin polarization. A prerequisite for that is an external magnetic field and low temperatures. These spin-polarizers have been used to demonstrate the first electrical spin injection into semiconductors [2]. To exploit the possibilities of spin polarized currents at room temperature, alternative coupling mechanisms need to be involved, leading to ferromagnetic behavior. It has been suggested by Dietl [6] that Mn containing semiconductors can be made ferromagnetic, if a sufficiently large p-type carrier concentration can be achieved. However, the required hole concentrations are for ZnO beyond all presently realistic possibilities. See Chap. 5. This Zener model description of ferromagnetic coupling in zinc blende semiconductors could successfully describe the Curie temperatures of ferromagnetic GaMnAs as a function of Mn concentration and, in addition, point out that GaMnN and ZnMnO would particularly be interesting materials for room temperature ferromagnetism in semiconductors. The Zener model described a hole mediated exchange coupling, with the degree of exchange coupling depending on the free hole concentration. The same coupling mechanism is at least in principle possible with electrons, but the exchange coupling is less pronounced, and room temperature ferromagnetism would be difficult to achieve [6]. Other theoretical calculations based on a local density approximation [7] demonstrated that ZnXO with X D V, Cr, Fe, Co, and Ni is supposed to show ferromagnetic ordering without additional doping, with the possibility to fabricate transparent ferromagnets. These theoretical publications initiated a large amount of experimental effort to demonstrate room temperature ferromagnetism in ZnO doped with magnetic ions. Also, nonmagnetic impurities such as Cu, Ag, Sn, Li, or intrinsic defects have been considered in the context of ferromagnetism in ZnO. See further.

10.2 Short Overview of the Situation in ZnO Numerous publications on magnetic ZnO have been published over the last years. SQUID measurements often indicated a hysteresis at room temperature, and the occurrence of ferromagnetism was consequently assumed. More thorough investigations, however, demonstrated that the magnetic influence of nominally nonmagnetic substrates such as sapphire (Al2 O3 / must not be neglected [8]. Obviously, magnetic contamination in the substrate plays an important role here, especially if thin magnetic films with a small overall magnetization are to be analyzed. After subtracting the influence of the substrate, no more ferromagnetic response could be detected in the referenced case [8]. One can only speculate to what extent the substrates have lead to erroneous conclusions concerning the magnetic properties of magnetic ZnO thin films. In the Zener model theoretically describing ferromagnetic coupling in ZnO [6], a p-type doping level of 3  1020 cm3 has been assumed for the calculations. As has been mentioned above and in Chap. 5, p-type doping in ZnO is a problem, and

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reported p-type concentrations are usually orders of magnitude lower. The assumed prerequisite for ferromagnetic coupling cannot be fulfilled in ZnO up to this point. Frequent attempts have been undertaken to measure the spin polarization and Zeeman splitting in magnetic ZnO, with only limited success. In conventional semimagnetic semiconductors such as CdMnTe, the large Zeeman splitting can easily be analyzed by magneto-optical spectroscopy. Such an analysis has also been performed for both GaMnN and ZnCoO to get information on the Zeeman splitting in these materials [9, 10]. Absorption and luminescence confirm the incorporation of Co as Co2C -ion into the ZnO matrix [10]. Each Co-Ion carries a spin 3/2. The splitting of the A and B excitons could be measured at low Co concentration, leading to a value of the exchange integral difference jN0 .˛  ˇ/j D 0:4 eV [10] for a Co-concentration of 0.4%. The Zeeman splitting of the A and B excitons was 1.6 meV, which is 15 times larger when compared with the nonmagnetic ZnO reference sample [10]. However, when the A excitonic transition moves up in energy as the magnetic field increases, the corresponding B excitonic transition moves down. This symmetry makes it difficult to observe Zeeman splittings, especially when A and B excitons cannot be distinguished any more due to line broadening in ZnCoO. Magnetic ZnO has also been investigated by magnetic circular dichroism (MCD) [11] for Sc, Ti, V, Cr, Mn, Co, Ni, and Cu incorporation into ZnO. Pronounced negative MCD peaks were seen for ZnMnO, ZnCoO, ZnNiO, and ZnCuO, and it was concluded that these materials are magnetic semiconductors with strong sdand pd-interaction. After ion implantation, Mn has been found to be in a Mn2C state by electron spin resonance [12]; however, a substantial amount of Mn ions was also found in clusters. In implanted ZnFeO, tiny Fe clusters were found to be responsible for the ferromagnetic response [13]. In ZnO/Cu, ferromagnetic behavior has been reported [14]. Other studies have concluded that the ferromagnetism originates from defects, without correlation to Cu incorporation [15]. In ZnO/Ni, the ferromagnetism has been assigned to a strong tendency for Ni aggregation [16]. The important role of defects for the magnetic coupling of Co ions in ZnCoO has been identified by a hybrid density-functional-theory study [17]. These are just a few examples indicating the complexity of analyzing potential ferromagnetism in ZnO. Recently an increasing amount of literature points to the fact that ZnO without any magnetic ions also shows ferromagnetic behavior. Ferromagnetism has been found in undoped ZnO [18, 19], and also in ZnO doped with nonmagnetic ions [20] such as carbon [21], Sc [22], Cu, and Al [22,23], as well as implanted Ar [24], often the ferromagnetism even being more pronounced than in ZnO doped with magnetic impurities. A strong correlation of magnetic properties and defects has been revealed by positron annihilation experiments [25]. Figure 10.1 shows the room temperature magnetization as a function of magnetic field for different ZnO materials: chemically prepared ZnO, with and without firing at 550ı C, ball milled ZnO and as received ZnO; for details see [26]. The nanocrystalline, chemically prepared ZnO shows paramagnetic behavior, in contrast to as-delivered ZnO, which is diamagnetic, as should be expected. The 550ı C

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271

Magnetisation (emu/gm)

(1) Nano-ZnO (fired at 550°C) (2) Nano ZnO (3) As received ZnO (4) Nano-ZnO ball milled

(1)

(2)

(3)

(4)

–2.10–3 –3.0

3.0 Magnetic Field (kOe)

Fig. 10.1 Room temperature magnetization curves for different ZnO samples without additional magnetic ions. After [26]

fired ZnO even shows room temperature ferromagnetism, whereas the ball milled ZnO shows an even more pronounced diamagnetism. Correlations between defects and the occurrence of ferromagnetisms have also been reported by other groups, as referenced earlier. All these results indicate that either the ZnO is contaminated with magnetic impurities, or that the magnetic behavior of nonmagnetic ZnO is a complex function of the defect situation in the material. These correlations are not yet understood in detail, and are likely to be the main origin of the large number of inconsistent results on magnetic ZnO, which have been published in the past. Recent detailed X-ray magnetic circular dichroism studies of ZnCoO have shown that the Co system is paramagnetic and that the occurrence of ferromagnetism is indeed due to defects in the material [27]. The results suggest that oxygen vacancies are the defects causing a ferromagnetic response. Without any doubt, Co could be excluded being the source of ferromagnetism, even though Co was identified to replace Zn on a Zn site without any clustering. This result is also corroborated by a switching of ferromagnetism by annealing nonmagnetic ZnO in zinc or oxygen environment, or hydrogen implantation, which is known to increase the number of oxygen vacancies [28–35]. Unexpected room temperature ferromagnetism has also been observed in carbon doped ZnO/C [36, 37]. Carbon has been introduced either during pulsed laser deposition or by ion implantation. Because of a comparison to neon implanted samples, the clear involvement of carbon in the ferromagnetic behavior has been concluded, even though ion implantation increases the amount of point defects drastically. Similar magnetic phenomena have recently also been found in other materials, and even in silicon, without a generally accepted explanation [38]. The phenomenon is either new and relevant or based on artifacts that are not yet under control. For

272

A. Waag

silicon, the origin of a magnetic response has been identified to be the contamination with Fe particles [38] in one case. Room temperature ferromagnetism has also been observed in nominally nonmagnetic materials such as CeO2 , Al2 O3 , In2 O3 , and SnO2 [39]. Recent theoretical calculations in the frame of density functional theory also revealed the importance of point defects [40]. Native point defects have been found to have a large effect on the magnetic properties. Some p-type defects such as Zn vacancies stabilize ferromagnetism in Zn1x Crx O, Zn1x Mnx O, and Zn1x Fex O thin films, while O vacancies or Zn interstitials greatly enhance the ferromagnetic coupling in Zn1x Cox O thin films. It is pointed out that such a complicated behavior can be the reason for the numerous conflicting experimental results [40]. In addition, Co has theoretically been predicted to form clusters with antiferromagnetic coupling [41]. The given references are not supposed to give a complete overview on the vast amount of literature on magnetic ZnO (for that see, e.g., [42]). Instead, they should give an impression of the dilemma that in the former literature on magnetic ZnO, the important role of defects had not been acknowledged. The inconsistency of many reported results might be due to this fact, since magnetic ZnO has been fabricated by a manifold of techniques resulting not only in a variety of different defect levels but also in clustering, doping levels, etc. This makes comparison of data very difficult. As a matter of fact, the dream of a transparent ferromagnet at room temperature based on a semiconductor, including a high spin polarization, which can be used for spin electronic devices, has not yet become true, but is still a fascinating goal. More work has to be done in the future to get a detailed microscopic model of ferromagnetism occurring in ZnO under certain circumstances.

References 1. S. Datta, B. Das, Appl. Phys. Lett. 56, 665 (1990) 2. R. Fiederling, M. Keim, G. Reuscher, W. Ossau, G. Schmidt, A. Waag, L. Molenkamp, Nature 402, 787 (1999) 3. G. Schmidt, D. Ferrand, L.W. Molenkamp, A.T. Filip, B.J. van Wees, Phys. Rev. B 62, R4790 (2000) 4. E.I. Rashba, Phys. Rev. B 62, R16267 (2000) 5. A. Fert, H. Jaffr`es, Phys. Rev. B 64, 184420 (2001) 6. T. Dietl, H. Ohno, F. Matsukura, J. Cibert, D. Ferrand, Science 287, 1019 (2000) 7. K. Sato, H. Katayama-Yoshida, Jpn. J. Appl. Phys. 39, L555 (2000) 8. A. Che Mofor, A. Elshaer, A. Bakin, A. Waag, H. Ahlers, U. Siegner, S. Sievers, M. Albrecht, W. Schoch, N. Izyumskaya, V. Avrutin, Appl. Phys. Lett. 87, 062501 (2005) 9. P. Koidl, Phys. Rev. B 15, 2493 (1977) 10. D. Ferrand, S. Marcet, W. Pacuski, E. Gheeraert, P. Kossacki, J.A. Gaj, J. Cibert, C. Deparis, H. Mariette, C. Morhain, J. Supercond.: Incorporating Novel Magn. 18, 15 (2005) 11. K. Ando, H. Saito, Z. Jin, T. Fukumura, M. Kawasaki, Y. Matsumoto, H. Koinuma, J. Appl. Phys. 89, 7284 (2001) 12. A. Che Mofor, F. Reuss, A. Elshaer, R. Kling, E. Schlenker, A. Bakin, H. Ahlers, U. Siegner, S. Sievers, M. Albrecht, W. Schoch, W. Limmer, J. Eisenmenger, T. Mueller, A. Huebel, G. Denninger, P. Ziemann, A. Waag, Appl. Phys. A. 88, 161 (2007)

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13. K. Potzger, S. Zhou, H. Reuther, A. M¨ucklich, F. Eichhorn, N. Schell, W. Skorupa, M. Helm, J. Fassbender, T. Herrmannsd¨orfer, T.P. Papageorgiou, Appl. Phys. Lett. 88, 052508 (2006) 14. T.S. Herng, S.P. Lau, S.F. Yu, H.Y. Yang, L. Wang, M. Tanemura, J.S. Chen, Appl. Phys. Lett. 90, 032509 (2007) 15. Q. Xu, H. Schmidt, S. Zhou, K. Potzger, M. Helm, H. Hochmuth, M. Lorenz, A. Setzer, P. Esquinazi, C. Meinecke, M. Grundmann, Appl. Phys. Lett. 92, 082508 (2008) 16. M. Snure, D. Kumar, A. Tiwari, Appl. Phys. Lett. 94, 012510 (2009) 17. C.H. Patterson, Phys. Rev. B 74, 144432 (2006) 18. N.H. Hong, J. Sakai, V. Brize, J. Phys. Condens. Matter 19, 036219 (2007) 19. S. Banerjee, M. Mandal, N. Gayathri, M. Sardar, Appl. Phys. Lett: 91, 182501 (2007) 20. J.M.D. Coey, Solid State Sci. 7, 660 (2005) 21. H. Pan, J.B. Yi, L. Shen, R.Q. Wu, J.H. Yang, J.Y. Lin, Y.P. Feng, J. Ding, L.H. Van, J.H. Yin, Phys. Rev. Lett. 99, 127201 (2007) 22. J.M.D. Coey, M. Vankatesan, C.B. Fitzgerald, L.S. Dornneles, P. Stamenov, J. Luney, Magn. Mater. 290, 11405 (2005) 23. D. Chakraborti, G. Trichy, J.T. Prater, J. Narayan, J. Phys. D: Appl. Phys. 40, 7606 (2007) 24. R.P. Borges, R.C. Da Silva, S. Magalhaes, M.M. Cruz, M. Godinho, J. Phys.: Conden. Matter, 19, 476207 (2007) 25. D. Sanyal, M. Chakrabarti, T.K. Roy, A. Chakrabarti, Phys. Lett. A 371, 482 (2007) 26. S. Dutta, S. Chattopadhyay, A. Sarkar, M. Chakrabarti, D. Sanyal, D. Jana, Prog. Mater. Sci. 54, 89 (2009) 27. Th. Tietze, M. Gacic, G. Sch¨utz, G. Jakob, S. Br¨uck, E. Goering, New J. Phys. 10, 055009 (2008) 28. K.R. Kittilstved, D.A. Schwartz, A.C. Tuan, S.M. Heald, S.A. Chambers, D.R. Gamelin, Phys. Rev. Lett. 97, 037203 (2006) 29. R.D.A. Schwartz, D. Gamelin, Adv. Mater. 16, 2115 (2004) 30. T. Zhu, W.S. Zhan, W.G. Wang, J.Q. Xiao, Appl. Phys. Lett. 89, 022508 (2006) 31. S.H. Liu, H.S. Hsu, C.R. Lin, C.S. Lue, J.C. Huang, Appl. Phys. Lett. 90, 222505 (2007) 32. H.S. Hsu, J.C.A. Huang, Y.H. Huang, Y.F. Liao, M.Z. Lin, C.H. Lee, J.F. Lee, S.F. Chen, L.Y. Lai, C.P. Liu, Appl. Phys. Lett. 88, 242507 (2006) 33. H.S. Hsu, J.C.A. Huang, S.F. Chen, C.P. Liu, Appl. Phys. Lett. 90, 102506 (2007) 34. V.K. Sharma, G.D. Varma, J. Appl. Phys. 102, 056105 (2007) 35. H.J. Lee, C.H. Park, S.Y. Jeong, K.J. Yee, C.R. Cho, M.H. Jung, D. Chadi, Appl. Phys. Lett. 88, 062504 (2006) 36. H. Pan, J.B. Yi, L. Shen, R.Q. Wu, J.H. Yang, J.Y. Jin, Y.P. Feng, J. Ding, L.H. Van, J.H. Yin, Phys. Rev. Lett. 99, 127201 (2007) 37. S. Zhou, Q. Xu, K. Potzger, G. Talut, R. Gr¨otzschel, J. Fassbender, M. Vinnichenko, J. Grenzer, M. Helm, H. Hochmuth, M. Lorenz, M. Grundmann, H. Schmidt, Appl. Phys. Lett. 93, 232507 (2008) 38. P.J. Grace, M. Venkatesan, J. Alaria, J.M.D. Coey, G. Kopnov, R. Naaman, Adv. Mater. 21, 71 (2009) 39. A. Sundaresan, R. Bhargavi, N. Rangarajan, U. Siddesh, C.N.R. Rao, Phys. Rev. B 74, 161306(R) (2006) 40. Q. Wang, Q. Sun, P. Jena, Y. Kawazoe, Phys. Rev. B 79, 115407 (2009) 41. D. Iuan, M. Kabir, O. Gr˚an¨as, O. Eriksson, B. Sanyal, Phys. Rev. B 79, 125202 (2009) 42. F. Pan, C. Song, X.J. Liu, Y.C. Yang, F. Zeng, Mater. Sci. Eng. B R62, (2008)

Chapter 11

Nonlinear Optics, High Density Effects and Stimulated Emission C. Klingshirn

Abstract Nonlinear optics is a wide field, comprising in principle all phenomena, where one observes a nonlinear response (e.g. of the polarization of a medium) on the stimulus such as the incident electromagnetic field. It starts with the typical effects such as second or third harmonic generation, four wave mixing or the rectification of the electromagnetic field (the so-called dc-effect) and continues over two and multi photon absorption to the phenomena of extreme nonlinear optics. Another branch deals with the phenomena in dense electron–hole pair systems (socalled high exciton, high density or many particle effects), which can be created, for example by optical excitation, but also by biasing a p–n junction in forward direction or by excitation with an electron beam. The third aspect concerns the stimulated emission resulting (e.g.) from the high excitation effects and the laser emission, which is influenced by the shape of the samples and resonators, (e.g.) of bulk materials, nano rods or powders. All three aspects overlap. We present in the following selected results for ZnO following roughly the above ordering.

11.1 Nonlinear Optics ZnO has no centre of inversion. Consequently, it shows phenomena that come with even powers of the electric field like X .2/ effects in addition to odd powers, for example in X .3/ phenomena. Second harmonic generation (SHG) as a typical X .2/ phenomenon has been reported rather early [1–4]. The efficiency of this phenomenon has not only been investigated far from resonance (e.g.) by an Nd-laser but also approaching the excitonic resonances [5,6]. Starting from the 1980s, SHG is investigated also in epitaxial layers, nano rods and powders [7–17]. Third harmonic generation has been reported (e.g.) in [18–22].

C. Klingshirn Institut f¨ur Angewandte Physik, Karlsruher Institut f¨ur Technologie KIT, Karlsruhe, Germany e-mail: [email protected]

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The field has been expanded to extreme nonlinear optics using ultra-short pulses with the duration of only a few cycles of light, where perturbation theory collapses, and the phase between the carrier wave and its envelope matters [23–25]. The rectification of Nd laser pulses in ZnO has been observed in [26], where also the relation of this effect to the Pockels effect in ZnO has been presented [26, 27]. Two photon absorption or more precisely two polariton absorption (TPA) of 30 ns pulses from a Q-switched ruby laser was an early means to create a high density of electron–hole pairs in relatively large (a few mm3 / almost homogeneously excited volumes of bulk ZnO [26, 28–31, 215, 216]. Values of the two photon absorption coefficient ß, defined by (11.1a)  dI D .˛I C ˇI 2 /dx; where I is the intensity and ˛ and ˇ the one- and two-photon absorption coefficients have been obtained of the order of [26, 28–32]. 0:04  107 cm=W  ˇ  .0:35 ˙ 0:09/107 cm=W

(11.1b)

For three photon absorption values in the range of 1020 cm3 =W2 have been deduced from Z-scan measurements with a TiSa laser around photon energies corresponding to 0:45Eg [33]. Later, various exciton (-polariton) states have been investigated by two- and three-photon absorption [34–41] exploiting the fact that the combination of various polarizations allows to reach different final states according to Fig. 11.1. These measurements confirm also the exciton spectra and the valence band ordering presented in Sect. 6.1. Also transitions from deeper valence bands have been observed in TPA [43]. The X .3/ processes four wave mixing (FWM) or hyper-Raman scattering (also known as two-photon Raman scattering) have been also used to determine the dispersion curve of exciton polaritons in ZnO [44, 45]. The polariton dispersion curves obtained from all these measurements agree essentially with those presented in Chap. 6 and are therefore not repeated here. The use of TPA to determine the level scheme of biexcitons will be outlined below.

Fig. 11.1 Schematic drawing of the symmetries of ground, intermediate and final states reached in ZnO for various combinations of polarizations in dipole approximation. From [42]

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11.2 High Excitation Effects With increasing generation rate G (i.e. increasing number of electron–hole pairs created per unit of volume and time), interaction processes between excitons or between excitons and free carriers or phonons become more frequent. These interaction processes change the optical properties and therefore belong to the regime of nonlinear optics. These phenomena can be roughly sorted into two groups namely those at densities where excitons are still (reasonably) good quasi particles – the socalled intermediate density regime – and the high-density regime, where the binding of excitons is screened by the many carriers and a new collective phase is formed, called the electron–hole plasma (EHP) [42,46–50]. It should be noted in this context that the transition from the intermediate to the high density regime is in a direct gap semiconductor such as ZnO with electron–hole pair lifetimes in the 100 ps to 1ns regime (see Chap. 12), a continuous and not an abrupt one occurring for ZnO in the range around np  1018 electron–hole pairs per cm3 depending on temperature as shown in Sect. 11.2.3.

11.2.1 The Intermediate Density Regime In Fig. 11.2, we give a schematic overview of processes in the intermediate density regime.

Fig. 11.2 Schematic drawing of the following processes: recombination of an exciton under emission of one (or more LO) phonons (a), decay of a biexciton into a photon like and an exciton like polariton (b), inelastic exciton–exciton scattering (c) and inelastic exciton-free electron scattering (d). According to [42, 46]

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In the following, we discuss these processes and give some examples: The recombination of an exciton under emission of one or more LO-phonons (X–mLO) in Fig. 11.2a is a luminescence process occurring already in the regime of linear optics. See, for example Fig. 6.15. Since it can easily be inverted at low temperature and leads to stimulated emission in low loss cavities (see Sect. 11.3), it is also included here. The formation and decay of biexcitons or excitonic molecules shown in Fig. 11.2b was in ZnO for a certain period a point of controversial discussion b of the biexciton relative to two free especially concerning the binding energy Exx excitons [51, 52]. Values between 10 and 20 meV had been given in the literature. The issue has been solved in a cooperation of two research groups [51] using a technique called luminescence assisted two-photon spectroscopy (LATS) [52]. In this example of TPA spectroscopy, one photon comes from a spectrally narrow, tuneable pump laser at „!l and the second from the broad band luminescence of the sample itself at „!d excited by the pump laser. This technique assures for ns excitation pulses automatically spatial and temporal overlap of the two photon sources. The TPA process manifests itself in a reabsorption dip in the luminescence spectrum at „!d , which shifts in a way that the sum   b „!l C „!d D Ebiex D 2 Eg  Exb  Exx

(11.2)

remains constant. In Fig. 11.3 we show two sets of spectra and the relation „!d D f .„!/l . Actually three biexciton levels have been found with this technique, which contain either two holes from the A VB, or one A and one B hole or two B holes. The binding energies of these three states relative to the parent excitons, that is relative to two free A1 , an A1 and a B6 or two B6 (spin-triplet) excitons (or transverse A5 and B5 spin singlet excitons) is almost the some in all three cases, namely

b

Luminescence - intensity ( arb.units )

1.7 K

3.330

c I9

ZnO Eexc II c

hw1 hw2 hw3

I6

hw1

hw2

3.350

3.3936

3.3869

hw2 hw2

3.3887

3.3916

3.3927 3.3936

(2)

3.340

3.3945 3.3953

3.3884

3.370

(3)

hw3

3.3896

3.350

1.7 K

(eV) 3.386

( eV )

3.3910

ZnO

hwexc

hwexc

3.3924

1.8 K

hwm ( eV)

a

3.346 3.350 3.354 3.358 3.362

Photon energy of luminescence ( eV )

(1) 3.390

3.400

hwexc ( eV)

Fig. 11.3 Luminescence spectra for two different ZnO samples showing the dip at „!d for various values of „!l (a, b) and the relation of „!d D f .„!l / with data from the two different samples showing in all cases the characteristic slope – 1(c). According to [51]

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b Exx  .14 ˙ 1/ meV. More recently a biexciton containing two C holes (or excitons) has been observed [53]. The binding energy of 1 meV claimed there seems, however, unlikely since the C valence band and exciton have in ZnO parameters concerning effective masses or binding energy very similar to A- and B-bands or excitons (see Chaps. 4, 6 or [54] and references therein). Indeed, it has been outlined in [55] that the data of [53] can be reinterpreted resulting also for a biexciton containing two C-holes in a more realistic binding energy between 10 and 20 meV. The radiative decay of a biexciton results in a photon (more precisely a photonlike polariton), which is detected as luminescence and an exciton-like polariton on the LPB, on the longitudinal branch or in a mixed mode state. The corresponding emission band is usually called M-band. The intensity Iem of the biexcitonic M-band increases generally super linearly with the generation rate G as

Iem  G ˛ ;

(11.3a)

but one does generally not observe the value ˛ D 2 expected from simple recombination kinetics but values 1<˛2 (11.3b) This finding can be explained by more elaborate kinetic models like the ones in [56–58]. Energy and momentum conservation result for the line shape of the decay of a biexciton into a luminescence photon and a single exciton state in an inverted b to lower energies Boltzmann distribution [42,45,46] extending from Eg  Exb  Exx folded with a Lorentzian taking care of homogenous broadening. This line shape must not be decomposed into various Gaussians, since there is no justification for b is not given by the energetic dissuch a procedure. Furthermore, the value of Exx tance from the exciton energy to the maximum of the M-band, but rather to its high energy side, for example to the point of inflection. In [59–65] we give in addition to the ones mentioned (e.g.) in [45, 46, 51, 52] a few more references to M-band luminescence. It must be kept in mind that several other processes have been identified, which may also contribute to the luminescence in the spectral region of the M-band but are not related to biexcitons [46], especially processes involving bound exciton complexes (BEC). This spectral coincidence is not surprising, since both a biexciton and an exciton bound to a neutral acceptor or donor (Aı X or Dı X) consist of a bound state of two negatively and two positively charged particles. The direct recombination of a BEC at low temperature leads to spectrally narrow luminescence features (see Fig. 6.15 or Chap. 7), which can be easily distinguished from a biexciton decay, while the decay of the BEC under emission of a photon and an acoustic phonon (the acoustic phonon side band [46]) or under inelastic scattering with a free carrier [66, 67] may lead to relatively broad emission bands, which could easily mimic the properties of a biexcitonic M-band. Even the application of uniaxial stress as an additional parameter [68] did not lead to a unique identification of biexciton luminescence as shown in [45]. Therefore, the observation of an M-band is alone no proof but only a hint to the existence of biexcitons.

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Fig. 11.4 Luminescence spectra of ZnO-based multiple quantum wells with increasing fs-pulsed excitation. According to [76]

Such hints for the existence of biexcitons (which have to be expected in structures of reduced dimensionality as well) have been also found in epilayers (see, e.g. references in [64, 65] or [69, 70]), nano rods [71–73], quantum wells [74–76] or nano crystallites [77]. Although the properties are again identical to the ones of bulk samples for epilayers, rods and larger nano crystallites, the binding energy b is increased in narrow quantum wells to values above 20 meV [74–76] as Exx expected for the reduced dimensionality [42,78,79] and the luminescence feature is blue-shifted compared with bulk. In addition to the comments on the origin of the M-band and on the determination of the binding energy from luminescence given above, localization effects come into play for quantum wells. We give in Fig. 11.4 an example for a ZnO quantum well between Znx Mg1x O barriers. The emission at 3.36 eV comes from a ZnO buffer layer, the one above 3.44 eV from the barriers. The peaks around 3.40 eV and 3.415 eV are due to localized and/or bound excitons. The peak around 3.39 eV growing superlinearly with excitation is attributed to b around 30 meV. biexciton luminescence, resulting in a binding energy Exx The two remaining processes in Fig. 11.2c,d are so-called inelastic scattering processes [80, 81]. Inelastic, because they occur under energy and momentum conservation (see [42, 46, 82–84] and references therein) but the kinetic energy is not conserved, which is the definition of elastic scattering. Figure 11.2c shows the inelastic exciton–exciton scattering (X–X scattering). In this process, two excitonlike polaritons with nB D 1 interact (e.g.) via their dipole moments. In this interaction process one exciton is scattered under energy and moment conservation into a state with nB D 2, 3 . . . or into the ionization continuum, while the other is scattered onto the photon-like part of the LPB and appears as luminescence photon. These so-called P-bands (sometimes resolved into P2 , P3 : : : P1 / have their emission maxima at

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Fig. 11.5 The P2 and P1 bands of ZnO in the intermediate density regime, together with the M-band and some linear recombination process. According to [85]

  XX „!max D Eg .T /  Exb 2  1=n2B  ıkB T

(11.4)

with kB D Boltzmann’s constant, and the parameter ı is assumed to be 0 < ı  1 [80,81]. In Fig. 11.5 we show an example for the P2 and P1 bands and the M-band. Actually the peak labelled I9 in the upper spectrum of Fig. 11.5 is the M band, while the bound exciton emission line I9 is situated at slightly higher photon energies as can be seen by comparison with the lower trace. Similar data are found (e.g.) in [82, 83]. The P-bands have been observed in bulk samples only up to temperatures around 100 K [82, 83, 85]. At higher temperatures, the inelastic exciton-free carrier scattering process takes over, which is shown in Fig. 11.2d. There, an exciton scatters inelastically with a free carrier (generally an electron, because ZnO is usually n-type) and ends up again on the photon like part of the LPB, while the electron reaches under energy and momentum conservation a state of higher kinetic energy. The Stokes part of this X–el emission band starts ideally (i.e. without reabsorption) at the energy of the free exciton and extends from there to lower energies. Energy and momentum conservation show that the emission maximum shifts with increasing temperature T faster to lower energies than the band-gap does roughly as [45, 46, 82–84] Xel D Eg .T /  Exb  kB TM x =me „!max

(11.5)

282

C. Klingshirn 3.4

BL BT AL Ex AT

BEx

Ex-Ex

(hw)max(eV)

Ex–LO

3.3

}BEx–LO Ex–EI Ex–2LO BEx–2LO

3.2

Ex-3L0

3.1

0

200 100 Crystal temperature (K)

300

Fig. 11.6 The temperature dependence of the maxima of various emission bands in ZnO. According to [82, 83]

where Mx is the translational exciton mass and again with  of the order of or below unity. In Fig. 11.6 we show the experimentally observed temperature dependences of the spectral positions of various emission maxima. The pronounced red-shift of the X–el (or Ex–El) band maximum is obvious. Note that various processes may be spectrally degenerate in some temperature intervals like around 100 K. The exact position may be further influenced by heating of the exciton and carrier gases above lattice temperature by the high excitation, by reabsorption and of course by stimulated emission treated in Sect. 11.3. The transition from the X–X to the X–el process around 100 K has several reasons. One is the increasing thermal ionization of the excitons and of neutral donors with increasing temperature resulting in an increase of the electron density, the other the fact that the interaction cross section for X–X scattering (i.e. dipole–dipole interaction) is smaller than for the dipole–monopole interaction of the X–el process. Consequently, there were hardly any claims for X–X scattering in ZnO at RT or above until recently when many authors claimed inelastic X–X scattering, that is the P bands to be the laser process in ZnO at RT and above. As we shall show in Sect. 11.3, this is in most cases a misinterpretation.

11.2.2 Electron–Hole Plasma With increasing excitation or generation rate or electron–hole pair density, various things are happening. The increasing scattering rates lead to a shorter dephasing time (know as excitation induced dephasing to contrast it with the dephasing occurring with increasing temperature due to the thermal population of phonons, as shown in Fig. 6.10), that is to an increasing homogenous width or damping of the exciton resonances. This excitation induced dephasing is by itself a typical high excitation

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or many particle effect. There are two more of them. One is an increasing screening of the Coulomb interaction between electron and hole by the other carriers, leading together with phase-space filling (or Pauli blocking) to a decrease of the excitonic binding energy Exb 0 .np /, where np is the density of electron–hole pairs, until the exciton becomes unbound and disappears at a density known as Mott density nM . The frequently used approach for the Mott density (see [42,55,86,87] and references therein) (11.6) aB3 nM D 1 over estimates nM by more than one up to even two orders of magnitude. For ZnO with the excitonic Bahr radius aB D 1:8 nm (11.6) would result in nM D 1:7  1020 cm3 , while a reasonable value following (e.g.) from the Saha equation and other approaches [42, 55] is nM  5  1017 cm3 while [49, 88] result in even lower values. Examples where (11.6) has been applied are [219–222]. Consequently either the experimental values of the density or the interpretation of the data may be open for discussion. The third aspect is that the value of the forbidden gap is a monotonously decreasing function of np due to exchange and correlation effects. For details see, for example [42, 46, 49, 50] and references therein. The decreases of the exciton binding energy and of the band gap with increasing np compensate each other to a large extend in the sense that the exciton energy remains in absolute terms almost unchanged up to nM at which density the excitons cease to exist as a individual quasi particles. All these effects are shown in Fig. 11.7 for room temperature (RT).

Fig. 11.7 Calculated values of the band gap renormalization Eg of ZnO as a function of the electron–hole pair density np (dashed line) according to [88,89] and deduced from an average over experimental data for many different IIb –VI semiconductors (solid line) [42], the almost constant absolute position of the exciton resonance and its homogeneous width (FWHM) shown by the shaded area, which starts at low densities at RT with 40 meV FWHM (see Fig. 6.15), and the density dependence of the chemical potential .np ; Tp D 300 K/. The quasi-Fermi levels Efe and Efh of electrons and holes are counted in the notation of this figure from their respective band extrema. According to [55]

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C. Klingshirn

The vanishing of the exciton binding energy occurs around nM D .6 ˙ 3/1017 cm3 , but due to the large homogenous width of the exciton, which starts at RT already with a FWHM value of about 40 meV as mentioned already above, the intermediate density regime, where excitons are still good quasi particles, is left at RT already around or even slightly below np D 1017 cm3 . At lower temperatures, where the damping is smaller (see Fig. 6.15) this value might be higher, but always below nM . Furthermore, we show in Fig. 11.7 the chemical potential of the electron hole pair system .np ; Tp / D 300 K, which is defined as the energetic distance between the quasi-Fermi levels of electrons and holes. They describe the distribution of the carriers in their respective bands. Population inversion between CB and VB occurs if .np ; Tp / Eg 0 ;.np /:

(11.7)

We come back to this aspect in Sect. 11.3. The transition to an EHP is in direct gap semiconductors usually a continuous one, even below the critical temperature Tc for the formation of an electron–hole liquid (EHL) in the form of droplets surrounded by a lower density gas phase [42, 46–48]. The reason for the suppression of this phase separation is the short electron– hole pair life time, which is for ZnO at high densities typically in the 100 ps regime (see Chap. 12). In the optical reflection spectra, the creation of an EHP is connected first with a broadening and then with the disappearance of the excitonic features as shown already in Fig. 6.10. In the luminescence and absorption spectra, the excitonic features should consequently disappear, too. However, there are at least two reasons, why broadened (exciton-like) luminescence and absorption peaks may still occur at the position of the exciton. One is the excitonic enhancement of the oscillator strength around .np ; T ) (see [42, 46, 49, 50] and references therein) and the other is inhomogeneous excitation either laterally over the excitation spot or into the depth of the sample (or even temporally over the excitation pulse) allowing the coexistence of excitonic and EHP features in the spectra. See [47,48]. The observation of optical gain due to band-to-band transition in an EHP will be reported below in Sect. 11.3. Similarly as for the linear optical properties in Chap. 6, it can be stated that the high excitation phenomena are in epilayers, nano rods and larger nano crystals similar to the ones in bulk samples. Possibly the excitation intensities to reach an EHP are lower in thin epilayers, because carrier diffusion into the depth of the sample is restricted or the P-band emission may be influenced by the mode pattern of the quasi one-dimensional wave guide structure of a nano rod [76, 90–92]. For nano rods, the presence of an EHP at sufficiently high pumping is also well established. See [93, 94] and examples in Sects. 11.3 or 12.3. The presence of an uni-polar plasma of electrons in ZnO, resulting from a high doping level, results often in a blue shift of the absorption edge. This effect is known as Burstein–Moss shift. It is the result of a delicate balance between the decrease of the band gap, which is approximately one half of the band gap renormalization (BGR) of a bipolar plasma of the same electron–hole pair density, the filling of the states and the screening of the Coulomb interaction. See also the comment in Sect. 6.2. Especially the two latter effects have been investigated in detail in [95].

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The blue shift of the onset of the absorption edge occurs if the band filling dominates over the BGR. For the luminescence these two effects do not result in a simple blue shift, but in a broadening seen e.g. in (e,A0 / transitions. Furthermore, plasmon–phonon mixed states occur both in uni- and bi-polar plasmas, if the plasmon frequency approaches or exceeds the one of transverse optical phonons as detailed in [42] and in Sect. 2.5 for uni-polar plasmas. Some examples for the formation of an EHP in quantum wells are found in [96–98]. Here localization effects have to be taken into account, too [99].

11.3 Processes for Stimulated Emission Several of the radiative recombination processes which are presented in Chap. 6, and all of the high excitation processes introduced above are capable to show optical gain stimulated emission and lasing. In the following parts, we proceed from bulk material to structures of reduced dimensionality finishing with a few comments on polariton lasers and within every subchapter we go from excitonic processes in the intermediate density regime to EHP related emission in the high density regime, stressing here again, that the transition between the two regimes is a continuous one. For first reports on stimulated emission in ZnO see [82, 83, 85, 100–113]. The pump sources where at the beginning electron beams using acceleration voltages from a few ten to a few hundred keV and current densities on the sample in the range of kA=cm2 . This way of excitation is very unselective and produces electron–hole pairs with a lot of excess energy of the order of a few Eg . Then optical excitation came into play, starting with pulses of a few ten ns from Q-switched ruby lasers using two-phonon absorption (TPA), which allows to pump or to excite relatively large volumes (several mm3 / rather homogeneously (see, e.g. [82,83,109,110,113]) or to create first the second harmonic and use then one photon absorption (OPA) in a thin layer close to the surface (see, e.g. [82, 83]). The generation rate and excitation density are in the latter case higher but spatially generally rather inhomogeneous into the depth of the sample. The thickness of the excited layer is determined in this case by the penetration depth of the exciting light lex D ˛ 1  0:1 m (see Figs. 6.11 and 6.12), by the diffusion length of the excited species (in bulk typically around 1 to a few m) and/or by the thickness of the layer or quantum well. Only if the thickness of the layer is small or comparable to the absorption or diffusion length (whatever is longer) one can obtain by OPA a homogeneous generation rate into the depth of the sample. In the next step N2 and excimer lasers have been used for OPA with excitation pulse duration from 5 ns to 50 ps ([100, 111–113]) as well as tuneable lasers for resonant excitation of (e.g.) the exciton resonance. More recently, the frequency doubled or tripled output of Ti sapphire lasers is used, which goes from the ps down to the 100 fs regime (e.g. [93, 94]) and this can be used for the investigation of coherent processes (see Chap. 12) or extreme nonlinear optics if the pulses are made sufficiently intense and short as a few fs to avoid sample damage and to remain below the dephasing time T2 . See [23–25] and Chap. 12.

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For excitation pulse durations Tp much longer than the lifetime T1 of the excited electron hole pairs or excitons (1 ns T1 0:1 ns see Chap. 12), quasi stationary conditions may be reached in the temporal centre of the excitation pulse, otherwise dynamics has to be considered. The upper limit of the incident intensity is given by the damage threshold and depends on the pulse durations and on the preparation of the surface. For pulses with 50 ns Tp 5 ns the limiting value for surface damage is of the order of a few 10 MW=cm2 and 5 MW/cm2 for TPA and OPA, respectively. For pulses in the (sub-) ps regime, it is more the fluence F that matters, that is the temporally integrated energy per unit of area. A rather general value is the onset of damage when approaching F D 1 kJ=m2 (see, e.g. [114, 115] and references therein). In the case of TPA, self-focussing in the sample may also lead to damage. Pumping via a forward biased p(i)n homo- or hetero-junction led to light emission (see references in Chaps. 1 and 13) but hardly any claims of stimulated emission can be found in literature until now for this type of creation of electron–hole pairs.

11.3.1 Bulk Samples and Epilayers We start with the inelastic scattering process depicted in Fig. 11.2. Most of them can be mapped onto a four level laser system (sometimes coming also under names like threshold less lasing or lasing without inversion, though these terms are also used for other phenomena). The X–mLO process is in principle inverted, if there is one exciton in the sample and no LO phonon. The inelastic X–X P2 -process is inverted, if there are two excitons in the sample and none of them in the state nB D 2. Similar approaches hold for the other processes. Finite losses require of course finite densities to reach net optical gain and possibly laser emission. One loss mechanism would be a reabsorption process, which occurs if there is finite thermal population of the LO-phonons or of the nB D 2 exciton states. We start with some data on the X–mLO process. As mentioned, it can be easily inverted at low temperatures; however, its gain values are relatively small. Consequently, stimulated emission of this process can be observed best if large volumes (with low diffraction and other losses) are excited and inverted by TPA. As for most other gain processes, stimulated emission and laser modes emerge on the low energy side of the maximum of the spontaneous emission band [116]. We show in Fig. 11.8 some experimental results. See also [110–113, 217]. The sample has been pumped by TPA with a Q-switched ruby laser. The resonator consisted of two plan-parallel as grown surfaces of the hexagonal ZnO sample. Because of this resonator geometry clear threshold behaviour can be observed of the light output as a function of generation rate G, together with spatially directed emission above threshold [109–113]. At low temperatures, the stimulated emission occurs on the first LO-phonon replica. Caused by increasing losses due to population of the LO phonons and the extension of the Urbach tail in absorption to lower photon energies, the stimulated emission goes in the range around (100˙10) K over to the second LO replica. We show in Fig. 11.8a the light output as a function of the

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Fig. 11.8 The emission intensity LExmLO of the first three LO phonon replica of the free A and B 5 excitons as a function of TPA generation rate G at a lattice temperature of 115 K (a) and the generation rate at threshold as a function of temperature compared with a model calculation (b) According to [82, 83, 109, 110, 113]

TPA generation rate G in this transition region. The threshold behaviour is clearly visible for the first two LO-phonon replica. The densities at threshold resulting from G  2  1026 cm3 s1 with a lifetime of about 0:2  109 s (see Chap. 12) is with 4  1016 cm3 at low temperatures still in the intermediate density regime. In Fig. 11.8b we show for the LO phonon replica the calculated temperature dependence of the threshold density for fixed resonator losses [109, 110]. The steep increase around 100 K is caused by the onset of reabsorption effects mentioned above. In contrast to theory, the experimental data for the generation rate at threshold Gth show first a decrease above 50 K, because excitons bound in BEC are increasingly thermally released from their centres and form free excitons (see Sects. 6.1.1 and 6.5) and then an increase, which is less pronounced in experiment than in theory, because the stimulated emission goes over to the second LO phonon replica where reabsorption is less. If the (diffraction-) losses are higher, for example in thin excited layers, the stimulated emission of the X–mLO process is less favoured. Instead one can observe at temperatures below 100 K the stimulated emission from the P2 and P1 bands, i.e. X–X scattering as shown in Fig. 11.9, which is for 10 K actually an extension of Fig. 11.5 to higher excitation densities. This process has been never observed in bulk samples as a laser process at temperatures above 100 K as mentioned earlier. We come back to frequent recent claims of stimulated emission due to the X–X process at RT and above in connection with the stimulated emission from an EHP below.

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3.35

Photon energy (eV) 3.2 3.3 3.25 ZnO 10 K

Photon energy (eV) 3.35 3.3 3.25 3.2

40 KeV

ZnO 60 K

J =3.5 A/cm2

J =2.5 A/cm2

P

Relative Emission Intensity

Relative Emission Intensity

40 KeV

J = 1.5 A /cm2

P Ex-LO Ig-LO

J =0.4 A /cm2 Ex-2LO I -2LO g

Ig

3700

Ig-LO Ig-2LO

ExLO

J =0.4 A/cm2

n =2 n=∞

P-LO

3750 3800 3850 Wavelength (Å)

3700

3750 3800 3850 Wavelength (Å)

3900

Fig. 11.9 Spontaneous and stimulated emission of the P2 and P1 bands at 10 K and 60 K. See also Fig. 11.5. According to [85]

Some reports on optical gain due to the recombination of excitonic molecules (Dbiexcitons) can be found in [59–65,77,96–98,117,118]. Since the binding energy b is about 15 meV in bulk and around 20 meV to 30 meV in of the biexciton Exx quantum wells, the radiative decay of biexcitons is hardly an efficient gain process at RT because both the homogeneous broadening and the thermal energy exceed at b : RT Exx When a substantial fraction of the excitons are ionized or if there are electrons from (un-) intentional doping, the X–el process takes over among others due to the larger scattering cross section of the dipole–monopole scattering compared with dipole–dipole scattering. As mentioned earlier, the emission maximum of this process shifts faster to lower energies than the band gap does and this is even more so for stimulated emission. Other excitonic processes discussed for stimulated emission in ZnO are processes involving bound exciton complexes (BEC) like the stimulated emission out of the acoustic phonon sideband or due to inelastic scattering processes between BEC and free carriers. These processes are spectrally degenerate with the biexcitonic M band

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and are again limited to lower temperature because of the relatively low binding energies of BEC [42, 45, 46, 59–65, 82, 83]. It should be noted that at higher temperatures (above, e.g. 80 K) usually several gain processes may contribute in the same spectral range (see Fig. 11.5) so that an identification based alone on the spectral position may be frequently debatable. At densities around the Mott density nM , the excitons cease to exist as individual quasi particles as mentioned earlier and the new collective phase of an EHP is formed accompanied with the disappearance of excitonic features from the optical spectra, for example from the reflection. See Fig. 6.10. However, it should be remembered that even in an EHP there is some remainder of the Coulomb correlation between electrons and holes leading especially for photon energies around the chemical potential of the electron–hole pair system .np ; Tp / (see below) to an enhancement of the optical transition matrix element and possibly to a peak (e.g.) in luminescence or absorption. See, for example [42, 46, 49, 50]. This feature and related phenomena are known under names such as excitonic enhancement, Fermi edge singularity or Mahan exciton. Optical gain due to the direct band-to-band transition in an EHP occurs at electron–hole pair densities npg at which the chemical potential of the electron–hole pair system .np ; Tp / (the energetic difference of the quasi Fermi levels describing the distribution of electrons and holes in their respective bands) is larger than the reduced band gap Eg0 .np / that is if the population of carriers is degenerate .npg ; TP / Eg0 .npg / with .np ; Tp / D EFe .np ; TP /  EFh .np ; TP /

(11.8)

At low temperatures, nM and npg are similar. If an EHP is created, there is also gain due to band-to-band recombination. At higher temperatures, npg may be considerably larger than nM . The reason is the fact that nM depends only weekly on temperature, npg and .np ; T / in contrast strongly, see Fig. 11.6. We show in Fig. 11.10 some EHP gain spectra at lattice temperatures around 10 K measured by the pump-and-probe beam technique on a platelet type sample (b) and by variation of the excitation stripe length for an epitaxial layer (a) and a bulk sample (c). For these techniques see [42]. The spectra in Fig. 11.10c are fitted with a model assuming recombination of the electron–hole pairs without k-conservation or with a sum of such spectra (Fig. 11.10b). This was the state of the art at that time [47, 48]. Now, we know that a fit based on k-conservation but including Coulomb enhancement, which is especially important around .np ;Tp / and final state damping (or Fermi sea shake up which includes the emission of plasmons) is physically more adequate for direct gap semiconductors [46, 49, 50]. The gain starts at the lowest excitation with a small peak in the M- or P-band region and then broadens rapidly stretching from 3.34 eV down to 3.20 eV at the highest excitation and involving values of np reaching 1019 cm3 [47, 48, 90]. This shows among others that no liquid like EHL state is reached because of the short electron hole pair lifetime, though the temperature is well below a possible critical temperature for this first-order phase transition, as stated in [47, 48].

290 2

4600 kW/cm 2 2600 kW/cm 2 1400 kW/cm 2 825 kW/cm 2 570 kW/cm 2 325 kW/cm

250 200

gain (cm–1)

c

300 T=10K

1

400 2

100

0 3.20 3.22 3.24 3.26 3.28 3.30 3.32 3.34 Photon energy (eV)

Zn0

Optical gain (103cm–1)

Zn0

150

50

b

600

6

E c

Optical gain (cm–1)

a

C. Klingshirn

200 3

0

4 2 0

3.36

–2 3.36

3.34 3.32 Photon energy (eV)

3.30

3.34 3.32 3.30 Photon energy (eV)

Fig. 11.10 Spectra of the optical amplification of an epitaxial ZnO layer (a) and for a platelet type and a bulk sample (b, c) at a bath temperature T around 10 K and in (a, c) for increasing excitation intensity. According to [46–48, 55, 90]

The maximum gain values gmax could be in principle as high as the band-toband absorption coefficients (without excitonic contributions, i.e. gmax  104 cm1 /. Actually, the experimental values do generally not much exceed 103 cm1 . This is due to the facts that some of the light “leaks out” of the epilayers into the substrate and/or that the EHP does not homogenously fill the excited volume as discussed in [42, 47, 48, 90] for direct gap semiconductors. The band gap renormalization (BGR) Eg D Eg .np D 0/  Eg0 .np / can be deduced from the gain spectra, however, only using well developed theoretical models for the shape of the spectra, which include the excitonic enhancement, final state damping (Fermi sea shake-up) including coupling to plasmons and LO phonons (or plasmon-phonon mixed state quanta, see Sect. 2.5) and the valence band structure [42, 46, 49, 50]. One of the consequences of such a line shape fit is that the high energy edge of the gain spectrum (i.e. the transition from gain to absorption) is still identical with .np; T /, but the low energy edge of the gain extends below Eg0 .np /. The value of .np; T / for the broadest gain spectrum in Fig. 11.10a is consequently around 3.3 4eV, the value of Eg0 .np / is at np of a few 1019 cm3 in the upmost spectrum of Fig. 11.10a around 3.24 eV resulting in a value of Eg of approximately 190 meV in agreement with Fig. 11.7. In [119] Eg has been deduced from luminescence spectra. But since Eg0 .np / has been identified with the low energy end of these spectra, the values of Eg have been overestimated resulting e.g. for np D 1019 cm3 in Eg in 300 meV. The fact that Eg .np / is overestimated in [119] becomes also clear from the too small value of the Mott density nM D 1015 cm3 ,

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which would follow from these data and which results actually from the condition that Eg equals the exciton binding energy, that is Exb .np / is zero. As can be seen from the inspection of Fig. 11.7 and as stated earlier, there is at RT a significant difference between nM .2  1017 cm3 / and npg ( 3  1018 cm3 /. On the one hand, this means that gain due to an inverted direct band-to-band recombination in an EHP will occur at RT only at the highest densities (approaching the damage threshold of the sample). On the other hand, stimulated emission has been observed independently by many different authors at RT and even above in the density regime roughly between 1017 cm3 and 1018 cm3 . The frequently repeated claim of inelastic X–X scattering with low threshold at RT (see, e.g. [120–125] and references therein) does not seam to be justified at RT, though being well established to low temperatures, because Fig. 11.7 shows that the exciton is gone at RT at these densities. Consequently, alternative explanations had to be put forward in [55, 86, 87] like inelastic scattering between carriers in a Coulomb correlated EHP (in analogy to the X–el process) or recombination of an electron–hole pair in such an EHP under emission of one or two LO-phonon (-plasmon mixed state) quanta. The data in Fig. 11.11 show the temperature dependences of the free A and B5 exciton resonances and of various emission maxima extending the older data from Fig. 11.6 to

Fig. 11.11 The temperature dependence of the free A and B5 exciton resonances and of various emission maxima for temperatures up to 550 K including data from various authors listed in [120– 126]. Compare with Figs. 6.15d and 11.6. According to [55, 86, 87, 116, 126, 127]

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higher temperatures by including data from various authors. These data support the above assignment: At densities np between some 1017 and 1018 cm3 the reduced gap coincides with the exciton energy at low densities as shown in Fig. 11.7. The data from [126] shown in Fig. 11.11 by open and full stars extrapolate the temperature dependence of the X–2LO and of the X–el processes from lower temperatures beautifully up to 550 K. The continuous transition from excitonic processes to an EHP with increasing density means in this context that the inelastic scattering between an exciton and an electron (the X–el process discussed above) goes continuously over to a scattering process between a still Coulomb correlated e–h pair and another electron in a not yet inverted (or degenerate) EHP or that the X–mLO emission goes over to a process where again an e–h pair in an EHP recombines under emission of a photon and one or two LO-phonons or more precisely phonon–plasmon mixed state quanta, see Sect. 2.5. For more details of this approach see [55, 86, 87]. Unfortunately, these aspects have been completely missed in the recent review [218]. There only the concept of lasing due to inelastic exciton–exciton scattering at and above RT is presented without any critical comments. An over interpretation of the data in the other direction has been given in [128] in the sense that EHP recombination has been claimed at densities below the Mott density. Stimulated emission from a ZnO platelet type sample has been claimed at 2 K and at pump powers of 4 W/cm2 only. The only argument in favour of lasing was the appearance of modes. However, such modes can be also seen in spontaneous emission [129, 130]. For the gain process, the recombination in a degenerate EHP has been suggested, but the calculated density is with 1:4  1017 cm3 , which was necessary to explain the observed width of the emission band, in this case well below the Mott density at low temperatures. A lifetime T1 of the e–h pairs of microseconds had to be assumed to model with the low pump power even this value. This value of T1 is order of magnitude off as shown in Chap. 12, even if shallow donor states are involved as suggested in [128] to overcome the lifetime problem. The final claim in [128] ‘. . . that this is the first report of lasing in ZnO by optical pumping’ is clearly wrong, bearing in mind [82, 83, 100–113] and the references given therein. A few words on another claim of stimulated emission under optical pumping with power densities as low as 10 W m2 [131]. Also here the density obtained with reasonable values for lifetime (1 ns, see below) and excitation depth (1 m) determined essentially by diffusion in a density np D 51014 cm3 is too low to produce significant X–X scattering. Slopes above one [131] can be explained without stimulated emission by simple (e.g. quadratic) recombination kinetics [42] as well. The gain processes are in bulk samples, in epitaxial layers, nano rods (see Sect. 11.3.3) and nano crystals essentially the same. In epilayers or nano rods and  crystals, the optical pump power at threshold is partly lower than in bulk samples if there is no fast surface or interface recombination, because the diffusion of the carriers is limited by the geometry. Tuneable laser emission under TPA from prism shaped ZnO samples serving simultaneously as dispersive element in a wavelength selective resonator has been reported in [31].

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11.3.2 Quantum Wells and Superlattices In single and multiple QW or in superlattices (SL), the exciton and biexciton binding energies are (usually only moderately) enhanced if the well thickness lz becomes comparable to the diameter of the exciton, (i.e.) for lz  5 nm. The gain process will be in most cases the recombination in an EHP, especially at RT or above. Inelastic X–X scattering may be of importance at lower temperatures [132], but in most cases not at RT and above, since the value of Exb increases in most wells only moderately and the above arguments remain valid [91,92]. Stimulated emission out of localized states may play a role in very narrow wells at lower temperatures, since well width fluctuations result in narrower wells in stronger potential fluctuations than in wider ones, or in structures where the well itself is an alloy [99, 119]. For some reports on stimulated emission in (M-)QW see, e.g. [99, 120–125, 132–137]. We show as an example in Fig. 11.12 the stimulated emission of Cd1-x Znx O MQW between ZnO barriers under optical pumping with 20 ns pulses being absorbed in the ZnO barrier and also in the wells. In the upper panel, one sees the stimulated emission at 5 K for samples with various well widths grown on sapphire substrates (1–4) and on a ZnO

a Zn1-xCdxO/ZnO, MQWs T = 5K (5) (4)

dW (Xn)

1

0.10

2.6 nm, (x7)

2

0.10

3.2 nm, (x7)

3

0.15

2.4 nm, (x5)

4

0.17

2.0 nm, (x10)

5

0.16

2.7 nm, (x10)

PL intensity [arb.units]

XCd

(3) (2) (1)

Iexc = 1 MW/cm2

PL intensity [arb.units]

Lasing threshold [kW/cm2]

b

290 K 5 K

350 300 250 200 150 100 50 0 0 50 100 150 200 250 300 T [K]

2.3

2.4

2.5

2.6

2.7

2.8

2.9

Photon energy [eV]

Fig. 11.12 Normalized stimulated emission from Cd1x Znx O QW under optical excitation. According to [99]

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substrate (5) and in the lower one the variation of the emission of structure (2) from 5 to 290 K. The inset gives the temperature dependence of the optical pump power at laser threshold. As mentioned already such structures are meant to close the gap in the green spectral range of laser diodes.

11.3.3 Nano Rods and Their Cavity Modes We mentioned in Sect. 6.1 that the usual nano rods of ZnO do not show any quantization effects for excitons. Consequently, the gain process should be the same as in bulk samples, but the pronounced one-dimensional wave-guiding properties could bring some differences. Therefore, we address stimulated emission from nano rods separately in this subsection. Lasing from ensembles of nano rods has been reported several times preferentially at RT. See, e.g. [138–196] for stimulated emission in various types of nano structures. This finding raises the question if the stimulated emission of the ensemble is just the sum of the contributions of the individual rods, or if it is a cooperative effect in the sense of random lasing (discussed below in Sect. 11.3.4 for ZnO powders). The answer could come from the investigation of single rods [152–160]. Therefore, we show below preferentially such results. The other question is, if the laser processes are the same as in bulk and epilayers. There the answer is yes, but in some cases emission processes are suppressed by the mode structure of the rods [76, 157–162], presented already in Sect. 6.4.2. In the X–X process, one exciton is scattered on to the photon like part of the polariton dispersion. If there is no cavity mode to be reached under energy and momentum conservation for the outgoing photon-like polariton, this emission process may be suppressed in stimulated emission. This is especially true in rather narrow and not too long rods where the mode spacing my reach several tens of meV, and indeed the P2 or P1 bands failed to show in such samples laser emission in contrast to thicker samples with narrower mode spacing [76, 157–159]. We start a survey over some experimental results in Fig. 11.13 with data obtained at 10 K with a single rod prepared on a Si support (Fig. 11.13b). The excitation is under quasi stationary conditions with the third harmonic of an Nd-YAG laser (Texc D 5 ns; „!exc D 3:49 eV). A well developed mode structure can be seen, which starts in the M – band region (see Sect. 11.2.1) and extends at the highest pump power from 3.34 eV down to 3.20 eV corresponding to the width of the gain spectrum of an EHP with a density around 1019 cm3 . Compare with Fig. 11.10. The preferential emission of the various laser modes through the end facets of the rod is documented in Fig. 11.13c. Stimulated emission can be observed up to RT as shown in Fig. 11.14a. In Fig. 11.14a lasing spectra are shown for temperatures T between 9 and 290 K. For the three spectra at lower T , the pump power has been kept constant, for 290 K

11

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295

Fig. 11.13 Stimulated emission spectra (a) of a single ZnO rod shown in (b) at 10 K with increasing excitation intensity (Texc D 5 ns; „!exc D 3:49 eV) while (c) shows the preferential emission from the end facets of the rod. According to [160–162]

it had to be increased to stay above the threshold. In Fig. 11.14b, the temperature dependence of the pump power at laser threshold is shown defined by the appearance of the first laser mode. The curve starts around 30 kW=cm2 at 9 K and reaches 600 kW=cm2 at RT. These data can be fitted by an exponential with a characteristic temperature To D 70 K. Figure 11.14c shows finally the spectral spread of the laser modes in the pump power range of Fig. 11.14a. The gain region can be further shifted down with increasing pump power. Now we present an example using pulsed excitation with 150 fs pulses from the second harmonic of a TiSa laser tuned to 3.49 eV for comparison with the ns pulsed excitation above. Figure 11.15 shows laser emission of several modes at 11 K. In this case, the nano rod sample was still standing upright on the GaN=Al2 O3 substrate, and a single rod is pumped through the top end facet. The gain is again due to the recombination in an EHP. There are clear signatures of mode competition as can be seen in the inset. For the dynamics of the emission see Sect. 12.3 below. The nano-rods might form (once electrical pumping via a p–n junction becomes possible) a highly interesting version of nano lasers for application. See Chap. 13. A few more references on lasing in nano rods and related structures like fourlings also known as tetrapods are found in [171–196].

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Fig. 11.14 Lasing spectra of two rods excited simultaneously and prepared on a Si chip (a), the temperature dependence of the pump power at laser threshold (b) and the width over which the stimulated modes extend (c). According to [93, 94, 160–162]

11.3.4 Quantum Dots and Random Lasing The interest in the stimulated or laser emission of ZnO nano crystallites is not so much the blue-shift resulting from quantization, since this effect is much less pronounced compared (e.g.) with CdS(e) [42] because of the small exciton Bohr radius of ZnO and the relatively large translational exciton mass. The main interest is lasing in random media [163–200] (short ‘random lasing’) and connected thus with phenomena of slow light or the storage of light [163, 164]. Usually one expects that amplified spontaneous emission (ASE) can occur in every medium with optical gain resulting, for example from population inversion or parametric effects such as four wave mixing. For the appearance of laser modes one anticipates, however, the contribution of a cavity. In the case of random lasing, the latter contribution is replaced by elastic light scattering in a random medium (in our case ZnO powder, [42, 163–170]) partly combined with the effect of enhanced backscattering or weak localization. If the ZnO crystallites (e.g.) of a ZnO powder are in the size range of a few ten to hundreds of nm, the optical pump light excites and inverts an ensemble containing many hundred or thousand nano crystallites. The scattering at the crystallites keeps the light longer in the inverted volume compared with a single straight passage increasing thus the effect of ASE. Furthermore, enhanced backscattering may occur, keeping light on a ‘closed loop’, which replaces

11

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297

Fig. 11.15 Lasing spectra of a single nano rod exited with 150 fs-pulses at 3.49 eV. For higher excitation densities the spectral gain region shifts to the red. This causes the appearance of new lasing modes on the low energy side, while modes on the high energy side loose intensity in the mode competition as shown in the insert. According to [93, 94, 160–162]

the cavity modes. Random lasing in ZnO powders has been reported several times [163–200]. Most of the investigations concentrate on room temperature (RT). We show in Fig. 11.16a single pulse emission spectra of a ZnO powder (Emprove, from Merck – average particle size 260 nm) at RT excited with 5 ns pulses at 3.49 eV, that is, with the third harmonic of an Nd YAG laser, for an excitation intensity Iexc slightly above the threshold for random lasing. In some cases, random lasing occurs, in others it does not. The fraction of nominally equal excitation pulses that result at the same spot of the sample in random lasing increases with Iexc . This fraction is plotted in Fig. 11.16b and defines clearly a threshold. If no random lasing occurs one observes the well known emission band centred on 3.2 eV with a FWHM around 100 meV. See Fig. 6.15 for comparison. (Sometimes much broader emission features are reported in this spectral range casting some doubts on the quality of the used powder.) If random lasing occurs, narrow spikes are observed, which correspond to laser modes forming in the random medium along the ideas given above. Small fluctuations in the spatial and temporal profile of the pump laser pulse are responsible if and which random modes come above threshold. The randomness of the lasing is further demonstrated by Fig. 11.17. A relatively big area of 1 mm in diameter of a pressed ZnO powder sample has been excited

298

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Fig. 11.16 Single shot spectra of a ZnO powder at RT for an excitation intensity close to the random lasing threshold (a) and the probability that stimulated emission occurs as a function of the excitation intensity (b). According to [197–200]

again with 5 ns pulses at 3.49 eV, and the excited area has been photographed in the near edge spectral range. On top of a continuous background hot spots appear, which are due to the emission from random laser modes. The spatial emission pattern fluctuates from shot to shot for nominally equal excitation conditions on the same sample and on the same excitation spot, but some features seam to occur more frequently like the bright spot a third from the centre towards the upper left corner or the bright horizontal feature slightly below the middle line. In Fig. 11.18 we show emission spectra for various temperatures. At low temperatures the threshold for random lasing is rather low and it is sometimes difficult to stay with a reasonable signal-to-noise ratio for pulsed excitation below threshold. The reason for this fact (which is also important for thin epilayers) is that diffusion of the electron–hole pairs out of the directly excited volume is suppressed by the grains of the powder. If there is no fast surface recombination, an excitation intensity of 10 kW=cm3 may result with reasonable values of absorption coefficient (˛  105 cm1 / and lifetime (T1  0:3 ns) under quasi stationary conditions already in electron–hole pair densities above 1018 cm3 , enough to create at low temperatures an inverted EHP in the nano crystals. By a decrease of the size of the powder sample to values in the 10 m range, the spectral mode spacing could be increased, that is, their density per spectral interval decreased. Under these conditions it was possible to reproducibly observe modes and to measure the spatial extension of these random laser modes. Modes extending

11

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299

Fig. 11.17 Spatial, single shot photographs of the emission from a relatively large (diameter  1 mm) excited spot under single shot excitation. According to [197–200]

over the whole sample and strongly confined ones extending only over a few ten nano crystallites were found to coexist in the same sample [197–200]. For a theoretical modelling of both cases see [201, 202] and references therein. In Fig. 11.19 we show an example. A small hole has been prepared in a GaAs chip with lateral dimensions in the range of 15 m and a depth of a few m by a focussed ion beam (FIB). This hole has been filled with ZnO powder with an average crystallite size comparable to the emission wavelength. The figure shows colour coded the spectrally integrated and spatially resolved emission intensity (a), the spectrally resolved emission from the stripe marked by the two vertical lines showing some laser modes (b), and finally the vertical extension of the modes in (c). It is obvious that modes extending over the whole height of the sample coexist with other ones confined to a much smaller volume. It has been also verified (not shown here) that the horizontal extension of the strongly confined modes is similar as in the vertical direction. The observation of the coexistence of more extended and strongly localized laser modes (extending over a small number of powder grains only) has solved a controversy in literature [197–202]. Some indications on random lasing in disordered nano rod ensembles have been published recently by Ursaki et al. [195, 196].

11.3.5 Cavity Modes, Photonic Crystals and Polariton Lasers The term ‘polariton laser’ is enigmatic and not well defined. The quanta of every light field propagating in matter with a refractive index different from unity consist

300

C. Klingshirn

Fig. 11.18 Emission spectra of a ZnO powder sample for various temperatures and excitation fluences, increasing from 0.5 to 2:5 MW=cm2 . According to [197–200]

of a mixture of an electromagnetic wave and a polarization wave. Consequently, these quanta are not pure photons but polaritons [42] and – as an extreme interpretation – every laser emission from solid, liquid or even gas could thus be called ‘polariton laser’ including e.g. the inelastic exciton–exciton (or better polariton–polariton)

11

Nonlinear Optics, High Density Effects and Stimulated Emission 1

b PL Intensity (arb.units)

a

301 2

horizontal cut

c

Integrated PL-Intensity (norm.) 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

0

0.2

0.4

0.6

0.8

1

PL-Intensity (norm.) 3.15

3.20

3.25

Photon-Energy (eV)

Fig. 11.19 Spatially and spectrally resolved random laser modes in a ZnO powder sample. From [197–200]

scattering introduced above. Generally, the term is used to describe stimulated and/or laser emission from (micro-) cavities containing one or a few quantum wells (QW) or a thin semiconductor film, in which the exciton states from the QW and the photon dispersion from the cavity form a cavity polariton in the case of strong coupling (see Sect. 6.4.4 and references given there) and stimulated emission may occur from some state on this polariton dispersion [42]. In the other extreme, some authors tend to almost identify polariton lasing with Bose–Einstein condensation (BEC) of cavity exciton polaritons [203–209]. To the best of the knowledge of the author, no experimental results exist presently (December 2008) to verify the theoretical concepts of [203–209] in ZnO-based structures at RT. Although the longitudinaltransverse splitting of the B5 and of the C1 excitons are underestimated by a factor of two in [201, 202] (see the comments in Sect. 6.1.2 with Fig. 6.8 on how to fit reflection spectra), this approach is highly questionable, since a BEC is a transition occurring in thermodynamic equilibrium if either the density n of Bosons is increased at constant temperature T above a critical density nc or the temperature of a Bose gas is lowered at constant n below a critical temperature Tc . In contrast, frequently no thermal equilibrium exists among the cavity polaritons under laser conditions. Furthermore, the claim of RT BEC [203–205] does not take into account the strong homogeneous broadening occurring already at low densities at RT. See in this context Sect. 6.4.4. However, considerable progress has been made concerning BEC of cavity polaritons in other II–VI compounds as detailed recently in [210– 212] and references given there, since thermodynamic equilibrium conditions have been obtained in the ground state of the cavity polaritons and a linear dispersion relation has been observed, which is characteristic for a condensate.

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In bulk ZnO ‘polariton lasing’ on the photon like part of the lower exciton polariton branch (LPB) is known since decades as mentioned earlier. All the excitonic processes discussed above (e.g.) X–m LO or inelastic X–X scattering, contribute to optical gain, stimulated emission and lasing on this part of the LPB. In contrast, lasing on the exciton-like part of the polariton dispersion is not possible in bulk samples. The absorption coefficient exceeds in this region 105 cm1 and the density necessary to overcome these losses is beyond the Mott density in an EHP. Because of the short dephasing times of the electron–hole pair states in an EHP, (e.g.) due to final state damping, the aspect has to be carefully considered whether one can be in the presence of an EHP still in the strong coupling regime or not. In principle one can define a polariton dispersion also in the presence of an (degenerate or inverted) EHP with density np via c 2 k 2 =! 2 D ".np ; !/ (11.9) where ".np ; !/ is the dielectric function in the presence of the EHP, and then one could also define ‘polariton lasing’ in the range between .np Tp / and roughly the reduced gap Eg0 .np /. See the introduction to Sect. 11.3. Note that the polariton dispersion following from (11.9) must not be called plasmon polariton, because this term is already used otherwise [42]. The interaction of cavity modes in laser emission has been treated in [213]. In contrast to the open situation described earlier, clear laser emission from the whispering gallery modes (WGM) has been observed recently at 10 K in [214]. It will be interesting to see how these laser modes develop with increasing temperature. In [217] a preliminary and partly controversal discussion is given on the dispersion and lasing of cavity - and WGM polaritons. Exciting new results can be expected in this field in the future.

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Chapter 12

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Abstract The purpose of this chapter is to present the results of the dynamics of exciton (polariton)s or more generally of electron–hole pairs. For a recent review of this topic concentrating on quantum wells, see Davies and Jagadish (Laser Photon. Rev. 3(1), 1(2008)). We neither consider the dynamics of carriers, for example, their relaxation time entering in Hall mobility or electrical conductivity, nor the dynamics of phonons or spins, respectively. We give here only a very small selection of references to these topics (Baxter and Schmuttenmaer, J. Phys. Chem. B, 110:25229, 2006; Queiroz et al. Superlattice Microstruct. 42:270, 2007; Niehaus and Schwarz, Superlattice Microstruct. 42:299, 2007; Lee et al., J. Appl. Phys. 93:4939, 2003; A. K Azad, J. Han, W. Zhang, Appl. Phys. Lett. 88:021103, 2006; Janssen et al., QELS 2008 IEEE 2; D. Lagarde et al., Phys. Stat. Sol. C 4:472, 2007; S. Gosh et al., Appl. Phys. Lett. 86:232507, 2005; W. K. Liu et al. Phys. Rev. Lett. 98:186804, 2007). The main characteristic time constants relevant to optical properties close to the fundamental absorption edge are the dephasing time T2 , (i.e. the time after which the polarization amplitude of the optically excited electron–hole pair loses the coherence with the driving light field), the intra band or inter sub band relaxation times T3 (i.e. the time it takes for the electron–hole pairs to relax from their initial state of excitation to a certain other state e.g. to a thermal distribution with a temperature equal to or possibly still above lattice temperature) and finally the lifetime T1 (i.e. the time until the electron–hole pairs recombine). The characteristic time constants T2 and T1 are also known as transverse and longitudinal relaxation times, respectively. Their inverses are the corresponding rate constants. T2 is inversely proportional to the homogeneous width  , and T1 includes both the radiative and the generally dominating non-radiative recombination (Hauser et al., Appl. Phys. Lett. 92:211105, 2008). For this point, recall Figs. 6.16 and 6.33. Since the polarisation amplitude is gone in any case after the recombination process, there is an upper limit for T2 given by T2  2 T1 . The factor of two comes from the fact that T2 describes

C. Klingshirn Institut f¨ur Angewandte Physik, Karlsruher Institut f¨ur Technologie KIT, Karlsruhe, Germany e-mail: [email protected]

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the decay of an amplitude and T1 the decay of a population, which is proportional to the amplitude squared. Sometimes T2 is subdivided in a term due to recombination described by T1 and another called ‘pure dephasing’ called T2 with the relation 1=T2 D 1=2 T1 C 1=T2 . The quantity T2 can considerably exceed 2 T1 . In the part on relaxation processes that is on processes contributing to T3 , we give also examples for the capture of excitons into bound, localized, or deep states. For more details on dynamics in semiconductors in general see for example, the (text-) books [Klingshirn, Semiconductor Optics, 3rd edn. (Springer, Berlin, 2006); Haug and Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 4th edn. (World Scientific, Singapore, 2004); Haug and Jauho, Quantum Kinetics in Transport and Optics of Semiconductors, Springer Series in Solid State Sciences vol. 123 (Springer, Berlin, 1996); J. Shah, Ultrafast Spectroscopy of Semiconductors and of Semiconductor Nanostructures, Springer Series in Solid State Sciences vol. 115 (Springer, Berlin, 1996); Schafer and Wegener, Semiconductor Optics and Transport Phenomena (Springer, Berlin, 2002)]. We present selected data for free, bound and localized excitons, biexcitons and electron–hole pairs in an EHP and examples for bulk materials, epilayers, quantum wells, nano rods and nano crystals with the restriction that – to the knowledge of the author – data are not available for all these systems, density ranges and temperatures. Therefore, we subdivide the topic below only according to the three time constants T2 , T3 and T1 .

12.1 Dephasing Dynamics Basically, it is impossible to learn from linear optical spectroscopy alone something about dephasing and homogeneous broadening or the difference between homogeneous and inhomogeneous broadening. The width of a spectral feature such as that of an absorption or luminescence band gives only an upper limit of its homogeneous broadening under the assumption that the contribution of inhomogeneous broadening is negligible that is a lower limit of T2 . Some additional information is necessary, which may come from non-linear optics [four wave mixing (FWM), spectral hole burning, etc.] or from other knowledge. Since there are only few data of FWM in ZnO (see later) we start, nevertheless, with T2 values deduced from linear spectroscopy. A short additional comment: the line shape of a homogeneously broadened absorption or luminescence band is in simplest approximation a Lorentzian. See for example Fig. 6.15. The frequently found approach to deconvolute a band of arbitrary shape into various Gaussians lacks therefore the physical justification, though it is mathematically simple. As a first example for T2 measurements, we consider free excitons in bulk samples, remembering that these data are also relevant for good epilayers or nano rods. The low temperature reflection spectra of Fig. 6.8 have been fitted assuming that the damping  is the homogeneous width. The obtained values depend slightly on

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the sample (and on the abc model used, see [1]) but in all cases the value is around 1 meV at low temperatures (T  10 K) for high quality samples corresponding to a T2 of approximately 1 ps. At room temperature, this value increases to 20 meV HWHM or T2 below 100 fs due to scattering with acoustic and optic phonons (see Fig. 6.15, the references given there or [2]) assuming that the free exciton luminescence and absorption features are homogeneously broadened at higher temperatures and that the folding of the line shape of the LO-phonon replica with a Lorentzian gives also the homogeneous width. In [3] the dephasing of excitons in 70-nm thick nano rods has been investigated and very similar data have been deduced from the luminescence width. The low temperature value of 5 meV FWHM is, however, possibly overestimated by the improper inclusion of the splitting between lower and upper polariton branches (see Fig. 6.14), but the 230 K value of 70 meV FWHM is only slightly above the value of Fig. 6.15 of 40 meV. Spin triplet excitons like the A1 and 2 have at T  4 K in the linear luminescence or absorption spectra FWHM values around 0.2 meV ([4, 5] and Fig. 6.13) and necessarily T2 values of at least 5 ps, which is under the assumption that this width is entirely due to homogeneous broadening. Bound and localized excitons are notorious for long dephasing times at low T [1]. Indeed the FWHM of the luminescence of various neutral donor and acceptor bound excitons is below 0.1 meV (see Chap. 7 and [4–7]) resulting in a lower limit of their T2 times above 10 ps. At moderately high temperature, the FWHM value increases quadratically with temperature T due to interaction with, at lower T , primarily acoustic phonons [6, 7], resulting in an analogous decrease of T2 . As stated earlier, these data rely on the a priori knowledge or assumption of homogeneous broadening, which is, however, for the above-mentioned examples generally a rather save one. In contrast to some other materials like GaAs or quantum wells based on this material [1,8–12], there are only some but not too many data from non-linear optics essentially four wave mixing (FWM) for ZnO concerning dephasing. In general, these data agree rather well with the ones given above. We cite here a selection: For an early example see [13] giving response times decreasing from 270 to 160 fs from 4.2 K to RT. In [14] values for the homogeneous broadening  of 0.3 meV have been deduced at 10 K for the free exciton resonance increasing at 70 K to 3 meV. The parameters used for the fit are again similar though not identical to the ones used in the equation shown in the insert of Fig. 6.15 to describe  (T) up to room temperature. The same statement holds for the data in [15, 16]. See Fig. 12.1. The unusual values of the binding energies for B and C excitons stated in [15, 16] and the unlikely high numerical parameters used in [17] to describe the temperature dependence of the homogeneous damping have been discussed already in Chap. 6 and in [18–20]. In [15,16] also the spectral shape of the FWM signal is shown revealing for E ?c a narrow and a broad peak. Their widths coincide with the LT values of the A and B 5 excitons, respectively. For E jjc a signal is observed, which is by three orders of magnitude smaller than the one for E ?c but occurs at the same position and has

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Fig. 12.1 The homogeneous width of excitons and biexcitons in ZnO as a function of temperature (b) as deduced from FWM signals with the indicated polarizations and three different excitation energies a: 3.3685 eV, b: 3.3765 eV and c: 3.3783 eV (a). According to [15, 16]

the same width as the one for the A5 exciton. This signal is considered there as a proof for the normal valence band ordering in ZnO. The author of this chapter cannot follow this argument. The 1 exciton state has very small oscillator strength and homogeneous width (see above and Figs. 6.13 and 6.14 or [20] and [21]) independent if it results from the A or B valence band. Therefore, a very narrow feature should result in FWM in contrast to the experimental findings. On the other hand, the orientation in Fig. 1b in [15, 16] was not a pure E jjc orientation as stated there and the small signal can be attributed to the small component E ?c. Relatively short decay times of the FWM signal reported in [21] are partly not compatible with the data given above and might be influenced by the fact that spatial overlap of the two pulses necessary for FWM experiments is not trivial in bulk samples, if these two laser pulses producing the two propagating polariton wave packets impinge on the sample with some delay [1]. In [22] FWM experiments have been carried out on the C1 exciton at 10 K. The decay time of the signal is around 200 fs indicating for this resonance slightly shorter T2 values than for the A and B 5 states given above. The reason might be the fact that the C1 exciton is situated in the (quasi-)continuum states of A and B excitons. Concerning the statements in [22] on the binding energy of a biexciton containing two C excitons see the discussion in Sect. 11.2.1. In a QW of 3-nm width [23] found at RT dephasing times of (280 ˙ 40) fs slightly longer than for bulk samples. The difference might come from the reduced phase space of excitons in the QW system or from some residual influence of localization from well width fluctuations and/or alloying. Both effects tend to result in localization and in longer dephasing times as mentioned earlier. Biexciton states involving various combinations of A and B holes (see Sect. 11.2.1) have been observed in FWM in [24] for negative delays showing characteristic beat frequencies and signatures in the spectra. The binding energies correspond for the AA and AB biexcitons essentially to the ones given in

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Sect. 11.2.1. Their homogeneous width increases with temperature faster than for excitons and linearly as seen in Fig. 12.1. The experimental data in [23] provide hints to a biexciton dephasing time of 100 fs in quantum wells at RT. The dephasing times of electron–hole pairs in an EHP depends strongly on their density, temperature and additionally on the energetic distance to the chemical potential and the (reduced) band edges [1]. To the knowledge of the author no direct measurements are available for ZnO, but these dephasing times enter in the calculation and fit to the experimentally observed luminescence and gain spectra [8–11, 25] and are most probably situated in the (sub-) 100 fs regime.

12.2 Relaxation Dynamics In this subchapter, we consider the relaxation processes of electron–hole pairs in the band(s). Similarly to the case of dephasing not too many papers exist. The information is in most cases deduced from the temporal evolution of luminescence spectra, for example from a spectral shift or a narrowing indicating relaxation or cooling but also recombination treated in Sect. 12.3. See e.g. [28, 125, 127] If an electron–hole pair is created with an excess energy above the free exciton larger than the one of a LO-phonon, one expects in the strongly ionic material ZnO a fast relaxation by the emission of LO-phonons (typical timescales around or even below 1 ps [26–28]) followed by a slower relaxation or thermalisation via emission of acoustic phonons [1]. In [29] indeed a delay of a few ps has been observed in the appearance of an emission band around 3.19 eV at RT under 100 fs pulsed excitation with an excess energy of about 1.35 eV. This delay is attributed just to the relaxation from the states high in the bands (or for lower densities, high in the excitonic ionisation continuum) to the EHP (or exciton-) ground state with the argument that the delay is absent, if the excitons are directly excited resonantly. This argument remains essentially valid, even if one doubts the interpretation of this band as P-band that is inelastic X–X scattering, since the claimed densities of 2 1019 cm3 are well above the Mott density in ZnO as can be seen from Fig. 11.7. In Fig. 12.2 we show data from [30–32] reflecting the relaxation between the various A5 polariton branches at low temperature after excitation with 100 fs pulses. Compare with the steady state data of Fig. 6.14. The luminescence from the upper polariton branch (UPB) has short rise and decay times, while both times are longer for the lower branch (LPB). The slower rise and partly also the longer decay time of the emission from the LPB have been attributed in [30–32] to a feeding process that is to the relaxation of (exciton-like) polaritons or of longitudinal excitons from the UPB to the LPB, presumably under emission of acoustic phonons. The time delay between the two maxima of about 40 ps in Fig. 6.14 hints to a low temperature relaxation time between the upper and lower (exciton) polariton branches of this order of magnitude. We come back to the values of the life time T1 resulting from these data in the next section.

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Fig. 12.2 Unpolarized emission spectra for k perpendicular to c for different time delays after a short, non-resonant excitation pulse (a) and the rise and decay dynamics of the high and low energy peaks (b). According to [30]

There are a few examples of pump-and-probe beam spectroscopy near the band edge [53, 126]. In [128] another approach has been used, the probing of the sample in the THz regime after pulsed excitation in the band-to-band transition or exciton regions. As discussed already in Sect. 11.2.2 the (Mott) density is in some cases over estimated. The capture time of free excitons into bound exciton states (BEC) – and their decay, see below – has been investigated in [33] at 1.8 K and it has been found that the capture time increases with increasing binding (or localization-) energy of the complex that is with the energy, which has to be dissipated by emission of acoustic phonons. The conclusions drawn from these findings might be too ‘sharp’ since the generally accepted value of the translational exciton mass is smaller than the 1:06m0 claimed there (see Chaps. 4 and 6), and the agreement of the decay time trend with a model assuming only radiative recombination lacks the proof that non-radiative processes do not give a similar trend. The formation sequence of free and bound (bi-)excitons has been investigated at 10 K in [34] from an analysis of the rise and decay times of various luminescence bands and the following sequence has been established: free excitons are formed first which then partly relax to BEC or form at intermediate densities excitonic molecules. Bound biexcitons emerge from the capture of a free exciton by a BEC. The emission band of the decay of such a bound biexciton is claimed to be situated at 3.353 eV. The problems with this later interpretation are twofold. A biexciton bound to a neutral donor or acceptor contains either three electrons or holes as properly discussed in [35, 36]. Because of the only twofold degeneracy of both A valence and conduction bands, this requires the transfer of one carrier into a higher shell (or a deeper valence band) with a substantial decrease of the binding energy of the complex which might be easily smaller than the 16.4 meV claimed in [34]. On the other hand, the emission around 3.355 eV has been attributed by various authors to quite different processes like the recombination of donor or acceptor bound excitons, the I10 line, to states bound to defects close to the surface. See for example [4,5,37–43].

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The capture rate of excitons from Mg0:12 Zn0:88 O barriers into ZnO quantum wells has been deduced from the dependence of the ratio of barrier to well luminescence as functions of temperature and well width [44]. From the fact that this ratio decreases with increasing temperature a repulsive barrier at the interface has been suggested, which restricts the relaxation of carriers from the barrier into the well. In addition to (or instead of) this explanation, simple localisation effects in the barrier alloy may also play a role. See also [124]. The trapping of carriers in ZnO clusters was investigated by sub ps pump-andprobe experiments [45]. The pump photon energy exciting the carrier pairs in the clusters was 4 eV and the probe at 2 eV, being sensitive to trapped carriers. The signal rise and decay times are faster for larger (6.2-nm diameter) clusters compared with smaller (3.2 nm) ones. Several papers treat the dynamics of an electron–hole plasma (EHP) in thin epitaxial layers and nano rods [26–28, 46–55, 126, 128]. In the context of this subsection, it is important that agreement exists that the formation time of the EHP (i.e. the time it takes that the screening of the Coulomb interaction between the carriers becomes effective) is roughly inversely proportional to the plasmon frequency and thus in all cases mentioned here below experimental resolution (e.g., [26, 27, 48, 49, 126,128]) as expected [1,56,57]. In some cases (e.g., [26,27,49,51,53]) a delay of a few ps has been reported between the excitation pulse and the onset of EHP luminescence if a large excess energy beyond 1 eV is involved. This delay is attributed – as mentioned earlier – to the relaxation of the carriers by LO-phonon emission towards the band extrema. Further cooling is slower by emission of acoustic phonons. Note that elastic scattering processes between carriers or excitons alone may change their distribution function, e.g., from a non-thermal one towards a thermal one – possibly with a temperature well above lattice temperature. However, these elastic scattering processes alone cannot lower the average kinetic energy or the temperature of the carrier system. The next step is a decrease of the carrier density in the EHP due to either recombination, which is actually the topic of the next subsection, or diffusion if the sample geometry permits. This density reduction is accompanied by the recovery of excitonic processes after typically 10 or a few ten ps [48,49,51,54,126,128]. In Fig. 12.3 we show an example for a single nano rod with 300-nm diameter and a length of 1:5 m at 24 K. For epilayers see [28]. The sample has been excited with the second harmonic of a TiSa laser. Immediately after the excitation pulse, one observes the emission from an EHP between 3.38 and 3.35 eV i.e. with relatively low carrier density. Compare to Figs. 11.10 and 12.6. Both width and intensity decay rapidly. After 400 ps only the emission from BEC (called BX in Fig. 12.3a) is left at this spectral position. The excitonic P-band (see Sect. 11.2.1) rises with same delay reaching its maximum after 150 ps. It should be noted that an EHP and excitonic processes may coexist in the spectra since one integrates usually over spatial regions with different densities even in temporally resolved experiments [1]. For the situation above laser threshold see the right panel of Figs. 12.3 or 12.6 below.

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Fig. 12.3 The temporal evolution of the normalized luminescence of a single rod with 100 fs excitation pulses with above band gap energy at 24 K for two different fluences. According to [54]

12.3 Recombination Dynamics In this subsection, we consider the recombination of excited carriers or in other words their lifetime T1 . A rather early guess for the lifetime of BEC at low temperatures of about 10 ns has been given in [6, 7]. This value is well in the range of presently accepted ones for high quality samples at low temperature and at low to moderate electron–hole pair or exciton densities. In contrast to the dephasing and relaxation processes discussed above, there are many results concerning the lifetime, which we cannot mention or cite here all. Most data are deduced from luminescence decay measurements after pulsed optical excitation. See for example for bulk samples [6, 7, 30, 58–71], for epilayers [13, 26, 27,34,35,46–51,68,72–76], for nano rods [41,42,52–54,77–86], for quantum wells [87–91], for alloys [125] and for nano crystals [92–99, 127]. Frequently the authors identify the luminescence decay time with the radiative lifetime. This approach is only correct if quantitative measurements are presented showing that the luminescence yield is close to unity. This point is, however, in most cases, not verified quantitatively. In contrast many samples show values of the luminescence yield around 0.1 at low and 0.01 at room temperature below laser threshold. See Figs 6.16 and 6.33 or [100]. Under these conditions, the luminescence decay is essentially determined by non-radiative processes and/or capture into deep centres described by a non-radiative lifetime Tnr resulting in T1 D Tnr Tr =.Tnr C Tr /:

(12.1)

Another aspect of concern is that in decay measurements a certain quantity like the luminescence intensity should be followed over at least three orders of magnitude to claim a decay time constant, which is to make sure that one has a single exponential decay. In many cases, a variation over one order of magnitude (or even less) is used to claim a single or even a double exponential decay, though such small variations

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can usually equally well be fitted by a stretched exponential [1] or by a power law [125], for example. Indeed a bimolecular recombination process between independent electrons and holes of equal density would result in a t1 dependence. If the dynamics is followed only over a small intensity interval, the value deduced from the data has to be considered rather as an ‘effective decay time’ for this intensity interval. The numbers cited here are in this sense mainly effective values. An alternative possibility is to investigate T1 via the decay dynamics of non-linear optical phenomena (e.g.) in pump-and-probe or laser induced grating spectroscopy, to which the whole population of excited carriers contributes [1]. Examples are found in [26, 27, 49, 50, 53, 126, 128]. In these experiments one is usually in the high density regime. Consequently effective decay times with short components of a few to a few tens of ps are observed. In some other cases, the lifetime is deduced from the dynamics of photoconductivity [101–103] or from anisotropic diffusion in a Dember-effect-like phenomenon [60, 104, 105] resulting also in values of T1 of a few hundred ps. After these rather general remarks and first examples, we present some more selected results: First, we come back to the data of Fig. 12.2 and [30]. At a temperature of 150 K, the free A and B zero phonon exciton luminescence bands show two decay time constants of 100 ps and 2 ns. These time constants have been explained in [30] by various contributions namely the diffusion of the excited excitons or polaritons from the thin excited layer either back to the surface, where they can leave the sample as luminescence quanta with a certain transmission probability [1], or deeper into the sample over distances larger than the escape depth of the zero phonon luminescence. Furthermore, the fact comes into play that only exciton polaritons with small kjj vector within the light cone can contribute to this emission [1]. This fraction is strongly temperature dependent. In contrast, all excitons contribute to the LO-phonon replica (see the analysis with Fig. 6.15). This latter fact explains also that the LO-phonon replica decay is with effective time ‘constants’ around 5 ns more slowly than even the LPB component of the zero phonon line. A further contribution to the slow decay time in the spectral range of the X-mLO bands could come from other recombination processes like surface exciton states or free to bound transitions, which are spectrally almost degenerate and the importance of which increases with increasing surface to volume ratio and is therefore strongest in nano crystals or  powders [98]. See also Sect. 6.4.3. Apart from the few examples already mentioned earlier, there are many reports showing that the typical exponential or non-exponential effective decay times of the near edge luminescence in ZnO bulk samples lay in the range from several hundred ps to one or a few ns. A small selection of references from the above cited ones is [34, 73–75]. These values are also confirmed by photo-conductivity measurements, in which the decay of the signal is governed by electron–hole pair recombination [101–103]. Therefore, it is safe to state that the effective total radiative and nonradiative lifetime [see (12.1)] of excitons or more generally electron–hole pairs in high quality ZnO is at low densities and temperatures of the order of 1 ns:

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300 ps  T1  5 ns

(12.2)

Intensity (a.u.)

The shorter values may indicate an increasing influence of fast non-radiative decay. In this context, we mention [68] where it has been found that the luminescence decay is around 1 ns for a bulk sample, while it can be as short as a few ten ps for a low quality epilayer sample. In this case also the spectrum of the near edge emission is strongly broadened. Annealing in a suitable atmosphere may improve the sample quality [69]. In this context, this means sharper emission features at low temperature and a longer decay time. Within the accuracy of (12.2), this statement is true both for free and bound excitons and their phonon replica and for bulk samples, but also for high quality epilayers and nano rods or even for quantum wells and nano crystals. We shall come back below to a discussion of the influence of higher temperatures and with Fig. 12.6 to data obtained, when an EHP is formed and/or stimulated emission sets in. Before some data for bound exciton complexes (BEC) are given. It has been found by various authors [65, 98, 106] that the decay time of the different bound exciton complexes (BEC) increases with increasing binding energy. We present in Fig. 12.4 an example. Such behaviour can be calculated for radiative recombination [107]. The conclusion that this is a proof for dominant radiative recombination at least of BEC once they have been formed is not stringent, since a similar dependence on the overlap integral of electron and hole wave function can be expected also for non-radiative processes.

I9 I7 I6 I4

I3

Intensity (a.u.)

3.354 3.360 3.366 energy (eV)

I6 I7 I6 I4 I3 FE ZnO T = 1.8 K 0

600 1200 Time (ps)

1800

Fig. 12.4 The rise and decay dynamics of free (FE) and bound exciton complexes I3 to I9 in ZnO after pulsed excitation. According to [33]

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Furthermore, it has been found that the decay time of an emission band attributed by some authors to excitons bound to defects at or close to the surface is significantly longer than that of the other BEC [98] but other authors give also shorter values around only 70 ps [62]. A clearly non-exponential decay of donor–acceptor pair luminescence in n-type ZnO has been reported in [99] at 5 K with effective decay times in the ns range. There is a general trend that the luminescence decay time increases with increasing temperature T [1, 30, 75, 76], though some components like the fast one in [30] get shorter with increasing temperature. It must be taken into consideration that the dominating radiative decay channel changes with T from BEC to free excitons [75]. In [75], the luminescence decay time varies from below 100 ps at 10 K to 450 ps at 180 K. In this contribution, the radiative decay time Tr has been deduced from the data with the help of a theoretical approach, which connects the spectral width with Tr [108]. It is open for discussion whether the assumptions of [108] are fulfilled in [75]. See in this context also [1, 109, 110] and references therein. In [76] the luminescence decay time increases also from 100 ps at10 K to 1 ns at 300 K. It is decomposed into Tr increasing from 100 ps at 10 K to 10 ns at 300 K and Tnr decaying from more than 20 ns at 20 K to 1 ns at 300 K. In other words, the luminescence decay should be only radiative at low T but mainly non-radiative at temperatures above 150 K. Indeed the luminescence intensity drops for constant excitation conditions between 50 and 300 K by more than a factor 10 in agreement with our data in [100] (see Figs. 6.16 and 6.33), but the crucial proof that the luminescence yield is one at low T is missing. See the comment above. Since ZnO has a polar c-axis the luminescence properties depend even on the surface, i.e. if a zinc-, or an oxygen terminated or if a non-polar surface is excited [74]. A rather detailed study on the influence of defects on the recombination dynamics of epilayers has been published by [67]. Now we proceed to a few examples from quantum wells. The radiative and non-radiative decay of luminescence has been investigated in (Cd,Zn)O/(Mg, Zn)O multiple quantum wells (e.g.) in [88]. Similarly as for alloys and other quantum well systems [1, 111–115, 125], localization leads to a strong variation of the decay times over the rather broad emission band increasing at low temperatures from the mobility edge to deeper localized states, in [112] from below 1 ns to more than 2 ns. Furthermore, the well known [1] non-monotonous shift of the spectral position of the emission maximum with increasing temperature can be seen. Since ZnO is a piezoelectric material, the recombination dynamics in strained quantum wells or superlattices may be strongly influenced by the piezoelectric fields as known for other blende or wurtzite type II–VI or III–V structures. See for example Fig. 6.29 or [1] and references therein. In a phenomenon similar to the quantum confined Stark effect (QCSE), electrons and holes are separated in piezo-superlattices from each other and driven against the opposite sides of the quantum well. This effect reduces the overlap of electron and hole wave functions as explained already with Fig. 6.29b and thus both the radiative and non-radiative recombination rates. In Fig. 12.5, we show calculated and measured lifetimes for ZnO/(Zn, Mg)O quantum wells as a function of the well width including this effect.

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Fig. 12.5 The lifetime of excitons in ZnO/(Zn, Mg)O quantum wells as a function of well width, assuming a piezo field of 0.9 MV/cm. According to [89]

The effective lifetime is drastically enhanced with values up to 100 s for a well width of 7 nm. This effect is accompanied by a decrease of the transition energy with increasing well width and otherwise identical sample parameters. Since the piezo field can be screened by a high density of carriers, one should be able observe both a strongly non-exponential decay dynamics and a spectral red-shift of the emission with time after pulsed excitation, when the system returns from almost flat band conditions to the situation with piezo field. See [1] and [89–91] for ZnO quantum wells. In nano crystals with a diameter of several 10 nm or more, the luminescence properties are not much altered compared with an epilayer except for a stronger influence of the surface. We gave already some references and examples above. The situation changes for diameters in the rage of a few nm or below. There, quantisation effects become important even for ZnO with an excitonic Bohr radius of only 1.8 nm [45, 92–95]. A fast initial decay (t  50 ps) is attributed in [45] to recombination of carriers trapped in the interior of 3–6 nm sized nano clusters. Also [95] report decay times in the 50 ps regime. In [92] a luminescence decay time of 33 ps has been found in a 55-nm-thick film consisting of micro crystallites with a grain size of 50 nm. The luminescence yield decreases also here strongly with increasing temperature and an activation energy of 57 meV. Values of the luminescence decay ranging from 30 ps down to 5 ps have been observed in mesoporous ZnO structures [127]. Under conditions of stimulated emission, the decay time may become as short as a few ps. Unfortunately the near edge emission has not been monitored together with the THz signal in [128]. This statement holds independent of the specifics of the sample that is bulk, layer, rod or dot and essentially also of the recombination process responsible for the stimulated emission. For nano crystallites see [92]. References for the intermediate density regime are [82, 116]. For the stimulated

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Fig. 12.6 Time resolved emission spectra of a single rod pumped by 150 fs pulses at 3.5 eV for different excitation fluences F (a) the emission intensity of various modes as a function of excitation fluence (b) and the overall shift of the emission maxima over the fluence (c). According to [92]

emission from and the decay of an electron–hole plasma, one finds typical decay times in the range of few 10 ps range. See for example Fig. 12.3b, [26–28, 46– 51,86,92,126,128] and below. We give with Fig. 12.6 an example showing emission spectra of a single rod pumped by 150 fs pulses at 3.5 eV from the second harmonic generation of a TiSa laser. Every line in Fig. 12.6a corresponds to an emission spectrum for a given excitation fluence F temporally resolved over an interval of 60 ps by a streak camera. The emission intensity is normalized and colour coded. The emission starts at the M-band region for low F (see also [34]) shifts red and broadens with increasing F due to the transition to an EHP. Distinct laser modes start to develop for F around 0:4 mJ=cm2 . The ensemble of the laser modes shows an increasing red shift with increasing pump energy. This fact reflects the increasing band gap renormalization and band filling. The individual laser modes show in contrast a blue shift with increasing F due to the decrease of the refractive index with increasing np . This

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phenomenon results via Kramers–Kronig relations from a decrease of the refractive index due to the progressive bleaching of the excitonic and near edge absorption. As a consequence, various modes shift spectrally into or out of the gain region resulting in mode competition (Fig. 12.6b). See also Fig. 11.15. Within every 60 ps trace, there is the opposite trend that is a red shift because the refractive index tends to recover during the recombination of carriers. See also [51]. Now a few words on the dynamics of deep centre luminescence treated in more detail in Chap. 9. The Cu (or Vanadium) centre in ZnO is for example known to give at low densities rise to one of the various green emission bands in ZnO characterized by a well-developed phonon structure. See for example [117–119] and references therein. However, samples containing a lot of Cu in the range of several ten ppm or more show hardly any luminescence from the UV through the whole visible spectrum. This phenomenon is known as concentration quenching. This means that Cu in ZnO acts at high concentrations as luminescence killer. The conclusions deduced from an increase of the green luminescence with a decrease of the Cu concentration produced via the decay of a radioactive Cu isotope in [120] are therefore not stringent. For more data on luminescence quenching by Co, Fe or Ni see [121]. The rise and decay dynamics of deep centre luminescence is frequently slower than the one of the near band edge emission. For a few examples see [58, 59, 73]. In [73] a decay dynamics of the green emission has been found, which follows a t1 law over one order of magnitude while the near edge emission is fast and fitted by a double exponential with time constants of 30 and 150 ps. A very slow spatiotemporal expansion of deep centre luminescence over mm distance in ms has been reported in [122]. In contrast to the rather fast excitonic recombination processes, it has been found also for nano crystals that the luminescence in the visible involving deep centres decays much slower [93, 94] with temperature dependent effective decay times in the range of a s. With these few examples from the field of deep centre luminescence, we finish the presentation on dynamic processes.

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Chapter 13

Past, Present and Future Applications C. Klingshirn

Abstract While we presented in the preceding chapters to a large extend basic physical properties of ZnO, which are, however, in many cases just the basis of and thus relevant for applications, we concentrate in this chapter on the applications themselves. We go from past applications in Sect. 13.1 to present and emerging ones in Sect. 13.2. Applications, which are according to the point of view of the author presently still highly speculative, will be presented in Sect. 13.3 as visions of future uses of ZnO and ZnO-based structures. A more humorous overview of ZnO based applications can be found in [ZnO and you, Kentucky Fried Movie (1977)].

13.1 Past Applications Here, some applications of ZnO are presented for curiosity, which are in most cases no longer in the market. See also [1, 2].

13.1.1 The Electro Fax Copy The intrinsic sensitivity spectrum for photo-conductivity of pure ZnO starts only in the near UV because of its large band gap. See Chap. 4 or 6. Consequently, ZnO can be used as a photo conducting material in this spectral range (see also below in Sect. 13.2), while it is insensitive to longer wavelengths. This effect has been used in a photocopy process known as electro fax (wet or dry) copier [1–3]. A paper had to be used, which was coated with ZnO powder and has been charged electro-statically. The image of the original was projected on this paper in the near UV range, and the paper was discharged in the illuminated areas. Subsequently, a dry or wet toner was

C. Klingshirn Institut f¨ur Angewandte Physik, Karlsruher Institut f¨ur Technologie KIT, Karlsruhe, Germany e-mail: [email protected]

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applied, which adheres only in the still charged (i.e.) non-illuminated areas. After a (thermal) fixation, the photocopy was ready. This electro-fax photocopy procedure disappeared essentially from the market because it needed the special ZnO-coated paper. This was a big disadvantage compared with indirect methods, which can use standard papers.

13.1.2 Ferrite Properties Ferrites are mixed oxides with the formula (MO  Fe2 O3 / where M stands for a divalent metal. The crystal structure corresponds generally to the one of spinell. In natural magnetite, M is Fe. In usual ferrite, M stands for Ni. It has been found by [4] that a replacement of NiO by up to 35% of ZnO significantly improves the magnetic properties of this ferrite. Consequently, this ZnO containing mixed oxide has been and still is used as cores for coils and transformers at elevated frequencies, because the low electrical conductivity suppresses eddy currents and reduces thus the losses. Ferrite beads are presently widely used on data cables as filters for electromagnetic interference (EMI). Ferrites have also been used for data storage in magnetic or ferrite core memories up to the seventies. Later on Si-based RAMs replaced these.

13.2 Present and Emerging Applications As mentioned already in the introduction (Chap. 1), ZnO is used presently by several 100,000 tons per year. Subsequently, we outline some of the present and emerging applications. More references than the few ones given here may be retrieved from data collections such as INSPEC or Web of Science but also from wikipedia. We start with some present applications for which ZnO is used in large quantities and proceed then to applications centred on electronics, sensing and optics including devices that are already on the market and others, which are in the state of development.

13.2.1 Cement, Rubber, Paint and Glazes ZnO serves in large quantities as additive to cement or concrete. It prolongs the cement setting time and improves the hydraulic properties. As an additive to rubber, it improves the rubber cure. Because of its high heat conductivity, it contributes additionally to the transport of heat e.g. out of tires resulting from the crunching.

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ZnO is a white pigment used in paints, also known as Chinese white. In contrast to (e.g.) Pb containing pigments, it is not poisonous, does not react with H2 S and does not change its colour under illumination. Partly, TiO2 is replacing it nowadays. Furthermore, ZnO can be added to the glazes of ceramics.

13.2.2 Catalysts, Pharmaceutics, Cosmetics and Food Additives ZnO is known since decades as a catalyst. See [1, 2] for some older references and [5–14] for a few recent ones in this field. It is used for the production of methanol (CH3 OH) out of CO and/or CO2 and H2 . The combination of Cu=ZnO=Al2 O3 seems to be very efficient as catalyst. Because of its high absorption over the whole UV spectral range and its good photo stability, ZnO is used as absorber in sun blockers, but also in other cosmetics and pharmaceuticals. ZnO is known to have anti-inflammatory and bacteriostatic properties. Therefore, it is used in cr`emes, ointments and on fabrics [11, 12]. It is also found as an additive to human and animal food to compensate Zn deficiencies in nutrition. A nano rod has been used successfully to measure the membrane potential across a human fat cell or the intracellular pH value [13, 14].

13.2.3 Electronics In electronics, ZnO is used since many years to build varistors [15–19]. See also Sect. 5.7. ZnO is sintered with smaller amounts of other oxides such as Bi-, Cror Mn-oxides. Ceramic pellets are formed from this mixed oxide, which are then contacted. The device has a symmetric I(V) characteristics in contrast to a Zener diode with the property that it has a high resistance up to a certain threshold voltage. Above, the resistance drops very sharply. See Fig. 13.1. Therefore, varistors (variable resistor or VDR D voltage-dependent resistor) can be used for voltage limiting or the protection of sensible and/or expensive devices. The critical voltage can reach several hundred volts. The effect is based on the contacts between the various grains. ZnO-based varistors are sold in huge numbers. For some recent publications on ZnO-based varistors see [21–27]. A device that is also very common but is not yet in the ZnO-based version on the market is the Schottky diode. This semiconductor metal contact works especially well for the combination of n-type ZnO with a Pd contact [28]. An example of the I(V) characteristics is given in Fig. 13.2. In forward direction, one sees first the exponential increase of the current followed by the transition to a linear characteristic, while the reverse bias results in the expected, almost constant saturation current. The absolute values of the current density are still rather small, compared with commercial Si-based devices. For a few more details and references to ZnO-based Schottky diodes and their surface barriers see [29–37] and Sect. 5.5.

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Fig. 13.1 Comparison of the current–voltage characteristics of a ZnO and a SiC-based varistor. According to [20]

Fig. 13.2 The I(V) characteristics of a Pd/ZnO Schottky diode. The modulus of the current is plotted in a logarithmic scale vs. the voltage. According to [28]

The field effect is known in ZnO since half a century [38, 39]. An accumulation layer has been produced on the surface of a high resistivity bulk crystal by exposure to atomic Hydrogen. The carrier density of this channel could be influenced by heating, by an Oxygen treatment or by a gate voltage. This latter effect is the essence of the field effect (transistor). Since devices based on this field effect do not necessitate ambipolar doping, which is still difficult on the p-type side as discussed in Chap. 5, many scientists tried recently to circumvent this problem by designing field effect transistor (FET) struc-

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Fig. 13.3 Possible arrangements of TFT with a ZnO cannel (a), the drain current as a function of the voltage between source and drain (b, d) and the drain current as a function of the voltage between gate and source for constant voltage between drain and source (c); (a) to (c) according to [59] and (d) according to [60]

tures. Partly, single crystals are used [38, 39], but generally thin (epitaxial) layers resulting in thin film transistors (TFT) [40–60] but also quantum wells may serve as channel [61] and partly even nano rods or belts [62–70]. Sometimes, ZnO is used for the channel only and sometimes alloys such as Indium Zinc Oxide (IZO). Since they are transparent in the visible, they also come under the name transparent thin film transistors (TTFT). First attempts have been reported recently to involve also p-type doped ZnO [71, 72]. In Fig. 13.3a various layout concepts are shown, in all cases with a ZnO channel using partly opaque Si gates, partly transparent ITO gates on glass substrates. The characteristics of such devices are shown in Fig. 13.3b–d. The absolute values of the currents are again relatively small in these examples. Recently, a ZnO-based FET has been used to drive an organic light emitting diode (O-LED). The whole structure was grown on a transparent polymer substrate. See the contribution [52]. This approach makes the complete device transparent. See also the results and suggestions in [40]. The photoconductivity of ZnO has been also investigated since long [1, 2, 73– 79]. For a few, more recent results see, for example [80–83], references therein and Sect. 5.8. Trivially, one expects the onset of photoconductivity for photon energies around the band gap. Consequently, the idea is close at hand to use ZnO or alloys

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Fig. 13.4 The I(V) characteristics of a ZnO:As/ZnO pn junction without and with UV illumination. According to [87]

with even larger band gap as solar- or visible-blind photo detectors [84, 85]. The typical response times are in the 10 ns range. Surprisingly, photoconductivity has been also observed at smaller photon energies as well, down to the red part of the spectrum [1–3,83,86]. Here the participation of defect states in the sample or of ador absorbed surface species comes into play. ZnO pn junctions and Schottky diodes have also been used as photoconductive devices or as UV photocells (see Fig. 13.4), using partly again nano rods, however, still with small efficiencies. For references on these topics, see [87–104, 306]. A common advantage of ZnO for all applications in electronics and optoelectronics (see below) is its radiation hardness. This means its insensitivity against high energy radiation like electrons in the MeV range [105]. This does not mean that the bonds in the lattice of ZnO would be so strong that no damage occurs during exposure to high energy radiation, but that radiation damages are annealing quickly at moderately elevated but even at low temperatures [106, 107] or that defects created by the irradiation are compensating each other [108, 109]. In [105] this radiation hardness has been demonstrated for varistors.

13.2.4 Gas Sensors It is also known since more than half a century [110–113] that the surface conductivity of ZnO can be strongly modified by the surrounding gas atmosphere, for example by oxygen or hydrogen. See also Sect. 5.8. These gases are adsorbed to the surface

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Fig. 13.5 The layout and operation of ZnO nano wires acting as sensor for ethanol in air. According to [119]

and shift the Fermi level with respect to the bands. In this sense, the action as catalyst is rather directly connected with the sensor application. Some more recent reports on applications of ZnO as gas sensor are given in [114–124] or in the contributions [63, 70]. One idea is to use ZnO nano rods because of their huge surface-to-volume ratio [120–122]. Other developments aim at selective coatings of the surface of ZnO, which allow the docking of specific molecules only. This concept can be extended even into the range of ZnO-based biosensors [123, 124]. In Fig. 13.5, the dynamics of the temporal response of a nano rod is shown, exposed to ambient air and to air with the given concentrations of ethanol. It is assumed that the oxygen absorbed to the surface of the nano rod captures the electrons forming O 2 and leaving the rod in a high resistivity state while the carrier concentration recovers in a reducing atmosphere. See also Sect. 5.8 and Fig. 5.18 there for another example. Partly as a point of curiosity, it should be mentioned that not only the surface conductivity can be changed by an ambient gas but also the luminescence yield [125]. A variation of the band bending towards the surface and/or of the carrier concentration by adsorption or desorption of some species influences also the excitonic reflection features (e.g. via a variation of the exciton-free or dead layer, see Chap. 6) and of the luminescence spectra. This effect will also allow an optical reading of such sensors.

13.2.5 TCO, Solar Cells and Some Further Applications ZnO can be easily n-type doped reaching electron concentrations beyond 1020 cm3 . The doping is generally on the Zn site with Al, Ga or In. See Chap. 5, Sect. 2.5 or [126]. Doping with halides on the anion site is very efficient in other II–VI compounds like ZnSe but has been less investigated in ZnO [127–129]. These highly n-doped samples are essentially transparent in the visible, but bulk, highly Ga-doped

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samples show a slight bluish colour presumably because the tail of the free carrier absorption reaches into the red spectral region. These highly doped wide band gap semiconductors are generally called transparent conducting oxides (TCO). The prototype is indium tin oxide (ITO), but ZnO/X with X D Al, Ga or In is cheaper and especially for X D Al not poisonous. For a small selection of references see [130–139]. The ZnO-based TCOs can be produced by many square meters (e.g.) by stuttering. They serve (e.g.) as transparent front contacts for solar cells, liquid crystal displays, in MESFETS or as heat protecting and energy saving coatings for windows, which transmit the visible but reflect the IR. For a small collection of references, see [140, 141]. Recently, ZnO/Al, so-called AZO, has been used as TCO contacts to drive an organic O-LED. The whole structure was grown on a transparent glass substrate [142, 143]. This concept might lead to ‘entirely see through’ displays. Concerning photovoltaic, early examples of aqueous systems with ZnO electrodes are referenced in [1, 2]. In more recent work (see [144–162, 306] for some references, which demonstrate also the diversity of present day activities in this field), ZnO does not only serve as contact material as mentioned above, but also as a functional one, for example in hybrid solar cells made from n-type ZnO and a p-type semiconductor like Cu2 O or from ZnO nano particles and conjugated polymers. Alternatively, ZnO nano wires can be used in dye sensitized solar cells. In any case, a medium is necessary to extend the absorption spectrum towards longer wavelengths. A completely different approach is the use of ZnO in a solar reactor. The ZnO is reduced with graphite to metallic Zn and CO2 by the heat, i.e. the thermal energy of sunlight concentrated by a collimator [163]. For hydrolysis of water at ZnO electrodes under the influence of UV (sun-)light to O2 and H2 O2 see, for example already [1, 2]. As discussed in detail in Sect. 2.3, ZnO has a substantial fraction of ionic binding and lacks a centre of inversion. Consequently, it shows a strong piezo electric effect [164–166]. This effect can be used, for example to produce piezo electric oscillators from bulk samples [166, 167] but also from nano wires [168]. Since the eigen frequency of such an oscillator depends on temperature, it can be used as temperature sensor [166,167]. The piezo effect allows to couple to and to propagate surface acoustic waves (SAW). Such devises may serve as acousto-optic modulators [169–174]. Since the SAW reacts sensitively on the mass (and elastic constants) of species adsorbed to the surface, SAW-based devices allow to detect surface layers. If the surface is functionalized, the sensitivity can be very selective, for example for interleukin-6 or various gases [114–118, 120–122, 175–180].

13.3 Visions of Future Applications Here, we present possible applications and the commercial use of which would be huge, though their practical realization is presently less apparent because it involves partly serious unsolved problems, for example a high, stable and reproducible

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p-type doping, or because the concept underlying the application itself is still highly speculative like in spintronics.

13.3.1 pn Junctions For the first of the two above reasons, the situation is for ZnO-based semiconductor pn junctions similar to or possibly even less favourable than for Schottky diodes discussed earlier. The n-type region can be easily made from ZnO/X with X D Al, Ga or In. See Chap. 5. Since first reliable reports on p-type doping have been published recently, ZnO homo junctions have been produced. We show in Fig. 13.4 an example for the I(V) characteristic. Some more references are, for example [181–186]. The other possibility is to grow heterojunctions with n-type ZnO, its alloys or ZnO-based quantum wells and a p-type doped semiconductor such as SiC, Si, GaN, In1x Gax N, GaAs, NiO, SrCu2 O2 , CuCrO2 , ZnRh2 O4 or even a p-type organic semiconductor. Examples including MIS structures can be found in [187–197] and in the references for solar cells [144–162] and for LEDs [198–206]. One has to ask, however, in the case of heterojunctions why one should use n-type ZnO with p-type GaN, since n-type In1x Gax N is also readily available. For LEDs there are both arguments in favour of and drawbacks for heterojunctions as shown below. Recently, non-volatile memory devices based on resistance switching including ZnO-based selector elements have been suggested as an application of Schottky or pn junctions [207]. One of the main advantages is said to be the ability to stack these cross-bar memory structures shown in Fig. 13.6 in three dimensions, since there is no need for single crystallinity, such as in silicon. In such a cross-bar memory, a selector element as well as a memory element needs to be realized. As a selector element, a ZnO-based Schottky diode or p-n-diode can be used. For the bit storage element, resistance switching has been demonstrated in another oxide semiconductor, NiO. In NiO, different conduction paths are created after employing high current densities, leading to a reversible resistance switching.

Fig. 13.6 An array of TiAu/ZnO/Ag Schottky diodes for cross-bar memories. According to [207]

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13.3.2 Light Emitting Diodes The most important aspect that drives the present renaissance (or hype) of ZnO research and development (R&D) is the hope to obtain with ZnO a material alternative to or instead of group III-Nitrides for a blue optoelectronics. More specifically, light emitting diodes (LED) or even laser diodes (LD) are meant from the green over the blue to the near UV spectral range using the combination Zn1x Cdx O=ZnO in the first case and the combinations Zn1x Mgx O=ZnO or Zn1x Bex O=ZnO in the second. For examples of rather enthusiastic statements concerning this aspect, see [198–205]. Since a simple p(i)n homo junction will not work at RT in a cw mode as a LD, even not for the III–V compounds, more elaborate structures are necessary. In one case, one uses n- and p-type doping in ZnO-based layers and a thin undoped layer or a (M)QW as zone for the recombination of the injected electrons and holes. We showed in Figs. 6.29 and 11.12 already an example for an optically pumped Zn1x Cdx O quantum well between ZnO barriers. In Fig. 13.7, the luminescence spectrum of a ZnO QW between Zn1x Bex O barriers is shown under electric pumping. For further examples of homo junctions including structures containing apart from ZnO also Zn1x Mgx O, Zn1x Bex O or Zn1x Cdx O and including also examples of simple pn homo junctions also in nano rods see [181–197, 209–224]. For heterojunctions using (e.g.) the p-type semiconductors mentioned above, including directional emission from random media see [187–197, 206, 225–264, 307, 308].

Fig. 13.7 The luminescence spectrum of a MQW ZnO=Zn1x Bex O-based LED. According to [208]

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Fig. 13.8 (a) The electroluminescence spectrum of a ZnO homo junction at 110 K. According to [269] and (b) from a ZnO nano rod array using ZnO/As for the p-type material. According to [270]

The spectra in Fig. 13.7 and 13.8b show a substantial fraction of near edge luminescence around 3.36eV resulting from localized and/or bound excitons in the ZnO MQW. See for another example [265]. This is a significant progress compared with earlier results (e.g.) [266–268] in which the luminescence is dominated by deep centre emission. See for example [265] or Fig. 13.8a. Figure 13.8a shows a recent electroluminescence spectrum of a ZnO:Al/ZnO:Na homo junction at 110 K. The luminescence is attributed to the p-type ZnO/Na layer. The deep centre emission is decomposed into two Gaussians (though there is no stringent argument that deep centre emission should be Gaussian) and the near edge emission at 3.03 eV, which is here hardly visible and, which is in good bulk samples at this temperature centred around 3.36 eV (see Fig. 6.15). At RT the electroluminescence of this structure is quenched. Figure 13.8b shows the electro luminescence of a ZnO nano rod ensemble grown on semi insulating GaAs. The p-type doping is assumed to result from As diffusion from the GaAs substrate into the naturally n-type nano rods during a post growth annealing procedure in O2 . It should be mentioned in this context that one observes frequently the opposite behaviour in Zn-group VI compounds grown on GaAs (or Al2 O3 / namely diffusion of Ga (or Al) into the II–VI layer resulting in n-type doping. The current is sent in the device of Fig. 13.8b from an ITO covered glass plate through an Au/Zn contact electrode into the GaAs and from there into the rods containing the pn junction. It is collected on the other side by another ITO coated glass sheet. The peak position of the luminescence around 3.25 eV comes close to the RT value (see Fig. 6.15). The forward voltages of several 10 V are surprisingly high, because the I(V) curve of this device shows an onset voltage of 5 V only. To circumvent the problem of p-type doping of ZnO, several research groups use again a heterojunction approach. They combine easily accessible n-type ZnO material with a different p-type-doped semiconductor such as GaN, SiC, Si or even organic p-type semiconductors [206, 225–264, 271–274, 307, 308]. In the contribution [262] even the opposite approach is used namely the combination of n-type

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Fig. 13.9 The luminescence of a n ZnO/p-type organic structure at RT. According to [271, 272]

SiC with p-type ZnO/Cu. In Fig. 13.9, an example is given for the system n ZnO/p organic material. The ZnO is in the form of nano rods, and the organic material is a blend of different compounds with good p-type conductivity and luminescence [271,272]. As seen from the lower trace of Fig. 13.9, the emission originates mainly from the organic material, (i.e.) electrons are (also here) preferentially injected from the n-type ZnO into the organic p-type semiconductor. A calcium (2) acetylacetonate layer between ZnO and the organic p-type material (upper trace) reduces the potential step in the VB into two smaller steps and one hopes to increase in this way the hole injection into ZnO. Until now, no RT near edge emission of ZnO is seen. However, the approach of heterojunctions like n-type ZnO with (e.g.) p-type GaN has its own problems: as discussed in Chap. 4 or shown in Fig. 5.1 the band alignment between ZnO and (e.g.) GaN is of type II. This means that the recombination is spatially indirect across the hetero interface, which tends to have a rather large number of defects, which will act at least partly as non-radiative recombination centres. Furthermore, the emission is necessarily red shifted compared with the near edge emission of the parent materials of the heterojunction. A possible further drawback of this approach is the fact that some of the above-mentioned constituents of a heterojunction (SiC, Si or GaP) are indirect gap materials with intrinsically low luminescence yield. This means that it is necessary that the holes are injected into the ZnO and not the electrons from the ZnO into the indirect gap material. This requirement imposes severe and generally not fulfilled restrictions on the band alignment because of the low laying valence band in ZnO. See Fig. 5.1. However, an advantage of the approach to use heterojunctions is the possibility to obtain a better outcoupling of the electroluminescence from the LED, if the refractive index of ZnO cover layer is lower than that of the p-type material and consequently the angle for total internal reflection becomes larger. Another improvement of the

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out coupling efficiency occurs, if the n-type ZnO forms a rough layer with large scattering efficiency. For some references, see [206,225–264]. Possible applications of ZnO (nano) pn junctions in lightening have been mentioned already in Sect. 3.3.2. A severe drawback of all reported LEDs is the small luminescence yield, which has been addressed already in the introduction to Chap. 3. To the knowledge of the author, there are presently (June 2009) only very few reports on ZnO-based LDs, that is electrically pumped laser diodes. An exception is the work [273, 309, 310]. The authors report on laser emission from a ZnO QW between Mg1x Znx O barriers at RT under electrical pumping with current densities as low as 10 A=cm2 . This structure is embedded between ZnO/Sb as p-type and ZnO/Ga as n-type material. The stimulated emission is also here attributed to inelastic exciton–exciton scattering. The fact that it extends from 3.38 down to 3.122 eV makes also here the recombination in an electron–hole plasma more probable. See the discussion with Figs. 11.7 and 11.11. The luminescence yield is also in this case rather low with optical output powers of 0:5 W at injection currents of 70 mA at 20 V. Even if one takes into account the losses by the Si substrate, the yield is still significantly below the best one in ZnCdSe-based LD, which reached 10%. Interestingly, the emission is attributed in [273] to random lasing (see Sect. 11.3.2), and the scattering is being provided by small grains forming the ZnO layer. The state of the art is among others characterized by the fact that very few systematic investigations of the lifetimes of ZnO-based LEDs exist. Furthermore, the efficiency of the LEDs, that is the number of emitted photons per injected electron–hole pair is generally not given in the references, or if given it is very small. See above. However, even if data are not given, it can be guessed to be usually considerably below unity (e.g.) from the signal-to-noise ratio of the published electroluminescence spectra or from a statement that a ‘bright luminescence’ is characterized by the fact that it is ‘visible to the naked eye’. See also Chap. 5. According to the subjective feeling of the author, the pace of the development of ZnO-based LED seams to have decreased over the last 2 years, because one finds sometimes the same figures in papers published in 2005 and in 2008 [198–205]. Although beautiful physics and considerable technical progress is seen in the investigation of ZnO-based homo- and heterojunction LEDs, the above data may explain why the author listed this topic still under ‘highly speculative applications’. ZnSe-based LEDs and LDs have been reported in the 1980s and 1990s of the last century with optical output powers for the latter case in the range of several ten mW. On the one hand, this means that these devices were much more advanced when compared with the present state of ZnO; nevertheless, they did not make it on the market, because the longest reported lifetimes did not exceed a few 100 h. See [275– 277] and references therein. On the other hand, the breakthrough in the case of GaN-based LEDs and LDs [278], which came for many scientists rather unexpected, is an encouragement to continue the efforts on ZnO for some while.

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13.3.3 Field Emitters The pointed tips of etched or as-grown, needle-like bulk ZnO crystals enhance the electric field strength if a voltage is applied between the ZnO needle and a counter electrode in vacuum. This fact triggered rather early the idea of field emission from ZnO. For an early experimental realization, see [279]. Therefore, it is not surprising that the idea came up again with the availability of nano rods, which have a tip with a small radius of curvature. As a further application-friendly aspect, these nano rods grow in well-defined places on pre-structured substrates. Besides the interesting physics and material properties, which can be learned from this effect like the density of surface states, the idea came up to use ZnO nano rods as field emitters in flat panel displays [280–301] by accelerating the field emitted electrons onto a phosphor screen. The questions, which have to be answered before a large-scale application becomes possible, concern again the lifetime or degradation of the rods. ZnO is a relatively soft material compared (e.g.) with tungsten, and degradation has been seen even for bulk samples at rather low currents below 1 A [279].

13.3.4 Spintronics The last examples in the category ‘highly speculative’ are connected with the magnetic properties of ZnO. We neglect in this discussion the aspect to which extend the ferromagnetism observed by some authors is an intrinsic property of doped ZnO:X with X D Co, Mn, Fe, Cu, etc., or if it is due to inclusions or precipitates of other phases. See for this point the discussion in Chap. 10. There is a lot of speculation in the literature about spintronics in connection with diluted magnetic semiconductors (DMS) or ferromagnetic ones in the sense to use not or not only the electric charge of an electron for data storage and manipulation as it is presently done, in every computer or lap top, but also the spin of the electron. The experimental and theoretical work on this field produced again many extremely beautiful physical results. For a short overview, see, for example [302]. However, the aspect of application is according to the opinion of the author highly overestimated. The application of spintronics in the above sense requires spin alignment, spin transport, spin manipulation, spin storage and read-out. Most of these aspects are treated on a laboratory scale only and no up scaling exists so far nor does viable computer architecture. To elucidate these problems just two numbers are mentioned. The magnetic flux density necessary to align the spins in a DMS is of the order of 1T. See, for example [303] and references therein. However, the field strengths resulting from the magnetization of the ferromagnetic semiconductors is in contrast only of the order of several pT and thus about seven orders of magnitude smaller than the magnetic field of the earth of about 20 T [268]. This ratio makes simple fan-out architectures completely impossible. Even if all these problems would be solved, one gains only a factor of two for the two possible spin orientations compared with one elementary charge. Therefore, the concept of quantum computing

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is usually evoked in the context of spintronics. The author is rather sceptic about quantum computing in general [304] and even more so in context with spintronics, and not only he [305]. In addition to the problems mentioned earlier, there is the one of dephasing. A large number of interacting spins must be encoded to handle big numbers, subsequently processed and stored without dephasing. Furthermore, obligatory features for a computer like fan-out and cascadability are by no means trivial nor solved, nor does a highly developed computer architecture exist. It looks very unlikely that these aims can be reached in the near future to an extend that the product is technically and economically superior to Si-based electronics. To conclude this section on future applications, we present another vision concerning ferromagnetic ZnO/X, which is independent of its extrinsic or intrinsic nature. If it becomes possible to create nano rods, which are ferromagnetic at RT, and if it becomes possible to increase their magnetization by several orders of magnitude (see above) and if it becomes possible to either flip the direction of magnetization of a pixel on a magnetic data carrier by an external magnetic field and to read this process by the voltage induced in an nano coil around the nano rod or vice versa to control the magnetization of the pixel by an external current through the nano-coil, then the ZnO nano rods may be used as nano-sized read/write heads for magnetic data storage. The future must show if there are in the above sentence many or too many ‘ifs’ [268].

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Chapter 14

Conclusion and Outlook C. Klingshirn

Abstract In this final chapter, we summarize in the conclusions some aspects of ZnO research and some prospects of applications in the outlook.

14.1 Conclusions In the introduction, we mentioned (and verified with several references in various chapters) that in spite of the present research renaissance (or hype) ZnO is a long known and investigated semiconductor material with first publications going back to the first quarter of the last century. One possible reason for this long-lasting scientific interest in ZnO could be the fact that it is possible to study in ZnO not all but a very substantial fraction of the properties and phenomena which make up solid-state physics. See in this context also the comment to Fig. 2 in [1]. Indeed the approach to “study solid-state physics on one material” has been followed in the Institut f¨ur Angewandte Physik der Universit¨at Erlangen by Prof. Dr. Erich Mollwo and his coworkers from the beginning of the fifties to the mid seventies of the last century, contrasting thus the much more frequently used approach to center the research activities of one institute around one or a few physical effects investigated on a rich variety of different materials. The research topics on ZnO start, for example, with chemical binding and lattice dynamics including IR- and Raman-spectroscopy or specific heat and the piezoelectric effect, continuing then with transport properties for heat and charge carriers, including the quantum Hall effect, and by far do not come to an end with magnetic properties including, for example, ESR or ODMR but also the aspects of diluted magnetic semiconductors and ferromagnetism. Another wide field of ZnO research comprises many aspects of surface physics such as surface reconstruction, surface states, and catalytic properties. Yet another topic is doping (up to the metallic

C. Klingshirn Institut f¨ur Angewandte Physik, Karlsruher Institut f¨ur Technologie KIT, Karlsruhe, Germany e-mail: [email protected]

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limit resulting in plasmon-phonon mixed states) and also the problem of ambipolar doping and defects of intrinsic as well as extrinsic nature and deep centers. An especially rich part of solid-state physics, which can be studied in ZnO, is solid-state optics. The spectral range of interest extends from the IR over the visible and near UV to the VUV and the X-ray regime, where Auger spectroscopy or perturbed angular correlation (PAC) give information on chemical binding and the atomic environment of some species. The optical properties close to the fundamental absorption edge in the near UV see ZnO as a model substance for exciton physics, including bulk and surface polaritons or bound or localized exciton states. ZnO allows to study in detail stimulated emission of semiconductors, with the advantage (which partly also causes problems in the interpretation) that both excitonic gain processes and recombination in an electron–hole plasma are observable. Another aspect comprises all types of optical nonlinearities ranging from the “classical” phenomena like second or third harmonic generation and the dc-effect over four wave mixing to the regime of extreme nonlinear optics. The growth techniques involve gas transport, hydrothermal methods, and growth from melt. For thin layers or for various nano structures, molecular beam epitaxy (MBE), pulsed laser deposition (PLD), metal-organic vapour phase deposition (MOVPE or MOCVD) or the vapor-liquid solid (VLS) technique and for large areas sputtering, pyrolysis, and other coating techniques are used. The growth (and subsequent investigation) of nano structures covers the full range from epitaxial layers over quantum wells to nano rods and quantum wires down to nano crystallites and powders. As mentioned in the introduction already, the investigation of many of the abovelisted effects goes back well into the last century. There are, however, also very beautiful new phenomena discovered only recently. Without trying to be complete, we mention the self-organized growth of nano rods and related structures, the successful (though not yet reproducible) p-type doping, the observation of random lasing in ZnO nano powders with strongly localized or more extended modes, the growth of diluted or possibly even ferromagnetic ZnO:X or the observation of phenomena of extreme nonlinear optical phenomena in ZnO or of the quantum Hall effect.

14.2 Outlook Following from the above “tour d‘horizon,” we can expect from ZnO also in the years to come some beautiful results in physics. But since the present research boom on ZnO is driven mainly by expectations for applications, we address this aspect in the outlook. Since ZnO is used already on a scale of 100,000 tons per year in various fields, the application relevance of ZnO is clearly given. What one expects as new high-tech applications for the near future is the use of ZnO in blue/UV optoelectronics, especially in the form of light emitting or laser diodes, as a transparent field effect transistor (TFT), as a transparent conducting oxide (TCO), as a component in

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solar cells, as a field emitter, and possibly in spintronics. Although the applications centered on TCOs are already taking off, the future of all applications involving a p–n junction are still unclear. If high, stable, reproducible, and reliable p-type doping becomes available in the next few years, ZnO will remain and become even more a major topic in semiconductor R&D. If not, ZnO will (once again) disappear from the landscape of application-oriented research and remain limited to academia. The author has the subjective feeling that the other application-oriented topics mentioned earlier will alone not help ZnO toward a major breakthrough in applications. Therefore, it makes sense to invest for a few years to bring more ideas, work, and money into ZnO research to see how far one can get. A positive result is, at our present state of knowledge, not guaranteed, but concerning this aspect, the author has the objective feeling that this point is not limited to ZnO.

References 1. C. Klingshirn, Phys. Stat. Sol. B 244, 3027 (2007)

Index

A0 , 240 AC , 240 Absolute deformation potential, 220 Absorption spectroscopy, 134 Acceptor, 181 Acceptor binding energies (BEs), 182, 188, 190, 191, 194 Acceptor bound excitons, 196, 203, 206, 207 Accidental degeneracy, 134 Acoustic phonon, 140 scattering, 104 side band, 279 Acoustic wave devices, 14 Activation energies, 185 Additional boundary conditions, 131 Ag, See Silver Al, See Aluminium Alloy, 147 Alloy fluctuations, 145, 149 Aluminum (Al), 97, 236 Ambipolar doping, 2 Amphoteric, 97 Amphoteric behavior, 96 Amplified spontaneous emission, 296 Angular momentum, 123, 203 Anion vacancies, 236 Anisotropy, 206, 214 Antiferromagnetic, 268 Antimony, 99 Arsenic (As), 98–100, 182, 193, 194, 239 As, See Arsenic Atomic terraces, 43 Attenuated total reflection (ATR), 151 Au, 106 Au/Ni contacts, 107 A0 X, 182, 183, 192, 206 B0 , 240 B , 240

Band alignment, 155 Band discontinuities, 84, 91 Band filling, 319 Band gap, v, 1, 51, 148, 149 difference, 91 energies, 85, 88 renormalization, 283, 290, 319 Band offset, 153 Band structure, 122 Band to acceptor transition, 192 Band-to-band absorption, 290 Band-to-band transition, 149 Bandoffset, 91 Barrier height, 106 BE, 170 BEC, 138, 142, 143, 169 BeO, 84, 145 BeZnMnSe, 268 Bex Zn1x O, 88 Biaxial strain, 83, 215 Biaxial stress, 228 Biexcitons, 278, 310 Bi2 O3 , 113 Bipolar doping, 189 Birefringence, 126, 129, 131 Bleaching, 320 Bohr magneton, 267 Boltzmann occupation probability, 138 Bond polarity, 9 Bond strength anisotropy, 19 Born effective charge, 22 Bose–Einstein condensation, 162, 301 Bose–Einstein statistics, 138 Bottleneck, 122 Boundary conditions, 131 Bound excitons, 79 complexes, 121, 143, 169, 279, 288, 316 states, 312 Breakdown voltage, 113

351

352 Brillouin scattering, 216 Buffer, 57 Buffer layer, 46 Burstein–Moss shift, 150, 284

C, See Carbon C0 , 240 c-axis, 124 Calorimetric absorption spectroscopy, 262 CaO, 236 Capacitance-voltage data CV, 101 Capture rate, 313 Capture time, 312 Carbon (C), v contamination, 103 incorporation, 53 Carrier mobility, 95, 104, 141 Cascadability, 339 Cathodoluminescence, 48 Cavity, 296 mode, 162 polariton, 162, 301 CdMnTe, 270 CdO, vi, 48, 84, 124, 145 CdS, 188 CdSe, 244 CdTe, 244 Cd1-x Znx O, 293 CdZnO/ZnO, 91 Central cell effects, 181 Centre of inversion, 275 Characteristic temperature, 295 Charge transfer, 97 Charge-transfer transition, 262 Chemical binding, 7 Chemical potential, 284, 289, 311 Chemical shift, 174, 175 Circular polarized light, 208 Clusters, 270, 313 Co, 28 Co2C , 241 Co3C , 240 Compliance tensor, 215 IIb –VI compounds, 1 III–V compounds, v Compression, 220 Concentration quenching, 320 Conductive polymer, 107 Conductivity, 70 Confined modes, 299 CoO, 113 Cooling, 311 Correlation effects, 283

Index Coulomb enhancement, 289 Cr3C , 240 Crystal field, 77, 239, 245, 247 Crystal field splitting, 124, 228 Crystec, 43 Cu, 98, 100, 243 Cu3C , 240 Cu acceptor, 234 Cubic phase, 85 Cyclotron energy, 201

cr , 124

so , 124

EDia , 202

EZ , 202 Damage threshold, 286, 291 Damping, 133, 138 DAP, 189, 191, 237 Datta-transistor, 268 dc-effect, 275 Debye temperature, 12 Decay time, 114 Decay time constant, 314 Deep acceptors, 182, 189 Deep centres, 169, 233, 264 emission, 140 luminescence, 320 Deep donor, 96, 241 Deep double donor, 264 Deeper valence bands, 276 Defect density, 40 Defect passivation, 97 Deformation potential, 23, 216, 218 2DEG, 108 Degenerate electron gas, 150 Dember-effect, 315 Density, 1 Density functional theory, 79 Dephasing, 339 Dephasing time, 138, 307 Depletion region, 70 Deuterium, 98 Diagonal stress tensor, 220 Diamagnetic shift, 202 Dichroism, 129 Dielectric function, 144 Dielectric response, 33 Diffusion, 141 Diffusion length, 285 Dilatation, 220 Diluted magnetic, 3 Diluted magnetic semiconductor (DMS), 28, 210, 268, 338

Index Dipole-forbidden, 134 Dislocations, 100, 141 Disorder, 121 Disorder-induced Raman scattering, 27 DMS, See Diluted magnetic semiconductor Donor, 180 Donor binding energies, 175 Donor bound exciton, 203 Donor–acceptor pair, 190, 194, 317 Donor–acceptor-pair transition, 99 Dopant concentration, 105 Doping, 26, 67 D0 X, 171, 183, 185, 206, 234 DC X, 171, 185 Dynamic Jahn–Teller effect, 252, 254 Dynamical bond polarity, 21

eA0 , 190, 285 Excitonic molecules (Dbiexcitons), 288 Effective g-factors, 269 Effective exciton g-factor, 214 Effective mass approach (EMA), 109, 130, 172, 181 Effective piezoelectric charge, 16 Effective Rydberg, 81, 174 EHP, See Electron-hole plasma Elastic moduli, 21 Electrical properties, 69 Electromechanical coupling, 14 Electron g-factor, 204 Electron affinity, 105 Electron beam lithography, 69 Electron beam-induced current (EBIC), 106 Electron holography, 100 Electron mass, 174 Electron nuclear double resonance, 175, 236 Electron paramagnetic resonance (EPR), 175, 202, 233, 241, 247, 258 line width, 235 Electron–hole correlations, 80 Electron–hole liquid, 284 Electron–hole plasma (EHP), 144, 277, 289, 293, 295, 311, 313, 318, 319 Electronic excited states, 187, 188 Electronic transition level, 97 Ellipsometry, 148 EMA, See Effective mass approach EMT, 188 ENDOR, 175 Energy gap, 78 Enhanced backscattering, 296 Epilayer, 141 ESR, 175

353 Etch pit density, 44 Etch pits, 42 Eutectic, 67 Evanescent wave, 151 Exchange, 283 Exchange coupling, 268 Exchange interaction, 209 Exchange splitting, 208 Excitation induced dephasing, 282 Excited states, 174 Exciton, 81 Exciton binding energies, vi, 81, 83, 154 Exciton physics, 348 Exciton polariton, 121 Exciton series, 130 Exciton–exciton scattering, 280 Exciton–phonon bound state, 146 Excitonic enhancement, 284 Excitonic enhancement, Fermi edge singularity, 289 Excitonic molecule, 278 Excitonic Rydberg energy, 130 Excitons bound to ionized impurities, 203, 207 External luminescence yield, 159 Extreme nonlinear optics, 276

Fabry–Perot resonator, 162 Faraday configuration, 206, 210, 214 Fe3C , 240 Fe2C -defect complexes, 251 Fe3C=2C donor level, 245 Fermi function, 150 Fermi sea shake up, 289 Ferromagnetism, 3, 28 Ferromagnets, 268 Field effect, 328 Field effect transistor, 103, 328, 348 Field emission, 338 Final state damping, 289 Four level laser system, 286 Four wave mixing (FWM), 275, 276, 308, 309 Fourier transform infrared spectroscopy, 250 Fourier transform infrared spectroscopy (FTIR), 249 Fourlings, 295 Fr¨ohlich scattering, 23 Free excitons, 121, 203 Frenkel pairs, 237 FTIR, See Fourier transform infrared spectroscopy FWM, See Four wave mixing

354 Ga, 177, 241 GaAs, v Gain processes, 292 Gain spectra, 289 GaMnN, 270 GaN, vi, 92 GaP, 194 Gap states, 249 Gas sensor, 69, 331 Gate dielectric, 108 Gaussian, 138, 308 Ge, v g-factor, 202 Giant Zeeman splitting, 268 Gr¨uneisen parameters, 12, 225 Grain, 141, 298, 318 Grain boundaries, 113 Grating, 151 Green luminescence, 106 Group-III donors, 181 Group III-nitrides, vi Group theory, 123, 212 Group velocity, 144 g-value, 235

HO , 97 Half-width at half-maximum, 140 Hall effect, 100, 101, 193 Hall mobilities, 108 Haynes rule, 175, 188 Heat conductivity, 326 Hetero-epitaxy, 215 Heterojunction, 334 Heterostructrures, 45 High electron mobility transistors (HEMT), 108 High-density regime, 277 High-field drift velocity, 110 History, 1 Hole g-factor, 204, 210 Homoepitaxially, 39 Homogeneous broadening, 133, 138, 140, 308 Homogenous width, 282 Hot spots, 298 HRXRD, See X-ray diffraction, high resolution Huang–Rhys factor, 138, 170, 191, 234, 237 Hydrogen, 53, 95, 236 diffusion, 98 Hydrothermal growth, 39, 41 Hyper-Raman scattering, 276 Hyperfine interaction, 175, 235 Hysteresis, 269

Index ICPS, 3 Implantation, 29 Impurity bands, 99 incorporation, 42 In, 179, 241 In-donor, 235 Inelastic exciton-free carrier scattering, 281 Inelastic scattering processes, 280 Inelastic X–X scattering, 291, 293 Inhomogeneous broadening, 145, 308 Inhomogeneous distribution, 100 InP, v INSPEC, 2, 326 Integer filling factors, 110 Integrating sphere, 140 Interaction processes, 277 Interdiffusion, 175, 177 Interface, 141 Interface dipoles, 92 Intermediate density regime, 277 Intermediate polariton branch, 135 International Conference on II–VI Compounds, 3 Interstitial hydrogen, 96 Intra band or inter sub band relaxation times, 307 Intra-centre, 262 Intracentre transitions, 245, 262 Intrinsic defects, 95, 233 Inverted valence band (VB), 125 ordering, 136 Ionization continuum, 129 Ionized acceptor, 239 Ionized bound exciton, 208 Ionized donor, 171, 239 Ionized donor-bound exciton, 99 Ionized impurity scattering, 104, 105, 108 Irreducible representation, 126 Isoelectronic charge state, 249 Isotope, 26 shifts, 247, 262 splitting, 257 Isotropic point, 135, 210 Jahn–Teller, 239 coupling, 247, 248 Keywords, 5 k-linear, 133, 138 k-linear term, 126, 136 KOH, 42 Kramers degenerate, 208

Index Kramers doublets, 247, 262 Kratzer potential, 187 Kronecker product, 212

Landau levels, 202 Laser diode (LD), v, 3, 334, 337 Laser modes, 286, 319 Lattice constants, 9, 86 Lattice mismatch, 145, 215 LD, See Laser diode LED, See Light-emitting diode Level repulsion, 125 Li, See Lithium LiZn acceptors, 236 Lii donors, 236 Lifetime, 141, 292, 307, 314 Light-emitting diode (LED), v, 40, 52, 56, 68, 98, 101, 329, 333, 334 Line shape, 308 Line shape fit, 138 LiOH, 42 Liquid phase epitaxy, 67 Lithium (Li), 42, 100, 179, 182, 189, 233 LO-phonon replica, 138, 309 Local bond softening, 263 Local density approximation, 269 Local vibrational modes, 25, 250 Localization, 285, 310, 317 effects, 145 energies, 171, 181 Localized excitons, 121, 309 Localized states, 147, 293 Longitudinal energy, 133 Longitudinal exciton, 127 Longitudinal exciton branch, 122 Longitudinal optical phonon, 18 Longitudinal optical phonon replicas, 191 Longitudinal–transverse splitting, 127 Lorentz-model, 21 Lorentzian, 138, 308 Low field approximation, 202 Lower polariton branch (LPB), 122, 136, 302, 311 Lower-lying d bands, 79 Luminescence, 126, 169 decay time, 314 killer, 320 line shape, 140 of free, 138 spectra, 136 yield, 140, 141, 314, 317, 318, 331, 337 Luminescence assisted two-photon spectroscopy, 278

355 Magnetic anisotropy, 203 Magnetic circular dichroism, 270 Magnetic ions, 239 Magnetic moment, 267 Magnetic resonance, 175 Magnetite, 326 Mahan exciton, 289 Main section, 129 Many particle effects, 150, 275 Mass ratio, 181 MBE, See Molecular beam epitaxy M-band, 279, 319 Melt growth, 183 Melting temperature, 8 Metal organic chemical vapor deposition (MOCVD), 39, 103 Metal–insulator transition, 108 MgO, vi, 58, 84, 145, 236 Micro-crystallites, 57 Misfit dislocations, 58, 86 Mixed longitudinal modes, 34 Mixed mode polariton, 217 Mixed oxides, 326, 327 Mixed-mode polaritons, 129, 132, 135 Mn, 29 Mn2C , 241 Mn3C , 240 MnO, 113 MOCVD, See Metal organic chemical vapor deposition Mode competition, 295, 320 Mode spacing, 298 Modulation doping, 84, 108 Modulation spectroscopy, 130 Modulation-doped ZnMnO/ZnO, 110 Molecular beam epitaxy (MBE), 39, 192, 237 Mott density, 283, 289, 311 Murnaghan equation, 220

N, 194 .N2 /O , 103 NO acceptor, 103 n-type doping, 141 Na, 42, 177, 189 NaZn , 236 Na acceptor, 234 Nano crystallites, 153, 280 Nano pillars, 66, 70 Nano rods, 3, 67, 102, 141, 143, 155, 280, 284, 294, 295, 309, 348 Nanowires, 153, 221 Native point defect, 96 Negative spin–orbit

356 coupling, 77 splitting, 125 Negative thermal quenching, 141, 185 Neutral acceptor bound excitons, 182, 192 Neutral acceptors, 171 Neutral donor bound excitons, 99, 179 Neutral shallow donors, 171 Ni, 106 Ni3C , 240, 241 NiO, 108, 326, 333 Nitrogen, 98, 99, 182 NO, 103 Non-crossing rule, 162 Non-Kramers configuration, 249 Non-local response, 131 Non-radiative decay, 316 Non-radiative lifetime, 314 Non-volatile memory, 333 Nonaqueous solution growth, 41 Nonlinear response, 275 Nuclear moment, 259 Nuclear spin, 236

ODMR, See optically detected magnetic resonance Ohmic contacts, 105, 107 Omega-scan, 42 One-particle state, 121 Optical band gap, 149 Optical cycle, 236 Optical gap, 160 Optical phonon, 140 Optical phonon eigenmodes, 17 Optical phonon scattering, 108, 111 Optical spectroscopy, 308 Optically detected magnetic resonance (ODMR), 202, 234–237 Optoelectronics, 334, 348 Organic p-type semiconductor, 336 Oscillator, 129 Oscillator strength, 124, 126, 127, 136, 228 O vacancies, 272 Oxygen source, 56 Oxygen vacancies, 96, 233, 237, 271 Oxygen vacancy F-centre, 236 Oxygen-terminated face, 44

P, See Phosphorous P-bands, 280, 313 p-type, 237 doping, vi, 40, 52, 68, 95, 99, 103, 189 ZnO, 107

Index Paramagnetic, 268 Pauli blocking, 283 PbS, v Pd, 106 Phase-space filling, 283 Phonon, 7 branches, 20 confinement effects, 31 oscillator strength, 21 structure, 170 Phonon–plasmon mixed, 7 Phonon–plasmon mixed excitations, 34 Phosphorous (P), 98, 99, 182, 193, 194, 239 Photo detectors, 330 Photo stability, 327 Photo-conductivity, 315, 325 Photo-Hall effect, 115 Photocell, 330 Photoconductive response, 114 Photoconductivity, 95, 115, 315, 329 Photocopy, 325 Photoelectron emission, 144 Photoluminescence, 48, 72 Photoluminescence excitation spectra, 183 Photovoltaic, 332 Piezo electric effect, 108, 332 Piezo electric fields, 154, 317 Piezo-superlattices, 317 Piezoelectric interactions, 104 Piezoelectric strain coefficients, 16 Piezoelectric stress moduli, 15 Piezoelectric tensor, 14 Pigment, 327 Plasma frequency, 22 Plasma oscillation, 32 Plasma-assisted epitaxy, 191 Plasmon frequency, 32 Plasmon polariton, 302 Plasmon scattering, 105 Plasmon–phonon mixed states, 285 PLD, 39, 146 PLD targets, 66 PLE, 183, 187 p–n-diode, 70 Pockels effect, 229, 276 Point defects, 143 Point group Td , 123 Point group C6v , 124 Poisson distribution, 191 Polar hexagonal c axis, 129 Polar optical scattering, 104 Polar phonon mode, 17 Polariton, 311 Polariton dispersion, 129, 144, 302

Index Polariton laser, 299 Polaron correction, 81 Polaron mass, 174 Polaron self energy, 174 Pollmann–B¨uttner potential, 181 Porto-notation, 23 Precursor, 47, 48, 52 Pressure coefficient, 220, 222, 225, 228 Pseudo-donor model, 188 Pseudomorphic growth, 86 Pure dephasing, 308 Quantum computing, 338 Quantum confined Stark effect, 317 Quantum confinement, 160 Quantum dots, 160 Quantum Hall effect, 95, 109 Quantum structure, 67 Quantum wells, 39, 48, 63, 66, 68, 84, 99, 153, 280, 309, 313 Quasi stationary conditions, 286 Quasi-Fermi levels, 284 Ryeff , 81 Radiation hardness, 330 Radiative decay, 279 Radiative lifetime, 314 Radiochemical doping, 259 Raman spectrum, 23 Raman tensor, 23 Raman-active phonon modes, 23 Random lasing, 294, 296, 348 Random media, 296 Rare-earth-ions, 264 Reabsorption, 140, 287 Reactor, 41 Recombination, 314 Recombination center, 169 Reconstruction, 98 Rectifying behavior, 106 Red-shift, 282 Reflection spectra, 129, 308 Refractive index, 140 Relaxation processes, 311 Research peak, 2 Resonant excitation, 285 Resonant Raman scattering, 26 Response time, 330 Reststrahlenbande, 21 RF plasma source, 60 RHEED, 60 Rock salt, 10, 145 structure, 84

357 Room temperature ferromagnetism, 269 Rotation energies, 187 Rotational quantum numbers, 188

Saha equation, 283 Sapphire, 65 Sapphire substrates, 46 Saturation velocity, 108 Sb, 194 Sb2 O5 , 113 SCAM, 45, 56, 101, 143, 193 Scandium-Aluminum-Magnesium-Oxide, 45 Schottky contacts, 105 Schottky diode, 105, 327 Scientific correctness, 4 Scratch, 45 Screening, 283 Se, v Second harmonic generation (SHG), 275 Second-order Raman scattering, 25 Second-order Raman spectra, 25 Second-phase detection, 28 Secondary phases, 145 Selection rules, 21 Selective coatings, 331 IIb -selenides, 124 Self-absorption, 207 Self-compensation, 97 Self-focussing, 286 Self-organization, 52 Self-organized growth, 3, 67 II–VI semiconductors, vi III–V semiconductors, 3 Semimagnetic semiconductors, 268 Shallow acceptors, 182, 237 3d shell impurities, 239 Shubnikov de Haas oscillations (SdH), 108 SiC, v Silver (Ag), 98, 100, 106, 182 SiN, 98 SiO2 , 98 Solar cells, 332 Solar reactor, 332 Solid state lighting, 68 Solid-state optics, 348 Solid-state physics, 347 Solubility, 145 Solubility limitations, 99 Sound velocities, 20 sp3 hybridization, 8 Space-charge-limited currents, 114 Spatial dispersion, 128, 131 Spectral hole burning, 308

358 Spin injection, 268 Spin triplet excitons, 309 Spin–flip, 134, 136, 266 forbidden, 124 transition, 245 Spin-Hamiltonian, 242, 247 Spin–orbit coupling, 77, 252 interaction, 249 splitting, 124 Spin-polarized current, 268 Spin-polarizers, 269 Spin-transistor, 268 Spinell, 326 Spintronics, 244, 267, 333, 338 Sputtering, 40 Stacking fault, 100, 196 Stark effect, 245 Static crystal field model, 256 Sticking coefficient, 60 Stiffness constants, 216 Stiffness tensor, 215 Stimulated emission, 285, 318 Stoichiometry, 60 Stokes shift, 153, 160 Strain, 83, 141, 154 Strain deformation potentials, 215 Strain tensor, 215, 216 Stress tensor, 215, 217 Strong coupling, 301 Strong coupling limit, 162 Substrate, 42, 65 IIb -sulphides, 124 Sun blocker, 327 Surface, 141, 331 acoustic waves, 332 chemistry, 114 conductivity, 331 contamination, 129 depletion, 114 exciton, 151 morphology, 62 passivation, 72 polarity, 106 Surface-exciton polaritons, 151

T1 , 307 T2 , 307 T3 , 308 Tauc regime, 147, 150 IIb -tellurides, 124 Temperature sensor, 332 TES, See Two-electron satellite

Index Tetrahedral coordination, 1 Tetrapods, 295 Thermal conductivity, 13 Thermal decay, 185 Thermal equilibrium, 41 Thermal expansion, 11 Thermal expansion coefficient, 215 Thermal phonon shift, 31 Thermal population, 126 Thermal quenching, 141 Thermalization, 206 Thermally activated hopping, 148 Thermodynamic equilibrium, 301 Thin film transistors, 329 Third harmonic generation, 275 Three photon absorption, 276 Three-photon difference frequency generation, 218 Threshold, 286, 294, 298 Ti3C , 240 Time-of-flight, 144 Tokyo Denpa, 44 Transistor, v Transition metal, 28 Transparent conducting oxides, 332, 348 Transparent ferromagnet, 272 Transverse exciton polariton, 126 Transverse optical phonon, 18 Trap, 169 Trigonal symmetry, 248, 249 Tuneable laser emission, 292 Tunneling, 114 Two photon absorption, 276 Two-electron satellite (TES), 143, 171, 172 Two-electron transition, 142 Two-oscillator model, 140 Two-particle exciton state, 121 Two-phonon absorption, 285 Two-photon excitation spectroscopy, 218 Type I, 84, 91 Type II, 336 Type-II, 92

Ultrasonic measurements, 216 Uni-polar plasma, 284 Uniaxial, 129 distortion, 217 pressure, 217 stress, 215, 279 UPB, See upper polariton branch Upper polariton branch (UPB), 122, 136, 311 Urbach rule, 139 Urbach tail, 134, 147, 149, 150, 286

Index VZn , 237 V3C , 240 VOx , 97 Vacuum level, 95 Valence band, 214 offset, 92 ordering, 83, 124, 213, 228, 310 Valence band splitting, 80, 82 Van der Pauw configuration, 100 Vapor phase transport (VPT), 39 Vapour–liquid–solid approach (VLS), 67 Varistors, 95, 111, 327 Varshni formula, 140 Vegards law: lattice parameter, 88 Vibration eigenmodes, 17 Vibrational states, 188 Vibrational-rotational excited states, 187 Vibronic coupling, 252 Voigt configuration, 204, 214 Voigt geometry, 208 Voigt notation, 215

Wave guide, 156 Weak localization, 296 Web of Science, 2, 326 Wet chemical growth, 39 Whispering gallery cavity polaritons, 163 Whispering gallery modes, 156, 302 White light LED, vi Wikipedia, 326 Wurtzite, 1, 7, 8, 124

X–el process, 288 X–mLO, 278 X–mLO process, 286 X–X scattering, 287 X-ray diffraction, high resolution (HRXRD), 42, 57 XPS, 103

359 Zeeman effect, 134 Zeeman spectra, 247 Zeeman splitting, 202, 249 Zener model, 269 Zero field splitting, 243 Zero phonon line, 135, 138, 247, 250 Zinc (Zn) vacancies, 96, 237, 252, 272 Zinc-blende, 1, 77 Zinc-blende structure, 8 Zinc-blende-type, 123 Zinkit, 1 ZnI , 97 Zn interstitials, 96, 272 Zn1x Bex O, 153 ZnCdO, 51 Zn1x Cdx O, 153 ZnCdSe, 337 ZnCoO, 270 Zn1x Cox O, 210 Zn1x Mgx O, 146, 153 ZnMnO-ZnO heterostructures, 110 ZnO/AlN, 93 ZnO/C, 271 ZnO/Co, 254 ZnO/Cu, 336 ZnO/GaN, 92 ZnO/MgZnO, 91 ZnO/N, 196 ZnO/Na, 237 ZnO1x Sx , 89 ZnO1x Sex , 89 ZnO=Ni2C , 256 ZnO/SiC, 93 ZnO:Al, 99 ZnO:Ga, 99 ZnO:P, 99 ZnO:Sb, 107 ZnS, 189, 244 ZnSe, 3, 189, 191, 239, 244, 331