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

Citation preview

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

vi

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

vii

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

•

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

x

3

4

Contents

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

Contents

xi

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

7

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

xii

Contents

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

Contents

xiii

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

2

C. Klingshirn

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].

1

Introduction

3

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.

4

C. Klingshirn

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.

1

Introduction

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]

7

8

J. Geurts

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

2

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].

10

J. Geurts

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

2

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

2

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.

14

J. Geurts

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

2

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).

16

J. Geurts

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

2

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.

20

J. Geurts

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 ( 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.

2

Crystal Structure, Chemical Binding, and Lattice Properties

35

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)

36

J. Geurts

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

2

Crystal Structure, Chemical Binding, and Lattice Properties

37

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

40

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

3

Growth

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

42

A. Waag

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

3

Growth

43

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]

44

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

3

Growth

45

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

b

MgO

MgO

c

ZnO

ZnO

d

ZnO

ZnO

e

ZnO

ZnO

AI2O3

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 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

3

Growth

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].

References 1. B. Pecz, A. Elshaer, A. Bakin, A. Che Mofor, A. Waag, J. Stoemenos, J. Appl. Phys. 100, 103506 (2006) 2. Tadashi Takahashi, Atsuko Ebina, Akira Kamiyama, Jpn. J. Appl. Phys. 5, 560 (1966) 3. Michael H. Huang, Yiying Wu, Henning Feick, Ngan Tran, Eicke Weber, Peidong Yang, Adv. Mater. 13, 113 (2001) 4. A. Che Mofor, A. Bakin, B. Postels, M. Suleiman, A. Elshaer, A. Waag, Thin Solid Films 516, 1401 (2008) 5. R. Helbig, J. Cryst. Growth 15, 25 (1972) 6. H. Schneck, R. Helbig Thin Solid Films, 27, 101 (1975) 7. R. Tena-Zaera, M.C. Mart´ınez-Tom´as, S. Hassani, R. Triboulet, V. Mu˜noz-Sanjos´e, J. Cryst. Growth 270, 711 (2004) 8. V. Mu˜noz-Sanjos´e, R. Tena-Zaera, C. Mart´ınez-Tom´as, J. Z´un˜ iga-P´erez, S. Hassani, R. Triboulet. Phys. Stat. Solidi. C2, 1106 (2005) 9. C. Klingshirn, Phys. Stat. Sol., b 244, 3027 (2007) 10. D. Ehrentraut, H. Sato, Y. Kagamitani, H. Sato, X. Akira Yoshikawa, T. Fukuda, Prog. Cryst. Growth Charact. Mater. 52, 280 (2006) 11. R.A. Laudise, A.A. Ballman, J. Phys. Chem. 64, 688 (1960) 12. K. Oka, H. Shibata, S. Kashiwaya, J. Cryst. Growth 237, 509 (2002) 13. D.C. Reynolds et al., J. Appl. Phys. 95, 4802 (2004) 14. J.W. Nielsen, E.F. Dearborn, J. Phys. Chem. 64, 1762 (1960) 15. J. Nause, B. Nemeth, Semicond. Science an Technol. 20, S45 (2005) 16. D. Schulz, S. Ganshow, D. Klimm, M. Neubert, M. Rossberg, M. Schmidbauer, R. Fornari, J. Cryst. Growth 296, 27 (2006) 17. Byrappa, in Handbook of Crystal Growth, ed. by D.T. Hurle. Bulk Crystal Growth, Basic Techniques, 2a (North-Holland, Amsterdam, 1994) 18. J. Bl¨asing, A. Krost, J. Hertkorn, F. Scholz, L. Kirste, A. Chuvilin, U. Kaiser, J. Appl. Phys. 105, 033504 (2009) 19. D. Zwingel, J. Luminesc.5, 385 (1972)

74

A. Waag

20. 21. 22. 23. 24. 25.

D. Zwingel, F. G¨artner, Sol. Stat. Commun. 14, 45 (1974) E. Ohshima et al., J. Cryst. Growth 260, 166 (2004) K. Maeda et al., Semicon. Sci. Technol. 20, S49 (2005) E.P. Warekois, M.C. Lavine, A.N. Mariano, H.C. Gatos, J. Appl. Phys., 33, 690 (1962) A.N. Hanneman, R.E. Mariano, J. Appl. Phys. 34, 384 (1963) Xing Gu, Sh. Sabuktagin, Ali Teke, D. Johnstone, H. Morkoc¸, B. Nemeth, J. Nause, J. Mater. Sci. Mater. Electron. 15, 373 (2004) S. Graubner, C. Neumann, N. Volbers, B.K. Meyer, J. Bl¨asing, A. Krost, Appl. Phys. Lett. 90, 042103 (2007) G.A. Wolff, B.N. Das, F.H. Cocks, J. Appl. Crystallogr., 4, 379 (1971) V. Petukhov, A. Bakin, A. Elshaer, A. Che Mofor, A. Waag, Electrochem. Solid State Lett., 10, H357 (2007) E.S. Hellman, C.D. Brandle, L.F. Schneemeyer, D. Wiesmann, I. Brener, T. Siegrist, G.W. Berkstresser, D.N.E. Buchanan, E.H. Hartford, Internet J. Nitride Semicond. Res. 1, 1 (1996) A. Ohtomo, A. Tsukazaki, Semicond. Sci. Technol. 20, S1 (2005) Th. Gruber, C. Kirchner, R. Kling, F. Reuss, A. Waag, F. Bertram, D. Forster, J. Christen, M. Schreck, Appl. Phys. Lett. 83, 3290 (2003) Ishihara Junji et al., IEIC Tech. Rep. 103, 69 (2003) R. Kling, C. Kirchner, Th. Gruber, F. Reuss, A. Waag, Nanotechnology 15, 1043 (2004) B.P. Zhang, K. Wakatsukia, N.T. Binha, N. Usamic, Y. Segawa, Thin Solid Films 449, 12 (2004) B. Hahn, G. Heindel, E. Pschorr-Schoberer, W. Gebhardt, Semicond. Sci. Technol. 13, 788 (1998) C. Kirchner, Th. Gruber, F. Reuss, K. Thonke, A. Waag, Ch. Giessen, M. Heuken, J. Cryst. Growth 248, 20 (2003) A. Waag, Th. Gruber, K. Thonke, R. Sauer, R. Kling, C. Kirchner, H. Ress, J. Alloys Compd. 371, 77 (2004) Y. Kashiwaba, K. Haga, H. Watanabe, B.P. Zhang, Y. Segawa, K. Wakatsuki, Physica Status Solidi B, Vol. B, 229, 921 (2002) Th. Gruber, C. Kirchner, R. Kling, F. Reuss, A. Waag, Appl. Phys. Lett. 84, 5359 (2004) Th. Gruber, Dissertation, Universit¨at Ulm, 2003 Seung Yeop Myong, Seung Jae Baik, Chang Hyun Lee, Woo Young Cho, Koeng Su Lim, Jpn. J. Appl. Phys. 36, L1078 (1997) A. Behrends, A. Bakin, A. Waag, private communication Th. Gruber, Ch. Kirchner, F. Reuss, R. Kling, A. Waag, unpublished A. Elshaer, PhD Thesis, TU Braunschweig, Germany (2008) A. Elshaer, A. Bakin, A. Che Mofor, J. Bl¨asing, A. Krost, J. Stoimenos, B. P´ecz, M. Kreye, M. Heuken, A. Waag, Phys. Stat. Sol. (b) 243, 768 (2006) 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) A. Tsukazaki, A. Ohtomo, T. Onuma, M. Ohtani, T. Makino, M. Sumiya, K. Ohtani, Sh.F. Chichibu, S. Fuke, Y. Segawa, H. Ohno, H. Koinuma, M. Kawasaki, Nat Mater 4, 42 (2004) A. Ohtomo et al., Appl. Phys. Lett. 75, 2635 (1999) P. Fons, K. Iwata, S. Niki, A. Yamada, K. Matsubara, J. Cryst. Growth 201–202, 627 (1999) Y. Chen, D.M. Bagnall, H.-J. Koh, K.-T. Park, K. Hiraga, Z.-Q. Zhu, T. Yao, J. Appl. Phys. 84, 3912 (1998) A. Elshaer, A. Bakin, A. Che Mofor, J. Bl¨asing, A. Krost, Phys. Stat. Sol. (b) 4, 768 (2006) P.F. Palmstrøm, C.J. Miceli, Phys. Rev. B 51, 5506 (1995) T. Metzger, R. H¨opler, E. Born, S. Christiansen, M. Albrecht, H.P. Strunk, O. Ambacher, M. Stutzmann, R. St¨ommer, M. Schuster, H. G¨obel, Physica Status Solidi A 162, 529 (1997) A. Boulle, R. Guinebreti`ere, A. Dauger, J. Appl. Phys. 97, 073503 (2005) V.M. Kaganer, R. K¨ohler, M. Schmidbauer, R. Opitz, B. Jenichen, Phys. Rev. B 55, 1793 (1997) A. Elshaer, A. Bakin, A. Che Mofor, J. Stoimenos, B. Pecz, A. Waag, Superlattices Microstruct 42, 158 (2007)

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.

3

Growth

75

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)

76

A. Waag

90. J. Fallert, R. Hauschild, F. Stelzl, A. Urban, M. Wissinger, Huijuan Zhou, C. Klingshirn, H. Kalt, J. Appl. Phys. 101, 073506 (2007) 91. J. Grabowska, A. Meaney, K.K. Nanda, J.-P. Mosnier, M.O. Henry, J.-R. Ducl`ere, E. Mc Glynn, Phys. Rev. B 71, 115439 (2005) 92. M. Al-Suleiman, A. Che Mofor, A. Elshaer, A. Bakin, H.-H. Wehmann, A. Waag, Appl. Phys. Lett. 89, 231911 (2006) 93. M. Al-Suleiman, A. Bakin, A. Waag et al. J. Appl. Phys. 106, 063111 (2009) 94. Z.L. Wang, J. Phys. Condens. Matter. 16, R829 (2004) 95. Z. Fan, J.G. Lu, J. Nanosci. Nanotechnol. 5, 1561 (2005) 96. A. Waag, Th. Gruber, Ch. Kirchner, D. Klarer, K. Thonke, R. Sauer, F. Forster, F. Bertram, J. Christen, Adv. Solid State Phys. 42, 81 (2002) 97. E. Schlenker, A. Bakin, H.-H. Wehmann, A. Waag, Th. Weimann, P. Hinze, A. Melnikov, A.D. Wieck, J. Korean Phys. Soc. 53, 119 (2008)

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 ,

4

Band Structure

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

4.2

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)

88

B.K. Meyer

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

4

Band Structure

89 2.0X105

3.4

1.5

1.0

y =0

Eg (n)= 3.28–4.40y+5.93y2

Eg (eV)

Absorption coefficient (cm–1)

Zn1–x Cdx O Room temp.

3.2

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

2.5

3.0

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

90

B.K. Meyer

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

4

Band Structure

91

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

92

B.K. Meyer

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

4

Band Structure

93

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)

94

B.K. Meyer

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]

95

96

A. Waag SiO2

–0

Cds

Cdse

CdTe

GaSb

AIAs

InN

SiC

GaP

InAs

Si

Energy (eV)

H2O

ZnTe

InSb

ZnSe

ZnS

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

5

Electrical Conductivity and Doping

97

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

98

A. Waag

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

5

Electrical Conductivity and Doping

99

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

100

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

104

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

114

A. Waag

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

5

Electrical Conductivity and Doping

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].

5

Electrical Conductivity and Doping

117

References 1. C.G. van de Walle, J. Neugebauer, Lett. Nat. 423, 626 (2003) 2. A. Janotti, C.G. van de Walle, Phys. Rev. B. 78, 165202 (2007) 3. A. Janotti, C.G. van de Walle, Phys. Rev. B. 76, 165202 (2007) 4. Y.S. Kim, C.H. Park, Phys. Rev. Lett. 102, 086403 (2009) 5. G.C. van de Walle, J. Negebauer, Ann. Rev. Mater. Res. 36, 179 (2006) 6. A. Janotti, C.G. van de Walle;Nat. Mater. 6(1), 44 (2007) 7. F.A. Selim, M.H. Weber, D. Solodovnikov, K.G. Lynn, Phys. Rev. Lett. 99, 085502 (2007) 8. D.M. Hofmann, A. Hofstaetter, F. Leiter, H. Zhou, F. Henecker, B.K. Meyer, S.B. Orlinskii, J. Schmidt, P.G. Baranov, Phys. Rev. Lett. 88, 045504 (2002) 9. M. Kunat, S.G. Girol, T. Becker, U. Burghaus, C. W¨oll, Phys. Rev. B. 66, 081402 (2002) 10. C. W¨oll, Prog. Surf. Sci. 82, 55 (2007) 11. B. Meyer, Phys. Rev. B. 69, 045416 (2004) 12. H. Qiu, B. Meyer, Y. Wang, C. W¨oll, Phy. Rev. Lett. 101(23), 236401 (2008) 13. W. Liu, S.L. Gu, J.D. Ye, S.M. Zhu, Y.X. Wu, Z.P. Shan, R. Zhang, Y.D. Zheng, S.F. Choy, G.Q. Lo, X.W. Sun, J. Cryst. Growth 310, 3448 (2008) 14. Y.-L. Wang, H.S. Kim, D.P. Norton S.J. Pearton, F. Ren, Appl. Phys. Lett. 92, 112101 (2008) 15. Y.L. Wang, F. Ren, H.S. Kim, S.J. Pearton, D.P. Norton, Appl. Phys. Lett. 90, 092116 (2007) 16. Y.J. Li et al., J. Appl. Phys. 104, 053711 (2008) 17. H.J. Ko, Y.F. Chen, S.K. Hong, H. Wenisch, T. Yao, D.C. Look, Appl. Phys. Lett. 77, 3761 (2000) 18. T. Makino, Y. Segawa, S. Yoshida, A. Tsukazaki, A. Ohtomo, M. Kawasaki, Appl. Phys. Lett. 85, 759 (2004) 19. J.D. Ye, S.L. Gu, S.M. Zhu, S.M. Liu, Y.D. Zheng, R. Zhang, Y. Shi, Appl. Phys. Lett. 86, 192111 (2005) 20. F. Reuss, S. Frank, C. Kirchner, R. Kling, Th Gruber, A. Waag, Appl. Phys. Lett. 87, 112104 (2005) 21. T. Makino, Y. Segawa, S. Yoshida, A. Tsukazaki, A. Ohtomo, M. Kawasaki, J. Appl. Phys. 98, 093520 (2005). 22. V. Bhosle, A. Tiwari, J. Narayan, Appl. Phys. Lett. 88, 032106 (2006) 23. H.C. Park, D. Byun, B. Angadi, D.H. Park, W.K. Choi, J.W. Choi, Y.S. Jung, J. Appl. Phys. 102, 073114 (2007) 24. Z. Yang, D.C. Look, J.L. Liu, Appl. Phys. Lett. 94, 072101 (2009) 25. J. Meyer, P. G¨orrn, S. Hamwi, H.H. Johannes, T. Riedl, W. Kowalsky, Appl. Phys. Lett. 93, 073308 (2008) 26. B. Bayraktaroglu, K. Leedy, R. Bedford, Appl. Phys. Lett. 93, 022104 (2008) 27. D.C. Look, B. Claflin, H.E. Smith, Appl. Phys. Lett. 92, 122108 (2008) 28. A. Tsukazaki, A. Ohtomo, T. Onuma, M. Ohtani, T. Makino, M. Sumiya, K. Ohtanis, S. Chichibu, S. Fuke, Y. Segawa, H. Ohno, H. Koinuma, M. Kawasaki, Nat. Mater. 4, 42 (2005) 29. C.H. Chia, T. Makino, K. Tamura, Y. Segawa, M. Kawasaki, A. Ohtomo, H. Koinuma, Appl. Phys. Lett. 82, 1848 (2003) 30. T. Aoki, Y. Hatanaka, D. Look, Appl. Phys. Lett. 76, 3257 (2000) 31. F.X. Xiu, Z. Yang, L.J. Mandalapu, D.T. Zhao, J.L. Liu, W.P. Beyermann, Appl. Phys. Lett. 87, 152101 (2005) 32. B.C. Cao et al., Phys. Stat. Sol. (RRL) 2, 37 (2008) 33. M. Brandt et al., J. Appl. Phys, 104, 013708 (2008) 34. J.G. Lu et.al., Appl. Phys. Lett. 89, 113 (2006) 35. H.S. Kang, B.D. Ahn, J.H. Kim, G.H. Kim, S.H. Lim, H.W. Chang, S.Y. Lee, Appl. Phys. Lett. 88, 202108 (2006) 36. Y. Kanai, Jpn. J. Appl. Phys. 30, 703 (1991) 37. C.X. Xu, X.W. Sun, X.H. Zhang, L. Ke, S.J. Chua, Nanotechnology 15, 856 (2004) 38. J.B. Kim, D. Byun, S.Y. Ie, D.H. Park, W.K. Choi, J.W. Choi, B. Angadi, Semiconduct. Sci. Technol. 23, 095004 (2008)

118

A. Waag

39. I. Vurgaftman, J.R. Meyer, C.A. Hoffman, D. Redfern, J. Antoszewski, L. Faraone, J.R. Lindemuth, J. Appl. Phys. 94, 4966 (1998) 40. M. Schirra, R. Schneider, A. Reisera, G.M. Prinz, M. Feneberg, J. Biskupek, U. Kaiser, C.E. Krill, R. Sauer, K. Thonke, Physica B. 401, 362 (2007) 41. E. M¨uller, D. Gerthsen, P. Br¨uckner, F. Scholz, T.h. Gruber, A. Waag, Phys. Rev. B. 73, 245316 (2006) 42. A. Dadgar, A. Krtschil, F. Bertram, S. Giemsch, T. Hempel, P. Veit, A. Diez, N. Oleynik, R. Clos, J. Christen, A. Krost, Superlattice Microst. 38, 245 (2005) 43. T. Ohgaki, N. Ohashi, S. Sugimura, H. Ryoken, I. Sakaguchi, Y. Adachi, H. Haneda, J. Mater. Res. – Rapid Commun. 23, 2293 (2008) 44. D.C. Look, J. App. Phys. 104, 063718 (2008) 45. M. Kawasaki, SPIE Photonics West, Invited Talk (2009) 46. B. Xiang, P. Wang, X. Zhang, S.A. Dayeh, D.P.R. Aplin, C. Soci, D. Yu, D. Wang, Nano Lett. 7, 323 (2007) 47. B.Q. Cao, M. Lorenz, A. Rahm, H. von Wenckstern, C. Czekalla, J. Lenzner, G. Benndorf, M. Grundmann, Nanotechnology 18, 455707 (2007) 48. Y. Yang, X.W. Sun, B.K. Tay, G.F. You, S.T. Tan, K.L. Teo, Appl. Phys. Lett. 93, 253107 (2008) 49. B.Q. Cao, M. Lorenz, H. von Wenckstern, C. Czekalla, M. Brandt, J. Lenzner, G. Benndorf, G. Biehne, M. Grundmann, Proc. SPIE 6895, 68950V (2008) 50. H.S. Kim, F. Lugo, S.J. Pearton, D.P. Norton, F. Ren, J. Vac. Sci. Technol. B. 26, 968 (2008) 51. C.L. Perkins, S.H. Lee, X. Li, S.E. Asher, T.J. Coutts, J. Appl. Phys. 97, 034907 (2005) 52. A.R. Hutson, Phys. Rev. 108, 222 (1957) 53. H. Rupprecht, J. Phys, Chem. Sol. 6, 144 (1958) 54. M.A. Seitz, D.H. Whitmore, J. Phys. Chem. Sol. 29, 1033 (1968) 55. C. Klingshirn, Z. Physik 248, 433 (1971) 56. P. Wagner, R. Helbig, J. Phys. Chem. Sol. 35, 327 (1974) 57. D.C. Look, D.C. Reynolds, J.R. Sizelove, R.L. Jones, C.W. Litton, G. Gantwell, W.C. Harsch, Sol. Stat. Commun. 105, 399 (1998) 58. D.C. Look, D.C. Reynolds, J.R. Sizelove, R.L. Jones, C.W. Litton, G. Cantwell, W.C. Harsch, Solid State Commun. 105, 399 (1998) 59. D.L. Rode, Semiconduct Semimet 10, 1 (1975) 60. D.C. Look, J.W. Hemsky, J.R. Sizelove, Phys. Rev. Lett. 82, 2552 (1999) 61. A. Tsukazaki, A. Ohtomo, T. Onuma, M. Ohtani, T. Makino, M. Sumiya, K. Ohtani, S.F. Chichibu, S. Fuke, Y. Segawa, H. Koinuma, M. Kawasaki, Nat. Mater. 4, 42 (2005) 62. K. Miyamoto, M. Sano, H. Kato, T. Yao, Jpn. J. Appl. Phys., Part 2, 41, L1203 (2002) 63. K. Ellmer, J. Phys. D 34, 3097 (2001) 64. T. Makino, Y. Segawa, A. Tsukazaki, A. Ohtomo, M. Kawasaki, Appl. Phys. Lett. 87, 022101 (2005) 65. J.R. Lowney, H.S. Bennett, J. Appl. Phys. 69, 7102 (1991) 66. K. Seeger, Semiconductor Physics: An Introduction, 8th edn. (Springer, Heidelberg 2002) 67. S. Liang, H. Sheng, Y. Liu, Z. Huo, Y. Lu, H. Shen, J. Crystal Growth 225, 110 (2001) 68. H. von Wenckstern, E.M. Kaidashev, M. Lorenz, H. Hochmuth, G. Biehne, J. Lenzner, V. Gottschalch, R. Pickenhain, M. Grundmann, Appl. Phys. Lett. 84, 79 (2004) 69. R.C. Neville, C.A. Mead, J. Appl. Phys. 41, 3795 (1970) 70. M.W. Allen, M.M. Alkaisi, S.M. Durbin, Appl. Phys. Lett. 89, 103520 (2006) 71. K. Ito, Surf. Sci. 86, 345 (1979) 72. S. Kim, B.S. Kang, F. Ren, K. Ip, Y.W. Heo, D.P. Norton, S.J. Pearton, Appl. Phys. Lett. 84, 1698 (2004) 73. C. Weichsel, O. Pagni, A.W.R. Leitch, Semiconduct. Sci. Technol. 20, 840 (2005) 74. L.J. Brillson, H.L. Mosbacker, M.J. Hetzer, Y. Strzhemechny, G.H. Jessen, Appl. Phys. Lett. 90, 102116 (2007) 75. H.L. Mosbacker, Y.M. Strzhemechny, B.D. White, P.E. Smith, D.C. Look, D.C. Reynolds, C.W. Litton, Appl. Phys. Lett. 87, 012102 (2005)

5

Electrical Conductivity and Doping

119

76. Q.L. Gu, C.C. Ling, X.D. Chen, C.K. Cheng, A.M.C. Ng, C.D. Beling, S. Fung, G. Brauer, H.C. Ong, Appl. Phys. Lett. 90, 122101 (2007) 77. W.I. Park, G.-C. Yi J.-W. Kim, S.-M. Park, Appl. Phys. Lett. 82, 4358 (2003) 78. Y.W. Heo, L.C. Tien, D.P. Norton, S.J. Pearton, B.S. Kang, F. Ren, J.R. LaRoche, Appl. Phys. Lett. 85, 3107. (2004) 79. M. Nakano, A. Tsukazaki, R.Y. Gunji, K. Ueno, A. Ohtomo, T. Fukumura, M. Kawasaki, Appl. Phys. Lett. 91, 142113 (2007) 80. H.K. Kim, S.H. Han, T.Y. Seong, W.K. Choi, Appl. Phys. Lett. 77, 1647 (2000) 81. H.K. Kim, K.K. Kim, S.J. Park, T.Y. Seong, I. Adesida, J. Appl. Phys. 94, 4225 (2003) 82. K. Ip, Y.W. Heo, K.H. Baik, D.P. Norton, S.J. Pearton, F. Ren, Appl. Phys. Lett. 84, 544 (2004) 83. L.J. Mandalapu, Z. Yang, J.L. Liu, Appl. Phys. Lett. 90, 252103 (2007) 84. Y.F. Lin, W.B. Jian, C.P. Wang, Y.W. Suen, W.u. Z.-Y., F.R. Chen, J.J. Kai, J.J. Lin, Appl. Phys. Lett. 90, 223117 (2007) 85. Th. Weimann, P. Hinze, E. Schlenker, A. Bakin, A. Che Mofor, A. Behrends, A. Waag, Microelectron. Eng. 85(5–6), 1248 (2008) 86. K. Miyamoto, M. Sano, H. Kato, T. Yao, J. Crystal Growth, 265, 34 (2004) 87. A. Tsukazaki, A. Ohtomo, M. Kawasaki, Appl. Phys. Lett. 88 (2006) 88. M.W. Allen, S.M. Durbin, J.B. Metson, Appl. Phys. Lett. 91, 053512 (2007) 89. P. Wagner, R. Helbig, Journal of Physics and Chemistry of Solids, 35, 327 (1974) 90. D.C. Look, G.C. Farlow, P. Reunchan, S. Limpijumnong, S.B. Zhang, K. Nordlund, Phys. Rev. Lett. 95, 225502 (2005) 91. K. Maeda, M. Sato, I. Niikura, T. Fukuda, Semiconduct. Sci. Technol. 20(4), S49 (2005) 92. A. Tsukazaki, A. Ohtomo, D. Chiba, Y. Ohno, H. Ohno, M. Kawasaki, Appl. Phys. Lett. 93, 241905 (2008) 93. A. Tsukazaki, A. Ohtomo, T. Kita, Y. Ohno, H. Ohno, M. Kawasaki, Science, 315, 1388 (2007) 94. A. Tsukazaki, H. Yuji, S. Akasaka, K. Tamura, K. Nakahara, T. Tanabe, H. Takasu, A. Ohtomo, M. Kawasaki, Appl. Phys. Express 1, 055004 (2008) 95. K. Koike, K. Hama, I. Nakashima, G. Takada, M. Ozaki, K. Ogata, S. Sasa, M. Inoue, M. Yano, Jpn. J. Appl. Phys. 43(2), L1372 (2004) 96. H. Tampo, H. Shibata, K. Maejima, A. Yamada, K. Matsubara, P. Fons, S. Kashiwaya, S. Niki, Y. Chiba, T. Wakamatsu, H. Kanie, Appl. Phys. Lett. 93, 202104 (2008) 97. A. Tsukazaki, A. Ohtomo, T. Kita, Y. Ohno, H. Ohno, M. Kawasaki, Science 315, 1388 (2007) 98. T. Edahiro, N. Fujimura, T. Ito, J. Appl. Phys. 93, 7673 (2003) 99. J.D. Albrecht, P.P. Ruden, S. Limpijumnong, W.R.L. Lambrecht, K.F. Brennan, J. Appl. Phys. 86, 6864 (1999) 100. K. Eda, IEEE Electr. Insul. Mag: (5)28 (1989) 101. M. Matsuoka, Matsushita Electric, Japan, (1968) 102. M. Matsuoka, Jpn. J. Appl. Phys. 10, 736 (1971) 103. L.M. Levinson, H.R. Philipp, J. Appl. Phys. 46, 1332 (1975) 104. G.E. Pike, Phys. Rev. B. 30, 795 (1984) 105. K. Eda, in Materials Research Society Symposia Proceedings: Grain Boundaries in Semiconductors ed. by H.J. Leamy, G.E. Pike, C.H. Seager, B de. (Elsevier, New York, 1982), p. 381 106. H.R. Philipp, L.M. Levinson, J. Appl. Phys. 50, 383 (1979) 107. F. Stucki, F. Greuter, Appl. Phys. Lett. 57, 446 (1990) 108. E. Schlenker, A. Bakin, T. Weimann, P. Hinze, D.H. Weber, A. G¨olzh¨auser, H.H. Wehmann, A. Waag, Nanotechnology 19, 365707 (2008) 109. S.A. Studenikin, N. Golego, M. Cociveraa, J. Appl. Phys. 87, 2413 (2000) 110. W. G¨opel, U. Lampe, Phys. Rev. B. 22, 6447 (1980) 111. R.K. Willardson, T.C. Harman, A.C. Beer, Phys. Rev. B. 96, 1512 (1954)

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]

121

122

C. Klingshirn

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.

6

Intrinsic Linear Optical Properties Close to the Fundamental Absorption Edge

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