Springer Series in

materials science 120

Springer Series in

materials scienceEditors: 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. Recognizingthe increasing importance of materials science in future device technologies, the book titles in thisseries ref lect the state-of-the-art in understanding and controlling the structure and propertiesof all important classes of materials.

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

Claus F. KlingshirnBruno K. MeyerAndreas WaagAxel HoffmannJean Geurts

Zinc OxideFrom Fundamental PropertiesTowards Novel Applications

123

With 226 Figures

Professor Dr. Claus F. KlingshirnInstitute for Applied PhysicsKarlsruhe Institute of Technology (KIT)Wolfgang-Gaede-Str. 176131 Karlsruhe, GermanyE-mail:

Professor Dr. Andreas Waag

Institut fur HalbleitertechnikHans-Sommer-Str. 6638106 Braunschweig, GermanyE-mail: a.waag@tu-bs.de

Professor Dr. Bruno K. MeyerUniversitat Gießen, Physikalisches InstitutHeinrich-Buff-Ring 1635392 Gießen, GermanyE-mail:Bruno.K.Meyer@exp1.physik.uni-giessen.de

Professor Dr. Axel HoffmannTU Berlin, Fakutat IIMathematik und NaturwissenschaftenInstitut fur FestkorperphysikHardenbergstr. 3610623 Berlin, GermanyE-mail: hoffmann@physik.tuberlin.de

Professor Dr. Jean Geurts¨ ¨

Am Hubland, 97074 Wurzburg, Germany

Series Editors:

Professor Robert HullUniversity of VirginiaDept. of Materials Science and EngineeringThornton HallCharlottesville, VA 22903-2442, USA

Professor Chennupati JagadishAustralian National UniversityResearch School of Physics and EngineeringJ4-22, Carver BuildingCanberra ACT 0200, Australia

Professor R. M. Osgood, Jr.Microelectronics Science LaboratoryDepartment of Electrical EngineeringColumbia UniversitySeeley W. Mudd BuildingNew York, NY 10027, USA

Professor Jurgen ParisiUniversitat Oldenburg, Fachbereich PhysikAbt. Energie- und HalbleiterforschungCarl-von-Ossietzky-Straße 9–1126129 Oldenburg, Germany

Dr. Zhiming WangUniversity of ArkansasDepartment of Physics835 W. Dicknson St.Fayetteville, AR 72701, USA

Professor Hans WarlimontDSL Dresden Material-Innovation GmbHPirnaer Landstr. 17601257 Dresden, Germany

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Preface

After the invention of semiconductor-based rectifiers and diodes in the first half ofthe last century, the advent of the transistor paved the way for semiconductors inelectronic data handling starting around the mid of the last century. The transistorswidely replaced the vacuum tubes, which had even been used in the first generationof computers, the Z3 developed by Konrad Zuse in the 1940s of the last century.

The first transistors were individually housed semiconductor devices, which hadto be soldered into the electric circuits. Later on, integrated circuits were developedwith increasing numbers of individual elements per square inch.

The materials changed from, e.g., PbS and Se in rf-detectors and rectifiers usedfrequently in the first half of the last century over the group IV element semiconduc-tor 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 dependencesignificantly. Therefore, the logical step was to try GaAs with a band gap of 1.4 eVnext. However, the technology of this semiconductor from the group of III–V com-pounds proved to be much more difficult, though beautiful device concepts had beendeveloped. Therefore, GaAs and its alloys and nano structures with other III–V com-pounds like AlGaAs or InP remained restricted in electronics to special applicationslike transistors for extremely high frequencies, the so-called high electron mobilitytransistors (HEMT). The IT industry is still mainly based on Si and will remain soin the foreseeable nearer future. The story up to the mid 1980s of the last centuryhas been written up, e.g., by H. Queisser in his book “Kristallene Krisen,” 2nd ed.,Piper, Munchen (1987).

However, the III–V compounds mentioned above found their place in the fieldof light-emitting semiconductor devices like light-emitting diodes (LED) or laserdiodes (LD), since many of the III–V compounds are direct gap materials, whilethe group IV element and compound semiconductors like Ge, Si, SiC, or C (dia-mond) 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, orporous or amorphous Si. The use of inorganic and organic semiconductors (LEDsand O-LEDs) for lighting purposes is envisaged, while the use of the former indata storage and reading (CD, DVD, and blue ray discs), in scanners, displays,traffic lights, in data transmission through glass fibres, etc., is already well estab-lished. 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 ofoptoelectronics.

LEDs exist for the whole visible spectral range including the near IR for glassfibre data transmission and the near UV, but for LDs, there is still a gap in the yellow-green spectral range, which prevents the use of LDs in full color, high brightnessdisplays, e.g., in projectors. On the other hand, the (near) UV is technically veryattractive since shorter wavelengths allow increasing the data density in optical stor-age, to write smaller structures for the masks of integrated circuits and to excitea wide variety of phosphors covering the whole visible spectrum and being usedalready as one possibility to produce white light LEDs.

The first successful attempt to produce short wavelength LDs was based on theII–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 opti-cal 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 commercialproduct, 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 isdocumented, e.g., by S. Nakamura, S. Pearton, and G. Fasol in their book “The BlueLaser Diode: the Complete Story,” 2nd ed., Springer, Heidelberg (2000). A mainproblem to solve was ambipolar doping. Many of the wide gap semiconductors areeasily 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 GaNsingle 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 foralternative materials. An obvious choice is the II–VI semiconductor ZnO. It has aband 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 manyauthors as big advantage. Indeed, it allows doing nice basic exciton physics but ismuch less important for the applications in optoelectronics in contrast to what isclaimed 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 begrown as large single crystals by various methods, or that it has a strong tendencyto grow in a self-organized way in the form of nano- and microrods with diametersranging from a few ten nanometers to a micrometer and lengths of several to beyondten micrometers. These nanorods hold big promises in miniaturized optoelectronicsand sensing. By alloying with MgO or CdO, the band gap can be shifted either fur-ther into the UV or down into the green spectral ranges, respectively. Additionally,there are many other existing or emerging applications of ZnO. The big drawbackof 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 itsgrowth or its electronic, phononic, magnetic, and optical properties, with someemphasis on the latter since the hope for optoelectronic devices based on ZnO isthe 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-baseddevices. More details about the contents of this book and the philosophy behind aregiven in the introduction.

The book is equally well suited for graduate students and scientists in physicswho have a good background in solid state physics and are entering the field ofZnO research and development and for those coming from engineering disciplineswho frequently do not yet have this background. For them, the book by one of theco-authors (CK) on “Semiconductor Optics,” 3rd ed., Springer, Heidelberg (2007)might be additionally helpful.

Karlsruhe, Claus Franz KlingshirnGießen, Bruno K. MeyerBraunschweig, Andreas WaagBerlin, Axel HoffmannWurzburg, Jean GeurtsMay 2010

•

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1C. Klingshirn1.1 History of ZnO Research and Contents of This Book . . . . . . . . . . . . . . . . 21.2 Aim of This Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Crystal Structure, Chemical Binding, and LatticeProperties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7J. Geurts2.1 Crystal Structure and Chemical Binding .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.1.1 ZnO Polytype Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.1.2 Phase Transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.1.3 Crystal Axis Polarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2 Thermal Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2.1 Thermal Expansion Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2.2 Specific Heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.2.3 Thermal Conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.3 The Piezoelectric Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.3.1 Principle and Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.3.2 The Piezoelectric Tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.4 Lattice Dynamics .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.4.1 Phonon Symmetry and Eigenvectors of the

Wurtzite Lattice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.4.2 Phonon Dispersion Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.4.3 Infrared Optical Phonon Spectroscopy . . . . . . . . . . . . . . . . . . . . . . 212.4.4 Raman Spectroscopy of Phonon Modes . . . . . . . . . . . . . . . . . . . . . 232.4.5 Vibration Modes in Doped ZnO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.4.6 Incorporation of Transition Metal Atoms in ZnO .. . . . . . . . . . 282.4.7 Raman Scattering from ZnO Nanoparticles . . . . . . . . . . . . . . . . . 30

2.5 Phonon–Plasmon Mixed States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312.5.1 Collective Charge-Carrier Oscillations . . . . . . . . . . . . . . . . . . . . . . 322.5.2 Coupling to Polar Longitudinal Phonons .. . . . . . . . . . . . . . . . . . . 33

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

ix

x Contents

3 Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39Andreas Waag3.1 Bulk Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.1.1 Vapor Phase Transport. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403.1.2 Solvothermal Growth .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.2 Epitaxial Growth Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423.2.1 Metal Organic Chemical Vapor Deposition . . . . . . . . . . . . . . . . . 463.2.2 Molecular Beam Epitaxy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533.2.3 Pulsed Laser Deposition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

3.3 Growth of Self-Organized Nanostructures .. . . . . . . . . . . . . . . . . . . . . . . . . . . 663.3.1 Growth Techniques for Nano Pillars. . . . . . . . . . . . . . . . . . . . . . . . . 673.3.2 Properties of Nanopillars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

4 Band Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77B.K. Meyer4.1 The Ordering of the Bands at the Valence Band Maximum in ZnO . 774.2 ZnO and Its Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

4.2.1 Cationic Substitution: Mg, Cd, Be in ZnO . . . . . . . . . . . . . . . . . . 854.2.2 Anionic Substitution: S, Se in ZnO . . . . . . . . . . . . . . . . . . . . . . . . . . 89

4.3 Valence and Conduction Band Discontinuities . . . . . . . . . . . . . . . . . . . . . . . 914.3.1 Iso-Valent Hetero-Structures .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 914.3.2 Hetero-Valent Hetero-Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

5 Electrical Conductivity and Doping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95Andreas Waag5.1 Introduction .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 955.2 Hydrogen in ZnO.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 975.3 Donors in ZnO: Al, Ga, In . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 985.4 Acceptors in ZnO.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 995.5 Mobility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1045.6 Ohmic and Schottky Contacts on ZnO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1055.7 Two-Dimensional Electron Gas and Quantum Hall Effect . . . . . . . . . . .1085.8 High-Field Transport and Varistors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1105.9 Photoconductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .114References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .117

6 Intrinsic Linear Optical Properties Closeto the Fundamental Absorption Edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .121C. Klingshirn6.1 Free Excitons in Bulk Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .121

6.1.1 Free Excitons in Bulk Samples, EpitaxialLayers, and NanoRods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .125

6.1.2 Experimental Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1296.2 ZnO-Based Alloys. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .145

Contents xi

6.3 Surface Exciton Polaritons .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1506.4 Excitons in Structures of Reduced Dimensionality . . . . . . . . . . . . . . . . . . .153

6.4.1 Excitons in Quantum Wells and Superlattices . . . . . . . . . . . . . .1536.4.2 Quantum Wires . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1556.4.3 Quantum Dots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1586.4.4 Cavity Polaritons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .162

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .163

7 Bound Exciton Complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .169B.K. Meyer7.1 ZnO Luminescence: An Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1697.2 Neutral Donor Bound Excitons (A-Valence Band)

and Their Two Electron Satellites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1727.3 Ionized Donor Bound Excitons (A-Valence Band) . . . . . . . . . . . . . . . . . . .1777.4 A Comparison of the Localization Energies with

Theoretical Predictions (the Haynes Rule) . . . . . . . . . . . . . . . . . . . . . . . . . . . .1807.5 Excited State Properties of the Bound Excitons . . . . . . . . . . . . . . . . . . . . . .1837.6 Donor–Acceptor Pair Transitions.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .189References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .197

8 Influence of External Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .201M.R. Wagner and A. Hoffmann8.1 Excitons in Magnetic Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .201

8.1.1 Zeeman Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2028.1.2 Free and Bound Excitons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2038.1.3 Selection Rules for Zeeman Splitting of

Exciton States in Magnetic Fields . . . . . . . . . . . . . . . . . . . . . . . . . . .2128.1.4 Symmetry of Exciton Hole States . . . . . . . . . . . . . . . . . . . . . . . . . . .213

8.2 Excitons in Strain Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2158.2.1 Uniaxial Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2178.2.2 Hydrostatic Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2198.2.3 Biaxial In-Plane Strain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .225

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .229

9 Deep Centres in ZnO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .233A. Hoffmann, E. Malguth, and B.K. Meyer9.1 The Green and Yellow Emission Bands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2339.2 Transition Metal Ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .239

9.2.1 ZnO/V .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2419.2.2 ZnO/Fe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2449.2.3 ZnO/Fe3C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2459.2.4 ZnO/Fe2C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2499.2.5 ZnO/Co. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2539.2.6 ZnO/Ni . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2549.2.7 ZnO/Cu. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .258

9.3 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .264References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .264

xii Contents

10 Magnetic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .267Andreas Waag10.1 General Overview of the Topic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26710.2 Short Overview of the Situation in ZnO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .269References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .272

11 Nonlinear Optics, High Density Effects and StimulatedEmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .275C. Klingshirn11.1 Nonlinear Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27511.2 High Excitation Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .277

11.2.1 The Intermediate Density Regime . . . . . . . . . . . . . . . . . . . . . . . . . . .27711.2.2 Electron–Hole Plasma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .282

11.3 Processes for Stimulated Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .28511.3.1 Bulk Samples and Epilayers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .28611.3.2 Quantum Wells and Superlattices . . . . . . . . . . . . . . . . . . . . . . . . . . . .29311.3.3 Nano Rods and Their Cavity Modes . . . . . . . . . . . . . . . . . . . . . . . . .29411.3.4 Quantum Dots and Random Lasing . . . . . . . . . . . . . . . . . . . . . . . . .29611.3.5 Cavity Modes, Photonic Crystals and

Polariton Lasers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .299References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .302

12 Dynamic Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .307C. Klingshirn12.1 Dephasing Dynamics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30812.2 Relaxation Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31112.3 Recombination Dynamics.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .314References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .320

13 Past, Present and Future Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .325C. Klingshirn13.1 Past Applications .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .325

13.1.1 The Electro Fax Copy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32513.1.2 Ferrite Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .326

13.2 Present and Emerging Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32613.2.1 Cement, Rubber, Paint and Glazes . . . . . . . . . . . . . . . . . . . . . . . . . . .32613.2.2 Catalysts, Pharmaceutics, Cosmetics and Food Additives . .32713.2.3 Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32713.2.4 Gas Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33013.2.5 TCO, Solar Cells and Some Further Applications . . . . . . . . . .331

13.3 Visions of Future Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33213.3.1 pn Junctions .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33313.3.2 Light Emitting Diodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33413.3.3 Field Emitters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33813.3.4 Spintronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .338

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .339

Contents xiii

14 Conclusion and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .347C. Klingshirn14.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .34714.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .348References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .349

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .351

Chapter 1Introduction

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 andthe intentions of the authors.

Zinc oxide (ZnO) is a IIb–VI compound semiconductor. This group comprisesthe binary compounds of Zn, Cd and Hg with O, S, Se, Te and their ternary and qua-ternary alloys. The band gaps of these compounds cover the whole band gap rangefrom Eg � 3:94 eV for hexagonal ZnS down to semimetals (i.e., Eg D 0 eV) formost of the mercury compounds. ZnO itself is also a wide gap semiconductor withEg � 3:436 eV at T D 0 K and (3:37 ˙ 0:01) eV at room temperature. For moredetails on the band structure, see Chaps. 4 and 6 or for a recent collection of data onZnO, for example, [Rossler et al. (eds) Landolt-Bornstein, 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 atetrahedral coordination. In contrast to several other IIb–VI compounds, which occurboth 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 inthe 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. Solids15:86, 1960], the largest among the IIb–VI compounds, but by far not the largest forall semiconductors since, for example, CuCl and CuO have exciton binding ener-gies around 190 and 150 meV, respectively. See, for example, [Rossler et al. (eds)Landolt-Bornstein, 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;Honerlage et al., Phys. Rep. 124:161, 1985] and references therein. More details onexcitons will be given in Chap. 6.

ZnO has a density of about 5:6 g=cm3 corresponding to 4:2 � 1022 ZnOmolecules per cm3 [Hallwig and Mollwo, Verhandl. DPG (VI) 10, HL37, 1975].

ZnO occurs naturally under the name zinkit. Owing to the incorporation of impu-rity atoms such as Mn or Fe, zinkit looks usually yellow to red. Pure, synthetic ZnO

C. KlingshirnInstitut fur Angewandte Physik, Karlsruher Institut fur Technologie KIT, Karlsruhe, Germanye-mail: claus.klingshirn@kit.edu

1

2 C. Klingshirn

is colourless and clear in agreement to the gap in the near UV. The growth of ZnOand ZnO-based nano-structures is treated in Chap. 3.

ZnO is used by several 100,000 tons per year, for example, as additive to concreteor to the rubber of tires of cars. In smaller quantities, it is used in pharmaceuticalindustries, as an additive to human and animal food, as a material for sensors and forvaristors or as transparent conducting oxide. For more details and aspects of presentand 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 ZnOper 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 ZnOgoes back to the first half of the last century and started, for example, with investiga-tions of ion radii and crystal structure, the specific heat, even at low temperatures, itsdensity or its optical properties [1–10] and references given therein. Early examplesof ZnO growth, even in the form of thin (partly epitaxial) layers or of tetrapods canbe found, for example, in [11–18] and first reviews on ZnO including the electronictransport (see Chap. 5) and optical properties (see Chaps. 6–9, 11 and 12) appearedstarting 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 mid1980s, driven by the availability of good bulk single crystals and first epitaxial lay-ers [14–18]. The central topics at that time were, apart from the growth, dopingand electric transport (see Chap. 5), the band structure and free or bound exci-tons (Chaps. 4 and 6–8, respectively), deep centres investigated in luminescenceor 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 var-ious reviews, which are partly or completely dedicated to ZnO and entered also asexamples in some textbooks [26–32]. In the mid of the 80s, the interest in ZnO fadedaway essentially for two reasons:

One was the problem of ambipolar doping of ZnO. Although ZnO can be easilyn-type doped by Al, Ga or In on Zn site up to the range of n � 1020cm�3 [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 semi-conductor applications in opto-electronics. The absence of p-doping at that timedestroyed the hope to obtain with ZnO a material for semiconductor laser-diodesin the blue, violet, or near UV spectral ranges. The other reason was the adventof structures of reduced dimensionality such as quantum wells and superlatticesand later on of quantum wires and dots. In their early years, these structures werealmost exclusively based on III–V compounds, especially on the lattice matchedsystem GaAs=Al1�yGayAs. For recent textbooks or data collections of this topicsee for example [32, 39].

1 Introduction 3

The need for blue/UV laser-diodes (LD) remained and after an intermezzo withZnSe-based LD structures, which unfortunately never exceeded a lifetime of a few100 h, the group III nitrides made it [40]. However, gradually it became evident thatGaN and its alloys with AlN and InN are rather difficult materials because patentsconcerning LD are in the hands of a few companies with partly rather restrictivelicence politics and ZnO and its alloys with MgO, BeO or CdO have partly similarproperties as GaN (e.g., concerning band gap, crystal structure, carrier mobilitiesor heat conductivity) and also some advances, for example, the availability of largesingle crystals for homo epitaxy, the insensitivity against radiation damage, the factthat ZnO is cheaper and not poisonous or the fact that magnetic dopants such asCo, Mn or Fe do not introduce simultaneously carrier doping as is the case in III–Vsemiconductors. Finally, the patent situation is for ZnO still more open.

Additionally ZnO has a strong tendency for self-organized growth of nano-structures, above all of nano-rods (see Chap. 3) but also of many other types ofnano-structures like tetrapods (or fourlings), nano-belts, -ribbons, -nails, -combs,-flowers, -walls, -castles, -tubes, -wool, -corals, or -cabbage, etc., depending on theimagination of the respective author and from which especially the last mentionedones 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, dilutedmagnetic ZnO-based samples may be formed, which possibly show weak ferromag-netism up to RT (see Chap. 10).

All these partly application-oriented aspects, for example, progress in the growthof nano-structures such as quantum wells and nano-rods, progress in p-type dopingand first reports of light emission from electrically pumped ZnO-based homo orhetero junctions (e.g., see the reviews [41–52] and the references given therein) andsome more application aspects, which we present in Chap. 13, are the reason for therenaissance of ZnO research during the last decade. The progress of the field can beseen in the contributions to and proceedings of international or national conferencesand workshops such as the proceedings of the International Conference on II–VICompounds 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 prop-erties of ZnO are being rediscovered – but also beautiful new results are obtainedby research groups from all over the world – and this is the main aspect. The topicsof research and development are partly the same as in the 1970s and 1980s (andthus partly to some extent a kind of repetition), such as growth, doping, linear andnonlinear optics, including the aspects of stimulated emission; new ones are alsoadded such as the growth of nano-structures, p-type doping and the developmentof light emitting or even laser diodes (L(E)Ds), the investigation of semi magneticalloys, the use of ZnO as transparent conducting oxide (TCO) in solar cells, as sen-sor 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 ofZnO in a didactical way without too much of theoretical ballast, especially thosethat are relevant for present and possible future applications, and second to reviewjust these applications. The topics that we shall treat to this end have been alreadymentioned in the subsection above.

Despite of the numerous recent review articles, books or conference proceedingslisted above and some other ones, which will be most probably under way duringthe writing of this book by other authors (actually the recent, over large parts alsovery good book [53] or [55,56] are example for this expectation), the authors of thisbook think that it is worthwhile to publish this work because there is, apart fromthe two aims mentioned above, a third one, namely, to really critically review ofthe old and new data concerning, for example, the valence band structure, magneticproperties 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 cer-tain amount of enthusiasm is necessary and helpful. However, the authors feel thatnot a too small fraction of papers or conference contributions is too euphoric andoveroptimistic in the sense that (frequently good) data are over interpreted, with-out taking too much care about consistency or plausibly of their interpretations norof past results. This aspect can be especially annoying when reviewing some ofthe recently submitted papers. The other aspect is that ambitious young scientistsfrequently either simply do not know or do not bother about the fact that manythings, which they enthusiastically want to present as new, are actually known sincedecades. For example, it is not acceptable that a group cites a paper for the exci-ton binding energy of 60 meV, which is just about 5 years old (possibly even fromtheir own group) without giving credit to much earlier work (in this case, e.g., byThomas and Hopfield and other authors [1, 54]) who published this value alreadymore than 40 years ago. The authors think that this phenomenon touches the boarderof scientific correctness.

The team of the authors of this book comprises young scientists, who started towork on ZnO only several years ago, and others, who are familiar with this materialsince over three decades. On the one hand, this combination may help to reach theabove aims. On the other hand, the authors are aware of the fact that they them-selves will make in this book their own mistakes and will inevitably miss relevantresults and references. Concerning the first aspect, the authors will appreciate com-ments from critical readers. The second point is an inherent problem. Nobody canread or know the over 26,000 ZnO-relevant publications mentioned at the beginningof this section nor the 2,000 new ones appearing every year. Therefore, the refer-ences of this book are necessarily limited and their choice is partly arbitrary or evenaccidental.

Concerning the (co-) authors of the cited references, we give in all chapters allof them up to a maximum number of three, while some of the authors give onlythe 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 fromthe own work of the authors of the respective chapters. Figures from other authorsare frequently modified for the purpose of this book, for example, by adding aphoton energy scale to a wave length scale to make the data of different figurescomparable, but in all cases the proper references are given. The authors like tothank their colleagues and various publishing houses for the permission to use theirmaterial in this book.

As a few minor final comments, it should be noted that every chapter, includingthis one, has at its beginning under the headline “abstract” a short summary of andpartly also an introduction to the topics of this chapter. The references for eachchapter are given directly at the end of this chapter. A collection of keywords andthe pages, where they appear, are given at the end of this book excluding generallyreferences to keywords appearing in the headlines of chapters or sections.

References

1. U. Rossler et al. eds., Landolt-Bornstein, 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. Kroger, Physica, 7, 1 (1940)9. F.A. Kroger, H.J. Meyer, Physica, 20, 1149 (1954)

10. C.W. Bunn, Proc. Phys. Soc. Lond. A Math. Phys. Sci. 47, 835 (1935)11. Landolt-Bornstein, 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. Stockmann, 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. Honerlage 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. Hummer, Exzitonische Polaritonen in einachsigen Kristallen, Habilitation Thesis, Erlangen

(1978)

6 C. Klingshirn

31. M. Ueta et al. Excitonic Processes in Solids, Springer Series in Solid State Science, 60 (1986)32. C. Klingshirn, Semiconductor Optics, 3rd edn. (Springer, Berlin, 2007)33. M. Ataev et al. Thin Solid Films 260, 19 (1995)34. M. Goppert et al. J. Lumin. 72–74, 430 (1997)35. S.Y. Myong et al. Jpn. J. Appl. Phys. 36, L1078 (1997)36. H. Kato et al. J. Cryst. Growth 237–239, 538 (2002)37. T. Makino et al. Appl. Phys. Lett. 85, 759 (2004)38. T.V. Butkhuzi et al. J. Cryst. Growth 117, 366 (1992)39. Landolt-Bornstein, New Series, Group III, Vol. 34C C. Klingshirn ed., Springer, Berlin (2001)40. S. Nakamura, G. Fasol, The Blue Laser Diode (Springer, Heidelberg, 1997)41. D.C. Look et al. Phys. Stat. Sol. A 201, 2203 (2004)42. C. Klingshirn et al. Adv. Solid State Phys. 45, 261 (2005)43. U. Ozgur et al. J. Appl. Phys. 98, 041301 (2005)44. C. Klingshirn et al. Phy. J. 5(1), 33 (2006)45. A. Osinsky, S. Karpov in ZnO Bulk, Thin Films and Nanostructures, ed. By C. Jagadish,

S.J. Pearton p525 (Elsevier, London, 2006), p. 52546. N.H. Nickel and E. Terukov eds., Zinc Oxide – A Material for Micro- and Optoelectronic

Applications, NATO Science Series II, 194 (2005)47. C. Jagadish, S.J. Pearton (eds.) Zinc Oxide Bulk, Thin Films and Nanostructures (Elsevier,

Amsterdam, 2006)48. C. Klingshirn, Chem. Phys. Chem. 8, 782 (2007)49. C. Klingshirn et al. Superlattice Microst. 38, 209 (2005)50. C. Klingshirn et al. NATO Sci Series II 231, 277 (2006)51. S. Tuzemen, E. Gur, Opt. Mater. 30, 292 (2007)52. C. Klingshirn, Phys. Stat. Sol. B 244, 3027 (2007)53. H. Morkoc, U. Ozgur, Zinc Oxide (Wiley-VCH, Weinheim, 2009)54. D.G. Thomas, J. Phys. Chem. Solids 15, 86 (1960)55. M. Willander et al. Nanotechnology 20, 332001 (2009)56. C. Klingshirn et al. Phys. Stat. Sol. B 247, 1424 (2010)

Chapter 2Crystal Structure, Chemical Binding,and Lattice Properties

J. Geurts

Abstract This chapter starts with an overview of the ZnO crystal structure and itsconjunction to the chemical binding. ZnO commonly occurs in the wurtzite struc-ture. This fact is closely related to its tetrahedral bond symmetry and its prominentbond polarity. The main part of the first section deals with the ZnO wurtzite crystallattice, its symmetry properties, and its geometrical parameters. Besides wurtziteZnO, the other polytypes, zinc-blende and rocksalt ZnO are also briefly discussed.

Subsequently, lattice constant variations and crystal lattice deformations aretreated. This discussion starts with static lattice constant variations, induced by tem-perature or by pressure, as well as strain-induced static lattice deformation, whichreduces the crystal symmetry. The impact of this symmetry reduction on the elec-trical polarization is the piezo effect, which is very much pronounced in ZnO and isexploited in many applications. See also Chap. 13.

Dynamic lattice deformations manifest themselves as phonons and, in case ofdoping, as phonon–plasmon mixed states. The section devoted to phonons startswith a consideration of the vibration eigenmodes and their dispersion curves. Spe-cial attention is paid to the investigation of phonons by optical spectroscopy. Themethods applied for this purpose are infrared spectroscopy and, more often, Ramanspectroscopy. The latter method is very common for the structural quality assess-ment of ZnO bulk crystals and layers; it is also frequently used for the study of theincorporation of dopant and alloying atoms in the ZnO crystal lattice. Thus, it playsan important role with regard to possible optoelectronics and spintronics applica-tions of ZnO.

The final section of this chapter focuses on phonon–plasmon mixed states. Theseeigenstates occur in doped ZnO due to the strong coupling between collective free-carrier oscillations and lattice vibrations, which occurs due to the high bond polarity.Owing to the direct correlation of the plasmon–phonon modes to the electronicdoping, they are an inherent property of ZnO samples, when applied in (opto-)electronics and spintronics. See also Chap. 12.

J. GeurtsPhysikalisches Institut der Universitat Wurzburg, Wurzburg, Germanye-mail: geurts@physik.uniwuerzburg.de

7

8 J. Geurts

2.1 Crystal Structure and Chemical Binding

ZnO is a semiconducting compound of the group-IIb element 30Zn and the group-VI element 8O. Zinc has five stable isotopes, the prevalent ones are 64Zn (48.89%),66Zn (27.81%), and 68Zn (18.57%), while oxygen almost purely consists of the iso-tope 16O (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 theresulting semiconducting crystal, the bonding sp3 states constitute the valence band,while the conduction band originates from its antibonding counterpart. The resultingenergy gap is 3.4 eV, i.e. in the UV spectral range, which has triggered interest inZnO as a material for transparent electronics. The cohesive energy per bond is ashigh as 7.52 eV [2], which also leads to a very high thermal stability: The meltingtemperature, Tm D 2;242 K. For comparison, the melting temperature of ZnSe isconsiderably lower: Tm;ZnSe D 1;799 K [1].

2.1.1 ZnO Polytype Structures

The tetrahedrally coordinated bonding geometry determines the ZnO crystal struc-ture. Each zinc ion has four oxygen neighbour ions in a tetrahedral configurationand vice versa. This geometrical arrangement, which is well known from, for exam-ple, the group-IV elements C (diamond), Si, and Ge, is also common for II–VI andIII–V compounds. It is referred to as covalent bonding, although the bonds mayhave a considerable degree of polarity when partners with different electronega-tivity are involved. The tetrahedral geometry has a rather low space filling and isessentially stabilized by the angular rigidity of the binding sp3 hybrid orbitals. In acrystal matrix, the neighbouring tetrahedrons form bi-layers in the ZnO case, eachone consisting of a zinc and an oxygen layer. Generally, this arrangement of tetra-hedrons may result either in a cubic zinc-blende-type structure or in a hexagonalwurtzite-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 arrange-ment of two interpenetrating face-centred cubic sub-lattices, displaced by 1=4 of thebody diagonal axis. The bonding orbitals are directed along the four body diagonalaxes. Note that the cubic unit cell is not the smallest periodic unit of a zinc-blendecrystal, i.e. it is not a primitive unit cell. See also the comment in [3]. The primi-tive unit cell of zinc-blende is an oblique parallelepiped and contains only one pairof ions, in our case, Zn2C and O2�. In group theory, this lattice is classified by itspoint group Td (Schoenflies notation) or N4 3m (international notation) and by itsspace group, denoted as T2

d or F N4 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 beenprinted upside down. Its distinct axis, referred to as c-axis, is directed along one of

2 Crystal Structure, Chemical Binding, and Lattice Properties 9

a

b

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

the tetrahedral binding orbitals. This implies that the hexagonal c-axis correspondsto a body diagonal axis of the cubic structure. In the plane perpendicular to thec-axis, the primitive translation vectors a and b have equal length and include anangle of 120ı. In contrast to zinc-blende, the wurtzite primitive unit cell containstwo pairs of ions, in our case, two ZnO units. In group theory, this lattice typeis classified by its point group 6 mm (international notation) or C6v (Schoenfliesnotation) and by its space group P 63mc or C 4

6v, respectively. The orientation ofaxes and faces in a wurtzite lattice is denoted by four-digit Miller indices hkil. Thec-axis direction is referred to as [0001], the surface perpendicular to the c-axis isthe hexagonal (0001) plane.

The natural crystal structure of ZnO is the hexagonal wurtzite structure. At ambi-ent 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 cm�3 [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 thePauling scale [6]. This is the second highest value of all chemical elements, it comesafter the fluorine value of 4.0. Together with the quite low zinc electronegativityvalue 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. theZnO binding is at the border between the semiconductors, the binding of which iscommonly classified as (predominantly) covalent, while the (predominantly) ionicbinding 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 effectivecharge 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 structureinstead of the zinc-blende structure, which occurs for tetrahedrally oriented bondswith lower polarity (e.g. in many II–VI compounds and in almost all III–V com-pounds, such as GaAs). The cubic zinc-blende-type structure of ZnO is obtainedonly by epitaxial growth on a zinc-blende type substrate, e.g. GaAs(100) with aZnS buffer or Pt(111)/Ti/SiO2/Si [8, 9]. Calculations by HF-LCAO (Hartree–Focklinear combination of atomic orbitals) yield the lattice constant a D 0:4614 nm forpressure p D 0 [10].

The experimentally observed preference for the wurtzite structure is confirmedby theoretical results. Among the various methods, best agreement with the exper-iment was obtained for DFT calculations within the generalized gradient approx-imation (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 underscoresthe preference of the wurtzite structure, although the energy difference to thezinc-blende structure is quite low. While numerical values of the reported theo-retical results depend on the applied method, they consistently favour the wurtzitestructure [2].

2.1.2 Phase Transitions

Owing to the near-ionic bond character of ZnO, it is plausible that the applicationof a hydrostatic pressure p leads already at a quite modest value of p � 10 GPa to aphase transition from the wurtzite to the close-packed rocksalt type structure (spacegroup Fm3m), which is the common crystal structure for the class of alkali halideionic crystals [11]. The NaCl structure has a sixfold coordination and a considerablyenhanced space-filling factor. The volume shrinkage at the ZnO phase transition isabout 17% [1]. The experimental values reported for the cubic lattice constant arebetween 0.4271 and 0.4283 nm, confirming the results of calculations with variousmodels [2]. Calculations also predict a further phase transition to the CsCl structureat considerably higher pressure values beyond 250 GPa [12].

A detailed discussion of the wurtzite-to-rocksalt transition behaviour, reportedby various experimental groups, as well as theoretical results, is found in [13] andin an extended ZnO review article [2]. Moreover, the latter article comprises a verydetailed general discussion of the ZnO crystal structure and binding properties witha rich survey of experimental results as well as modelling calculations according todifferent methods.

2.1.3 Crystal Axis Polarity

Because of the prominent bond polarity of ZnO, the c-axis [0001] has a pronouncedpolar 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 otherbonds [1], whereas the ideal tetrahedron value is ˛ D 109:47ı. Therefore, the axislengths ratio amounts to c=a D 1:602, which is about 2% below the value for theideal wurtzite geometry c=a D .8=3/1=2 D 1:633. As a further consequence, the ratiou between the bond length and the length of the c-axis is uZnO D 0:3820, which isenhanced 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 thelargest of all wurtzite-type semiconductors, together with the high-polarity III–Vcompound GaN. This underscores the crucial role of the bond polarity. For com-parison, the wurtzite polytype of the much less polar ZnSe has the ideal c=a ratiowithin 0:5 � 10�3. A systematic analysis of this parameter and its trend among thevarious wurtzite compounds was presented by Lawaetz [14].

Furthermore, the sequence of positively charged Zn2C and negatively chargedO2� ions in planes perpendicular to the c-axis implies two faces of opposite polar-ity for a c-cut ZnO crystal: the Zn-terminated (0001) face on one side and theO-terminated (000N1) face on the other. In contrast, a non-polar character occurs forfaces with equal numbers of Zn and O ions, e.g. the (11N20) plane (perpendicular tothe a-axis) and the (10N10) plane. The opposite polarity of the (0001) and the (000N1)face is reflected e.g. in different etching behaviour, defect characteristics and epi-taxial growth properties. Further consequences of the bond polarity are (1) a stronginfrared activity of some of the ZnO lattice vibration modes, and (2) a pronouncedpiezoelectricity. The latter is caused by the bond polarity together with the non-centrosymmetric crystal structure. These aspects will be discussed in more detail inthe 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 reflectsthe uniaxial character of its crystal structure: As shown in Fig. 2.2, the thermalexpansion coefficients ˛ are strongly direction-dependent. The ˛-values at 300 K,˛kc D 2:9 � 10�6 K�1 for expansion along the c-axis, and ˛?c

D 4:7 � 10�6 K�1

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 Kfor ˛?c

[1,15]. The negative thermal expansion coefficient in the temperature rangebetween roughly 20 and 120 K is a common feature of the tetrahedrally coordi-nated semiconductors. For its explanation, one must take into consideration thatgenerally the origin of thermal expansion is the anharmonicity of the phonon eigen-modes. The volume dependence of the vibration frequency !i (i D mode-index)

12 J. Geurts

c

|| c

ZnO8

6

4

2

0

Temperature (K)0 200 400 600 800 1000

th(1

0–6 K

–1)

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

of each mode is expressed quantitatively in terms of the Gruneisen parameter�i D �@.ln !i /=@.ln V /. For each temperature region, the expansion coefficient isgoverned by the Gruneisen parameters of the modes activated at these tempera-tures. Now, low-frequency phonon modes in the energy range around 100–150 cm�1

have an inverted Gruneisen parameter, resulting in a negative expansion in thecorresponding temperature region.

For possible future applications of the wide-gap material ZnO in high-temperature electronics, the thermal expansion coefficients at elevated temperaturesare of relevance. Ibach presented data up to T D 800 K. As shown in Fig. 2.2, ˛kcand ˛?c

strongly increase with temperature, to saturate near 800 K, yielding thehigh-temperature values ˛kc D 4:98 � 10�6 K�1, and ˛?c

D 8:30 � 10�6 K�1 [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 idealDebye theory were explained by contributions from interstitials (Einstein-term with�E D 56 K), the ordering of which is possibly responsible for a Schottky contri-bution 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 heatdata sets (2) and (3) fairly consistently give the value cp D 9:66 cal mol�1 K�1

and 41:086 J mol�1K�1, respectively. In agreement with the quantum mechanicaloscillator model, the specific heat increases with increasing temperature to level

2 Crystal Structure, Chemical Binding, and Lattice Properties 13

0

Cp (

cal m

ol-1

K-1

)

200 400 600 800 1000temperature (K)

12

10

8

6

4

2

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 mol�1 K�1, is slightly beyond the Dulong–Petit value, which amounts to11:92 cal mol�1 K�1 D 49:90 J mol�1 K�1.

2.2.3 Thermal Conductivity

From the application point of view, the thermal conductivity � is a crucial param-eter for high-power and/or high-temperature electronics. In semiconductors, heattransport essentially takes place by lattice vibrations. It is described by the rela-tion � D cvvs�=3, where cv is the specific heat, vs the sound velocity, and � themean free path of the phonons. In the temperature range above T � 50 K, the mainlimiting factor for the thermal conductivity by lattice vibrations is anharmonicity-induced phonon–phonon scattering. More specifically, with increasing temperature“Umklapp”-processes gain relevance, in which the sum of the involved phonon wavevectors exceeds the Brillouin zone edge, resulting in a decrease of �.

For ZnO, the uniaxial character also dominates the thermal conductivity: it man-ifests 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 from30 to 300 K, the relation is �11 � 1:2�33 [19]. The average thermal conductivity isobtained as �av D .1=3/.2�11 C �33/. Typical values reported for T D 300 K are inthe range �av � 0:6–1 Wcm�1 K�1 [19,20]. With decreasing T , � increases by aboutone order of magnitude to its maximum value �av � 0:55 to 10 Wcm�1 K�1 slightlybelow T D 30 K.

In the low-temperature range, a decrease of � with decreasing temperature isobserved, because the T -dependence of � D cvvs�=3 essentially corresponds tocv � .T=�Debye/

3. The numerical value of � strongly depends on the sample qual-ity because of the �-limitation by crystal defects, disorder, grain boundaries, etc.

14 J. Geurts

k33

103

WKm

102k ii

101 10 102 103K

k11

Zn0

∇T ⊥ C

∇T II C

T

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

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

2.3 The Piezoelectric Effect

2.3.1 Principle and Applications

Generally, the piezoelectric effect describes the connection between an externallyapplied mechanical stress and a macroscopic polarization at zero external electricfield, and vice versa. For ZnO, this effect is extraordinarily prominent. Its piezo-effect 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-IIInitrides, values comparable to ZnO are obtained [21]. Therefore, since many yearsZnO is extensively exploited for electromechanical coupling applications. See alsoSect. 13.2 in Chap. 13. Its realizations include a wide variety of micro- and nano-electromechanical systems (MEMS and NEMS), sensors, and applications in signalprocessing and telecommunications. Among the most ubiquitous applications areZnO acoustic wave devices, especially exploiting surface acoustic waves (SAW) ininterdigital transducers (IDT) for electronic band filtering. In such an IDT, the signalprocessing through a SAW delay line device relies on the generation of a SAW ina piezoelectric ZnO film by a voltage signal (up to �10 GHz) through a lithograph-ically deposited interdigital metal double-comb structure. This wave travels as amechanical distortion along the film, and its electrical polarization induces a voltageresponse in an adjacent similar receiver comb structure. The ZnO film depositionmay take place by a variety of techniques, such as sputtering, chemical vapour depo-sition, 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 awide market in consumer electronics. Recent developments are MgxZn1�xO ternaryfilms (0 � x � 0:3) and ZnO=MgxZn1�xO multilayer structures, which allow thetuneable enhancement of the acoustic wave velocity and the tuning of the piezoelec-tric coupling coefficient. A very detailed discussion of the widespread applicationsis given e.g. in an extended review by Y. Lu [22]. In this section, the fundamentalphysical reasons for the outstanding piezoelectric activity of ZnO are discussed, andits 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 6mmwurtzite crystal structure. The piezoelectric tensor components eij , which are calledpiezoelectric stress coefficients or stress moduli, give the polarization componentsPi as a result of the strain "j . For reasons of symmetry, the wurtzite piezoelec-tric tensor has three independent nonzero components. For comparison, only onenon-vanishing component exists for zinc-blende. In Voigt notation, the wurtzitepiezoelectric stress moduli are labelled e33, e31, and e15 (cf. zinc-blende: e14/,yielding the wurtzite piezoelectric tensor E:

E D0@

0 0 0 0 e15 0

0 0 0 e15 0 0

e31 e31 e33 0 0 0

1A (2.1)

Two of these components, e33 and e31, represent the contributions to the c-directedpolarization P3, induced by a strain "3 D .c � c0/=c0 along the c-axis, and by astrain "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 (orequivalently 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 parame-ter 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 inter-nal relaxation, called “internal-strain” contribution. The internal-strain contributionP .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 dis-placement gives rise to the additional polarization term P .2/; which scales with theeffective bond charge Z� (cf. LO phonon modes).

16 J. Geurts

All tetrahedrally coordinated compound semiconductors have in common oppo-site signs of the polarization contributions P .1/ and P .2/. Besides, for most ofthese materials the absolute values of P .1/ and P .2/ are nearly equal, which resultsin a rather effective cancellation. Therefore, II–VI compounds generally exhibitonly a very weak positive piezoelectric effect. For ZnO, an ab initio study of thepiezoelectric effect calculating the tensor elements e33 and e31 within the FLAPWmethod (full-potential linearized augmented-plane-wave method), was presented byDal Corso et al. [23]. It shows that ZnO forms an exception in the sense that theclamped-ion contribution P .1/ is extraordinarily low, which yields a reduced com-pensation of the internal-strain contribution P .2/ by P .1/ (as low as 50%). This isthe reason for the very pronounced piezoeffect in ZnO. The piezoelectric activitymay be expressed in terms of an effective piezoelectric charge eP

�. The experi-mental 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 to1:56 C=m2 [1]. In reasonable agreement with these experimental results are thecalculated 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 piezoelectricstrain coefficients dij � dPi=dXj [C/N] (D ŒV�1 m�). In this notation, the polar-ization is expressed with respect to the externally applied stress. Therefore, the setof coefficients dij is connected with the set of coefficients eij through the elasticmoduli cij. The ZnO piezoelectric strain coefficients are d33 � 12 � 10�12C=N,d31 � �5 � 10�12C=N, and d15 � �10 � 10�12C=N [1].

For the application in SAW devices, an essential parameter is the conversionefficiency between electrical and mechanical energy. A measure for this efficiencyis the electromechanical coupling coefficient K . It is defined by K2 D e2=c", wheree, c, and " are the piezoelectric, elastic, and dielectric constants, respectively, alongthe propagation direction of the acoustic wave.

2.4 Lattice Dynamics

The ZnO lattice vibration dynamics is essentially determined by three key param-eters: (1) the uniaxial crystal structure, (2) the pronounced mass difference of thezinc and oxygen ions, and (3) the strong bond polarity. The uniaxial structureinduces a classification of the vibration eigenmodes according to their symmetry(ion displacement either parallel or perpendicular to the c-axis). Furthermore, thepronounced mass difference is reflected in rather high frequencies of the oxygen-dominated modes, considerably beyond those of the zinc-dominated ones. Finally,the bond polarity results in a strongly polar character for some eigenmodes, whichmakes them readily accessible for far-infrared spectroscopy. Besides, almost allmodes 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 inSect. 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 theprimitive unit cell: two ZnO molecular units. The number of N D 4 atoms in the unitcell 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 eigenmodesbecause of the onefold degeneracy of the A� and B modes, and the twofold Emodes. One A1 mode and one E1 mode pair are the acoustical phonons. There-fore, �opt D A1 C 2B1 C E1 C 2E2 represents the optical phonon eigenmodes, thenumber 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 shownin Fig. 2.5. For the A1 and B1 modes, the displacements are directed along the c-axis, and they are distinct in the following way: The A1 mode pattern consists ofan oscillation of the rigid sublattices, Zn vs. O. Owing to the bond polarity, thisoscillating sublattice displacement results in an oscillating polarization. In contrast,for the B1 modes one sublattice is essentially at rest, while in the other one theneighbouring atoms move opposite to each other. For the B1

.1/ mode, the promi-nent displacements occur in the heavier sublattice (Zn), for the B1

.2/ mode in thelighter one (oxygen). No net polarization is induced by the B modes because the dis-placements of the ions within each sublattice sum up to zero. Thus, the three modeswith displacement along the c-axis are classified as one polar phonon mode A1 andtwo non-polar modes B1. The same scheme applies for the E modes with their atomdisplacement directions perpendicular to the c-axis. The E1 mode is an oscillationof 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

A1 B1 E1 E2 E2B1(2)(1) (2)(1)

Zn

O

Fig. 2.5 Eigenvectors of the ZnO optical phonon modes. For each mode, the bold arrows representthe 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 displacementratio Zn:O is given in the text