Properties of Semiconductor Alloys: Group-IV, III–V and II–VI Semiconductors Properties of Semiconductor Alloys: Group-IV, III–V and II–VI Semiconductors Sadao Adachi © 2009 John Wiley & Sons, Ltd ISBN: 978-0-470-74369-0 Wiley Series in Materials for Electronic & Optoelectronic Applications Series Editors Peter Capper, SELEX Sensors and Airborne Systems Infrared Ltd, Southampton, UK Safa Kasap, University of Saskatchewan, Canada Arthur Willoughby, University of Southampton, Southampton, UK Published titles Bulk Crystal Growth of Electronic, Optical and Optoelectronic Materials, Edited by P. Capper Properties of Group-IV, III–V and II–VI Semiconductors, S. Adachi Charge Transport in Disordered Solids with Applications in Electronics, Edited by S. Baranovski Optical Properties of Condensed Matter and Applications, Edited by J. Singh Thin Film Solar Cells: Fabrication, Characterization and Applications, Edited by J. Poortmans and V. Arkhipov Dielectric Films for Advanced Microelectronics, Edited by M. R. Baklanov, M. Green and K. Maex Liquid Phase Epitaxy of Electronic, Optical and Optoelectronic Materials, Edited by P. Capper and M. Mauk Molecular Electronics: From Principles to Practice, M. Petty Luminescent Materials and Applications, Edited by A. Kitai CVD Diamond for Electronic Devices and Sensors, Edited by R. S. Sussman Forthcoming Titles Zinc Oxide Materials for Electronic and Optoelectronic Device Applications, Edited by C. Litton, D. C. Reynolds and T. C. Collins MercuryCadmiumTelluride:Growth,PropertiesandApplications,EditedbyP.Capperand J. Garland PhotovoltaicMaterials:FromCrystallineSilicontoThird-GenerationApproaches,Editedby G. J. Conibeer Silicon Photonics: Fundamentals and Devices, J. Deen and P. K. Basu InorganicGlassesforPhotonics:Fundamentsls,EngineeringandApplications,A.Jha,R.M. Almeida, M. Clara Goncalves and P. G. Kazansky Properties of Semiconductor Alloys: Group-IV, III–V and II–VI Semiconductors SADAO ADACHI Gunma University, Gunma, Japan Thiseditionfirstpublished2009 #2009JohnWiley&SonsLtd Registeredoffice JohnWiley&SonsLtd,TheAtrium,SouthernGate,Chichester,WestSussex,PO198SQ,UnitedKingdom Fordetailsofourglobaleditorialoffices,forcustomerservicesandforinformationabouthowtoapplyfor permissiontoreusethecopyrightmaterialinthisbookpleaseseeourwebsiteatwww.wiley.com. Therightoftheauthorstobeidentifiedastheauthorsofthisworkhasbeenassertedinaccordancewiththe Copyright,DesignsandPatentsAct1988. Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystemortransmitted,inany formorbyanymeans,electronic,mechanical,photocopying,recordingorotherwise,exceptaspermittedbytheUK Copyright,DesignsandPatentsAct1988,withoutthepriorpermissionofthepublisher. Wileyalsopublishesitsbooksinavarietyofelectronicformats.Somecontentthatappearsinprintmaynotbe availableinelectronicbooks. 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LibraryofCongressCataloging-in-PublicationData Adachi,Sadao,1950 Propertiesofsemiconductoralloys:group-IV,III VandII VI semiconductors/SadaoAdachi. p.cm. Includesbibliographicalreferencesandindex. ISBN978-0-470-74369-0 1.Semiconductors Materials. 2.Semiconductors Analysis. 3.Siliconalloys.I.Title. TK7871.85.A322009 621.381502 dc22 2008046980 AcataloguerecordforthisbookisavailablefromtheBritishLibrary. ISBN 978-0-470-74369-0(HB) Typesetin10/12ptTimesbyThomsonDigital,Noida,India. PrintedandboundinGreatBritainbyCPIAntonyRowe,Ltd,Chippenham,Wiltshire FrontcoverimageofaphotodiodearrayreproducedbykindpermissionofDr.Jian-youngWu.CourtesyofWutech InstrumentsandRedShirtImaging. Contents Series Preface xvii Preface xix Abbreviations and Acronyms xxi Introductory Remarks 1 A.1 An Alloy and a Compound 1 A.2 Grimm Sommerfeld Rule 2 A.3 An Interpolation Scheme 4 References 7 1 Structural Properties 9 1.1 Ionicity 9 1.2 Elemental Isotopic Abundance and Molecular Weight 9 1.3 Crystal Structure 11 1.3.1 Random Alloy 11 1.3.2 Spontaneous Ordering 11 (a) Group-IV Semiconductor Alloy 11 (b) III V Semiconductor Alloy 14 (c) II VI Semiconductor Alloy 15 1.4 Lattice Constant and Related Parameters 15 1.4.1 CuAu Alloy: Ordered and Disordered States 15 1.4.2 Non-alloyed Semiconductor 16 1.4.3 Semiconductor Alloy 19 (a) Group-IV Semiconductor 19 (b) III V Semiconductor 22 (c) II VI Semiconductor 29 1.5 Coherent Epitaxy and Strain Problem 32 1.5.1 Bilayer Model 32 1.5.2 Elastic Strain and Lattice Deformation 33 1.5.3 Critical Thickness 37 1.6 Structural Phase Transition 39 1.7 Cleavage Plane 41 1.7.1 Cleavage 41 1.7.2 Surface Energy 41 References 42 vi CONTENTS 2 Thermal Properties 45 2.1 Melting Point and Related Parameters 45 2.1.1 Phase Diagram 45 (a) Group-IV Semiconductor Alloy 45 (b) III V Semiconductor Alloy 45 (c) II VI Semiconductor Alloy 48 2.1.2 Melting Point 51 2.2 Specific Heat 51 2.2.1 Group-IV Semiconductor Alloy 51 2.2.2 III V Semiconductor Alloy 54 2.2.3 II VI Semiconductor Alloy 56 2.3 Debye Temperature 56 2.3.1 General Considerations 56 2.3.2 Group-IV Semiconductor Alloy 57 2.3.3 III V Semiconductor Alloy 58 2.3.4 II VI Semiconductor Alloy 58 2.4 Thermal Expansion Coefficient 59 2.4.1 Group-IV Semiconductor Alloy 59 2.4.2 III V Semiconductor Alloy 61 2.4.3 II VI Semiconductor Alloy 63 2.5 Thermal Conductivity and Diffusivity 63 2.5.1 Thermal Conductivity 63 (a) General Considerations 63 (b) Group-IV Semiconductor Alloy 66 (c) III V Semiconductor Alloy 68 (d) II VI Semiconductor Alloy 74 2.5.2 Thermal Diffusivity 75 (a) General Considerations 75 (b) Alloy Value 75 References 76 3 Elastic Properties 81 3.1 Elastic Constant 81 3.1.1 General Considerations 81 3.1.2 Room-temperature Value 81 (a) Group-IV Semiconductor Alloy 81 (b) III V Semiconductor Alloy 81 (c) II VI Semiconductor Alloy 84 3.1.3 External Perturbation Effect 86 (a) Temperature Effect 86 (b) Pressure Effect 88 3.2 Third-order Elastic Constant 89 3.3 Young’s Modulus, Poisson’s Ratio and Similar Properties 89 3.3.1 Group-IV Semiconductor Alloy 89 3.3.2 III V Semiconductor Alloy 89 3.3.3 II VI Semiconductor Alloy 90 CONTENTS vii 3.4 Microhardness 92 3.4.1 Group-IV Semiconductor Alloy 92 3.4.2 III V Semiconductor Alloy 92 3.4.3 II VI Semiconductor Alloy 93 3.5 Sound Velocity 96 References 97 4 Lattice Dynamic Properties 99 4.1 Phonon Dispersion Relationships 99 4.2 Phonon Frequency 99 4.2.1 General Considerations 99 4.2.2 Room-temperature Value 100 (a) Group-IV Semiconductor Alloy 100 (b) III V Semiconductor Alloy 104 (c) II VI Semiconductor Alloy 109 4.2.3 External Perturbation Effect 112 (a) Group-IV Semiconductor Alloy 112 (b) III V Semiconductor Alloy 113 (c) II VI Semiconductor Alloy 115 4.3 Mode Gr€uneisen Parameter 119 4.3.1 Phonon Deformation Potential 121 References 123 5 Collective Effects and Some Response Characteristics 125 5.1 Piezoelectric Constant 125 5.1.1 General Considerations 125 5.1.2 Alloy Value 125 5.2 Fr€ohlich Coupling Constant 129 5.2.1 General Considerations 129 5.2.2 Alloy Value 129 References 131 6 Energy-band Structure: Energy-band Gaps 133 6.1 Introductory Remarks 133 6.1.1 Quasi-cubic Band Model 133 6.1.2 Bowing Parameter 136 6.1.3 Ordered Alloy 136 6.2 Group-IV Semiconductor Alloy 139 6.2.1 Binary Alloy 139 (a) CSi 139 (b) CGe 140 (c) SiGe 141 (d) GeSn 144 6.2.2 Ternary Alloy 145 (a) CSiGe 145 (b) SiGeSn 147 6.2.3 Summary 147 viii CONTENTS 6.3 III V Semiconductor Ternary Alloy 149 6.3.1 (III, III) N Alloy 149 (a) c-AlGaN 149 (b) w-AlGaN 150 (c) c-AlInN 152 (d) w-AlInN 152 (e) c-GaInN 152 (f) w-GaInN 152 6.3.2 (III, III) PAlloy 153 (a) AlGaP 153 (b) AlInP 153 (c) GaInP 155 6.3.3 (III, III) As Alloy 157 (a) AlGaAs 157 (b) AlInAs 160 (c) GaInAs 161 6.3.4 (III, III) Sb Alloy 163 (a) AlGaSb 163 (b) AlInSb 165 (c) GaInSb 166 6.3.5 Dilute-nitride III (V, V) Alloy 166 (a) General Considerations 166 (b) GaNP 170 (c) GaNAs 171 (d) GaNSb 172 (e) InNP 173 (f) InNAs 173 (g) InNSb 174 6.3.6 Al (V, V) Alloy 174 6.3.7 Ga (V, V) Alloy 175 (a) GaPAs 175 (b) GaPSb 176 (c) GaAsSb 178 6.3.8 In (V, V) Alloy 179 (a) InPAs 179 (b) InPSb 179 (c) InAsSb 181 6.3.9 Summary 183 6.4 III V Semiconductor Quaternary Alloy 184 6.4.1 Dilute-nitride Quaternary Alloy 184 (a) AlGaNAs 184 (b) GaInNP 185 (c) GaInNAs 185 (d) GaNPAs 185 6.4.2 (III, III) (V, V) Alloy 186 (a) AlGaPAs 186 (b) AlGaAsSb 187 CONTENTS ix (c) AlInAsSb 188 (d) GaInPAs 189 (e) GaInAsSb 191 6.4.3 (III, III, III) VAlloy 193 (a) AlGaInP 193 (b) AlGaInAs 194 6.4.4 III (V, V, V) Alloy 195 6.4.5 Summary 196 6.5 II VI Semiconductor Alloy 197 6.5.1 (II, II) O Ternary Alloy 197 (a) BeZnO 197 (b) MgZnO 197 (c) ZnCdO 198 6.5.2 (II, II) S Ternary Alloy 198 (a) MgZnS 198 (b) ZnCdS 200 (c) ZnHgS 200 (d) CdHgS 200 6.5.3 (II, II) Se Ternary Alloy 201 (a) BeZnSe 201 (b) BeCdSe 202 (c) MgZnSe 202 (d) MgCdSe 202 (e) ZnCdSe 203 (f) CdHgSe 203 6.5.4 (II, II) Te Ternary Alloy 204 (a) BeZnTe 204 (b) MgZnTe 205 (c) MgCdTe 206 (d) ZnCdTe 206 (e) ZnHgTe 207 (f) CdHgTe 208 6.5.5 Zn (VI, VI) Ternary Alloy 208 (a) ZnOS 208 (b) ZnOSe 209 (c) ZnSSe 209 (d) ZnSTe 210 (e) ZnSeTe 210 6.5.6 Cd (VI, VI) Ternary Alloy 210 (a) CdSSe 210 (b) CdSTe 211 (c) CdSeTe 211 6.5.7 (II, II) (VI, VI) Quaternary Alloy 212 (a) MgZnSSe 212 (b) MgZnSeTe 213 6.5.8 (II, II, II) VI Quaternary Alloy 213 (a) BeMgZnSe 213