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Chapter 1

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Further Reading

Bechstedt F., Enderlein R.: Semiconductor Surfaces and Interfaces (Akademie-Verlag, Berlin 1988)

Luth H.: Solid Surfaces, Interfaces and Thin Films, 4th ed. (Springer-Verlag,Berlin 2001)

Wyckoff R.W.G.: Crystal Structures, 2nd ed. (Interscience, New York 1963)

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Desjonqueres M.-C., Spanjaard D.: Concepts in Surface Physics, 2nd ed.(Springer-Verlag, Berlin 1996)

Zangwill A.: Physics at Surfaces (Cambridge University Press, Cambridge1988)

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Further Reading

Harrison W.A.: Electronic Structure of Solids (Dover, New York 1980)

Srivastava G.P.: Theoretical Modelling of Semiconductor Surfaces (World Sci-entific, Singapore 1999)

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Further Reading

Bechstedt F., Enderlein R.: Semiconductor Surfaces and Interfaces (Akademie-Verlag, Berlin 1988)

Monch W.: Semiconductor Surfaces and Interfaces, 3rd ed. (Springer-Verlag,Berlin 2001)

Chapter 5

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Index

π-bonded chain model 24, 139, 153k-resolved inverse photoemission

spectroscopy (KRIPES) 154, 195Xα approximation 111

Adatom 3, 78– H3 site 170– S5 geometry 171– T4 site 170Adatom model 174Adiabatic approximation 196Adsorption 46– energy 104– group-III elements 171Ag(100)– image states 229Angle resolved photoemission spec-

troscopy (ARPES) 154, 194Antisite 302Arrhenius behavior 107Atomic position 16Au(110)– driving force for reconstruction 51– missing row reconstruction 135

Back bond 98, 126Band structure 96– projected 100Band-structure energy 112, 123, 134Bethe–Salpeter equation (BSE) 255Bloch function 82Bloch sum 85, 120Bloch theorem 82Bond– covalent 83– heteropolar 83– polarity 84, 136Bond-contraction relaxation model

144Bond-rotation relaxation model 144Born–Oppenheimer approximation

103

Bound surface state 218Bravais indices 3Bravais lattice 4, 7– cubic 4, 5– hexagonal 6, 14– oblique 14– plane 14– quadratic 14– rectangular 14– square 166– surface 20– three-dimensional (3D) 9– two-dimensional (2D) 7, 19, 30Bridging group 169Brillouin zone (BZ)– high-symmetry line 36– high-symmetry point 36– irreducible 42– projection 37– three-dimensional (3D) 37– two-dimensional (2D) 34Buckling 51, 59, 128– amplitude 147, 152– gap opening 154

C(100)– band structure 160– dimer 159– quasiparticle band structure 223– wave functions 161C(111)– angle-resolved photoelectron spectra

197– band structure 154– electrostatic potential 213– surface states 155– TDB surface 157– trimer reconstruction 181Charge-asymmetry coefficient 137,

146, 147Charge-transition level 298Chemical potential 47, 66, 69

338 Index

– compound semiconductor 71– element 71Chemical trend– structural parameters 148Chemical vapor deposition (CVD) 70,

157Cleavage 2, 138Cluster method 119Cohesive energy 71, 124Coincidence lattice 19Complex band structure 220Conductance– differential 192– relative 193Constant-current mode 188Constant-height mode 188, 191Corner hole 176Correlation 203, 209– strong 225, 232Crystal slab– irreducible 9, 10– primitive 9Crystal system– plane 14Cu(100)– image states 229– two-photon photoemission 231

Dangling bond 97, 100, 109, 126, 140,158, 163, 176, 183, 232

de Broglie wavelength 74, 105Delta-self-consistent field (ΔSCF)

method 234Density functional perturbation theory

(DFPT) 275Density functional theory (DFT) 109Density of states (DOS) 134– electronic 193– local 190Desorption 46, 105Dielectric function– bulk Si 259– intraband contribution 269– inverse 207– longitudinal 207, 240, 254– macroscopic 254Diffusion 46, 105– barrier 46, 107Dimer 51– asymmetric 163– buckling 163– flipping 165– formation 158

– mixed 167– molecule levels 159– symmetric 140– tilting 141– twisting 163Dimer-adatom-stacking fault (DAS)

model 176, 178Dimer-row domain wall 176Dimerization 142– chain bonds 152Domain 23Dynamical matrix 274Dynamically screened Coulomb

potential 203, 208Dyson equation 122, 202, 205

Effective-mass approximation (EMA)227, 260

Einstein law 195Einstein relation 106Electron affinity 214Electron counting rule (ECR) 141,

183Electron density 110, 202, 211Electron energy loss 243Electron energy loss spectroscopy

(EELS) 246Electron transfer 129Electron–hole interaction 197, 257,

263Electron–hole pair– Hamiltonian 257– state 251Electron–phonon interaction 251Electron–photon interaction 195, 251Electronegativity 136Electrostatic energy 112, 122, 135Electrostatic potential 211Empirical tight-binding method

(ETBM) 83, 88, 115Energy density formalism 119Epitaxial growth 2, 45Equilibrium crystal shape (ECS) 52,

57, 59Ewald construction 31Ewald energy 113Exchange 111, 255, 257Exchange-correlation energy 111Excitation 187, 237Exciton 258– binding energy 261, 264– Frenkel 265– surface 262– two-dimensional case 262

Index 339

– Wannier–Mott 261, 265

Facet 58, 65Facetting 59Fermi’s Golden Rule 189, 195, 251Fock operator 202Force constant model 122Formation energy 296Frenkel exciton 262Frozen-phonon approach 275Fuchs–Kliewer phonon 284Full-potential linearized augmented

plane wave (FLAPW) 116Fundamental gap 96, 99, 150, 215

GaAs(111)– As trimers 182GaAs(100)– ζ(4×2) 108, 162– band structure 162– EELS spectra 247– LEED 34– phase diagram 76– potential energy surface 108– reflectance anisotropy 241– slab 118– surface structure 69– topmost As dimers 143– wave functions 163GaAs(110)– total energy surface 103– HREELS spectrum 285GaN(111)– electrostatic potential 212GaP(100)– STM image 168, 192Ge(100)– bands 163Ge(111)– adatom model 173– band structure 154, 175– cleavage 139– isomer 154– surface states 175Generalized gradient approximation

(GGA) 111Gibbs adsorption equation 67Gibbs free enthalpy 46, 66, 69Gibbs phase rule 72Gibbs–Duhem equation 47Green’s function 120, 202, 205– first iteration 206– perfect crystal 121

Ground state 187Growth 76Growth mode– Frank–van der Merve 61, 76– Stranski–Krastanov 61– Volmer–Weber 61GW approximation 203, 255

Huckel theory 124– extended 83Half-slab polarizability 243Harmonic approximation 105, 273Hartree potential 81, 110, 202Heat of formation 71Hellmann–Feynman force 104, 113Hellmann–Feynman theorem 104Helmholtz free energy 47, 66Heterodimer 166Hohenberg–Kohn theorem 110Hubbard parameter 184, 233Hybrid 91– sp 94– sp2 93– sp3 91, 99– dangling 97, 126, 158Hydrogen problem 228, 260

III-N(110)– band structure 149– ionization energy, electron affinity

216– structural parameters 146III-V(110)– combined photoemission and inverse

photoemission spectra 198– phonon energy 289– structural parameters 146Image charge 209Image plane 208, 226Image potential 210, 246Image state 226Impurity 3, 300Independent particles 110, 187Independent-particle approximation

195, 251, 258, 259Independent-quasiparticle approxima-

tion 254, 258, 259InP(100)– mixed-dimer model 167– phase diagram 76– STM image 168– surface structure 69InP(110)– deposition of As atoms 78

340 Index

– quasiparticle band structure 224– Raman spectra 253– STM 145– surface phonon dispersion 286InSb(110)– EELS spectra 273Interatomic force constant 274Interdiffusion 46Internal energy 47, 66, 68Interstitial 294Inverse photoemission spectroscopy

(IPES) 194Ion bombardment and annealing (IBA)

2, 45Ionization energy 214– semiconductors 216Island 46, 64Isomer 154

Jahn–Teller– displacement 17, 18, 163– theorem 17, 126Janak theorem 123Jellium model 208, 211

K/Al(111)– electron energy loss spectra 271Kink 3, 294Kohn–Sham (KS) eigenvalues 110Kohn–Sham (KS) states 112Kohn–Sham equation 110Kohn–Sham potential 110, 204Kramer’s grand potential 47, 66

Lowdin theorem 83Lattice plane 2, 3, 6, 8Lattice vibration 68, 274Layer-orbital representation 120, 122Lehmann representation 202Lifetime 187Linear combination of atomic orbitals

(LCAO) 82, 85Linearized muffin-tin orbital (LMTO)

method 116Local density approximation (LDA)

71, 109Local spin density approximation

(LSDA) 111, 235Local-field effects 208, 241, 255, 268Lone pair 140Low-energy electron diffraction (LEED)

29, 33– measurement 146

Madelung energy 18Mass action law 72Matrix notation 20Metal surface 18– exchange-correlation potential 210– image states 231– reconstruction 134– relaxation 133Metal-induced gap states (MIGS) 221Metal-organic chemical vapor deposi-

tion (MOCVD) 237Mg metal– photoelectron spectrum 200Milk-stool model 180Miller indices 3, 4, 53Molecular beam epitaxy (MBE) 2, 45,

70Mott–Hubbard insulator 172, 184, 234

Nearest-neighbor interaction 87, 95,151

Nearly-free-electron (NFE) approxima-tion 219

Ni(100)– image states 229– Rayleigh phonon 280

Optical absorption– bulk Si 259– with electron–hole attraction 261Overlap integral 83, 124

Partial pressure 74Peierls effect 141, 291Peripheral atomic state 87Phase diagram 74, 80Phonon– eigenvector 287– macroscopic mode 277– microscopic mode 277– surface mode 276Photoemission spectroscopy (PES)

194Plasmon– losses 199– shake-up 199– surface 271Pocket 100, 228Point defect 295Point group 42– holohedral 14, 25– plane 14, 15Polarity 9

Index 341

Polarization function 207, 208, 254,258

– Bloch representation 256– macroscopic 254Polytype 136, 312Potential energy surface (PES) 103– minimum 104Potential-energy surface (PES)– saddle point 107Primitive basis vector 7, 29, 33Primitive lattice vector 4, 8Principle of detailed balance 46Pseudohydrogen 118Pseudopotential 110Pseudopotential plane wave (PPPW)

method 116Pyramidal-cluster model 180

Quasielectron 196Quasihole 196Quasiparticle– band 221– energy 204– gap 225– holon 291– peak 199, 206– quasielectron 187, 257– quasihole 187, 257– shift 205– spinon 291– wave function 204Quasiparticle equation 201

Raman scattering 250– by optical phonons 251– selection rule 252Random phase approximation (RPA)

203, 255Rayleigh wave 280Reciprocal lattice 4, 29, 32Reconstruction 16, 19, 24– driving force 135– missing row 17– pairing 17– principles 138– vacancy 140Reflectance anisotropy (RA) 243Reflectance anisotropy spectroscopy

(RAS) 238Reflectance difference spectroscopy

(RDS) 240Reflection high-energy electron

diffraction (RHEED) 76

Rehybridization 126, 140Relaxation 16, 17, 19, 128, 135, 146– outward 133Repeated-slab method 116, 274Rest atom 173Ring structure 139Roughening 59Rumpling 18, 135

Sagittal plane 278Satellite structure 199, 206Scanning tunneling microscopy (STM)

188– Ge nanocrystal 63– InAs pyramid 63Scattering-theoretical approach 120Schrodinger equation– excitons 260– image states 227– one-dimensional 219– single-particle 81– two-particle 257Screening 207Seiwatz model 157Self-energy– exchange-correlation 202, 204– GW approximation 203– near surfaces 210Self-interaction 274Shuttleworth equation 50Si(100)– band structure 99– reflectance anisotropy spectra 308Si(110)– RA spectrum 266Si(111)– band structure 99, 154– buckling model 128– cleavage 139– differential reflectance spectrum

238, 264– electron energy loss function 248– photoelectron spectra 199– quasiparticle band structure 223– RA spectrum 262– relative conductance 193– step 310– STM image 179– surface phonon modes 290– surface states 178SiC(0001)– LEED 35SiC(111)– adatom geometry 172

342 Index

– band structure 172– electrostatic potential 212– phase diagram 185– slab 117– tetramer 183– twisted Si adlayer 183Single dangling-bond (SDB) surface

150, 156, 180Slab method 115Slater–Koster parameter 89Small point group 42Space group 10, 25– plane 25Spectral ellipsometry (SE) 238Spectral weight 205Spectral(-weight) function 187, 190,

196, 201, 206– core-hole 201– Si 206Stacking fault 139, 176, 312Stacking vector 8, 9Star of wave vector 42Step 2, 46, 52, 303– biatomic 306– height 293– microfacet notation 304– monatomic 306Stereographic triangle 54Strain 51Sudden approximation 196Superlattice 19Supersaturation 76Surface 49, 51– entropy 50, 66, 68– excess free energy per unit area 49– free energy 51, 55, 68– nonpolar 135– polar 136– strain 65– stress 50, 65, 134– tension 49Surface differential reflectance (SDR)

237Surface energy 67, 74, 128– sp-bonded metals 57– jellium model 56– metals (table) 56– semiconductors (table) 56Surface loss function 246Surface phase 74Surface photoabsorption (SPA) 238

Surface plane 13Surface reconstruction 16Surface resonance state 218Surface roughness 3Surface-state gap 225Symmetry– point 13– rotational 15– translational 16, 82

Terrace 3, 46, 52Tersoff–Hamann approach 191Tetrahedron direction 91Tetramer 183Tetramer-adlayer model 184Three-layer model 239, 247Three-step model 195, 201Tight-binding method 83, 123, 151,

160, 193Total energy 68, 103, 109, 112Transfer-matrix method 120Transition-state theory (TST) 106Translational group 13, 19Trimer 181Triple dangling-bond (TDB) surface

156, 181Tunneling current 190Tunneling microscope– ideal 190Twin boundary 313

Ultrahigh vacuum (UHV) 2, 45Ultraviolet photoemission spectroscopy

(UPS) 194

Vacancy 3, 294Vacuum level 214Vapor phase epitaxy (VPE) 2Vicinal surface 52, 304Virtual gap states (ViGS) 221

W(100)– reconstruction 134– relaxation 133Wannier–Mott exciton 261Wigner–Seitz cell 25, 33Wood notation 20Work function 214– typical metals 215Wulff construction 57Wulff plot 51