1. Introduction 1
2. Thermodynamical and Statistical Properties of Clean Surfaces 4
2.1 Thermodynamics of a Surface at Equilibrium 4
2.2 Equilibrium Shape of a Crystal 7
2.3 Facetting 13
2.4 The Roughening Transition 15
2.4.1 Generalities 15
2.4.2 Macroscopic Approach: The Continuum Limit 16
a） One Dimensional Case: Statistics of a Step 16
b） The Two Dimensional Case: Statistics of a Surface 25
2.4.3 Microscopic Approach 29
a） Equilibrium Shape of a Step Edge 29
b） Equilibrium Shape of a Surface:The Roughening Transition 34
2.4.4 Consequences of the Roughening Transition for the Equilibrium Shape of Crystals and for Crystal Growth 41
2.4.5 Experimental Evidences of the Roughening Transition 41
2.4.6 Special Cases of Vicinal Surfaces 43
Problems 43
3. Atomic Structure of Surfaces 48
3.1 Surface Crystallography 48
3.1.1 Two-Dimensional Lattices 48
3.1.2 Semi-Infinite Crystals.Relaxation.Reconstruction 49
3.1.3 Notations for Surface Structures 51
3.1.4 Vicinal Surfaces 53
3.1.5 Reciprocal Lattice and Brillouin Zones 53
3.2 Experimental Techniques 57
3.2.1 Observation of the Real Lattice 57
a） Field-ion Microscopy （FIM） 57
b） Scanning Tunneling Microscopy（STM） 60
3.2.2 Observation of the Reciprocal Lattice 63
a） Principles of Diffraction 63
b） Low Energy Electron Diffraction（LEED） 71
c） Atom Scattering 74
d） X-ray Scattering at Grazing Incidence 78
3.2.3 Indirect Methods 86
a） Photoelectron Diffraction（PhD） 86
b） Surface Extended X-ray Absorption Fine Structure（SEXAFS） 93
c） Other Methods 99
Problems 101
4. Vibrations at Surfaces 106
4.1 Elastic Forces in Crystals 106
4.1.1 Dynamical Matrix 106
4.1.2 Interatomic Forces 108
a） Central Forces 108
b） Angular Forces 111
4.2 Bulk Modes 112
4.3 Surface Modes 114
4.3.1 Semi-Infinite Linear Chain 115
a） M0≠M 115
b） β0 ≠ β 117
4.3.2 Semi-Infinite Crystals 118
a） The Slab Method 119
b） Exact Method for the Calculation of Surface Modes 120
c） Relaxation and Reconstruction of Surfaces from Phonon Calculations 124
d） Experimental Determination of Surface Modes 128
4.3.3 Brief Remarks on Adsorbed Layers 131
4.4 Spectral Densities of Modes 133
4.5 Vibrational Thermodynamical Functions 137
4.5.1 Surface Vibrational Entropy 138
4.5.2 Surface Internal Energy 139
4.5.3 Surface Specific Heat at Constant Volume 139
4.6 Mean Square Displacements 140
4.6.1 Theory 140
4.6.2 Experimental Techniques 143
a） Diffraction Experiments 143
b） PhD and SEXAFS Experiments 147
c） Conclusion 152
Problems 153
5. Electronic Structure of Surfaces 162
5.1 Jellium Model 163
5.1.1 The Free Electron Gas Bounded by Infinite Barriers 164
a） One-dimensional Electron Gas 164
b） Three-dimensional Electron Gas 167
5.1.2 The Free Electron Gas Bounded by Finite Barriers 170
5.1.3 The Jellium Model in the Local Density Functional Formalism 177
a） Homogeneous Jellium 178
b） General Case 180
5.2 Nearly Free Electron Model-Surface States 188
5.2.1 Nearly Free Electron Model for Bulk States 188
5.2.2 Surface States in Simple Gaps （Gaps of Type A） 197
5.2.3 Surface States in Gaps of Type B 204
5.2.4 An Example: Al（001） 210
a） Band Structure along the？？Direction 210
b） Band Structure along the？？Direction 211
5.2.5 Semiconductors 215
5.3 Tight-Binding Approximation 217
5.3.1 General Principles 218
5.3.2 Computation Techniques for Semi-Infinite Crystals 219
a） The Slab Method 220
b） The Continued Fraction Technique 220
c） Illustrative Examples 224
5.4 Application of the Tight-Binding Approximation to Transition Metal Surfaces 235
5.4.1 Brief Survey of Bulk Electronic Structure 235
a） Band Structure 235
b） Cohesive Energy 238
5.4.2 Surface Densities of States and Potential 242
5.4.3 Surface Energies 247
5.4.4 Relaxation and Reconstruction from Energy Calculations 251
5.5 Application of the Tight-Binding Approximation to Semiconductor Surfaces 254
5.5.1 Brief Survey of Bulk Electronic Structure 254
a） Band Structure 254
b） Cohesive Energy 265
5.5.2 Determination of the Surface Tight-Binding Parameters 267
5.5.3 Qualitative Discussion of Surface States in Semiconductors 268
5.5.4 Examples 271
a） The （111） Surface of Si 271
b） The （001） Surface of Si 275
c） Brief Remarks on Heteropolar Semiconductor Surfaces 283
5.6 Other Methods 284
5.6.1 The Propagation Matrix Method 284
a） Formulation of the Method 284
b） The Layer KKR Method 294
c） The Method of Appelbaum and Hamann 303
5.6.2 Methods Using the Slab Geometry 308
a） The Single Slab Geometry 309
b） The Periodic Slab Geometry 310
5.7 Surface Plasmons in Metals 310
5.7.1 Summary of Bulk Plasmons in a Jellium 311
a） Elementary Classical Theory: the Plasma Frequency 311
b） Relation with the Dielectric Function:Dispersion of Plasmons 312
5.7.2 Surface Plasmons in a Jellium 320
a） The Simple Case of Charge Oscillations Strictly Localized in the Surface Plane 320
b） The Surface Plasmon Dispersion 323
5.7.3 Brief Remarks on the Effects of the Crystal Potential 335
a） Bulk Plasmons 335
b） Surface Plasmons 338
5.8 Image Potential 338
5.8.1 Response of a Semi-Infinte Jellium to a Uniform External Electric Field 339
5.8.2 Interaction of an External Point Charge with a Semi-Infinite Jellium: the Image Potential 342
5.8.3 Image Potential in a Dielectric Medium 346
5.8.4 Image Surface States 348
a） Basics of Image Surface States 348
b） A New Formulation of the Criterion for the Existence of Surface States 349
c） Determination of the Electron Reflectivity of the Surface Barrier 351
d） Determination of the Reflectivity of the Crystal in the Nearly Free Electron Approximation 352
e） “An Example: Surface States in the L Gap of Cu（111） 353
f） Conclusion 355
5.9 Some Further Remarks on Exchange and Correlation Energies 355
5.9.1 Exchange and Correlations in a Semi-Infinite Jellium:Validity of the Local Density Functional Approximation 356
5.9.2 Correlations in the Tight-Binding Formalism:The Hubbard Hamiltonian 361
a） Electronic Correlations in a s Band 362
b） Electronic Correlations in Degenerate Bands 367
c） Influence on the Band Structure and Conclusions 369
5.10 Experimental Techniques for Investigating the Electronic Structure 370
5.10.1 Surface Core Level Spectroscopy 371
a） Microscopic Approach 372
b） Thermodynamical Model 373
c） An Example: Surface Core Level Binding Energy Shifts in Ta and W 375
5.10.2 Photoemission of Valence Electronic States 377
a） Principle of the Determination of Dispersion Curves from Photoemission Spectra 378
b） An Example of Bulk Dispersion Curves: Cu（110） 381
c） An Example of a Surface State Dispersion Curve:Al（100） 384
d） Brief Outline of the Principles of the Intensity Calculations in Photoemission 385
5.10.3 Inverse Photoemission 387
5.10.4 Spatially-Resolved Tunneling Spectroscopy 389
5.10.5 Measurement of Surface Plasmons 392
5.10.6 Measurement of the Work Function 393
a） Vibrating Capacitor Method or Kelvin Method 393
b） Field Emission 394
c） Thermionic Emission Method 394
d） Secondary Electron Method 394
5.10.7 Measurement of Surface Energies 395
a） Measurements Based on the Study of the Equilibrium Shape of Crystals 395
b） Thermal Creep Under Tension 395
c） Surface Energy of Liquid Metals 396
Problems 397
6.Adsorption Phenomena 411
6.1 Thermodynamical Approach 412
6.2 Statistical Methods 416
6.2.1 Adsorption Isotherms in the Absence of Lateral Interactions Between Adatoms 417
a） Monolayer Adsorption: Langmuir Isotherms 417
b） Multilayer Adsorption: Brunauer, Emmett and Teller（BET）Isotherms 420
6.2.2 The Two-Dimensional Lattice Gas 423
a） Study of Isotherms: Condensation Phase Transition 423
b） Order-disorder Transition in Adsorbed Layers 432
6.3 Physisorption 438
6.3.1 The Classical Electrostatic Interaction Between a Polar Particle and a Dielectric Surface 438
a） Interaction between Two Dipoles 438
b） Interaction between a Dipole and a Dielectric Surfa 439
6.3.2 Interaction Between a Neutral Atom and a Dielectric Surface 440
a） Van der Waals Interaction between Two Neutral Atoms in S-States 440
b） Van der Waals Interaction between a Neutral Atom and a Dielectric Surface 443
6.4 Chemisorption 452
6.4.1 Generalities on Charge Transfer in Chemisorption 455
a） Variation of the Ionization Energy 456
b） Variation of the Affinity Energy 457
6.4.2 Anderson -Grimley-Newns Hamiltonian 458
a） Hartree-Fock Treatment 458
b） Beyond the Hartree- Fock Treatment 467
6.4.3 Chemisorption in the Local Density Functional Formalism 469
a） Atomic Chemisorption on a Jellium Surface 469
b） The Effective Medium Theory 475
6.4.4 Chemisorption on Transition Metals in the Tight-Binding Approximation 491
a） General Characteristics of the Models 491
b） Analytical Models 493
c） Improved Models 498
d） An Example: Adsorption of Simple Elements on BCC Transition Metal Surfaces 500
6.4.5 Vibrations of an Adsorbate 505
a） Rigid Substrate Approximation: M.﹤M 505
b） General Case 512
c） Experiments 512
6.4.6 Conclusions 514
6.5 Interactions Between Adsorbates 515
6.5.1 Experimental Data 515
6.5.2 Theory of Adatom Adatom Interactions 517
a） Electronic Interactions 517
b） Dipolar Interactions 523
c） Elastic Interactions 524
6.5.3 Consequences of Adatom-Adatom Interactions and Conclusions 525
6.6 Electronic Structure of Ordered Overlayers.An Example:O on Ni（l00） 525
Problems 528
Appendices 539
A.Theory of Scattering by a Spherical Potential: Brief Summary 539
A.1 Solution of the Schr？dinger Equation for a Particle in a Spherical Potential 539
A.2 Scattering of a Free Particle by a Spherical Potential 541
A.3 Friedels Sum Rule 543
B.The Continued Fraction Technique 545
B.1 Principle of the Recursion Method 545
B.2 Principle of the Moment Method 547
B.3 Practical Calculations 549
C.Electromagnetic Waves in Matter 552
C.1 Brief Summary of Maxwell Equations in Vacuum 552
C.2 Maxwell Equations and Dielectric Properties in a Homogeneous and Isotropic Medium 553
C.3 An Equivalent Description of the Dielectric Properties of a Homogeneous and Isotropic Medium: Longitudinal and Transverse Dielectric Functions 554
D.Calculation of the Variation of the Total Energy Due 556
to a Perturbing External Charge Distribution Within the 556
Density Functional Formalism 556
E.Useful Relations for the Study of Many Body Interactions 558
E.1 Relation Between the Expectation Value of the Interaction Energy and the l oral Energy for a System of Interacting Particles 558
E.2 Derivation of the Fredholm Formula 558
F.Interaction of an Electron With an Electromagnetic Field and Theory of Angle-Resolved Ultra-Violet Photoemission （UPS） 559
F.1 The Optical Matrix Element 560
F.2 Expression of the Photoemitted Current in UPS 562
F.2.1 Some Useful Relations 562
F.2.2 Calculation of the Photoemitted Current in UPS 564
F.3 Conservation of the Wave Vector in Photoemission 567
G.Calculation of the Current in a Scanning Tunneling Microscope 571
H.Calculation of the Atomic Dynamic Polarizability 578
I.Variation of the Density of States Due to a Perturbing Potential 579
J.Energy of Chemisorption in the Anderson-Grimley-Newns Model Using Contour Integrals 580
K.Elastic Constants and Elastic Waves in Cubic Crvstals 581
K.1 Elastic Strain 581
K.2 Elastic Stress 582
K.3 Elastic Constants 583
K.4 Propagation of Elastic Waves in Cubic Crystals 583
K.5 Elastic Energy 584
References 585
Subject Index 599