## Basic Theory of Surface StatesThe theory of surface states underlies our knowledge of the behavior of electrons at solid surfaces, which is of paramount importance in understanding the mechanisms by which solid-state devices operate and catalytic reactions proceed. In this work, the subject is viewed through the "theoretical eye" of a physicist, but the topics are treated in an elementary fashion. The main features of the presentation are its instructive, model-based approach; detailed step-by-step derivations of the equations; smooth progression through the simple wave-function matching techniques to the more sophisticated Green-function methods; and the historical theme, which traces the evolution of the subject from its founding by the Nobel Laureate Igor Tamm in 1932, through the invention of the transistor in 1947 by Schockley, Bardeen and Brattain, to recent developments. The book will appeal to both theoretical and experimental surface scientists from chemistry, materials science, and electronic engineering. |

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### Contents

ELECTRONS IN INFINITE CRYSTALS | 4 |

ELECTRONS AT CRYSTAL SURFACES | 46 |

TIGHTBINDING APPROXIMATION | 61 |

NEARLYFREE ELECTRON APPROACH | 74 |

MATHIEU POTENTIAL MODEL | 87 |

FIELD VIRTUAL AND IMAGE STATES | 99 |

GREENFUNCTION METHODS | 116 |

HISTORICAL DEVELOPMENT | 151 |

APPENDICES | 195 |

AUTHOR INDEX | 215 |

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### Common terms and phrases

Airy functions Allen and Gobeli atomic orbitals band edges band of surface band structure Bartos Bloch's theorem boundary conditions Brillouin zone bulk band calculations cleavage coefficients conduction bands constant corresponding crystal surface curve Davison density electron energy bands energy levels energy spectrum existence of surface experimental finite Gadzuk gives Goodwin Hamiltonian Himpsel image potential infinite crystal inside the crystal integral interaction Koutecky lattice lattice constant leads Levine Mathieu functions Maue metals method obtained orbitals p-states parameter periodic potential perturbation photoemission Phys plane reduces resonance integral Schrodinger equation sem(z,q semi-infinite crystal semiconductor shown in Fig shows solid solutions Statz surface atoms surface bands surface potential surface-state energy symmetry Tamm and Shockley Tamm's theoretical theory of surface tion Tomasek two-band valence band values vector virtual surface wave function wave number zero