The properties of metal-to-semiconductor junctions and of free semiconductor surfaces are usually explained on the basis of surface states. The theory of the metal contacts is discussed critically, because strictly speaking localized surface states cannot exist in such junctions. However, it is shown that virtual or resonance surface states can exist which behave for practical purposes in the same way. They are really the tails of the metal wave functions rather than separate states. In the past, the length of this tail has often been ignored. Some estimates of its length are made and its consequences pointed out. A semiquantitative discussion is given of various recent data, including the effect of an oxide layer on barrier height, the variation of barrier height with the metal, the work function of a free surface at high doping, and the effect of a cesium layer on the work function.

Theory of Surface States

Photoemission studies of quantum well states in thin films

http://dipc.ehu.es/etxenike/admin/documentos/archivos/publicaciones/257SSR2004.pdf

Decay of electronic excitations at metal surfaces

Almost all metal-semiconductor or Schottky contacts exhibit rectifying behaviour which is caused by a depletion layer on the semiconductor side of the interface. The electronic properties of a Schottky diode are characterised by its barrier height which is the energy difference between the top of the valence band of the semiconductor and the Fermi level at the interface. The physical mechanism primarily determining barrier height is provided by the decay of the metal's electron wavefunctions into the semiconductor in the energy range between the top of the valence band and the Fermi level where the metal conduction band overlaps the semiconductor band gap. These wavefunction tails are described as the continuum of metal-induced gap states (MIGS) which are derived from the virtual gap states of the complex semiconductor band structure.

https://iopscience.iop.org/article/10.1088/0034-4885/53/3/001/pdf

On the physics of metal-semiconductor interfaces

REVIEW ARTICLE: Inverse photoemission

It is shown that in a crystal there exist states in which the electron is bound to a surface of the crystal and has an energy lying within a forbidden band. The wave functions and energies of these states are calculated, on the nearly free electron approximation, in terms of the constants of the crystalline potential field, which is represented by a triple Fourier series having the periodicity of the lattice. The method is shown to be applicable to a general crystal having a surface parallel to any one of the crystal planes.

E. T. Goodwin

Papers

Electronic states at the surfaces of crystals: I. The approximation of nearly free electrons