Metal-induced gap states

When the finite size of a crystal is taken into account, the wavefunctions of electrons are altered and states that are forbidden within the bulk semiconductor gap are allowed at the surface.

Since the Fermi levels of the two materials must match at the interface, there exists gap states that decay deeper into the semiconductor.

This pins the Fermi level in the semiconductor to a position in the bulk gap.

Shown to the right is a diagram of band-bending interfaces between two different metals (high and low work functions) and two different semiconductors (n-type and p-type).

Volker Heine was one of the first to estimate the length of the tail end of metal electron states extending into the semiconductor's energy gap.

The resulting positions of these states, as calculated by C. Tejedor, F. Flores and E. Louis,[3] and J. Tersoff,[4][5] must be closer to either the valence- or conduction- band thus acting as acceptor or donor dopants, respectively.

Tersoff argued In order for the Fermi levels to match at the interface, there must be charge transfer between the metal and semiconductor.

fits his theoretical model for Au in contact with 10 common semiconductors, including Si, Ge, GaP, and GaAs.

Another derivation of the contact barrier height in terms of experimentally measurable parameters was worked out by Federico Garcia-Moliner and Fernando Flores who considered the density of states and dipole contributions more rigorously.

In effect, the capacitance across the depletion layer in the semiconductor is bias voltage dependent and goes as

Band diagram of the band-bending at the interface of (a) a low work function metal and n-type semiconductor , (b) a low work function metal and a p-type semi conductor, (c) a high work function metal and an n-type semi conductor, (d) a high work function metal and a p-type semi conductor. (Figure adapted from H. Luth's Solid Surfaces, Interfaces, and Thin Films, p. 384. [ 1 ] )
Band diagram of the contact point potential barrier at the interface of a metal and semiconductor. Shown are , the energy of the barrier, and , the maximum band bending in the semiconductor. (Figure adapted from H. Luth's Solid Surfaces, Interfaces, and Thin Films, p. 408 (see Refs.)