Metal-induced gap states

In bulk semiconductor band structure calculations, it is assumed that the crystal lattice (which features a periodic potential due to the atomic structure) of the material is infinite. 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. Similarly, when a metal is deposited onto a semiconductor (by thermal evaporation, for example), the wavefunction of an electron in the semiconductor must match that of an electron in the metal at the interface. Since the Fermi levels of the two materials must match at the interface, there exists gap states that decay deeper into the semiconductor.

As mentioned above, when a metal is deposited onto a semiconductor, even when the metal film is smaller than a single atomic layer, the Fermi levels of the metal and semiconductor must match. 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. He calculated the variation in surface state energy by matching wavefunctions of a free-electron metal to gapped states in an undoped semiconductor, showing that in most cases the position of the surface state energy is quite stable regardless of the metal used.

It is somewhat crude to suggest that the metal-induced gap states (MIGS) are tail ends of metal states that leak into the semiconductor. Since the mid-gap states do exist within some depth of the semiconductor, they must be a mixture (a Fourier series) of valence and conduction band states from the bulk. The resulting positions of these states, as calculated by C. Tejedor, F. Flores and E. Louis, and J. Tersoff, must be closer to either the valence- or conduction- band thus acting as acceptor or donor dopants, respectively. The point that divides these two types of MIGS is called the branching point, E_B. Tersoff argued

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