Coverage dependence of Schottky barrier formation

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Abstract
When the metal coverage at the surface of a semiconductor is sufficiently small so that there are isolated metal adatoms and therefore localized states, there is a distinction between the energy (0,+) to remove an electron from a neutral adatom and the energy (−,0) to add an electron to a neutral adatom. The acceptor level (−,0) is higher in energy than the donor level (0,+) by an energy U*, just as in the free atom, but here U* is modified by the presence of the surface. For these isolated metal adatoms, the donor level (0,+) frequently lies in the semiconductor gap with the acceptor level (−,0) coming in the conduction band. This circumstance leads to an asymmetry between the low-coverage band bending for n-type semiconductors versus that for p-type. As the number of adatoms is increased, the (0,+) and (−,0) levels shift relative to the semiconductor bands at the surface. These shifts can be understood in terms of the polar bonds between the metal adatoms and the semiconductor surface atoms. At sufficiently large metal coverages the wavefunctions of adjacent metal adatoms overlap and the discrete levels broaden into bands. Eventually the donor and acceptor bands overlap and the asymmetry between n-type and p-type band bending disappears. This picture is modified if the metal adatoms are clustered rather than uniformly distributed.

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