Scattering from ionized dopants in Schottky barriers

Abstract

We calculate the true electrostatic potential that forms a Schottky barrier, arising from a random distribution of dopants in the depletion region. It is customary to model the electrostatic potential in a Schottky barrier by a one-dimensional quadratic potential, as would obtain from a jellium of charge in the depletion region. The difference between the true potential and the ‘‘ideal’’ one acts as a perturbation to electrons traversing the depletion region. This perturbation is found to be small, and effectively one dimensional. Its effect on the transmission probability of an electron tunneling through the depletion region is shown to be negligible. It is shown, however, that because of the large quantum dipoles near the metal–semiconductor interface, the image-force lowering correction does not in general vary as N1/4d, as is widely thought, at least for heavily doped materials. Local-density calculations of the Schottky barrier height were made for several metal/GaAs interfaces, to obtain the magnitude and range of the interfacial dipoles. They are found to be large and persist sufficiently far from the interface that they dominate the slowly varying potential from the ionized dopants. Thus, the interplay between the image-force potential and the interfacial dipoles determines the maximum in Schottky barrier height; moreover the quantum dipoles add an additional correction of the same magnitude as the image-force correction in the heavily doped case.