Theoretical discussion of the scanning tunneling microscope applied to a semiconductor surface

A free-electron model that we recently developed for a metal-metal microscope is extended to the case of a semiconducting sample. The probe, biased positive with respect to the sample, is taken to be a free-electron metal in the shape of a plane with a hemispherical projection. The sample, its surface being a parallel plane, is assumed to have spherical energy bands. The penetration probability is assumed to be the WKB result along the central axis using a potential energy which includes multiple image effects. We calculate current versus voltage curves at several electrode spacings for a tungsten/silicon combination.