The electrostatic image potential in metal semiconductor junctions

Abstract

The classical image potential of electrostatics is generalized to take into account a more realistic dielectric response of metal and semiconductor. The Fermi-Thomas dielectric function is used for the metal while in the semiconductor an interpolation formula is used to approximate the true dielectric function. This interpolation formula leads to an inhomogeneous Fermi-Thomas equation which has, as a particular solution, the classical dielectric case. The image potential near the interface shows rapid variations which are critically dependent upon the relative Fermi-Thomas screening lengths in the two materials but at longer distances the classical image potential is recovered. The physical basis for these results is described in terms of the screening of the test charge by the valence electrons of the semiconductor and the conduction electrons of the metal.