Interface exciton modes and superconducting transition temperature of a metal in contact with a semiconductor

The problem of superconductivity in a metal-semiconductor system has been studied, using the dielectric formulation of superconductivity. The charge redistribution due to the quantum penetration of the metallic electrons to the semi-conductor side is approximated by a simple exponential function. The interface exciton modes are obtained within the framework of classical electrostatics, and their effect in modifying the effective electron-electron interaction near the interface is investigated. It is found that the strength of the excitonic term is small, and by itself, insufficient to lead to superconductivity. Nevertheless, it can alter the superconducting transition temperature of a metal, if it is already superconducting due to some other mechanism. This has been studied as a function of the various parameters entering in the problem.