Surface exciton modes for plane and spherical semiconductor-metal interfaces

An approximate method is developed for investigating the nature of interface exciton modes in a composite spatially dispersive medium. The method is general enough to be applicable to any composite system, in which each component is described by an arbitrary bulk dielectric function ε(q, ω). It is based on the extension of the usual electrostatic-image method of solving the Poisson's equation, in the presence of an external point charge in the system. We have applied our general method to a composite system of a finite metal slab surrounded by a semiconductor on one side and the vacuum on the other side. Similarly, we have also considered the case of a metallic sphere of radiusR, surrounded by a semiconductor, with a spherical interface between them. With assumed spatially dispersive model dielectric functions for the bulk metal and the bulk semiconductor, the nature of the electron-electron interaction and the interface exciton modes in the metallic region are obtained in both the cases. For the relevant size of the metal large compared to the atomic dimensions over which the bulk dielectric functions are non-local due to the spatial dispersion, it is shown that one can obtain the interface exciton modes by first defining new effective dielectric functions for each of the media making the particular interface, and then using the usual expression which determines the modes in the non-dispersive case