Self-consistent theory of electronic states and dielectric response in semiconductors

Abstract

A new method is proposed for dealing with the dielectric response of a semiconductor to a constant macroscopic electric field. The ‘‘direct’’ approach we use is general, an alternative to linear-response theory, and not restricted to linear effects. It consists in incorporating the macroscopic field into the system and in dealing with the ‘‘perturbed’’ crystal as with a new system; the potential of the constant field is generated by building in a (periodically repeated) capacitor. We apply this method to Ge and GaAs within the local-density-functional framework and investigate the dielectric response: Macroscopic quantities (${\epsilon }_{\infty }$,$e_T^{\mathrm{*}}$) are obtained, as well as microscopic ones (variations of local fields). Our approach, self-explanatory in r space, is related here to the conventional linear dielectric theory, which is formulated in terms of dielectric matrices in reciprocal space. Our results shed new light upon the basic mechanisms and trends in electronic dielectric screening; the most popular models for microscopic response are judged in view of the present calculations for real materials.