Correlation Energy in a Model Semiconductor

Abstract

The correlation energy of the electrons in a semiconductor is expected to be less than in a metal with the same electron density. The reduction occurs because the existence of an energy gap between filled and empty states tends to increase the magnitude of the energy denominators of perturbation theory. This effect is studied in a simple model, based on the calculations of Gell-Mann and Brueckner, in which the semiconductor is represented as a free electron gas with an energy gap above the Fermi surface. The correlation energy then depends on the ratio of the energy gap to the valence bandwidth as well as on the density. It is shown that for an energy gap large compared to the bandwidth, second order perturbation theory is correct; while for a small energy gap, an explicit correction to the Gell-Mann-Brueckner series can be obtained.