On the ground state energy of free excitons in group IV and III–V semiconductors

Abstract

An approximate calculation of the ground state energy of direct and indirect free excitons for group IV and group III–V semiconductors is presented. The basic assumption in this treatment is that the anisotropy of the effective masses can be neglected, however, the degeneracy of the valence band cannot. The resulting exciton ground state energy has the usual form but with a reduced mass\(\overline \mu \) given by (\(\overline \mu \))−1=(me)−1+(mlh)−1+(mhh)−1. The agreement with experiments is considerably improved as compared to the conventional ground state energy comprising the reduced mass defined as (μ)−1=(me)−1+(mhh)−1. Anisotropy corrections are shown to be of minor importance in many cases. However, for the heavier III–V-compounds the neglect of linear terms inE(k) for the valence band results in more serious errors, which invalidate the present theoretical approach.