Band gap narrowing due to many-body effects in silicon and gallium arsenide

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Abstract
The authors present a theoretical study of band gap narrowing due to many-body effects in silicon and gallium arsenide at zero temperature. A principal aim of the paper is to give a detailed description of a self-energy approach to the band gap narrowing problem and the use of the plasmon pole approximation for dielectric response in the self-energy formalism. The particular problems arising from multiple and anisotropic bands, and direct and indirect band gaps are considered. Numerical results are presented for electrons, holes and an electron-hole plasma in both Si and GaAs. For the case of electrons in Si where reliable theoretical results already exist the results are seen to agree well with the earlier work. Also the theory of band gap narrowing in the electron-hole plasma case is found to be compatible with established independent work on electron-hole droplets. The results described in this paper are expected to be relevant to heavily doped or highly excited semiconductors and electronic devices based on these although it is recognized that the theory as it stands does not include impurity disorder effects.