Condensation of excitons in germanium and silicon

Abstract

The ground state energy of an electron-hole plasma in a Ge type semiconductor is calculated with the help of the 'improved RPA' approximation of Nozieres and Pines (1958). The detailed band structure is taken into account, except for the warping of the valence band. That is, the effects of the anisotropy, of the valence band coupling and of the multivalley structure are discussed, and are found to stabilize the plasma. The numerical results for Ge and Si are in very good agreement with experiments, which provides a check for the validity of the 'improved RPA' approximation.