Temperature dependence of the direct gap of Si and Ge

Abstract

The temperature dependences of the lowest direct gaps of germanium and silicon are calculated. They result from the effect of electron-phonon interaction on the corresponding electronic states. Both Debye-Waller (second-order interaction Hamiltonian) and "self-energy" (first-order interaction Hamiltonian) are included. It is shown that the latter are by no means negligible. They reduce the calculated temperature coefficients at constant volume by a factor of 1.7 in the case of Si and 1.3 in the case of Ge. Agreement with experimental data is satisfactory.