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.

• Received 18 October 1982

DOI:https://doi.org/10.1103/PhysRevB.27.4760