Electron-Phonon Self-Energies in Many-Valley Semiconductors

The temperature dependence of band edges is discussed in many-valley semiconductors for intermediate and high temperatures. Electron-phonon self-energies are evaluated using a sphericalized, nonparabolic conduction band model. The intravalley and intervalley contributions to the electron-phonon scattering are shown to have the characteristics of Debye and Einstein functions, respectively. The results are shown to be in agreement with measurements of the temperature dependence of the indirect gap ${\Gamma }_{{25}^{\prime }}-L_1$ in Ge.