The intervalley scattering time in $n$-type germanium from the $\Gamma$ valley to the $L$, $\Delta$, and $X$ valleys, has been computed ab initio with a method based on the density functional perturbation theory. We demonstrate that the pressure dependence of the lifetime of the exciton limited by the electron-phonon interaction is well described. Moreover, we discuss relaxation times measured by various pump-probe experiments at low and ambient temperatures. The contributions of the various phonons to the scattering are computed. Relaxation times due to the electron-phonon coupling are provided for each intervalley transition, as well as their behavior under pressure.

• Received 28 March 2011

DOI:https://doi.org/10.1103/PhysRevB.84.035201