Phonon-induced lifetime broadenings of electronic states and critical points in Si and Ge

We present calculations of the lifetime broadenings of electronic states produced by the electron-phonon interaction in semiconductors and of their dependence on temperature. This effect is evaluated as a complex self-energy of the electronic states. The real part of this self-energy describes a shift of the bands with temperature, whereas the imaginary part is responsible for the broadening of the states. For the calculations based on perturbation theory to second order in atomic displacement we use a local pseudopotential with a basis of 59 plane waves, the lattice dynamics of Weber’s bond-charge model, and a tetrahedron method for doubly constrained Brillouin-zone integrals. Results are given for points along the Λ and Δ direction of the Brillouin zone for Si and Ge, thus obtaining the temperature dependence of the broadening parameters of the interband critical points $E_0$, $E_0^{\mathcal{’}}$, $E_1$, and $E_2$. The results are compared with experimental data obtained from ellipsometric measurements of the temperature dependence of the dielectric function. Remarkable agreement between calculated and measured data is found.