Temperature dependence of the shifts and broadenings of the critical points in GaAs

We present calculations of the shifts of the electronic states and their lifetime broadening with temperature in GaAs. The Debye-Waller and self-energy terms of the deformation-potential-type electron-phonon interaction are considered. The self-energy term is complex; its real part partly cancels the shifts caused by the Debye-Waller term and the imaginary part is responsible for the lifetime broadening. Results are obtained for the interband critical points $E_0$, $E_0^{\mathcal{’}}$, $E_1$, and $E_2$ in GaAs. The shifts of these gaps, when corrected for the contribution of thermal expansion, show good agreement with ellipsometric data. The broadening of $E_0^{\mathcal{’}}$ and $E_2$ gaps are underestimated when compared to the experimental results while the broadening of the $E_1$ gap is consistent with experiment.