Interband critical points of GaAs and their temperature dependence

The complex dielectric function \ensuremath{\epsilon}(\ensuremath{\omega}) of GaAs was measured from 20 to 750 K with a scanning rotating-analyzer ellipsometer. The structures observed in the 1.3--5.5-eV photon-energy region, attributed to transitions near the \ensuremath{\Gamma} point of the Brillouin zone (${E}_{0}$, ${E}_{0}$+${\ensuremath{\Delta}}_{0}$, ${E}_{0}^{\mathcal{'}}$), along the \ensuremath{\Lambda} direction (${E}_{1}$, ${E}_{1}$+${\ensuremath{\Delta}}_{1}$), and near the X point (${E}_{2}$), are analyzed by fitting the second-derivative spectrum ${d}^{2}$\ensuremath{\epsilon}(\ensuremath{\omega})/d${\ensuremath{\omega}}^{2}$ to analytic critical-point line shapes. The ${E}_{0}^{\mathcal{'}}$ and ${E}_{2}$ critical points are best fitted in the whole temperature region by a two-dimensional line shape, whereas the ${E}_{1}$ and ${E}_{1}$+${\ensuremath{\Delta}}_{1}$ transitions are best fitted up to room temperature by a Lorentzian interacting with a continuum of interband transitions (Fano line shape). The excitonic character of the ${E}_{1}$ and ${E}_{1}$+${\ensuremath{\Delta}}_{1}$ transitions is discussed within several theoretical approaches. The experiments indicate that up to room temperature the localized Lorentzian interacting with the continuum is dominant, whereas at higher temperatures the modification of the two-dimensional Van Hove singularity due to the electron-hole attractive perturbation is a better description of the measurements. For all critical points, the energy decreases with increasing temperature while the broadening increases. This dependence on temperature is analyzed in terms of averaged phonon frequencies which cause a renormalization of the energies and a broadening of the band gaps.