Temperature dependence of the dielectric function and the interband critical points of InSb

Measurements performed with a rotating-analyzer ellipsometer have been used to determine the dielectric function of undoped InSb between 1.2 and 5.6 eV in the temperature range 100 to 700 K. The critical energies of the critical points (CP’s) $E_1$, $E_1$+${\Delta }_1$, $E_0^{\mathcal{’}}$, $E_0^{\mathcal{’}}$+${\Delta }_0^{\mathcal{’}}$, $E_2$, ${\Delta }_5^{\mathrm{vu}}$-${\Delta }_5^{\mathrm{cu}}$, ${\Delta }_5^{\mathrm{vl}}$-${\Delta }_5^{\mathrm{cu}}$, $E_1^{\mathcal{’}}$, and $E_1^{\mathcal{’}}$+${\Delta }_1^{\mathcal{’}}$, and their dependence on temperature, have been obtained. Separate critical contributions in the $E_0^{\mathcal{’}}$ region, which were assigned earlier to Γ- and Δ-symmetry transitions, have been resolved. The experimentally obtained CP energies have been fitted to the empirical expression given by Varshni and also to a phenomenological expression which follows from the Bose-Einstein statistical factor. The line-shape analysis of the derivative spectra allows us to obtain precise broadening parameters, amplitudes, and excitonic phase angles for the above-mentioned CP’s. A decrease in these phase angles with increasing temperature is observed. It suggests a corresponding decrease of excitonic interaction effects with increasing temperature.