Temperature dependence of the infrared dielectric function and the direct bandgap of InSb from 80 to 725 K

Abstract

The temperature dependence of the complex pseudodielectric function of bulk InSb (100) near the direct band gap was measured with Fourier-transform infrared ellipsometry between 30 and 500 meV at temperatures from 80 to 725 K in ultrahigh vacuum. Using the Jellison–Sales method for transparent glasses, the thickness of the native oxide was found to be 25±5 Å, assuming a high-frequency dielectric constant of about 3.8 for the native oxide. After this surface correction, the dielectric function was fitted with a Herzinger–Johs parametric semiconductor model to determine the bandgap and with a Drude term to determine the electron concentration and the mobility. We find that the bandgap decreases from 230 meV at 80 K to 185 meV at 300 K, as expected from thermal expansion and a Bose–Einstein model for electron-phonon scattering renormalization of the bandgap. Between 450 and 550 K, the bandgap remains constant near 150 meV and then increases again at even higher temperatures, presumably due to a Burstein–Moss shift resulting from thermally excited electron-hole pairs. The broadening of the direct bandgap increases steadily with temperature. The electron concentration (calculated from the Drude tail at low energies assuming parabolic bands with a constant electron mass of 0.014m0) increases from 2×1016cm−3 at 300 K to 3×1017cm−3 at 700 K, in reasonable agreement with temperature-dependent Hall measurements. The electron mobility was found to decrease from 105cm2/Vs at 450 K to 2×104cm2/Vs at 700 K, also in good agreement with Hall effect results. We describe a theoretical model that might be used to explain these experimental results.