Temperature dependence of the infrared dielectric function and the direct band gap of InSb from 80 to 725 K*

The temperature dependence of the complex pseudo-dielectric 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. After a native oxidesurface correction, the dielectric function was fitted with a Herzinger-Johs parametric semiconductor model to determine the band gap and with a Drude term to determine the electron concentration and the mobility. We find that the band gap decreases from 230 meV at 80 K to 150 meV at 450 K, as expected from a Bose-Einstein model for electron-phonon scattering renormalization of the band gap and thermal expansion. Between 450 and 550 K, the band gap remains constant 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 band gap 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 2×10¹⁶ cm⁻³ at 300 K to 3×10¹⁷ cm⁻³ at 700 K, in reasonable agreement with temperature-dependent Hall measurements. The electron mobility was found to decrease from 105 cm²/Vs at 450 K to 2×10⁴ cm2/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.