Anomalous temperature-dependent band gaps inCuInS2studied by surface-barrier electroreflectance

The lowest-energy gaps of ${\mathrm{CuInS}}_2$ have been studied by low-field surface-barrier electroreflectance in the temperature range from 10 to 300 K. Anomalous temperature dependence of $E_0$ and $E_0$+${\Delta }_0$ have been found. Below 120 K the temperature coefficient of the band gap is 4.3×${10}^{\mathrm{-}5}$ eV/K for $E_0$ and 5.8×${10}^{\mathrm{-}5}$ eV/K for $E_0$+${\Delta }_0$. Above 120 K the coefficients become -8.7×${10}^{\mathrm{-}5}$ eV/K and -4.4×${10}^{\mathrm{-}5}$ eV/K for $E_0$ and $E_0$+${\Delta }_0$. These temperature-dependent energy gaps are explained by the reduction of d levels in the upper valence band due to thermal expansion and the competition with the electron-phonon interaction. The temperature dependence of spin-orbit splitting in our experiment confirms this explanation.