Dielectric function, band-to-band transitions, and exciton properties of bulk single-crystal In2O3 from room temperature to 600 °C determined by <i>in situ</i> spectroscopic ellipsometry

Abstract

We investigate the temperature-dependent complex dielectric function of bulk single-crystal In2O3 over the spectral range of 1–6 eV and temperatures from room temperature to 600 °C under high-vacuum conditions using in situ spectroscopic ellipsometry. The dielectric function was modeled using wavelength-by-wavelength and critical-point model dielectric function analyses. The dielectric function exhibits pronounced alterations with increasing temperature, attributed to thermally induced changes in the band structure and carrier dynamics. We identify direct and indirect interband transitions and excitonic contributions associated with the direct bandgap near the onset of absorption. At elevated temperatures, features in the dielectric function due to indirect transitions emerge below the direct bandgap energy, which shift toward shorter photon energies with increasing temperature. Combining our results with low-temperature data from previous reports, both observed shifts of the direct and indirect transitions can be seamlessly explained with the Bose–Einstein model. The direct transition is coupled less strong to the phonon bath (average temperature θB=512 K), leading to a smaller high-temperature slope (γ=−0.2 meV/K) than for the indirect transition (θB=360 K, γ=−1.3 meV/K). The exciton contributions diminish toward higher temperatures reflected by the decrease in amplitude and increase in broadening model parameters. Our parameter set can be used to calculate the model dielectric function In2O3 at elevated temperatures.