Temperature dependence of the dielectric function of germanium

TLDR

Temperature‑dependent band‑structure calculations of Ge, incorporating Debye‑Waller and self‑energy effects, provide the context for this study. The authors performed temperature‑dependent ellipsometry on undoped Ge (100–850 K, 1.25–5.6 eV) to extract critical‑point energies, broadening, amplitudes, and phase angles. Critical‑point energies follow either Varshni’s empirical law or a Bose‑Einstein phonon factor, and excitonic interactions weaken as temperature rises.

Abstract

Ellipsometric measurements of the dielectric constant of undoped Ge were performed between 1.25 and 5.6 eV in the temperature range of 100 to 850 K. The dependence of the ${E}_{1}$, ${E}_{1}+${ensuremath{\Delta}}_{1}$, ${E}_{0}^{\ensuremath{'}}$, and ${E}_{2}$ critical energies on temperature was obtained. It can be represented either with Varshni's empirical formula or with an expression proportional to the Bose-Einstein statistical factor of an average phonon. Broadening parameters, amplitudes, and phase angles for the corresponding critical points were also obtained. A decrease of the excitonic interaction with increasing temperature was found. The results are discussed in the light of recent calculations of the effect of temperature on the band structure of Ge containing Debye-Waller and self-energy contributions.