Band-filling and relaxation effects in the transient dielectric function of Ge

Abstract

This study investigates the transient dielectric function of germanium at charge carrier densities of the order of 1020cm−3 using time-resolved spectroscopic ellipsometry. By employing a pump-probe technique, we explore the temporal evolution of the critical points E1 and E1+Δ1 after high-intensity laser excitation. Given the two-dimensional character of these critical points, the absorption of Ge is significantly enhanced by excitonic binding. Furthermore, at high carrier densities, intervalley scattering and band saturation play a significant role in the optical response of the material. To address these phenomena, we combined band-filling effects with a two-dimensional excitonic line shape to model the observed optical spectra. We also simulated the Fermi energies and electron temperatures governing the measurements using Fermi–Dirac statistics. Given the short timescales of the carrier relaxation and intervalley scattering, this analysis focuses exclusively on the first few picoseconds after excitation, with a minimum step size of 50 fs. The model successfully reproduces the main features of the experimental spectra, capturing the reduction in amplitude of the dielectric function and the redshift of the critical points due to bandgap renormalization. From these fits, we extract an energy relaxation rate of the order of 1.5meVfs−1 and provide a quantitative description of the ultrafast carrier dynamics in Ge.