Temperature dependent dielectric function and direct bandgap of Ge

摘要

The dielectric function of bulk Ge is determined between 0.5 and 6.3 eV in a temperature range of 10-738 K using spectroscopic ellipsometry. The authors provide the data in a tabulated format that can be interpolated as a function of photon energy and temperature using commercial software. Another focus of this paper lies on the analysis of critical points, in particular, on the investigation of the temperature dependence of the direct bandgap E-0 and the critical point E-0 + Delta(0), where Delta(0) is the spin-orbit splitting. To explore the temperature dependence of critical points, the parameters that characterize their line shapes are calculated using three different techniques. First, the common method of numerically calculating and analyzing the second derivatives of the dielectric function works well for critical points at higher energies. Second, an analysis in reciprocal space by performing a discrete Fourier transform and analyzing the resulting Fourier coefficients yields values for the energies of E-0 and E-0 + Delta(0). Third, the energy determined from a parametric semiconductor model is shown as a function of temperature. The authors observe a temperature dependent redshift of the E-0 and E-0 + Delta(0) critical point energies as well as an increase in the broadening of E-0 with temperature. Published under license by AVS.