Analysis of the Critical Point Parameters of E₀ and E₀+Δ₀ of Bulk Ge

Germanium is an indirect bandgap semiconductor having its onset of absorption at 0.8 eV at room temperature. Knowledge of the behavior of critical points (CPs) of Ge and other semiconductors is valuable for the further development of electronic and optoelectronic devices.
The dielectric function of Ge has been measured between 0.5 eV and 1.3 eV using spectroscopic ellipsometry at various temperatures between 10 K and 740 K. The interband CPs E₀ and E₀+Δ₀, where E₀ is the direct band gap of Ge and Δ₀ is the spin-orbit splitting occurring at the center of the Brillouin zone, lie in this energy range and are subject of our investigations. Applying an analysis in reciprocal space by performing a discrete Fourier transform of the data points and fitting the resulting Fourier coefficients, the parameters describing the line shape of E₀ are found as a function of temperature. Like for the CPs at higher energies, the authors find a red shift of the E₀ and E₀+Δ₀ energies which can be described by a Bose-Einstein factor taking into account electron-phonon interactions. The results of the reciprocal-space analysis are compared to the parameters determined by a parametric semiconductor fit.