Temperature dependence of the dielectric function and analysis of critical point parameters of bulk Ge

Detailed knowledge of the optical properties of Ge is of great importance for the development of Ge technology. We investigate the effect of temperature on the dielectric function (DF) and interband critical points (CPs) of bulk Ge in the spectral range of 0.5 to 6.3 eV in 10 meV steps. Using spectroscopic ellipsometry at an incident angle of 70° and a UHV cryostat we took a series of measurements at different temperatures between 10 and 738 K. For the investigation of the E₀ and E₀+Δ₀ CPs at 10 K we chose step sizes of 0.5 and 1 meV to resolve their structures. To measure the DF accurately, we performed an ultrasonic and an ozone clean to achieve a stable and thin native GeO₂ layer. The thickness is found to be 11 Å at 300 K.

Variations in temperature show a significant influence on structures of the DF. To obtain the temperature dependent CP parameters we numerically calculate the second derivatives of the real and imaginary parts of the DF with respect to energy. Furthermore, we analyze CPs in reciprocal space by studying Fourier coefficients. The results from both methods are compared with each other. We observe a red-shift and an increase of broadening with temperature of the CPs due to electron-phonon interaction and temperature independent spin-orbit splittings Δ₀ and Δ₁.