Temperature dependence of the optical spectra of Si, Ge, and Ge-Si alloys

The optical spectra of Ge-Si alloys ranging from pure Ge to pure Si are studied at liquid-nitrogen and room temperatures in the spectral regions of $E_1$ and $E_2$ interband transitions. Dielectric functions are obtained from Kramers-Kronig analysis of reflectance, and their accuracy is discussed; thermoreflectance spectra are reported. The average temperature shift of interband energies obtained from the dielectric function is (-2.0±0.5)×${10}^{\mathrm{-}4}$ eV/K for both $E_1$ and $E_2$ regions, nearly independent of the alloy composition. The temperature coefficient substantially increases in derivative spectra, where the critical points are better isolated. This effect decreases going from Ge to Si. The change of broadening is found to be important, with temperature coefficients from ${10}^{\mathrm{-}4}$ to 2×${10}^{\mathrm{-}4}$ eV/K.