Excitonic effects at the temperature-dependent direct bandgap of Ge

The temperature dependence of the complex dielectric function ∈1 1∈2 of bulk Ge near the direct bandgap was investigated with spectroscopic ellipsometry at temperatures between 10 and 710 K. Second derivatives of the dielectric function with respect to energy are obtained using a digital linear filter method. A model that incorporates excitonic effects using the Tanguy model for the Hulthén potential [C. Tanguy, Phys. Rev. B 60, 10660 (1999)] was used to fit the dielectric function and its second derivatives simultaneously. Using k â p theory and literature values for effective masses, reasonable agreement with the experiment is obtained for I 2 up to room temperature using the direct bandgap and its broadening as the only adjustable parameters.