Optical critical points of thin-film Ge1-ySny alloys:: A comparative Ge1-ySny/Ge1-xSix study

The E-0, E-0+Delta(0), E-1, E-1+Delta(1), E-0('), and E-2 optical transitions have been measured in Ge1-ySny alloys (y < 0.2) using spectroscopic ellipsometry and photoreflectance. The results indicate a strong nonlinearity (bowing) in the compositional dependence of these quantities. Such behavior is not predicted by electronic structure calculations within the virtual crystal approximation. The bowing parameters for Ge1-ySny alloys show an intriguing correlation with the corresponding bowing parameters in the Ge1-xSix system, suggesting a scaling behavior for the electronic properties that is the analog of the scaling behavior found earlier for the vibrational properties. A direct consequence of this scaling behavior is a significant reduction (relative to prior theoretical estimates within the virtual crystal approximation) of the concentration y(c) for a crossover from an indirect- to a direct-gap system.