First-principle calculation of the band structure of Ge 1−x Sn x alloy by screened-exchange local-density approximation theory

The electronic properties of Ge1−xSnx were studied by the sX-LDA method. It is found that the bowing coefficient of the direct bandgap energy depends on composition obviously while the bowing coefficients of the Γ–L and Γ–X bandgap energies depend on composition weakly. As the atom size mismatch (ASM) between Ge and Sn atoms is large and the electronegativity difference (ED) between them is relatively small, the ASM should play a more important role than the ED in determining the bowing coefficient. The decrease of the direct bandgap bowing coefficient is owing to that the direct bandgap energy goes through from the impurity-like region to the band-like region in the Ge-rich range. According to the fitting results, the transition from the indirect to direct bandgap occurs when about 6% of Ge atoms are replaced by Sn atoms. The larger band bowing of Ge1−xSnx than Si1−xGex can be attributed to the ASM. In addition, the larger bowing of the CBM than the VBM is relative to the components of the two bands and the band offsets between Ge and Sn.