Composition-dependent band gaps and indirect–direct band gap transitions of group-IV semiconductor alloys

We used the coherent potential approximation to investigate the band structures of group-IV semiconductor alloys, including SixGe1−x, Ge1−ySny and SixGe1−x−ySny. The calculations for SixGe1−x prove the reliability and accuracy of the method we used. For Ge1−ySny, the direct band gap optical bowing parameter we obtained is 2.37 eV and the indirect–direct band gap transition point is at y = 0.067, both consistent with the existing experimental data. For SixGe1−x−ySny, with the increase of the Si concentration, the compositional dependency of the band gap becomes complex. An indirect–direct band gap transition is found in SixGe1−x−ySny in the range of 0 < x ≤ 0.20, and the indirect–direct crossover line in the compositional space has the quadratic form of y = 3.4x2 + 1.11x + 0.07, not the linear form as suggested before. Furthermore, for the Ge lattice-matched alloy Ge1−x(Si0.79Sn0.21)X, our results show that those with 0.18 < X < 0.253 have band gaps larger than 0.8 eV at room temperature.