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 = 3.4x(2) + 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.