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 Si(x)Ge(1-x), Ge(1-y)Sn(y) and Si(x)Ge(1-x-y)Sn(y). The calculations for Si(x)Ge(1-x) prove the reliability and accuracy of the method we used. For Ge(1-y)Sn(y), 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 Si(x)Ge(1-x-y)Sn(y), 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 Si(x)Ge(1-x-y)Sn(y) 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 Ge(1-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.