Electronic structure calculation of Si1−xSnx compound alloy using interacting quasi-band theory

We investigate energy band structures of the Si1−xSnx compound alloy in the zincblende structure using interacting quasi-band (IQB) theory. We first extend the IQB theory for four-element compounds and subsequently calculate the electronic structures of the virtual Si1−xSnxSi1−ySny alloy where x = y. Diagonalizing a 20 × 20 non-Hermitian Hamiltonian matrix using sp3s* empirical tight-binding model with parameters obtained for the Si, Sn, and SiSn (zincblende) crystals, we obtain the electronic energy spectrum of the Si1−xSnx alloy for arbitrary x. Comparing the band structures, we reveal that the indirect–direct gap crossover in Si1−xSnx alloys occurs around x = 0.67 with Eg = 0.87 eV. Calculated Sn concentration dependence of energy gaps in Si1−xSnx alloy.