Si-C atomic bond and electronic band structure of a cubicSi1−yCyalloy

We apply the ${\mathrm{sp}}^3{s}^{*}$ tight-binding model to study the electronic energy band structure of the cubic ${\mathrm{Si}}_{1-y}{\mathrm{C}}_y$ alloy. First by the effective medium approximation where local atomic fine structures are averaged out, it is obtained that the energy band gaps of both relaxed and strained ${\mathrm{Si}}_{1-y}{\mathrm{C}}_y$ alloys increase with increasing C content. The effect of the local Si-C atomic bond structure on the energy band is studied in the real space in order to include the actual broken translational symmetry in the ${\mathrm{Si}}_{1-y}{\mathrm{C}}_y$ alloy. The electronic local densities of states are investigated and the following is concluded: (a) When Si-C bond length in the alloy assumes the crystal SiC one (strained alloy), an electronic state at the C atom and its surrounding Si atoms is induced in the energy band gap of crystal Si. The valence band edge is slightly lifted. The results indicate a type I energy band alignment for strained ${\mathrm{Si}}_{1-y}{\mathrm{C}}_y/\mathrm{Si}$ quantum well. (b) When the Si-C bonds assume the Si-Si bond length of the crystal Si (relaxed alloy), the electronic states are not much modified.