Electronic structure ofPb1−xSrxS. Application of the Haydock recursion method

The Haydock recursion method is used to study the electronic structure of the pseudobinary alloy semiconductor ${\mathrm{Pb}}_{1-x}{\mathrm{Sr}}_x\mathrm{S}$. Density of states and $\overrightarrow{\mathrm{k}}$-dependent spectral weight functions are calculated for a tight-binding model. Large deviations from virtual-crystal behavior are found. The density of cation $s$ states decreases below the valence band and increases above the gap as $x$ increases from 0 to 1. For Pb-rich alloys, the absorption edge (due to the direct gap at $L$) goes from the infrared to the visible as Sr is added, in agreement with experiment. Near $x=1\mathrm{}$ (Sr rich), the direct gap at $X$ increases slightly as the Pb concentration is increased. The gap in the density of states and the optical-absorption edge decreases, however, due to the formation on an electron-volt scale of an impurity band comprised mostly of Pb $p$ states. The advantages of the recursion method relative to the coherent-potential approximation for calculating the electronic structure of alloys are discussed. It is concluded that the recursion method represents a viable alternative for real materials.