Calculation of the electronic properties of pseudo-binary semiconductor alloys

A coherent-potential approximation calculation is presented for the concentration variation of the pseudo-binary semiconductor alloy band structures and scattering rates. The procedure yields accurate results that compare favorably with experiments for ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$, $\mathrm{Ga}{\mathrm{P}}_x{\mathrm{As}}_{1-x}$, and ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{P}$. A theory for the scattering energy in the Brooks mobility formula is also given.