Disorder effects in alloy superlattices

We examine the effects of disorder on superlattices made of semiconductor alloys by proposing a method for obtaining an approximate solution of the coherent-potential approximation for superlattices. Our method is tested on a model one-dimensional superlattice for which it is possible to generate the ‘‘exact’’ densities of states with a Monte Carlo method. Our results are shown to be in good agreement with the Monte Carlo results. As an example of how this method might be implemented for realistic systems, we have computed the density of states and self-energies for ${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As/${\mathrm{Al}}_{\mathrm{y}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{y}}$As superlattices.