Effects of compositional disorder on phonons in layered semiconductor microstructures

The random-element-isodisplacement (REI) model developed originally to describe zone-center optical phonons in ternary mixed crystals is generalized. Starting from a certain configurational average that defines an average composition within an atomic or a molecule layer perpendicular to a given growth direction, we derive equations of motion for the averaged atomic displacements and the correlation of fluctuations in composition and displacements. The long-range macroscopic electric field is included fully. We show that phonons with arbitrary wave vectors can be studied for the configurationally averaged layered system. The density of states resulting from this model is compared with that from a numerical simulation of the full disorder using extended supercells. The comparison shows that only disorder-induced broadening effects are neglected within the generalized REI model. The power of the model is explicitly demonstrated for pure mass disorder in (GaAs${)}_{\mathit{N}1}$(${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Al}}_{\mathit{x}}$As${)}_{\mathit{N}2}$(001) superlattices. Different cases of cation interdiffusion at the interfaces of (GaAs${)}_{\mathit{N}1}$(AlAs${)}_{\mathit{N}2}$ structures and the influence of barrier composition are studied.