Local-field effects and the ir optical properties of ternary semiconductor alloys

We present a calculation of the infrared dielectric function of a three-dimensional ternary semiconductor alloy $A{B}_{1-x}{C}_x$. The diagonal disorder (masses) is treated in the coherent potential approximation; the off-diagonal disorder (force constants) as well as all the electronic properties (background dielectric constant, electronic screening) is handled by the virtual-crystal approximation. We use a nearest-neighbor single-force-constant potential which is shown to be sufficient to account for the optical properties. With the data of ${\mathrm{Ga}}_{1-x}{\mathrm{Al}}_x\mathrm{As}$, the calculated density of states shows one acoustic band and two optical bands, one near the gap mode of Ga in AlAs, and the other near the localized mode of Al in GaAs. Particular attention has been given to the local-field effects caused by the ionic and electronic polarization and by the screening due to the electronic delocalization. The line broadening induced by the disorder forces one to make a precise definition of the longitudinal and transverse frequencies. In addition to the well-known two-mode behavior of ${\mathrm{Ga}}_{1-x}{\mathrm{Al}}_x\mathrm{As}$, the model predicts a third very weak mode (about a hundred times weaker), which is a disorder-activated zone-edge mode. The model also predicts a rapid variation of the longitudinal-transverse splitting of the two main modes when one approaches the pure-crystal limit. The numerical results agree well with the experimental data and are also compared with those of the linear diatomic chain.