Infrared dielectric properties ofGa1−xAlxAs: Disorder-activated longitudinal-and transverse-acoustic modes

We present a calculation of the infrared dielectric response of ${\mathrm{Ga}}_{1-x}{\mathrm{Al}}_x\mathrm{As}$. A reference density of vibrational states is calculated in the virtual-crystal approximation with a Born—von Kármán force model. The mass disorder and an additional core-shell internal degree of freedom are then simultaneously accounted for in an extended coherent-potential approximation. Finally, an effective susceptibility is derived; adding the local-field effects gives the dielectric function. The optical spectrum evidences two main optical resonances: one rather GaAs-like, and the other rather AlAs-like. In addition, the model predicts the occurrence of two weak optical bands, which are interpreted as disorder-activated longitudinal and transverse acoustic modes from the Brillouin-zone edge.