Effective dielectric response of semiconductor composites

Using a previously proposed diagrammatic approach for the calculation of the renormalized polarizability of spherical inclusions in a homogeneous matrix we obtain an effective dielectric response of a composite of nonpercolating inclusions taking into account a continuous distribution of sizes of the spheres. We apply this theory to semiconductor-doped glasses (SDG) calculating both the electron and phonon responses in the far-infrared and optical spectral regions, respectively, and also to a strongly inhomogeneous semiconductor alloy. For SDG, we compare our calculated results with available experimental data on interband optical absorption and obtain good agreement by choosing the appropriate distribution function of sizes of the spheres. In the case of the ${\mathrm{Cd}}_{\mathit{x}}$${\mathrm{Hg}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$Te alloy, we find an interesting interplay of the composite effects and phonon-plasmon coupling resulting in a rich structure for the reflectivity spectra. We compare these results to those calculated using another approach, which is widely used for describing the dielectric properties of composites, the self-consistent approximation, and discuss the relation between the two approaches. \textcopyright{} 1996 The American Physical Society.