The usual paradigm to describe long wavelength phonons in AB_1-xC_x semiconductor alloys is the virtual crystal approximation (VCA), corresponding to local averaging of alloy disorder. With this, bonds of like species are immersed into the same VCA-like continuum and thus contribute to a unique phonon mode (1-bond→1-mode, macroscopic insight). In fact three sub-types are distinguished: (i) pure 1-bond→1-mode, (ii) mixed-mode, and exceptionally (iii) modified 2-mode. Types (i) and (ii) are accounted for by the modified-random-element-isodisplacement (MREI) model from Chang and Mitra. A theoretical criterion was worked out by Elliott within the coherent potential approximation (CPA) to distinguish between those two types, which has finalized the picture.

However, careful analysis of the vibration spectra in the literature reveals that, in fact, even the leading alloys in each class, i.e. InGaAs (i), ZnTeSe (ii) and InGaP (iii) do not fit into the MREI-VCA/Elliott-CPA classification. Our view is that the VCA misses the essence of the phonon behavior in alloys. As phonons relate directly to the bond force constant, i.e. to a local property, we infer that their understanding requires insight into the (B,C)-topologies, which comes to the percolation site theory. In fact, we show that unified understanding of the phonon mode behavior of the representative alloys we discuss can be achieved via a percolation model (1-bond→2-mode, mesoscopic insight) that views an alloy as a composite of the B-rich and C-rich regions, not as a continuum (VCA). The percolation model is a sort of sophistication to the mesoscopic scale of the MREI model, that operates at the macroscopic scale. The basic parameters are estimated via a simple ab initio protocol.

This reveals that phonons have the quite unique privilege to provide natural insight into the alloy disorder at the unusual mesoscopic scale. In particular this is much promising for the study of long-range ordering/anticlustering effects.

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1. Manifestation of single and coupled impurities in the vibration spectra of III-V and II-VI semiconductor alloys