Percolation versus cluster models for multimode vibration spectra of mixed crystals: GaAsP as a case study

We reexamine the phonon mode behavior of GaAsP, the leading system among those alloys that exhibit ``anomalous'' vibration spectra of the one-$\text{bond}\ensuremath{\rightarrow}\text{multimode}$ type, the sign of a far-from-random substitution if we refer to the 1-$\text{bond}\ensuremath{\rightarrow}4$-mode cluster model (microscopic insight), which has been accepted through use. In fact, we show that the phonon behavior of GaAsP obeys a basic version of the 1-$\text{bond}\ensuremath{\rightarrow}2$-mode percolation model (mesoscopic insight), just as the phonon behaviors of InGaAs, InGaP, and ZnTeSe [O. Pag\`es et al., Phys. Rev. B 77, 125208 (2008)], the leading systems representing the three admitted variants of the ``nominal'' 1-$\text{bond}\ensuremath{\rightarrow}1$-mode type for random alloys as covered by the modified random element isodisplacement model (macroscopic insight). With this, GaAsP and its like are rehabilitated as random alloys in principle, and further, the percolation paradigm generalizes to all types and subtypes of the traditional classification of phonon mode behavior of semiconductor alloys, based on the virtual crystal approximation. The discussion is supported by phenomenological modeling of representative Raman and infrared-reflectivity spectra of GaAsP taken from the literature via the percolation model, ab initio insight into the phonon mode behavior of basic impurity motifs, and existing experimental/ab initio bond length data.