Features of the percolation scheme of vibrational spectrum reconstruction in the Ga$_{1-x}$Al$_{x}$P alloy

Specific features of the properties of Ga–P lattice vibrations have been investigated using the percolation model of a mixed Ga$_{1-x}$Al$_{x}$P crystal (alloy) with zero lattice mismatch between binary components of the alloy. In contrast to other two-mode alloy systems, in Ga$_{1-x}$Al$_{x}$P a percolation splitting of $\delta\sim$ 13 cm$^{-1}$ is observed for the low-frequency mode of GaP-like vibrations. An additional GaP mode (one of the percolation doublet components) split from the fundamental mode is observed for the GaP-rich alloy, which coincides in frequency with the gap corresponding to the zero density of one-phonon states of the GaP crystal. The vibrational spectrum of impurity Al in the GaP crystal has been calculated using the theory of crystal lattice dynamics. Upon substitution of lighter Al for the Ga atom, the calculated spectrum includes, along with the local mode, a singularity near the gap with the zero density of phonon states of the GaP crystal, which coincides with the mode observed experimentally at a frequency of 378 cm$^{-1}$ in the Ga$_{1-x}$Al$_{x}$P ($x<$ 0.4) alloy.