Percolation picture for long wavelength phonons in zinc blende alloys: application to GaInAs

We propose a 'one bond→two modes' model for the long wavelength optical phonons in random zinc-blende AxB1−xC ternary alloys, based on the percolation site theory. Our model takes into account the 'fractal→normal' object transition, which goes with the 'dispersion→continuum' topology transition at the percolation thresholds of the A-C and B-C bonds. We first introduce the basics of our model in the case of Zn1−xBex(Se,Te) mixed crystals, whose parent binaries display a high contrast in the bond stiffness, which enhances the percolation effects. We then focus our study on standard systems, which display a much weaker contrast in the bond stiffness. The multi-phonon behavior of GaInAs alloys is re-examined in the light of the percolation model, with much success.