Defect-Induced Lattice Vibrations in Zinc-Blende-type Crystals. A Modified Molecular-Model Calculation

The molecular model developed for the point-defect problem in alkali halides has been adapted to the zinc-blende structure to calculate the local- and gap-mode frequencies for selected substitutional defects in a number of II-VI and III-V compounds. The novel feature of this calculation is that no force-constant softening is assumed for the bonds surrounding a defect center. For substitutional impurities of the type which also forms a mixed crystal system, such as $A{B}_{1-x}{C}_x$, local- and gap-mode frequencies for $x\gtrsim 0$ or $x\lesssim 1$ have been computed. For a system $A\mathit{B}:C$ the local- or gap-mode frequencies are shown to be given by parameters pertaining to end members $\mathrm{AB}$ and $\mathrm{AC}$ only. The computed frequencies agree remarkably well with available experimental data.