BOND-LENGTH DEPENDENCE OF PHONON FREQUENCIES IN TETRAHEDRALLY COORDINATED SEMICONDUCTORS

A scaling law of force constants versus equilibrium bond length is found, which gives a good account of phonon energies in tetrahedrally coordinated semiconductors. The law gives the bond-length dependence of bond-stretching and bond-bending parameters which enter the valence force field model used to describe the lattice dynamics of these materials. This is obtained after a theoretical fitting to the experimental optic phonons in II-IV-V2 chalcopyrite semiconductors. To test the validity of the proposed law, we calculated phonon energies in several III-V zincblende compounds at different points in the Brillouin zone. A good agreement is found with experimental results for most of the phonon energies. The small discrepancies obtained at intermediate frequencies are mainly due to the limitation of the valence force field model used and cannot be imputed to the scaling law. The law permits us to predict phonon energies in other compounds within the family. As an example, we calculate optic phonons of CdSiAs2, one of the chalcopyrite compounds with a larger cation-anion bond length difference, and discuss the results in terms of phonon energies in zincblende analogues.