Polycrystalline Si under strain: Elastic and latticehyphen;dynamical considerations

摘要

Expressions are derived for the effective phonon deformation potentials of polycrystalline materials, based on the properties of tensor invariants and the Voigtndash;Reussndash;Hill averages lsqb;Proc. Phys. Soc. London Sect. A65, 349 (1952)rsqb;. These results, and similar ones for the elastic constants, are used to determine the effect of strains on the longhyphen;wavelength optical phonons exhibited by such materials. Application to polycrystalline Si shows that under a uniaxial or biaxial stress, the triply degenerate phonons split into singlet and doublet components that shift at different rates and appear indistinguishably in the Raman spectrum. The implications of such effects on the Raman band shape are discussed.