Polycrystalline Si under strain: Elastic and lattice-dynamical considerations

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Abstract
Expressions are derived for the effective phonon deformation potentials of polycrystalline materials, based on the properties of tensor invariants and the Voigt–Reuss–Hill averages [Proc. Phys. Soc. London Sect. A 6 5, 349 (1952)]. These results, and similar ones for the elastic constants, are used to determine the effect of strains on the long‐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.