Selection rules of Raman scattering by optical phonons in strained cubic crystals

Strain characterization of materials through Raman spectroscopy often requires the optical phonon wave vector to be in directions other than those of the strain-modified phonon eigenvectors. As a result, the observed mode frequencies are mixtures of the strain-modified eigenfrequencies. The selection rules for such generalized scattering configurations are derived here for the strained zincblende-diamond family crystals. The formulation is based on the relative magnitude of the LO-TO and the strain-induced splittings. The results are important for the analysis of strain-modified Raman lineshapes and of “forbidden” lines. Specific examples are worked out in detail for externally stressed bulk crystals (90° scattering geometry), and for [001], [111], and [110] strained heterojunctions (backscattering under oblique incidence and/or detection).