Helicity-Dependent Raman Spectroscopy of Diamond and Zinc-Blende Crystal Structures

We calculate polarized Raman intensity of diamond and zinc-blende crystal structure for arbitrary (Formula presented.) surfaces in a backscattering geometry using both linearly and circularly polarized light. Rotated Raman tensors are applied to the (Formula presented.) phonon mode of diamond and the (Formula presented.) (LO/TO) phonon modes of zinc blende to evaluate how the Raman intensity evolves as the surface orientation is varied from (100) toward (110) and (111). Polar plots versus sample rotation angle (Formula presented.) or analyzer angle (Formula presented.) show distinct behaviors for parallel (VV) and cross (VH) configurations under linear polarization, as well as helicity-dependent (Formula presented.) configuration. Helicity-dependent Raman spectroscopy reveals surface-dependent tilts of the polar pattern. We derive the analytical expressions for the Raman intensities and for the angular positions of maxima and minima as explicit functions of (Formula presented.). These surface orientation-sensitive signatures enable identification of unknown (Formula presented.), including sample miscut, and allow predictive modeling of polar-plot evolution, improving the precision of polarized Raman surface metrology.