Unusual helicity-resolved Raman characteristics in silicon surfaces

Helicity-resolved Raman spectra are measured for silicon (100), (110), and (111) surfaces in a back-scattering geometry using a 532 nm laser and compared with linearly-polarized Raman spectra. The polar plots of the helicity-resolved Raman intensity for the (110) and (111) surfaces as a function of the rotating angle of the polarizer for the scattered light are quantitatively described by rotating the Raman tensor from the (100) surface. Notably, the polar patterns of the (Formula presented) (Formula presented) phonon mode at 520 cm⁻¹ for the (110) surface exhibit a tilted angular dependence in the helicity-changing Raman spectra. For the (100) surface, a weak Raman peak is observed in the helicity-conserved spectra that cannot be captured by the standard (Formula presented) (Formula presented) Raman tensor, indicating a resonance-induced renormalization of the Raman tensor. This effect is reproduced by introducing a small diagonal component to the Raman tensor, which is supported by the first-principles resonant Raman calculations. The calculations further show that the relative value of the diagonal to off-diagonal component increases with increasing laser excitation energy. Our findings establish helicity-resolved Raman spectroscopy as a non-destructive method for probing symmetry-dependent Raman selection rules and identifying surface crystallographic orientation in silicon. This approach provides direct information on the Raman tensor and is applicable to other semiconductor materials.