Measurement of the absolute Raman cross section of the optical phonon in silicon

The absolute Raman cross section σ_RS of the first-order 519 cm⁻¹ optical phonon in silicon was measured using a small temperature-controlled blackbody for the signal calibration of the Raman system. Measurements were made with a 25-mil thick (001) silicon sample located in the focal plane of a 20-mm effective focal length (EFL) lens using 785-, 1064-, and 1535-nm CW pump lasers for the excitation of Raman scattering. The pump beam was polarized along the [100] axis of the silicon sample. Values of 1.0±0.2×10⁻²⁷, 3.6±0.7×10⁻²⁸, and 1.1±0.2×10⁻²⁹ cm² were determined for for 785-, 1064-, and 1535-nm excitation, respectively. The corresponding values of the Raman scattering efficiency S are 4.0±0.8×10⁻⁶, 1.4±0.3×10⁻⁶, and 4.4±0.8×10⁻⁸ cm⁻¹ sr⁻¹.The values of the Raman polarizability |d| for 785-, 1064-, and 1535-nm excitation are 4.4±0.4×10⁻¹⁵, 5.1±0.5×10⁻¹⁵, and 1.9±0.2×10⁻¹⁵ cm², respectively. The values of 4.4±0.4×10⁻¹⁵ and 5.1±0.5×10⁻¹⁵ cm² for |d| for 785- and 1064-nm excitation, respectively, are 1.3 and 2.0 times larger than the values of 3.5×10⁻¹⁵ and 2.5×10⁻¹⁵ cm² calculated by Wendel. The Raman polarizability |d| computed using the density functional theory in the long-wavelength limit is consistent with the general trend of the measured data and Wendel’s model.