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

The absolute Raman cross section σ R S 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 σ RS 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.