Measurement of the Absolute Raman Cross Section of the Optical Phonon in Silicon

Abstract

The absolute Raman cross section (\sigma_{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} cm^2) were determined for (\sigma_{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} cm^2), respectively. The values of (4.4±0.4×10^{−15}) and (5.1±0.5×10^{−15} cm^2) 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} cm^2) 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.