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

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 x 10(-27), 3.6 +/- 0.7 x 10-28, and 1.1 +/- 0.2 x 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 x 10(-6), 1.4 +/- 0.3 x 10(-6), and 4.4 +/- 0.8 x 10(-8) cm(-1) sr(-1).The values of the Raman polarizability vertical bar d vertical bar for 785-, 1064-, and 1535-nm excitation are 4.4 +/- 0.4 x 10(-1)5, 5.1 +/- 0.5 x 10(-15), and 1.9 +/- 0.2 x 10(-15) cm(2), respectively. The values of 4.4 +/- 0.4 x 10(-15) and 5.1 +/- 0.5 x 10(-15) cm(2) for ldl for 785- and 1064-nm excitation, respectively, are 1.3 and 2.0 times larger than the values of 3.5 x 10(-15) and 2.5 x 10(-15) cm(2) calculated by Wendel. The Raman polarizability Idl 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. (C) 2011 Elsevier Ltd. All rights reserved.