Measurement of the Absolute Raman Cross Section of the Optical Phonons in Type Ia Natural Diamond

Abstract

The absolute Raman cross section (\sigma_{RS})of the first-order (1332-cm^{−1}) optical phonons in type Ia natural diamond was measured using 785- and 1064-nm pump lasers for the excitation of Raman scattering. A small temperature-controlled blackbody was used for the signal calibration of the 785- and 1064-nm Raman systems. Measurements were made with a 0.9-mm thick (111) natural diamond sample. Values of (2.7\pm0.6×10^{−29}) and (0.95\pm0.2×10^{−29} cm^2) per carbon atom were determined for (\sigma_{RS}) for 785- and 1064-nm excitation, respectively. The corresponding values of the Raman scattering efficiency S are (3.8\pm0.8×10^{−7}) and (1.3\pm0.3×10^{−7} cm^{−1} sr^{−1}). The values of the Raman polarizability |d| for 785-, and 1064-nm excitation are (6.8\pm0.7×10^{−16}) and (8.1\pm0.8×10^{−16} cm^2), respectively. Our measured values of |d| are larger than the previously measured values of (4.4\pm0.3×10^{−16}) and (4.6\pm0.7×10^{−16} cm^2) using 514.5- and 694-nm excitation, respectively. |d| vs. excitation photon energy was computed for the range from 1.0 eV (1240 nm) to 4.0 eV (310 nm) using time-dependent density functional theory. The computed values of (5.8×10^{−16}) and (5.3×10^{−16} cm^2) for 514.4- and 694-nm excitation, respectively, are larger than the corresponding measured values of |d|. The computed values of (5.2×10^{−16}), and (5.0×10^{−16} cm^2) for 785- and 1064-nm excitation are smaller than the corresponding values of |d| measured in this work. The computed value of |d| in the static limit is (4.7×10^{−16} cm^2). Modification of |d| due to IaA and IaB defects, computed for a 64-atom supercell, is less than 5%.