Resonant Raman scattering in diamond

The first- and second-order Raman scattering have been investigated in diamond below but near the fundamental gap using a frequency doubler for the high-photon-energy region. No resonance was found for the first-order Raman scattering up to 4.8 eV, while the second-order spectrum was clearly resonance enhanced as the gap was approached. These facts are explained as the result of the interference of the contributions to the first-order Raman cross section from the ${E^{\prime }}_0$ and $E_2$ gaps resulting in a cancellation for the dispersion of the first-order Raman scattering. Explicit expressions for the ${E_0}^{\prime }$ and $E_2$ contributions to the first-order absolute Raman tensor (which turns out to be negative) are given. The electron-one-phonon deformation potentials at the $\Gamma$ and $X$ points which appear in these expressions are evaluated in analytic form by using pseudopotential theory. The absolute scattering cross sections so obtained are compared with experimental values reported in the literature. An electron-two-phonon deformation potential for the ${E_0}^{\prime }$ gap is determined.