Theory of two-phonon Raman spectrum of diamond

The Raman spectrum of diamond in the high-frequency part of the two-phonon region is investigated. An interpretation of the sharp line at the two-phonon cutoff as a simple overtone is supported in terms of a harmonic model for the potential and a bond polarizability approximation for the scattering Hamiltonian. Polarization features as well as the anomalous position and width of the peak are discussed and interpreted, giving general agreement between theory and experiment. A comparison is made with the Raman spectrum of silicon, and differences in the spectra are accounted for by a different behavior of the dispersion relation along $\Delta$ for the two lattices, which has its origin in the greater angle-stiffness forces in diamond, ultimately due to greater covalency in diamond. A new set of critical points for the LO branch of diamond is also proposed.