Calculation of optical excitations in cubic semiconductors. III. Third-harmonic generation

Abstract

Following the preceding two papers on the linear optical and second-harmonic-generation calculations on the 18 cubic semiconductors of group-IV, III-V, and II-VI compounds using the first-principles band-structure method, the two nonzero elements ${\mathrm{\ensuremath{\chi}}}_{1111}^{(3)}$(\ensuremath{\omega}) and ${\mathrm{\ensuremath{\chi}}}_{1212}^{(3)}$(\ensuremath{\omega}) of the third-order nonlinear susceptibility in these semiconductors are studied. Contributions to the third-harmonic generation from virtual-electron, virtual-hole, and three-state processes are investigated and the final results are compared with available experimental data. It is shown that the zero-frequency limits ${\mathrm{\ensuremath{\chi}}}_{1111}^{(3)}$(0) and ${\mathrm{\ensuremath{\chi}}}_{1212}^{(3)}$(0) in these crystals can vary over several orders of magnitude, yet the ratios ${\mathrm{\ensuremath{\chi}}}_{1212}^{(3)}$(0)/${\mathrm{\ensuremath{\chi}}}_{1111}^{(3)}$(0) show remarkable consistency and are in very good agreement with the available data. The frequency-dependent dispersion curves for the 18 semiconductors up to 10 eV are also calculated. For most crystals, structures are limited to the low-frequency range below 4.0 eV. For several crystals, \ensuremath{\Vert}${\mathrm{\ensuremath{\chi}}}^{(3)}$(\ensuremath{\omega})\ensuremath{\Vert} show additional resonance structures in the higher-frequency range that have never been revealed before. Correlations of ${\mathrm{\ensuremath{\chi}}}^{(3)}$(0) with direct band gap and ${\mathrm{\ensuremath{\chi}}}^{(2)}$(0) are investigated. There is a remarkable correlation between the direct gap and the triple of frequency of the leading peak in the dispersion curves. Our results are also compared with the other existing calculation by Moss, Ghahramani, Sipe, and van Driel on some of these crystals. We again emphasize the importance of having accurate conduction-band (CB) wave functions and in taking a sufficient number of CB states into the calculation in order to obtain converged results. This is far more important than other effects that are not taken into account in the present local-density calculation for the electronic states.