Calculation of optical excitations in cubic semiconductors. II. Second-harmonic generation

Abstract

The second-harmonic generations in 15 noncentral symmetric cubic semiconductors are systematically studied by the first-principles full band-structure method. The crystals studied are the III-V compounds AlP, AlAs, AsSb, GaP, GaAs, GaSb, InP, InAs, InSb; and the II-VI compounds ZnS, ZnSe, ZnTe, CdS, CdSe, and CdTe. Calculations are focused on the frequency-dependent complex second-order nonlinear optical susceptibilities ${\mathrm{\ensuremath{\chi}}}^{(2)}$(\ensuremath{\omega}) up to 10 eV and their zero-frequency limits ${\mathrm{\ensuremath{\chi}}}^{(2)}$(0). A simple scissor operator is applied to adjust the band gaps from the local-density calculations to the experimental values. Large numbers of k points in the sum over Brillouin zone are used which are important in resolving structures in the dispersion curves. Comparison with available experimental data on ${\mathrm{\ensuremath{\chi}}}^{(2)}$(0) and ${\mathrm{\ensuremath{\chi}}}^{(2)}$(\ensuremath{\omega}) shows general good agreement. It is shown that for a well-converged result, sufficiently high conduction-band (CB) states at least 40 eV from the top of the valence band must be included because of the large CB-CB transition-matrix elements. Correlations between the calculated nonlinear optical parameters and other physical parameters such as band-gap and static dielectric constants are also investigated. It is shown that the validity of the Miller's rule with regard to the ratio between linear and nonlinear susceptibilities is limited to the low-frequency range.