Ming‐Zhu Huang

The electronic structures and the linear optical dielectric functions of 18 cubic semiconductors are studied by the first-principles orthogonalized linear-combination-of-atomic-orbitals (OLCAO) method in the local-density approximation. The crystals studied include the group-IV semiconductors C, Si, and Ge; the III-V compounds AlP, AlAs, AlSb, GaP, GaAs, GaSb, InP, InAs, InSb; and the II-VI semiconductors ZnS, ZnSe, ZnTe, CdS, CdSe, and CdTe. Results are presented for the band structures, for the density of states, and for the real and imaginary parts of the linear dielectric functions for photon energies up to 12 eV. The results are compared with other existing calculations and experimental data. Some interesting correlations and trends among the 18 semiconductors studied are pointed out, and possible problems with the optical excitation calculation are discussed. These results provide the groundwork for the calculation of nonlinear optical properties on these crystals using the full band-structure approach in the two papers to follow. It is argued that optical excitations in semiconductors can be efficiently carried out using the OLCAO method without resorting to empirical methods or model studies. The present calculation gives band gaps larger than the well-converged result of first-principles pseudopotential calculations. The consequence of this difference on the optical properties is discussed.

The electronic and optical properties of ${\mathrm{C}}_{60}$ in the fcc lattice have been studied by a first-principles method. It is shown that ${\mathrm{C}}_{60}$ has a low dielectric constant and an optical spectrum rich in structures; this is drastically different from diamond and graphite. The spectrum shows five disconnected absorption bands in the 1.4 to 7.0 eV region with sharp structures in each band that can be attributed to critical-point transitions. This is a manifestation of the localized molecular structure coupled with long-range crystalline order.

The linear and nonlinear optical responses in a large number of cubic insulators are studied by means of first-principles local-density calculations. Complete results on band structures, frequency-dependent dielectric functions, and frequency-dependent third-order nonlinear susceptibilities ${\mathrm{\ensuremath{\chi}}}^{(3)}$(\ensuremath{\omega}) (in the simplest form as the third-harmonic generations) are presented for 27 alkali halides, alkali-earth fluorides, oxides, and sulfides. They are LiF, LiCl, LiBr, LiI, NaF, NaCl, NaBr, NaI, KF, KCl, KBr, KI, RbF, RbCl, RbBr, RbI, ${\mathrm{CaF}}_{2}$, ${\mathrm{SrF}}_{2}$, ${\mathrm{CdF}}_{2}$, ${\mathrm{BaF}}_{2}$, MgO, CaO, SrO, BaO, MgS, CaS, and SrS. The results are compared with the existing experimental data and other calculations. The effectiveness of using a ``scissor operator'' to correct the gap underestimation in the local-density-approximation theory is assessed. It is shown that the full band-structure approach for the ${\mathrm{\ensuremath{\chi}}}^{(3)}$(0) calculation in these crystals gives results in very good agreement with experimental data, especially in the anisotropic coefficient of the nonvanishing tensor elements.

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.