Y. F. Tsay

Pressure and Stress Dependence of the Refractive Index of Transparent Crystals

The pressure derivative of the refractive index (dn/dP) and the elastooptic constants (P(ij)) in the transparent frequency regime of semiconducting and ionic crystals are investigated theoretically. The electronic contribution to dn/dP of semiconductors is obtained by carrying out pseudopotential calculations of the band structure as a function of hydrostatic pressure, and the results compared with experiment. The lattice contribution to dn/dP is obtained by relating dn/dP to changes in the effective ionic charge and the phonon spectrum as functions of pressure. As for the P(ij), we perform a detailed application of the theory of Humphreys and Maradudin to calculate these for a variety of cubic crystals as functions of frequency in the transparent regime. The parameters required in the calculation are determined from improved prescriptions, which relate various microscopic functions to experimental data on the pressure dependence of phonon frequencies. The theoretical results are checked employing a relatio between dn/dP and the P(ij). Overall, one finds that frequency dispersion is most important for the ionic materials and is generally negligible for the more highly covalent materials.

Temperature dependence of energy gaps in some II–VI compounds

Abstract The Brooks-Yu theory is applied to the calculation of the temperature dependence of the energy band gaps in some II–VI compounds. The theory is applied in the framework of the empirical pseudo-potential method, and utilizes a recent lattice dynamical calculation of the Debye-Waller factors. The temperature dependence of several critical-point band gaps are determined and compared with a vailable experimental data. In general, reasonable agreement is obtained. The interesting case of HgTe, which exhibits an anomalous positive temperature coefficient of the fundamental band gap, is also discussed.

Nonlinear absorption in direct-gap semiconductors.

Nonlinear absorption coefficients have been calculated for certain direct-bandgap semiconductors at 0.694-microm, 1.06-microm, 1.318-microm, and 10.6-microm wavelengths and compared with experimental results. The second- order perturbation theories of Braunstein and Basov yield underestimates and overestimates, respectively, of the nonlinear absorption constants. The numerical values are dependent upon the use of appropriate effective band masses, dielectric constants, and electron spin degeneracy factors. However, the Keldysh model gives second-order absorption constants that are intermediate between the two perturbation calculations. Although the Keldysh model often underestimates the value, in general, it yields the estimate of the magnitude of the two-photon absorption coefficient. The one-photon band-edge absorption in GaAs and InSb is predicted surprisingly well by the Keldysh model.

Theory of Multiphonon Absorption in the Transparent Regime of Amorphous Solids

We predict the multiphonon absorption α in amorphous solids, utilizing the statistical theory of Mitra et al, which relates optical properties of amorphous solids to variations in their local density. We find that if the ratio η of the mean density of an amorphous solid to that of its crystalline counterpart is greater than unity, then α decreases more slowly in the amorphous solid; if η<l, then either an increase or decrease is possible, depending on the width of the density distribution function. As an application of the method, we perform calculations for III–V semiconductors, utilizing an exactly soluble single-particle model which accounts for both anharmonicity and nonlinear moments. Analysis of their fundamental lattice resonance demonstrates that η<1 for these solids. Broadening of α and suppression of the temperature dependence is predicted to occur to varying extents for the III-V’s investigated. This suggests that various amorphous solids may not be as attractive as their crystalline counterparts for infrared applications requiring high transparency.

Multiphoton Ionization Probability and Nonlinear Absorption of Light by Transparent Solids

The multiphoton ionization probability has been calculated as functions of wavelength and electric field intensity for a number of semiconductors and insulators using three different theoretical models. Although there is a large amount of disagreement among available experimental data, the values of two-photon absorption coefficients calculated by Keldysh treatment come closest, while the Basov formula over-estimates and the Braunstein formula underestimates. Surprisingly, Keldysh formula also predicts the absolute values and the wavelength dependence of the one-photon absorption coefficient (absorption edge) extremely well for direct gap semiconductors.

Optical properties of density-disordered solids

A statistical theory of the optical response in solids with a small degree of microscopic density disorder is formulated, in which the properties of the disordered solid are related to those of its crystalline counterpart. Both the electronic and lattice response are treated, by determining the changes in band structure and phonon spectrum as functions of local density. As an application of the theory, we deduce the optical properties of amorphous semiconductors such as Si, Ge, GaAs and InAs and compare them to those of their crystalline counterparts. Good agreement with experiment is obtained for the predicted optical and infrared absorption spectra, and for the Raman scattering spectrum. The analysis provides a quantitative gauge of the departure from crystallinity in the optical spectrum, i.e., the relative contribution of processes which do not conserve crystal momentum.