A study of the optical properties and superconductivity in semiconductors is presented using the highly precise all-electron full-potential linearized augmented plane wave (FLAPW) density functional calculations. Optical properties [$\varepsilon(\omega)$,$n(\omega)$,$k(\omega)$,$R(\omega)$ and $\alpha(\omega)$] of some III-V semiconductors [InAs, InSb, GaSb, and AlSb] and their critical point (CP) energies, are calculated from the eigenvalues and wave functions obtained from calculations using the screened-exchange local-density approximation (sX-LDA) with spin-orbit coupling included. The full $e^{i\qq\cdot\rr}$ expression for the optical matrix is incorporated instead of the momentum representation. The results show a remarkable improvement over the usual LDA and better agreement with experiment. The method employed has the following features: (i) it is based {\em purely} on first-principles without resorting to adjustable parameters and uses only the self-consistent eigenvalues and wave functions; (ii) the non-locality sX-LDA Hamiltonian requires using the longitudinal expression for the optical matrix elements. In order to explore the excitonic ({\em or} electronic) mechanism of superconductivity, CuCl/Si superlattices are studied. Experimentally, CuCl epitaxy on Si (111) substrate was reported by Mattes and Foiles to have a nearly ideal diamagnetism between 60 and 150 K. First, the superconducting transition temperatures ($T_C$'s) are estimated using the electron-phonon ({\em e-p}) pairing mechanism in the rigid muffin-tin approximation (RMTA). Interface metallicity with 2D character is found for all CuCl/Si superlattices as evidenced by band structure, Fermi surfaces, and charge densities. A Hopfield parameter calculation shows that the electron-phonon interaction is present mostly at the interfaces and $T_C$ is estimated to be $0.03\sim 4.4$ K. Although superconductivity is present even when invoking the {\em e-p} mechanism, it is not strong enough to account for the experimentally reported $T_C$ between 60 and 150 K. Other semiconductor heterostructures, such GaP/Si and ZnS/Si superlattices also reveal two dimensional metallicity at the interfaces but zero $T_C$. Although the {\em e-p} interaction is dominant at the interfaces, superconductivity is not present, which makes CuCl/Si superlattices special. To further explore the excitonic ({\em or} electronic) mechanism of superconductivity, the dynamical dielectric function, $\varepsilon(\qq,\omega)$ is evaluated for CuCl/Si superlattices. A theoretical formulation of the dielectric function and the inverse dielectric function, and the superconducting kernel function is provided. The pairing potentials $V_{\kk,\kp}$ and the kernel functions are evaluated. The results show that there is a range of energies from some CuCl/Si superlattices where there is an effective attractive electron-electron interaction involving the excitonic pairing mechanism.

Last modified

• 08/30/2018

Creator

• Sung-Hyon Rhim

DOI

• https://doi.org/10.21985/N21B1N

Subject

• Physics and Astronomy

Keyword

• superconductivity

Date created

• 2007-12-14

Resource type

• Dissertation

Rights statement

• In Copyright