George C. John

Porous silicon: theoretical studies

Abstract Porous silicon has attracted considerable scientific interest ever since the recent discovery of visible photoluminescence. We present a review of the theoretical work done on this material. We describe the classical theories and computer simulations of the growth of this brittle, spongy structure. The electronic structure calculations based on first principles local density approximation as well as semi-empirical methodologies are outlined. Phenomenological models for photoluminescence, its broad lineshape, decay and temperature dependence and excitonic effects on optical behavior are reviewed. Rudimentary theories of electroluminescence, transport and quantum efficiency are also described. A unified, consistent theoretical framework appears to be a distant goal. Broad suggestions for further theoretical work are outlined.

Simple scheme for the numerical evaluation of nearly singular integrals

Nearly singular integrals are encountered in the evaluation of the Green’s function for a variety of physical problems. One example is the evaluation of the electronic density of states in condensed matter physics. We propose a simple scheme for the accurate evaluation of a class of commonly encountered nearly singular integrals using panels of equal width. This scheme is an extension of a method introduced by Roth [Phys. Rev. B 7, 4321 (1973)]. We demonstrate the usefulness of the scheme by employing it to evaluate the electronic density of states of a one- and of a three-dimensional ordered solid within a nearest neighbor tight binding model. A Fortran version of the scheme is also presented.

Vibrational spectra of defects in silicon: An orbital radii approach.

A phenomenological approach to the stretching mode vibrational frequencies of defects in semiconductors is proposed. A novel quantum scale is defined in terms of the first principles pseudopotential based orbital radius and the principal quantum number of the element concerned. A universal linear relationship between the Sanderson electronegativity and this quantum scale is established. Next, we show that the stretching mode vibrational frequencies of hydrogen and chlorine in the silicon network scale linearly with this quantum scale. Predictions and identifications of defect environments around the Si-H and Si-Cl are possible. The assignments of vibrational modes in porous silicon are critically examined. We discuss our proposed scale in the context of Mendeleveyan scales in general, and suggest justifications for it. We believe that our approach can be gainfully extended to the vibrational spectra of other semiconductors.

MONTE CARLO EVALUATION OF THE AHARONOV-BOHM EFFECT

The electron propagator in the Aharonov-Bohm effect is investigated using the Feynman path integral formalism. The calculation of the propagator is effected using a variation of the Metropolis Monte Carlo algorithm. Unlike “exact” calculations, our approach permits us to include a nonvanishing solenoid radius. We investigate the dependence of the resulting interference pattern on the magnetic field as well as the solenoid radius. Our results agree with the exact case in the limit of an infinitesimally small solenoid radius.