THE MATHEMATICAL MODELING OF TIME-DEPENDENT PHOTOCONDUCTIVE PHENOMENA IN SEMICONDUCTORS.

Abstract

This dissertation presents results pertaining to the mathematical modeling of semiconductor photoconductors and includes the formulation, analysis, and solution of photoconductive device model equations. The fundamental semiconductor device equations of continuity and transport are derived for the case of a material which contains a large density of deep-level impurities. Electron and hole trapping on deep-level impurities is accounted for by trapping-kinetics rate equations. The coupling between carrier drift and the electric field is completed through Poisson's equation. Simple, nonlinear model equations are presented for bulk-material response based on the dynamics of electron and hole trapping and recombination on deep-level impurities. The characteristics of the solution to these model equations are observed to depend strongly on the excitation intensity. These model equations qualitatively reproduce observed experimental behavior of an iron-doped indium phosphide photoconductor. A theory of the effect of deep-level centers on the generation-recombination noise and responsivity of an intrinsic photoconductor is presented. It is shown that the deep-level centers can influence the generation-recombination noise and responsivity in three main ways: (i) they can shorten the bulk carrier lifetime by Schockley-Read-Hall recombination; (ii) for some values of the capture cross sections, deep-level densities, and temperature, the deep-level centers can trap a significant fraction of the photogenerated minority carriers. This trapping reduces the effective minority carrier mobility and diffusivity and thus reduces the effect of carrier sweep out on both generation noise and responsivity; (iii) the deep-level centers add a new thermal noise source, which results from fluctuations between bound and free carriers. The strength of this new noise source decreases with decreasing temperature at a slower rate than band-to-band thermal generation-recombination noise. Photoconductive device model equations based on time-dependent, convective/diffusive transport equations are presented. The system of model equations is solved numerically with boundary conditions that represent ideal ohmic contacts. Computed results are presented for different photoconductor lengths and bias voltages with spatially uniform, rectangular light-pulse illumination.