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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.

There are several important semiconductor devices in which the transport of carriers is controlled by punch-through space-charge effects. Examples include the Bipolar Mode Static Induction Transistor (BSIT), ultrasmall Punch-through MOSFETs, and BARITT diodes for microwave applications. The development of punch-through space-charge type of devices is a technology motivated by the demanding high density among the IC chips. This dissertation discusses a device which operates in a punch-through condition with space-charge control of currents. It is a two terminal device, which could be fabricated with no deviation from today's technology. The device structure is simple, with two n⁺ or p⁺ regions formed in p⁻ or n⁻ substrate, respectively. Punch-through space-charge limited structures both n⁺p⁻n⁺ and p⁺n⁻p⁺, were simulated using a general one-dimensional semiconductor device performance simulation program GESIM1 for dynamic and static analysis. The results of simulation show that the potential barrier height decreases with increasing applied potential and with a reduction of the spacing L between the n⁺ diffusion in an n⁺p⁻n⁺ structure. The resistance increases as the spacing L is increased. A two-dimensional analytical model of carrier transport in the device was developed. This model accounts for surface effects as well as the space-charge limited flow. Also, a one-dimensional model that includes mobile carriers effects on the device operation. Structures of various configurations were fabricated and tested. Electrical evaluations of these structures provided large value resistors in a remarkably small area compare to traditional integrated resistors. The resistance was observed to increase with the spacing L and with the resistivity of the starting substrate. These punch-through space-charge limited loads should have applications as an alternative approach for integrated resistors in high-speed VLSI applications. They can provide very small area, large value resistors based on the space-charge limiting action of the device. The range of resistance value is large, and small dimensions lead to small capacitance and fast switching times.

This dissertation considers multi-wave interactions in bulk semiconductors. Non-equilibrium Green's functions are used to derive an appropriate set of equations describing the interaction of a light field with a semiconductor. Many-body effects lead to the screening of the Coulomb potential in these equations, as well as, carrier-carrier scattering. The carrier-carrier scattering is studied within the context of the carrier Boltzmann equation which contains the dynamically screened Coulomb potential. The relation between carrier scattering and optical dephasing is also made. The carrier scattering rates are then used in the equations describing a two beam pump-probe experiment. The resulting equations are solved numerically for both passive and active systems, and effects such as spectral hole burning, coherent light scattering, and light induced band splitting are studied. Considering three CW beams (pump and two probes) allows for the study of four-wave mixing in semiconductors. By considering CW fields, the semiconductor may be treated in the quasi-equilibrium approximation allowing for greater detail in the treatment of the light field. The resulting probe absorption yields asymmetries which result in an asymmetric four-wave mixing spectrum. The four-wave mixing spectrum is then used to study the amount of squeezing in the light field exiting the cavity in a four-wave mixing experiment.

This dissertation presents research on the propagation and manipulation of excitons in GaAs. There are three main aspects to be addressed. In the first part, we provide a comprehensive understanding of the slow- and fast-light propagation based on excitonic resonances. Propagation (or transit) times of optical pulses through a medium near an absorptive resonance with and without spatial dispersion are studied and contrasted. We show that, when the broadening of the resonance (i.e., dephasing rate) is below a critical value, a frequency range exists near resonance where the transit times are determined by interference between co-propagating exciton-polaritons and deviate strongly from expectations based on the group velocities of the individual exciton-polariton branches. Our theory puts the well-known slow- and fast-light effects in systems without spatial dispersion into a broader context by interpreting them as a limiting case of systems with spatial dispersion. An important ingredient of the exciton theory is the light-matter coupling that can be expressed either in terms of the dipole or the momentum matrix elements. We re-examine the validity of a frequently used relation between the interband momentum and dipole matrix elements ('p-r relation') in semiconductors. An additional correction term was obtained when we applied the 'p-r relation' to finite-volume crystals treated with periodic boundary conditions. The correction term does not vanish in the limit of infinite volume. We illustrate this with numerical examples for bulk GaAs and GaAs superlattices. For bulk GaAs, the correction term is found to be always important; while for a GaAs superlattice, the importance of the correction term for the transition depends strongly on the origin of the unit cell.As an example for manipulation of excitons, we consider mechanical deformations of GaAs nanomembranes. The nanomembranes with lateral sizes much larger than their thicknesses exhibit great flexibility in non-planar deformations and thus promise applications in flexible electronic and photonic devices. These non-planar deformations do not fit in the well-established theory for planar deformations induced by lattice mismatch. Our theory relates the general mechanical deformations (planar or non-planar) of nanomembranes to their excitonic spectra, and is numerically evaluated within the average-strain approximation.

A selective sloped silicon dioxide etching method has been studied using a temperature controlled diode-type reactive ion etch system with CHCl₃, C₂F₆, H₂ and N₂ gases. The SiO₂ was covered by a polyimide mask with vertical sidewalls and window openings from 1.25-4 microns. Control of the sidewall slope in SiO₂ is possible through varying the ratios of CHCl₃ and C₂F₆. High percentages (95-100%) of CHCl₃ resulted in low etch rates of 420 angstroms/min. Large slopes of up to 65 degrees are possible. With C₂F₆ above 5%, larger etch rates close to 2000 angstroms/min. occur and etching becomes vertical with purely anisotropic profiles at 10% C₂F₆. In a simulation study, SiO₂ sidewall slope was found to be controlled by the isotropic deposition rate as well as the anisotropic etch rate. Optical Multichannel Analysis of the discharge showed an increase in silicon dioxide removal when the percentage of C₂F₆ was increased. (Abstract shortened with permission of author.)

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