A number of analytical theories related to disordered systems have been developed based on two major themes: (1) charge transport in non-crystalline semiconductor systems where localized states play the main role in the underlying mechanisms; and (2) crystal nucleation in the presence of a strong electric field. In this dissertation, five research topics based on these themes are presented: (1) charge transport through non-crystalline junctions; (2) admittance characterization of semiconductor junctions; (3) 1/f noise in chalcogenide glasses; (4) electric field-induced nucleation switching in chalcogenide glass threshold switches (TS) and phase change memory (PCM); and (5) relaxation oscillations in PCM. Although the theories are quite general in nature, their practical implications are discussed in the context of thin-film photovoltaics (PV), and chalcogenide glass TS and PCM.

It is shown that, even at practical temperatures, hopping conduction via optimum channels of localized states can be the prevailing charge transport mechanism in semiconductor junctions. That type of transport results in laterally nonuniform current flow that leads to shunting, device degradation, and variations between identical devices. Analytical expressions have been derived that relate important device characteristics, such as the diode ideality factor, saturation current, and open circuit voltage, to material parameters; the results are in agreement with experimental data. Consideration of the laterally nonuniform current formed the basis of the phenomenological theory of admittance spectroscopy that properly accounts for the decay of an a.c. signal in a semiconductor structure with resistive electrodes. The theory facilitates a more informative analysis of admittance measurements, including additional device characteristics and the distribution of shunts. An important new insight is that blocking the entrance to the optimum channels, perhaps with surface treatments, can improve the performance of thin-films devices.

Localized atomic and electronic excitations, and generation-recombination processes in chalcogenide glasses are internal degrees of freedom that can cause low frequency current noise. On that basis, several mechanisms of 1/ f noise are analyzed and quantified in terms of the standard measure of the Hooge parameter. Six experimentally testable expressions are derived with varying dependencies on material properties. Based on existing data, the most likely cause appears to be electronic double-well potentials (two-level systems) related to spatially close intimate pairs of oppositely charged negative-U centers.

The field-induced nucleation model describes how crystallization occurs in the presence of a strong electric field. As a thermodynamic model, it predicts in analytical form the observed features of threshold switching, including the characteristic voltages, delay time, and statistics. Here it is shown how the model forms a unifying framework for switching in chalcogenide TS and PCM devices, as well as others, which were previously considered to be fundamentally different. The unity is manifest in relaxation oscillations that are observed in both TS and PCM. Results for relaxation oscillation experiments are presented and discussed in terms of the field-induced nucleation model.