Comprehensive Theoretical Framework for Modeling Diverse Electron Transport Experiments in Parallel Plate Geometries

Abstract

A unified set of parameters and dynamic equations have been developed to describe the time-dependent surface voltage and currents measured for a broad range of electron transport experiments conducted in parallel plate geometry with a dielectric slab above a grounded electrode and with either a floating or fixed voltage upper surface. The framework can model measurements of constant voltage, time-of-flight and AC conductivity; radiation induced conductivity; surface voltage accumulation and decay; electrostatic discharge; electron emission and electron-induced luminescence. The broad applications of the theoretical framework are outlined in terms a comprehensive classification of the ways in which charge is injected into or excited within a material; these classifications include surface deposition, bulk deposition and penetrating radiation for pulsed, stepped and periodic applied voltages/charge from either surface electrodes or electron beams. A set of equations are developed to model evolving electron transport and related phenomena in highly disordered insulating materials over large ranges of time, electric field, temperature, absorbed dose, and adsorbed dose rate. These analytic equations derived from physics-based theories predict the equilibrium and time-dependent accumulation, dissipation and transport of charge carriers; these basic equations are (i) Gauss’ law, (ii) a 1D electron continuity equation with Ohm’s law and source terms, (iii) a 1D continuity equation for holes with source terms, and (iv) the sum of currents due to various conduction mechanisms (including contributions from drift, diffusion, dispersion, polarization, and radiation-induced processes). The total conductivity is modeled as the sum of contributions from three independent conductivity mechanisms: thermally activated hopping, variable range hopping, and radiation-induced conductivity using a concise, unified set of independent fitting parameters. At a microscopic level, modeling and understanding these conduction mechanisms in disordered insulating materials is fundamentally based on a detailed knowledge of the distribution and occupation of the density of states (DOS) of nearly-free and trapped charged carriers. The conduction is controlled by transitions between extended valence and conduction band states, between localized trap states and the extended valence and conduction band states, and hopping between localized states; constant, linear, power law, exponential and Gaussian localized DOS are considered. By analyzing the observed temperature, field, dose rate and time dependent conductivities that result from both extended and localized trap state conduction, this theoretical framework provides new insight into the role of the localized trap state DOS in myriad ground-based materials testing methods.