Unified Density of States Based Model of Electron Transport and Emission of Spacecraft Materials

A unified set of parameters and dynamic equations have been developed to describe the complex relationships between spacecraft insulators and their surroundings that are fundamentally based on a detailed knowledge of how individual materials store and transport charge. This set of equations models evolving electron transport and related phenomena in highly disordered insulating materials, such as spacecraft polymers, over the large ranges of electric field, temperature, absorbed dose, and adsorbed dose rate that are typically encountered in space environments. From a these dynamic 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. The total conductivity is modeled as the sum of independent conductivity mechanisms [e.g., thermally activated hopping (TAH) conductivity, variable range hopping (VRH) conductivity, and radiation induced conductivity (RIC)] using a concise, unified set of independent fitting parameters. We motivate a discussion of these three conduction mechanisms in terms of this theoretical framework with simple macroscopic physical concepts; this leads to understanding for a wide variety of observed physical processes, including (drift, diffusion, dispersion, polarization, and radiation-induced) conduction, electrostatic breakdown, electron emission, and luminescence. At a microscopic level, modeling and understanding electron transport 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. 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 for constant, linear, power law, exponential and Gaussian localized DOS are considered. Using the concepts of an effective transport level and a demarcation energy associated with the energy and spatial distribution and the occupation of the localized trap DOS, we extend the formalism of macroscopic static and dynamic multiple trapping models used to model activated and variable rage hopping transport mechanisms. The broad applications of the theoretical framework are outlined in terms a comprehensive classification of the experimental methods in which charge is injected into or excited within a material; these classifications include surface deposition, bulk deposition and penetrating radiation for a full range of pulsed, stepped and periodic applied voltages/charge. 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 the charging and dissipation of spacecraft materials, in spacecraft charging phenomena, and in myriad ground-based materials testing methods.