Electrostatic breakdown leads to the majority of anomalies and failures attributed to spacecraft interactions with the plasma space environment. It is therefore critical to understand how the electrostatic field strength (F ESD ) of spacecraft materials varies due to environmental conditions, such as duration of applied electric field, rate of field change, history of exposure to high fields, and temperature. We have developed a dual-defect, thermodynamic, mean-field trapping model in terms of recoverable and irrecoverable defect modes to predict probabilities of breakdown. Fits to a variety of measurements of the dependence of F ESD of insulating polymers on endurance time, voltage ramp rate, and temperature based on this model yield consistent results. Our experimental results for the prototypical materials, low-density polyethylene and polymer (PI or Kapton HN), suggest that the values of F ESD from standard handbooks, or cursory measurements that have been used routinely in the past, substantially overestimate the field required for breakdown in common spacecraft applications, which often apply subcritical fields for very long time periods as charge accumulates.

The Walden-Wintle model for charge injection and transport through highly disordered insulating materials has been extended to include charge injection with a charged particle beam. The original model is applicable to charge injection in a dielectric material from a pair of electrodes in a parallel-plate geometry. It provides a versatile approach to predict the time-dependent current at a rear grounded electrode and the incident surface voltage, as the injection current density evolves over time with the development of a space charge barrier near the injection electrode. The Walden-Wintle model has been applied to many standard cases including Fowler-Nordheim injection, Schottky injection, space charge limited injection, and various tunneling mechanisms. The present model modifies the approach to include electrode-less charge injection via a charged particle beam, along with concomitant effects for the injection current, surface voltage, and electron emission as a charge is built up in the insulator. The approach is equally valid for near-surface injection and for bulk injection of both non-penetrating and penetrating radiation. The results are based on our dynamic emission model for electron emission yields dependent on accumulating charge in both the positive and negative charging regimes. *This work was supported by funds from NASA Goddard Space Flight Center and NRC Senior Research Fellowship at AFRL.

Radiation induced conductivity (RIC) occurs when incident ionizing radiation deposits energy and excites electrons into the conduction band of insulators. The increased number of charge carriers, and hence the magnitude of the enhanced conductivity, is dependent on a number of factors including temperature and the spatial and energy dependence and occupation of the material’s distribution of localized trap states within the band gap—or density of states (DOS). Expressions for RIC in terms of the filling of the DOS up to an effective Fermi level were largely developed by Rose [RCA Review, 1951], and were extended by Fowler [Proc. of the Royal Soc. of London A, 1956], Vissenberg [Phys. Rev., 1998], and others. A general discussion of the DOS of disordered materials can be given using two simple distributions, one that monotonically decreases below the band edge and one that shows a peak in the distribution within the band gap. Three monotonically decreasing models (exponential, power law, and linear), and two peaked models (Gaussian and delta function) are considered, plus a limiting cases with a uniform DOS for each. Variations using the peaked models are considered, with an effective Fermi level between the conduction mobility edge and the trap DOS, within the peaked trapped DOS, and below the peaked distribution. Equations for RIC are typically expressed in a power law form in which the radiation dose rate (a measure of the energy deposited per unit time and unit mass) raised to the power ∆, with a proportionality constant, kRIC. Expressions are presented for both kRIC and ∆, as temperature-dependent material parameters for each of the DOS models described above. The models are compared to measured RIC values over broad temperature ranges for polyimide, polyethylene, and disordered silicon dioxide. *Supported through funding from NASA Goddard Space Flight Center and a Senior Fellowship from the National Research Council and AFRL. Jodie Corbridge Gillespie, JR Dennison and Alec M. Sim, “Density of State Models and Temperature Dependence of Radiation Induced Conductivity,” 13 Spacecraft Charging Technology Conference, (Pasadena, CA, June 25-29, 2014).

New instrumentation has been developed for noncontact, in vacuo measurements of the electron beam-induced surface voltage as a function of time and position for non-conductive spacecraft materials in a simulated space environment. The novel compact system uses two movable capacitive sensor electrodes to measure surface charge distributions on samples, using a noncontact method that has little effect on charge dissipation from sample. Design details, calibration, and characterization measurements of the system are presented, with <1 V to >30 kV surface voltage range, <0.5 V voltage resolution, and <1.5-mm spatial resolution. Used in conjunction with the capabilities of an existing ultrahigh vacuum electron emission test chamber, the new instrumentation facilitates measurements of charge accumulation, bulk resistivity, effects of charge depletion and accumulation on yield measurements, electron-induced electrostatic breakdown potentials, radiation-induced conductivity effects, and the radial dispersion of surface voltage. Three types of measurements of surface voltage for polyimide (Kapton HN serve to illustrate the research capabilities of the new system: 1) accumulation using a pulsed electron beam, while periodically measuring the surface voltage; 2) postcharging, as deposited charge dissipated to a grounded substrate; and 3) the evolution of spatial profile resulting from an incident Gaussian beam. Theoretical models for sample charging and discharge are outlined to predict the time, temperature, and electric field dependence of the sample's net surface voltage.

We have extended the Walden-Wintle model for charge injection and transport through highly disordered insulating materials to include charge injection with a charged particle beam. The original model is applicable to charge injection in a dielectric material from a pair of electrodes in a parallel plate geometry. It provides a versatile approach to predict the time-dependent current at a rear grounded electrode, as the injection current density evolves over time with the development of a space charge barrier near the injection electrode. The Walden-Wintle model has been applied to many standard cases including Fowler-Nordheim injection, Schottky injection, space charge limited injection, and various tunneling mechanisms. Our new model modifies the approach to include electrode-less charge injection via a charged particle beam, along with concomitant effects for the injection current, surface voltage, and electron emission as a charge is built up in the insulator. The approach is equally valid for near-surface injection and for bulk injection of both non-penetrating and penetrating radiation. The results are based on our dynamic emission model for yields dependent on accumulating charge in both the positive and negative charging regimes. Work supported through funds from NASA GSFC and a Senior Fellowship from the National Research Council and AFRL.

Recent advances are described in the techniques, resolution, and sensitivity of the constant voltage conductivity (CVC) method and the understanding of the role of charge injection mechanisms and the evolution of internal charge distributions in associated charge transport theories. These warrant reconsideration of the appropriate range of applicability of this test method to spacecraft charging. We conclude that under many (but not all) common spacecraft charging scenarios, careful CVC tests provide appropriate evaluation of conductivities down to ≈ 10-22 (Ωcm)-1, corresponding to decay times of many years. We describe substantial upgrades to an existing CVC chamber, which improved the precision of conductivity measurements by more than an order of magnitude. At room temperature and above and at higher applied voltages, the ultimate instrument conductivity resolution can increase to ≈ 4·10-22 (Ωcm)-1, corresponding to decay times of more than a decade. Measurements of the transient conductivity of low-density polyethylene using the CVC method are fit very well by a dynamic model for the conductivity in highly disordered insulating materials over more than eight orders of magnitude in current and more than six orders of magnitude in time. Current resolution of the CVC system approaches fundamental limits in the laboratory environment set by the Johnson thermal noise of the sample resistance and the radiation-induced conductivity from the natural terrestrial background radiation dose from the cosmic ray background.

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.

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.

Sensitive optical instruments and telescopes constructed of polymeric highly disordered insulating materials (HDIM) for use in the space environment are subject to the charging induced by plasma surroundings, which can result in harmful emission of light and charge from HDIM. Recent tests have demonstrated electron induced luminescence of insulating polymeric materials using a high energy electron beam. This behavior, known as cathodoluminescence, results from incident beam electrons exciting electrons in the material from the valence band into extended energy states in the conduction band, which subsequently transition back to either the valence band or a distribution of trap states within the band gap and emit light. The time-dependent interplay between two competing electron decay mechanisms— cathodoluminescence and radiation enhanced conductivity—has been studied in epoxy resin, an HDIM. This study compares evolution of the relative amplitudes of the photon emission and the electric current signatures from the material samples as: (i) space charge accumulates in the HDIM due to the incident electron beam and (ii) before and after electrostatic discharges. Measurements were made at temperatures from ~100 K to ~300 K at various incident electron energies and current densities while the samples were in ultra high vacuum. The complex time dependent behavior observed is described in terms of a microscopic band theory based-model. Electron transport and luminescence provide two competing decay modes for these excited electrons. Thus, the simultaneous measurement of luminescence intensity and electron current can provide information about the spatial and energetic distributions of the trapped charges in the HDIM, their transition rates, and the interaction of electrons within the material. Such knowledge is critical in constructing materials used on space telescopes that can withstand the harsh space environment without impeding the telescope’s mission.