Measurements of the Temperature Dependence of Radiation Induced Conductivity in Polymeric Dielectrics

This study measures Radiation Induced Conductivity (RIC) in five insulating polymeric materials over temperatures ranging from ~110 K to ~350 K: polyimide (PI or Kapton HNTM and Kapton ETM), polytetraflouroethylene (PTFE or TeflonTM), ethylene-tetraflouroethylene (ETFE or TefzelTM), and Low Density Polyethylene (LDPE). RIC occurs when incident ionizing radiation deposits energy and excites electrons into the conduction band of insulators. Conductivity was measured when a voltage was applied across vacuum-baked, thin film polymer samples in a parallel plate geometry. RIC was calculated as the difference in sample conductivity under no incident radiation and under an incident ~4 MeV electron beam at low incident dose rates of 0.01 rad/sec to 10 rad/sec. The steady-state RIC was found to agree well with the standard power law relation, σRIC(D) = kRIC(T) DÄ(T) between conductivity, óRIC and adsorbed dose rate, D. Both the proportionality constant, kRIC, and the power, Ä, were found to be temperature-dependent above ~250 K, with behavior consistent with photoconductivity models developed for localized trap states in disordered semiconductors. Below ~250 K, kRIC and Ä exhibited little change in any of the materials

Density of State Models and Temperature Dependence of Radiation Induced Conductivity

Expressions are developed for radiation induce conductivity (RIC) over an extended temperature range, based on density of states models for highly disordered insulating materials. A general discussion of the DOS of can be given using two simple types of DOS distributions of defect states within the bandgap for disordered materials are considered, one that monotonically decreases within the bandgap and one with a distribution peak within the band gap. Three monotonically decreasing models (exponential, power law, and linear), and two peaked models (Gaussian and delta function) are considered, plus limiting cases with a uniform DOS for each type. Variations using the peaked models are considered, with an effective Fermi level between the conduction mobility edge and the trap DOS, within the peaked trap DOS, and between the trap DOS and the valence band. The models are compared to measured RIC values over broad temperature ranges for two common materials, low density polyethylene (LDPE) and disordered silicon dioxide

Temperature Dependence of Radiation Induced Conductivity in Insulators

We report on measurements of Radiation Induced Conductivity (RIC) of thin film Low Density Polyethylene (LDPE) samples. RIC occurs when incident ionizing radiation deposits energy in a material and excites electrons into conduction states. RIC is calculated as the difference in sample conductivity under an incident flux and “dark current” conductivity under no incident radiation. The primary focus of this study is the temperature dependence of the steady state RIC over a wide range of absorbed dose rates, from cryogenic temperatures to well above room temperature. The measured RIC values are compared to theoretical predictions of dose rate and temperature dependence based on photoconductivity models developed for localized trap states in disordered semiconductors. We also investigated the variation of RIC as a function of material, applied electric field, and incident beam energy parameters

Density of State Models of Steady-State Temperature Dependent Radiation Induced Conductivity

Radiation induced conductivity (RIC) occurs when incident radiation deposits energy and excites electrons into the conduction band of insulators. 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 are developed for steady-state RIC over an extended temperature range, based on DOS models for highly disordered insulating materials. 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 developed, plus limiting cases with a uniform DOS for each type. Variations using the peaked models are considered, with an effective Fermi level between the conduction mobility edge and the trap DOS, within the peaked trap DOS, and between the trap DOS and the valence band. Explicit solutions, limiting cases, and applications of the models to RIC measurements are presented

Engineering Tool for Temperature, Electric Field and Dose Rate Dependence of High Resistivity Spacecraft Materials

An engineering tool has been developed to predict the equilibrium resistivity of common spacecraft insulating materials as a function of electric field (Ε), temperature (T), and adsorbed dose rate (Ď) based on parameterized, analytic functions used to model an extensive data set taken by the Utah State University Materials Physics Group. The ranges of E, T and Ď measured in the experiments were designed to cover as much of the ranges typically encountered in space environments as possible: (i) the typical electric field range was from 104 V-m-1 to 107 V-m-1 or from \u3c0.1% up to between 30% to 90%of the electrostatic breakdown field strength; (ii) temperature was measured and modeled over a typical range of 150 K to 330 K (within limits noted below); and the adsorbed dose rate was measured and modeled over a range of 10-5 Gray to 10-1 Gray. This Mathcad worksheet calculates the total conductivity and the individual contributions from each conductivity mechanism based on user inputs for E, T and Ď. The engineering tool also plots 2D and 3D graphs of the conductivites over the appropriate full ranges of E, T and Ď. The range of validity of the resistivity values predicted by the engineering tool are largely set by the lower limits of currents measurable by the test apparatus, on the order of 10-15 A to 10-14 A, which typically correspond to an upper bound in measurable resistivity of 1018 Ω-cm to 1020 Ω-cm. The engineering tool calculates the total conductivity as the sum of three independent conductivity mechanisms, a thermally activated hopping (TAH) conductivity, a variable range hopping (VRH) conductivity and a radiation induced conductivity (RIC). The models of the first two mechanisms are based on hopping conductivity models developed and validated for disordered semiconductor materials, and are applied here to polymeric materials as semi-empirical models. The model developed for thermally activated hopping has three physics-based parameters, the product of the density of states ntrap and the hopping frequency νTAC that sets the conductivity magnitude, the activation energy ΔH that sets the low temperature behavior or energy scale, and the mean separation between hopping states that sets the intermediate E-field behavior or the length scale. The physics-based model for variable range hopping extended by Apsley and Huges (1975) from the original work by Mott and Davis can be expressed in terms of a constant energy density of states, NEF; a hopping attack frequency, νVRH; and a real space decay constant of the localized state wave function, α. The standard semi-empirical power law RIC model sets the RIC proportional to the adsorbed dose rate raised to a power; the model used here incorporates both a temperature-dependant proportionality constant, k(T) and power Δ(T). To perform fits to measured data, it is more convenient to make a conversion from the physics based model parameters to reduced notation where conductivity, temperature and electric field are expressed in reduced units. There are a total of ten independent fitting parameters: three (σTAHo, TA, and EA) to scale the thermally activated hopping reduced conductivity, reduced temperature and reduced E-field, respectively; three (σVRHo, To, and Eo) to scale the variable range hopping reduced conductivity, reduced temperature and reduced E-field, respectively; and four (ko, k1 Δ1 and Tcr) to scale the RIC magnitude, the temperature dependence of the magnitude, the temperature dependence of the power, and the critical temperature above which k and Δ begin to exhibit temperature dependence. The engineering tool also provides a purely empirical exponential decay fit for the temperature dependence of the electrostatic breakdown field strength, with two fitting parameters as the temperature decay rate, TESD, and the asymptotic high temperature limiting electrostatic breakdown field strength, EESDmin. The available materials database is described and applications of the engineering tool for spacecraft charging calculations are discussed

Synergistic Models of Electron Emission and Transport Measurements of Disordered SiO2

An important way for the spacecraft charging community to address the expanding necessity for extensive characterization of electron emission and transport properties of materials is to expand the role of more fundamental materials physics. This includes the development of unifying theoretical models of the charge transport equations based on the creation, distribution, and occupancy of defect densities of states. Models that emphasize the synergistic relation between fitting parameters for diverse measurements can also lead to a better understanding of materials and facilitate solutions to spacecraft charging issues. As an example of this approach, we present results of many different measurements on similar samples of a single common insulating spacecraft material, disordered silicon dioxide. Measurements include time-, field-, and temperature-dependent conductivity, radiation induced conductivity, electron emission yields and spectra, surface voltage accrual and decay, cathodoluminescence, electrostatic discharge, endurance time, and optical transmission