## Document Type

Presentation

## Journal/Book Title/Conference

47th AIAA Aerospace Sciences Meeting American Institute of Aeronautics and Astronautics

## Publication Date

2009

## Abstract

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 10^{4} V-m^{-1} to 10^{7} V-m^{-1} or from <0.1% 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 10^{18} Ω-cm to 10^{20} 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 *n _{trap}* and the hopping frequency

*ν*that sets the conductivity magnitude, the activation energy

_{TAC}*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,

*NE*; a hopping attack frequency,

_{F}*ν*; 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,

_{VRH}*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 (*σ _{TAHo}*,

*T*, and

_{A}*E*) to scale the thermally activated hopping reduced conductivity, reduced temperature and reduced E-field, respectively; three (

_{A}*σ*,

_{VRHo}*T*, and

_{o}*E*) to scale the variable range hopping reduced conductivity, reduced temperature and reduced E-field, respectively; and four (

_{o}*k*,

_{o}*k*and

_{1}Δ_{1}*T*) to scale the RIC magnitude, the temperature dependence of the magnitude, the temperature dependence of the power, and the critical temperature above which

_{cr}*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, *T _{ESD}*, and the asymptotic high temperature limiting electrostatic breakdown field strength,

*E*.

_{ESDmin}The available materials database is described and applications of the engineering tool for spacecraft charging calculations are discussed.

## Recommended Citation

Dennison, JR; Hart, Steven; Corbridge Gillespie, Jodie; Dekany, Justin; Sim, Charles; and Arnfield, Dan, "Engineering Tool for Temperature, Electric Field and Dose Rate Dependence of High Resistivity Spacecraft Materials" (2009). 47th AIAA Aerospace Sciences Meeting American Institute of Aeronautics and Astronautics. *Conference Proceedings.* Paper 31.

https://digitalcommons.usu.edu/mp_conf/31