On the Computation of Secondary Electron Emission Models

Abstract

Secondary electron emission is a critical contributor to the charge particle current balance in spacecraft charging. Spacecraft charging simulation codes use a parameterized expression for the secondary electron (SE) yield delta(E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sub> ) as a function of the incident electron energy E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sub> . Simple three-step physics models of the electron penetration, transport, and emission from a solid are typically expressed in terms of the incident electron penetration depth at normal incidence R(E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sub> ) and the mean free path of the SE lambda. In this paper, the authors recall classical models for the range R(E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sub> ): a power law expression of the form b <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n1</sup> and a more general empirical double power law R(E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sub> )=b <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n1</sup> +b <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n2</sup> . In most models, the yield is the result of an integral along the path length of incident electrons. An improved fourth-order numerical method to compute this integral is presented and compared to the standard second-order method. A critical step in accurately characterizing a particular spacecraft material is the determination of the model parameters in terms of the measured electron yield data. The fitting procedures and range models are applied to several measured data sets to compare their effectiveness in modeling the function delta(E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sub> ) over the full range of energy of incident particles