The use of the Boltzmann transport equation to describe electron scattering in electron microscopy and electron probe microanalysis is discussed. A method of solution is given in which the transport equation is divided into angle and energy intervals. This gives rise to a number of coupled first order differential equations. Separation into forward and backward travelling components of the electron flux distribution enables the correct boundary conditions to be imposed. Solutions are derived which take the form of matrix operators analytic in both depth and target thickness. These matrices allow derivation of other physical quantities such as X-ray or Auger electron production.
Calculations using this method are fast and accurate. Results are presented showing angular distributions of backscattered electrons and the variation of the backscattered fraction with angle of incidence and atomic number. The variations of backscattered, transmitted and absorbed fractions with target thickness are presented. The theory has also been applied to the calculation of the energy distributions of backscattered electrons, energy dissipation and X-ray production as functions of depth and the Auger backscattering factor.
It appears that electron scattering in thick targets is not amenable to treatment using simple models. This is because most of the features of interest are determined by a combination of medium angle scattering (< 20°) and large angle scattering (20-90°). Nevertheless certain approximations within the present framework, which describe multiple scattering correctly, can give some useful insights.
Fathers, D. J. and Rez, P.
"A Transport Equation Theory of Electron Scattering,"
Scanning Electron Microscopy: Vol. 1982
, Article 17.
Available at: https://digitalcommons.usu.edu/electron/vol1982/iss1/17