Three-Dimensional Multiregion S_n Solutions of the Spencer-Lewis Electron Transport Equation

The S_n method for solving the Spencer-Lewis equation for electron transport has been extended to treat three-dimensional multiregion problems. The flux continuity condition, which holds when the flux is expressed as a function of path length for single material region problems, is generalized for multiregion problems by reexpressing the flux as a function of energy. Expressing the fluxes in terms of fixed energy increments, independent of material, rather than fixed path length increments, results in a set of S_n/diamond-difference equations that are nearly identical in form to conventional S_n/diamond-difference equations. The S_n method is then applied to calculate electron energy deposition due to 200-keV electron beams incident on problem geometries typical of silicon and gallium-arsenide semiconductor microelectronic devices. The energy deposition results were found to compare well with results of ACCEPT Monte Carlo calculations. Computer run times required for the S_n calculations were found to be lower than that required for Monte Carlo by factors ranging from 30 to 50.