Integration of an adaptive parallel N-body solver into a particle-by-particle electron-beam interaction simulator

An adaptively refinable Fast Multipole library called Pbody has been developed and used to rigorously analyze statistical electron-electron interactions at high density field free regions in crossovers in electron beam lithography systems. The parallel algorithm and associated interaction decision regimes, communication and processor load balancing are portable to multiple processor networks supporting C and MPI. Beam blur effects at beam currents up to 30 (mu) A can be analyzed in a few hours. A basic imaging system with a crossover and no initial angular or energy spread was analyzed. At a given time step, electrons which experience a transverse force sufficient to influence the beam blur were first recorded. This set of electrons was then analyzed for the number of close neighbors and their relative contributions to the transverse statistical force. The data indicates that interactions with multiple rather than nearest neighbors almost immediately becomes the norm rather than the exception once the current reaches a level at which the average spacing between the electrons is about 48 micrometer.