Simulation of Coulomb interactions in electron beam lithography systems—A comparison of theoretical models

The Loeffler effect (trajectory displacement) has been calculated for a magnetic lens doublet electron-optic system considered to represent the basic configuration for next generation lithography. The results of two analytic and two numeric (Monte Carlo) models are compared and presented graphically as well as by analytic approximations, revealing significant quantitative differences within the parameter space considered relevant. Less severe discrepancies in the trends appear to be useful as a guide for system design, but experimental verification is needed to determine the validity of any of the approaches compared.