Unified simulation of Coulomb interactions and aberrations in charged particle optics by direct ray tracing

The performance of electron and ion beam columns for micro-fabrication and inspection is limited by the combined effects of electron optical aberrations and discrete Coulomb interactions. The accurate simulation of such columns is essential for their design and optimization, particularly in the case of state-of-the-art charged particle lithography columns which use projection optics with high beam currents. Historically, the electron optical aberrations have been computed using paraxial rays and aberration integrals, while the Coulomb aberrations have been simulated using N-body Monte Carlo simulation with thin-lens approximations for the lenses. These approaches have many drawbacks, including: (a) The aberrations of cathode lenses cannot be accurately analyzed; (b) The thin-lens approximations don´t allow the lens aberrations to be properly combined with the Coulomb effects; (c) The conventional aberration theory divides the aberrations into terms of various orders, and it is hard to know a priori how many orders are required for an accurate solution; (d) The thin-lens approximations are quite unrealistic for electrostatic lenses with extended fields. A new simulation method has been developed that computes the aberrations and Coulomb interactions simultaneously in a unified way, by direct ray tracing. This new method overcomes all problems mentioned above and provides accurate results in a reasonable computation time.