Quasi-ray Tracing Method for Coulomb Interaction Estimation in Charged Particle Systems

Coulomb interaction (CI) is a crucial factor contributing to the degradation of resolution in charged particle imaging systems. For example, certain inspection applications of scanning electron microscopes (SEM) require high probe current, which exacerbates resolution degradation due to CI. However, current methods for estimating CI, such as direct ray tracing and analytical approaches, struggle to balance speed and accuracy. This limitation significantly impedes the efficient optimization of SEM design parameters. In this study, we propose a quasi-ray tracing method based on perturbation theory, which simulates CI-induced trajectory displacement and the Boersch effect using a Monte Carlo ray tracing approach. Our method eliminates the need for iterative solvers employed in conventional direct ray tracing, thereby increasing simulation speed by over 105 times. Benchmarking against the direct ray tracing method demonstrates an error margin of less than 1% over a broad parameter range covering typical SEM applications. This quasi-ray tracing approach offers a fast, accurate, and general solution for CI estimation in charged particle imaging systems.