Aberration analysis of wide-angle deflectors and lenses by direct ray-tracing and comparison with conventional aberration theories

摘要

Abstract: This paper describes numerical techniques for computing aberrations in focusing and deflection systems for charged particle beams, and electron sources and mirrors, by direct ray- tracing of electron or ion trajectories. For such computations to be meaningful and reliable, high accuracy in the computed potential distribution and field components is essential. Suitable methods for potential and field computation in 2D and 3D are outlined, including finite difference and second-order finite element methods, Biot-Savart law and charge density method. A method for direct ray-tracing through these fields is then summarized, using a Runge-Kutta formula. To compare the results of direct ray-tracing with conventional aberration theories, techniques for computing third and fifth-order aberrations using axial field functions and aberration integrals are described. The techniques are illustrated by several examples, including: analysis of spherical and chromatic aberration of an electrostatic lens by direct ray-tracing; analysis of a magnetic probe-forming SEM lens with wide-angle magnetic deflection, with either post-lens or pre-lens deflection; analysis of quadrupole lenses by direct ray-tracing and multipole aberration theory; aberration analysis of an electron mirror by direct ray-tracing; and analysis of the aberration of electron and ion sources.!17