Scanning Electron Microscopy


The success of computer-aided design in electron optics is no longer limited by computing facilities but by our understanding of numerical methods and underlying physical laws used for the computation. This paper deals mainly with the computation of vector potential in rotationally symmetric magnetic lenses. The finite element method, as introduced by Munro in 1971, seems to be the best tool for this purpose, and we aim to show in this paper how it is possible to improve it without losing the original clarity. Therefore we discuss the suitable choice of mesh and the calculation of the coefficients of the finite element equations to get better accuracy, the choice of boundary and boundary conditions for correct results and methods for solving the resulting system of linear algebraic equations to obtain a higher speed of computation. A survey of programs that can be used for lens design is given, with an emphasis on our recent work. Several examples illustrate some important problems in lens calculations.

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