Multi Electrode Lens Optimization Using Genetic Algorithms

Abstract

In electron lens design, finding the optimum lens system for theapplication at hand, is still quite a challenge. The situation becomes especially more complicated when many lens electrodesare involved, because the number of free parameters of the optimization, such as electrode thickness, radii, gaps between electrodes and voltages, increases rapidly. Therefore, fast optimization routines are needed to tackle the problem. In the past, there have been some attempts to develop such optimization programs. Szilagy et al. [1] and Adriaanse et al. [2], have published someresults in 1989 on rough optimization of electrostatic lenses. However, using the above-mentioned methods, one could not get very accurate results. Now that we have more powerful computers and significantly better software, we revisit the problem. First we applied the so called “SOEM” (Second Order ElectrodeMethod) [2] for a fast (∼0.1sec) calculation of the axial potential. However, the results of the optimization were not accurate enough. To improve the accuracy of the SOEM-based optimization, we integrated a finite element based potential calculation method (using COMSOL). This way the potential calculation and the objective function calculation is more accurate, although the optimization becomes much slower. We propose a new approach that improves on the low speed of optimization while keeping the high accuracy results of the finite element method based potential calculation. This is done by first using a rough optimization based on the SOEM approach, resulting in a few approximately optimized systems. Then, using the parameters of the systems found, new sets of systems were defined using a small range of values around these parameters. Then the more accurate, COMSOL-based optimization was applied to this set of limited systems. We have tested our method on multi electrode systems up to 7 electrodes. We succeeded to very accurately optimize these systems within a few hours, with the electrode radii, gaps and voltages as free parameters, and the focus position as a constraint. [1] M.Szilagi. Yakowitz and M. Duff, Appl. Phys.Lett. 44, pp. 7-9, 1984. [2] J.P. Adriaanse, H.W.G Van der Steen and J.E. Barth, J.Vac. Sci. Technol. B7, pp. 651-666, 1989.