In electrostatic charged particle lens design, optimization of a multi-electrode lens with many free optimization parameters is still quite a challenge. A fully automated optimization routine is not yet available, mainly because the lens potential calculations are often done with very time-consuming methods that require meshing of the lens space. A new method is proposed that improves on the low speed of the potential calculation while keeping the high accuracy of the mesh-based calculation methods. This is done by first using a fast potential calculation based on the so-called Second-Order Electrode Method (SOEM), at the cost of losing some accuracy, and then using a Genetic Algorithm (GA) for the optimization. Then, by using the parameters of the approximate systems found from this optimization based on SOEM, an accurate GA optimization routine is performed based on potential calculation with the commercial finite element package COMSOL. A six-electrode electrostatic lens was optimized accurately within a few hours, using all lens dimensions and electrode voltages as free parameters and the focus position and maximum allowable electric fields between electrodes as constraints.
In electron optics, the design of electron lens systems is still a challenge. To optimize such systems, the objective function which should be calculated, depends on the electric potential distribution in the space created by the lenses. To obtain the electric potential, the existing methods are generally based on some mathematical techniques which need to mesh the space of the lens system and derive the electric potential at all mesh points. Hence, calculation of the objective function for such systems are computationally expensive. Therefore, applying a fully automatic optimization routine has not yet been feasible, especially for lens systems with many free variables. Hence, the study of objective-function landscape of such problems has not yet been performed.One of the questions of interest for optical designers, that has not been studied in the literature, is whether this problem can be solved by a local optimizer or is it necessary to apply a global optimizer. Recently we succeeded in implementing a method (based on a so-called SOEM (Second Order Electrode Method) technique) which calculates the electric potential in a fast and reasonably accurate way. In this paper, that method, is implemented to perform the study of local versus global optimization for electron lens design. The global optimization method here is performed by GA (Genetic Algorithm). The objective function is taken to be the probe size of the electron beams at the image plane.The results of our study show that the objective function of this problem has many local minima and the optimization of such problems cannot be handled by a local optimizer. GA is shown to perform well by overcoming these multiple-local minima to arrive at a global minima.
The design of an electrostatic electron optical system with five electrodes and two objective functions is optimized using multiobjective genetic algorithms (MOGAs) optimization. The two objective functions considered are minimum probe size of the primary electron beam in a fixed image plane and maximum secondary electron detection efficiency at an in-lens detector plane. The time-consuming step is the calculation of the system potential. There are two methods to do this. The first is using COMSOL (finite element method) and the second is using the second-order electrode method (SOEM). The former makes the optimization process very slow but accurate, and the latter makes it fast but less accurate. A fully automated optimization strategy is presented, where a SOEM-based MOGA provides input systems for a COMSOL-based MOGA. This boosts the optimization process and reduces the optimization times by at least ∼10 times, from several days to a few hours. A typical optimized system has a probe size of 11.9 nm and a secondary electron detection efficiency of 80%. This new method can be implemented in electrostatic lens design with one or more objective functions and multiple free variables as a very efficient, fully automated optimization technique.
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