Multiple criteria optimization of electrostatic electron lenses using multiobjective genetic algorithms

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.