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Computations in Charged Particle Optics
Oral, Martin ; Radlička, Tomáš
The design of modern electron microscopes could not be possible without appropriate software tools. With the sub-nanometer resolution in SEM, and the sub-ångström resolution in TEM, one can see that the simulations involved in designing the instruments need to be tremendously accurate. A simulation starts with the computation of the electric and magnetic fields generated by various optical elements. That is followed by determinig the paraxial properties, aberrations and accurate particle trajectories (ray tracing). The distributions of the fields are mostly detemined with the Finite Element Method (FEM), the Boundary Element Method (BEM) or the Finite Difference Method (FDM). As the field data are at the input of all the subsequent calculations, they need to be very accurate, especially in the region close to the optical axis. Current expertise includes a set of rules that need to be applied in generating a FEM or BEM mesh. Advanced field interpolation techniques are necessary for accurate aberration analysis and particle tracing with high-order integration methods. Specialized software has been developped for the use in charged particle optics which aids the user in getting meaningful and accurate results. For instance, the EOD (Electron Optical Design) is a comprehensive package for particle optical sumulations. Field data produced by SIMION and Comsol need a specialized post-processing before their use in accurate ray tracing. Presented will be different methods of computing the optical aberrations, intensity distribution and probe size (resolution) on basic as well as more advanced examples (electron and ion optical columns, deflection systems, ToF spectrometers etc.) that were solved in the EOD and using custom programs.
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