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Parasitic Aberrations of Electrostatic Deflectors
Badin, Viktor ; Radlička, Tomáš (oponent) ; Sháněl, Ondřej (oponent) ; Lencová, Bohumila (vedoucí práce)
The present doctoral dissertation deals with parasitic aberrations in electrostatic multipole optical components arising due to mechanical misalignment of the electrodes. Manufacturing and alignment precision of the mechanical parts can have a significant influence on the performance of electron beam machines such as microscopes and lithography (EBL) systems. Defects, imprecisions, and all other symmetry violations generate so-called parasitic fields whose effects on the particle beam are referred to as parasitic aberrations. Perturbations of axially symmetric lenses are usually treated using Sturrock's principle. Displacement or tilt of an entire multipole component can be analyzed in a globally shifted or tilted coordinate system. The present thesis deals with the misalignment of individual electrodes, which cannot be easily described with the mentioned approaches and usually need to be solved in 3D. Calculations in 3D are generally slower and have higher computational requirements than 2D tools standardly used in charged particle optics programs. To calculate parasitic fields generated by electrode misalignment, a 2D perturbation method compatible with the finite element method (FEM) has been developed in this thesis based on shifting the coordinate system locally around the affected electrode. Electrodes misaligned in each axis of the cylindrical coordinate system (longitudinal, radial, and azimuthal) are studied. Possible applications of the derived general method are shown, such as ellipticity and transverse shift of the entire deflector. For each of these cases, the resulting parasitic axial field functions (AFF) calculated in 2D are validated against the 3D solution. In addition to comparing parasitic AFFs, a case study is provided where the effect of parasitic aberrations on the electron beam in an entire optical column of an EBL system is shown, again validated against the 3D solution. The proposed method of calculating parasitic fields in 2D allows understanding the effects of different manufacturing and assembling tolerances, characterizing these effects, designing aberration correction devices, and optimizing mechanical tolerance requirements. The developed method can be run on any standard PC and is 1--2 orders of magnitude faster than solving the perturbed system in 3D.
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