15 November 1999 Numerical ray tracing of electrons in different 3D fringing fields of spherical deflectors
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Abstract
This paper presents the results of numerical investigations on electron trajectories in different 3D fringing fields of spherical defectors. We start with a chosen set of geometrical values for the electrodes such as radius of curvature, electrode gap, angle between entrance and exit face. We do a first numerical calculation of the spatial potential distribution using a 3D electron optics program based on the finite difference method (FDM). Ray tracing through this potential distribution is then performed using another program, which also gives the potential and the electric field strength along the curved beam path. In the next step we estimate the position and the geometry of the field clamp using Herzog's formulae assuming the entrance of a parallel plate condenser to be a good approximation for the entrance of the spherical deflector in first order. For the consecutive numerical recalculations of the real potential distribution of the spherical deflector with clamps we alter the position of the field clamp in beam direction under the constraint that the curved trajectory in the main field of an electron with defined energy will be the same as without fringing field. In our case the edges of the clamps are curved in the same way as the deflector electrodes are curved in the plane perpendicular to the curved optical axis. To check if the constraint is fulfilled we do a ray tracing from outside the field of the deflector through the fringing field into the main field and compare the trajectories of different setups with each other. For a considered example it can be shown that the best position of the clamps is approximately 9% further away from the entrance plane of the spherical deflector than calculated with Herzog's method.
© (1999) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Armin Huber, Erich Plies, "Numerical ray tracing of electrons in different 3D fringing fields of spherical deflectors", Proc. SPIE 3777, Charged Particle Optics IV, (15 November 1999); doi: 10.1117/12.370136; https://doi.org/10.1117/12.370136
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