Synthesis of electrostatic electron and ion optical systems.

Abstract

Synthesis of electrostatic lenses was successfully achieved by using the cubic spline method or the a priori given multielectrode approach. In this dissertation, we propose synthesis of electrostatic deflectors with given source parameters, first-order properties, and minimum aberrations by using the cubic spline method or the a priori given multielectrode approach through a sequential optimization technique combined with the gradient method and the Hooke and Jeeves' method. Our calculations show that the third-order geometrical deflection aberrations can be reduced by 2-3 orders of magnitude using the electrodes of electrostatic spline deflectors reconstructed in terms of the optimized first harmonic field distribution (FHFD) functions or a multielectrode deflector with 3 units or 5 units, each having short cylindrical segments geometrically octupole symmetry. We also present synthesis of an ion beam column as a single entity, based on combined focusing and deflection (CFD). In a CFD system it is difficult to reconstruct the electrodes by using the cubic spline method because of the difference in the role of inflection points between axial potential distribution (APD) and FHFD functions. In this case, while the cubic spline method remains a valuable mathematical tool, the a priori given multielectrode approach is a better candidate for the synthesis of the CFD system. By using a sequential optimization technique for a multipurpose multipole system with 9 units, our calculations show that one can obtain a beam spot radius less than 7 nm and current density of 614 A/cm², scanned over a 2 mm-square field for a field ionization source. A sensitivity analysis is given, and the optimum working distances of a given CFD system are presented for the minimum beam spot radius.