Synthesis of electrostatic focusing and deflection systems

In this article, we present synthesis of an ion beam column as a single entity, based on combined focusing and deflection (CFD). We present seven cases as examples of designing CFD systems by synthesis. Four of those are examples resulting from the a priori given multielectrode approach using a multipurpose multipole system with nine or five units. In these cases, the units have short cylindrical rings or disks cut into segments with geometrically octupole symmetry. In one example we are using the cubic spline method. The other two cases are examples obtained by using both methods in the case of a separate group of axially symmetric electrostatic lenses and electrostatic postlens deflectors. By using a sequential optimization technique combined with the gradient method and the Hooke-Jeeve's method for a multipurpose multipole system with nine units, our calculations show that one can produce 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. We also present comparison of our CFD system with other published data. The results display substantial improvements, especially for a field ionization source with smaller energy spread ΔU = 1 eV and higher acceptance half-angle γ₀ = 2.3 mrad. A sensitivity analysis is given, and the optimum working distances of a given CFD system are presented for the minimum beam spot radius.