Electrostatic einzel lenses with reduced spherical aberration for use in field-emission guns

Abstract

Focusing properties and aberration coefficients are calculated for electrostatic einzel lenses suitable for use as preaccelerator lenses in field-emission electron guns. Various lens shapes are analyzed, and asymmetric designs with conical central electrodes are found to have reduced spherical aberration. A lens shape with optimized geometry is found to have a spherical aberration coefficient of less than six times the working distance from the lens to the focal point. This lens has a bored conical central electrode located close to a thin first electrode. Calculations indicate that a field-emission gun using such a lens should be able to provide a 0.24 μA beam from a 1100 Å effective source size into an emission half-angle of 2.4×10−2 rad. At lower emission angles the source size would be limited by chromatic rather than spherical aberration.