Unipotential electrostatic lenses: Paraxial properties and aberrations of focal length and focal point

Abstract

An experimental study of electrostatic electron lenses as a function of geometrical and electrical parameters is described. The lenses are of the symmetrical three-electrode unipotential type. The parameters are the thickness of the center electrode and the interelectrode spacing, both relative to the center electrode aperture diameter, and the ratio of lens voltage to cathode voltage. The lens properties are characterized in terms of the focal length and focal distance, and the spherical and chromatic aberrations of these quantities. In general, the principal surfaces of a lens are not plane, and the aberrations of focal length and focal distance are not the same. Expressions are derived relating the focal length and focal distance aberrations to the spherical and chromatic imaging aberration coefficients Cs and Cc, and the magnification aberrations. The advantages of formulating the lens properties in terms of focal length and focal distance and their aberrations, and the usefulness of the data presented here, are illustrated with several examples.

Aberration Corrected Photoemission Electron Microscopy with Photonics Applications

“…(1.4)-(1.7) are defined, but at the circles of least confusion optimized for spherical and chromatic aberration separately [60]. The axial locations of the spherical and chromatic circles of least confusion are generally not coincident, so the prefactors will typically be different than those given here.…”

“…The focal variations are of the lens at a particular potential V o /V C can be measured experimentally, as in Rempfer [60], or computed using suitable software.…”

“…However, refraction in electron optics is qualitatively different; electron trajectories change direction continuously whereas light rays do so discretely at lens surfaces. In light optics, the aberration coefficient of multiple refractions is the sum of the aberration of each individual refraction, 9) where the weighting coefficients a j depend on changes in magnification and effective refractive index [60,66]. For a continuous refraction, the aberration coefficients of a lens in electron optics are best expressed as integrals over the axial potential V = V (z).…”

Photoelectron Emission Microscopy and its Application to the Study of Polymer Surfaces

“…The optical system is designed on the basis of the tabulated properties of unipotential lenses measured by Rempfer [12] and consists of two electrostatic lenses, an accelerating objective and a projective lens giving a combined maximum magnification factor of 1000. Resolution tests were carried out on Cu patterns deposited on a Si oxidized wafer using the 10%/90% knife: edge resolution criteria.…”

Simulation study and analysis of a compact einzel lens-deflector for low energy ion beam

“…Many studies of this aberration have been carried out, one of the most thorough being Ref. [3]. As a result of this aberration only about a quarter of the internal diameter of the central electrode of a simple einzel lens is useful if the emittance of a typical low-energy ion beam is not to be significantly increased.…”