Optimal magnetic and electrostatic Russian Quadruplet microprobe lens system with high demagnification

Abstract

The goal for the microbeam is a lateral resolution in the nanometer range. Usually one needs a very small object diaphragm to obtain this which gives problems with scattering and is difficult to manufacture. Focusing systems with very high demagnification solve these problems. In this paper a focusing system consisting of a magnetic or electrostatic Russian Quadruplet (RQ) working in the second mode of excitation and with high positive demagnification (up to 10000) is investigated in detail. In this system it is possible to vary the focal distance and the demagnification within a wide range, changing the distance between the second and the third lenses. We call this RQ the Separated Russian Quadruplet (SRQ). A general method for optimising the quadrupole configuration is described and a numerical optimization has been performed. We consider the differential equation of motion of the particles accurate to terms of third order inclusive. The minimum spot size, the appropriate radii of the diaphragms and the distance between them are found. It is shown that for 1 μm object and aperture diaphragms it is possible to obtain 1 nm resolution.