Abstract
The aim of this paper is to describe the development of the electron-beam optic analysis algorithm for simulating the e-beam behavior concerned with electrostatic lenses and their focal properties in the micro-column of the multi-beam lithography system. The electrostatic lens consists of an array of electrodes held at different potentials. The electrostatic lens, the so-called einzel lens, which is composed of three electrodes, is used to focus the electron beam by adjusting the voltages of the electrodes. The optics of an electron beam penetrating a region of an electric field is similar to the situation in light optics. The electron is accelerated or decelerated, and the trajectory depends on the angle of incidence with respect to the equi-potential surfaces of the field. The performance parameters, such as the working distances and the beam diameters are obtained by the computational simulations as a function of the focusing voltages of the einzel lens electrodes. Based on the developed simulation algorithm, the high performance of the micro-column can be achieved through optimized control of the einzel lens.
