Electrostatic lenses of the antisymmetric quadrupole and symmetric octupole quadruplet
Abstract
Electrostatic quadrupole octupole lens systems are studied to focus a cone of electron beams emanating from a point source. The half angle of emission is 0.01 radian and the accelerating voltage is 10 KV. These are desirable parameters for e beam lithography. An antisymmetric quadruplet simulates a round lens which gives a regular image with the capability of aberration correction. The analytical solution for trajectories is obtained by assuming an ideal hyperbolic field and by neglecting the secondorder effects such as the fringefield, local voltage, and relativistic effect. An initial guess of the sign parameters is provided. For the real case design, a successive over relaxation technique is used to solve Laplace's equation for potential distribution in three dimensional cylindrical coordinates. The boundary values are imposed around the primary region which is the first 45 deg for a quadrupole and the first 22.5 deg for an octupole.
 Publication:

Ph.D. Thesis
 Pub Date:
 1981
 Bibcode:
 1981PhDT........78C
 Keywords:

 Electron Trajectories;
 Electrostatic Charge;
 Lens Design;
 Magnetic Lenses;
 Boundary Value Problems;
 Hyperbolic Coordinates;
 Laplace Equation;
 Potential Gradients;
 Electronics and Electrical Engineering