Generalization of electrostatic lens characteristics using the Picht ray trajectories

Paraxial electron/ion trajectories in rotationally symmetric fields are ana lyzed in the Picht space to derive analytical forms of thin lens characteri stics such as focal length F, magnification M, and chromatic and spherical aberration coefficients C-c and C-s. Dimensionless forms of T/F, {(C-c/T)/( T/F)}/(L-o/T)(2), and {(C-2/T)/(T/F)}/(L-o/T)(4), which are determined only by the normalized lens-potential distribution, are derived to evaluate the lens. Here, Tis the lens thickness and L-o is the distance from the object to the lens. As to bipotential or unipotential lenses composed of electrod es facing each other symmetrically, it is found that the accelerating mode at V-2/V-1 = a (> 1) and the decelerating mode at V-2/V-1 = 1/a (< 1) have relationships of F-accel = F-decel, C-c,C-accel = C-c,C-decel/a, and C-s,C- accel = C-s,C-decel/a(1/2), where V-1 and V-2 are the 1st and 2nd electrode potentials, respectively. Under constant lens fields, the known M-dependen t C, and C, expressions, i.e., C-c = C-c,C- infinity (1 - 1/M)(2) and C-s = C-s,C- infinity (1 - 1/M)(4), are analytically derived also in the present approach. (C) 1999 American Vacuum Society. [S0734-211X(99)04304-8].