Relativistic focus condition for E-beam projection lithography

In e-beam projection lithography (EPL) systems, the relativistic focus condition was derived and compared with the nonrelativistic focus condition to investigate the effect of a large acceleration field related to the initial energy and emission angle of an electron emitted from a cathode. The difference in confusion disk between the relativistic and nonrelativistic limits was 180 nm when 1 eV was used as the initial energy of the electron. The variation in the initial energy of the electron was more sensitive to change the confusion disk than the acceleration field. In this comparison, the focusing parameters are used as follows: axial magnetic field, 0.5 T, distance between the mask layer and the workpiece, 2mm and emission angle of the electron, 30°.