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The support device generations below 250 nm mask writing systems must improve productivity for smaller design address grids and simultaneously provide higher hose to support high resolution processes. Combining multipass writing techniques with higher pixel rate provides improved productivity and increased dose; however, many high resolution processes require even higher dose delivery. The optimization of field-emission systems for maximum effective brightness has been discussed previously, but the inclusion of electron-electron (e-e) interactions in the optimization process is a significant complication. There is little discussion in the general literature, except for Brodie and Meisburger [A.D. Brodie and W.D. Meisburger, Microelectron. Eng. 17, 99 (1992)] about the impact of e-e interactions on the design of columns for electron-beam lithography systems. This article discusses several formulations of the problem and the solutions. Closed-form solutions for particular special cases (spherical- and chromatic-aberration limited systems) have been derived using the computer algebra code Mathematica and will be presented. The design of an improved field-emission gun and column is described, based on these general considerations, and on an acceleration-mode gun lens with particularly low chromatic aberration. Several improvements in the column design are discussed. These include optimization of the gun and the column for highest dose (800 A/cm2) without increasing the beam energy of 10 keV.
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