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An effective three-dimensional finite element method analysis of electrical field is performed to obtain electric fields at field emitter tips in an array form. Considering the periodic characteristic of tips in an array form, the region for numerical analysis is reduced to a single cell with proper Neumann and Dirichlet boundary conditions. The evolution strategy is also adopted to find the optimal design condition. As an example, the maximum current density per anode area is found by the evolution strategy with design parameters of tip height and tip spacing. © 1998 American Vacuum Society.