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The geometry of an atomically sharp or nearly atomically sharp tip in proximity to a planar anode may be closely approximated in the prolate-spheroidal coordinate system. An exact three-dimensional electrostatic-potential solution for a free charge in such a tip/base junction is given in this letter, including calculations for both the symmetrical on-axis case and the asymmetric off-axis case. An exact solution for the potential-energy barrier is also given; this solution has immediate applications in three-dimensional tunneling studies and in calculations of electron trajectories in micron- and submicron-sized field-emitter arrays.
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Pan et al. (1994) studied this question.
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