Theoretical analysis demonstrates superior electric field magnification in rotationally symmetric tips over elliptical wedges, highlighting geometry's critical role in field emission.
An unambiguous comparison for the magnification factor, M, in field emission is derived by solving rigorously Laplace equations for the cases of individual prolate ellipsoids (cones) of revolution on one side, and for an elliptical wedge on the other side, under the assumption that a uniform electric field exists at some distance away from the emitting surface. Significant superiority of M for individual emitters with rotational symmetry is demonstrated as compared to the wedge. Also discussed is the case of a floating sphere.>
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H. G. Kosmahl (1991) studied this question.
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