Abstract
An analytical treatment of elliptical field emitting structures which includes image charge effects off axis and the variation of field along the tip is given. The angular distribution of electron emission along the tip, the total emitted current, and the area factor are calculated as a function of emitter to anode distance, tip radius, tip height, and the anode-tip voltage difference. Errors arise if the planar Fowler–Nordheim (FN) equation is used to govern electron emission; we show how to correct this by a modification of the FN equation which includes changes in fields and image charge due to curvature. An analytic form of the area factor is given and compared to a calculation based on the exact transmission coefficient and various Wentzel–Kramers–Brillouin-based approximations to it. The analysis is extended beyond diode geometries with the inclusion of additional electrodes, allowing devices such as triodes to be modeled.
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