Density-gradient analysis of field emission from metals

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Abstract
The conventional theory of field emission from metals consists of the Fowler-Nordheim tunneling analysis with space-charge effects accounted for using the ‘‘image-force’’ concept. This one-electron approach is highly questionable because the potential barrier through which the tunneling occurs is located very close (<3 Å) to the cathode interface, a region in which the charge density is quite high due to ‘‘spillover’’ effects. In this paper, we give an improved analysis of the field-emission current based on an approximate many-body quantum transport theory known as density-gradient theory. These calculations represent a much more realistic treatment of the emitting electrode in which the important interactions of the problem—the Coulomb interaction, exchange-correlation effects, and the finite screening capacity (field penetration) of the electrode—are treated in an approximate but fully coupled manner. From these calculations we find that the location, height, and bias dependence of the barrier differ sharply from those of conventional theory. Qualitatively, the calculated current remains Fowler-Nordheim-like and so remains in agreement with experiment. However, the size of the space-charge effect on the current is found to be very much smaller than predicted by image-force theory to the point that it is a much better approximation simply to ignore the space charge. This is in accord with most experimental observation and contrasts with the conventional theory whose prediction of unrealistically small effective emitting areas is well known.