Analysis of electric field screening by the proximity of two knife-edge field emitters

Abstract

The electric field of two semi-infinitely wide knife-edge cathodes with arbitrary separation is calculated by using a Schwarz–Christoffel transformation. This geometry could also represent a trench (or scratch) on a flat surface. It is found that the magnitude of the electric field on the knife-edge cathodes depends strongly on the ratio h/a, where h is the height of the knife-edge cathodes and 2a is the distance between the cathodes. When h/a increases, the magnitude of the electric field on the cathode’s surface decreases. This shows the screening of one cathode by another cathode; for example, keeping the height fixed and decreasing the distance between the cathodes, the field enhancement on the corner decreases. Analytic approximations for the divergent electric field in the immediate vicinity of the sharp edge are derived for the cases where h/a>>1, and h/a≪1. These results lead to insight on the relationship of the density of field emitter in field emitting arrays and field emission from rough surfaces.

Experimental study of electric field screening by the proximity of two carbon fiber cathodes

“…Since E is edge centered, a bilinear interpolation is used to determine its value at the sharp corner. Therefore, the sharp corner is effectively being smoothed out, and the electric field at that location is no longer infinite as theoretical analysis predicted, 11,21 and the current densities at the sharp corner become finite and integrable. In order to determine b eff as a function of the applied voltage, we employed the following procedure.…”

“…[6][7][8][9][10][11] Recently, we studied analytically the electric field screening of two semi-infinitely wide knifeedge cathodes with arbitrary separation by using conformal mapping and showed that the magnitude of the electric field on the knife-edge cathodes depends strongly on the aspect ratio h/a, where h is the height of the cathodes and 2a is the distance between the cathodes. 11 For experimental works, Nilsson et al reported that the emitted current density can be optimized by tuning the density of the carbon nanotubes (CNTs) on a film. 9 Later, Suh et al studied the field screening effect due to the proximity of neighboring CNTs by changing the height of the carbon nanotubes fabricated on porous anodic aluminum oxide templates.…”

Field emission characteristics of a small number of carbon fiber emitters

“…The cathode is negatively biased by using a computer controlled FX30N10 power supply, and in series with a 30 kΩ limiting resistor to reduce the effects of over-current on the power supply. 13,14,20 In situ diagnostics consist of a voltage divider providing voltage measurements across the A-K gap, and a current viewing resistor (CVR) for measuring the cathode current. We control the cathode current and voltage using the Lab Assistant 1.0 software package, developed by CCT, Inc., which also serves as the data acquisition software.…”

“…Hence, in previous work, we explored the emission characteristics of two-and four-fiber arrays of carbon emitters in a carefully prepared, simple geometry. [13][14][15][16][17][18][19] Our configuration allows a much more pristine and straightforward experimental geometry for isolating and interpreting the electric field screening from other effects such as work function variation across the cathode surface or statistical inhomogeneities in the geometry of the individual emitters that comprise the array.…”

Field emission from carbon nanotube fibers in varying anode-cathode gap with the consideration of contact resistance

“…Electric field screening by the proximity of neighboring emitters is found to have a profound effect on the field enhancement factor of the cathode. [18][19][20] Recently, it is shown that field enhancement factor strongly depends on the finite anode-cathode gap distance when the emitter tip-to-anode distance is comparable to or smaller than the emitter height. 8 In this paper, we study the FE characteristics of a CNT fiber emitter in different anode-cathode (AK) gap distances.…”