Field enhancement factor and field emission from a hemi-ellipsoidal metallic needle

Abstract

We present an exact solution for the electrostatic field between a metallic hemi-ellipsoidal needle on a plate (as a cathode) and a flat anode. The basic idea is to replace the cathode by a linearly charged thread in a uniform electric field and to use a set of "image" charges to reproduce the anode. We calculate the field enhancement factor on the needle surface and ponderomotive force acting on the needle. Using the Fowler-Nordheim theory we obtain an exact analytical formula for the total current.

Towards quantitative off-axis electron holographic mapping of the electric field around the tip of a sharp biased metallic needle

“…This value for k is very close to the usual value of 3 valid for a metallic half-sphere. 30 In Fig. 6, the main differences between the model and the experiment are at the very top of the tip.…”

“…[24][25][26][27][28][29] A simpler derivation of the same result can be obtained by considering the field that is generated by a linear distribution of charges, whose density increases linearly along its length. 24,30 The electron-optical phase shift can also be calculated easily in this case. It is useful to outline this derivation, starting from the electrostatic potential of two opposite point charges 6dq located at the variable coordinates (0, 6t, 0) in a Cartesian system (x, y, z), with the z-axis parallel to and in the same direction as the electron beam, in the form…”

Enhanced Cold Field Emission of Large-area Arrays of Vertically Aligned ZnO-nanotapers via Sharpening: Experiment and Theory

“…As for the theoretical models of field emission, most of the models have been established for carbon nanotubes (such as floating spheres18 and cylinders19) and metallic nanostructures (such as pyramids20, hemi-ellipsoidal21 and semi-infinite electrodes22). However, little has been reported on the semiconducting nano-emitters due to the complication mainly induced by the electric field penetration into the emitters and the surface states232425.…”

Carbon Nanotube Field Emitters

“…5(b)) was considered in many papers (for example Refs. (Forbes et al, 2003;Wang et al, 2004;Pogorelov et al, 2009) …”

“…We can replace the spheroid by a linearly charged thread as we show in our recent paper (Pogorelov et al, 2009). The thread is a green line in Fig.…”