Coherent field emission image of graphene predicted with a microscopic theory

Electrons in the mono-layer atomic sheet of graphene have a long coherence length of the order of micrometers. We will show that this coherence is transmitted into the vacuum via electric field assisted electron emission from the graphene edge. The emission current density is given analytically. The parity of the carbon pi-electrons leads to an image whose center is dark as a result of interference. A dragonfly pattern with a dark body perpendicular to the edge is predicted for the armchair edge whose emission current density is vanishing with the mixing angle of the pseudo-spin. The interference pattern may be observed up to temperatures of thousand Kelvin as evidence of coherent field emission. Moreover, this phenomenon leads to a novel coherent electron line source that can produce interference patterns of extended objects with linear sizes comparable to the length of the graphene edge.Comment: 6 pages, 3 figure

Analytical treatment of cold field electron emission from a nanowall emitter

This paper presents an elementary, approximate analytical treatment of cold field electron emission (CFE) from a classical nanowall. A simple model is used to bring out some of the basic physics of a class of field emitter where quantum confinement effects exist transverse to the emitting direction. A high-level methodology is presented for developing CFE equations more general than the usual Fowler-Nordheim-type (FN-type) equations, and is applied to the classical nanowall. If the nanowall is sufficiently thin, then significant transverse-energy quantization effects occur, and affect the overall form of theoretical CFE equations; also, the tunnelling barrier shape exhibits "fall-off" in the local field value with distance from the surface. A conformal transformation technique is used to derive an analytical expression for the on-axis tunnelling probability.Comment: 48 pages, 4 figure

Field electron emission characteristic of graphene

The field electron emission current from graphene is calculated analytically on a semiclassical model. The unique electronic energy band structure of graphene and the field penetration in the edge from which the electrons emit have been taken into account. The relation between the effective vacuum barrier height and the applied field is obtained. The calculated slope of the Fowler-Nordheim plot of the current-field characteristic is in consistent with existing experiments.Comment: 18 pages, 5 figures Copyright (2011) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. This article appeared in (J. Appl. Phys. 109 (2011) 044304) and may be found at (http://link.aip.org/link/?JAP/109/044304

Large-scale fabrication of ordered arrays of microcontainers and the restraint effect on growth of CuO nanowires

Technique has been developed to fabricate ordered arrays of microcontainers. We report that ordered microcontainer arrays of Cu can be fabricated on glass substrate by thin film deposition and self-assembly technology. In addition, CuO nanowires are found to grow only in the inner sides of microcontainers, which verifies the stress growth mechanism of CuO nanowires. High-resolution transmission electron microscopy study reveals that CuO nanowires grow along the [110] direction. Such structure may have potential application in micro-electron sources, which have the self-focused function

Screening effects on field emission from arrays of (5,5) carbon nanotubes: Quantum-mechanical simulation

The simulation of field electron emission from arrays of micrometer-long open-ended (5, 5) carbon nanotubes is performed in the framework of quantum theory of many electrons. It is found that the applied external field is strongly screened when the spacing distance is shorter than the length of the carbon nanotubes. The optimal spacing distance is two to three times of the nanotube length, slightly depending on the applied external fields. The electric screening can be described by a factor that is a exponential function of the ratio of the spacing distance to the length of the carbon nanotubes. For a given length, the field enhancement factor decreases sharply as the screening factor larger than 0.05. The simulation implies that the thickness of the array should be larger than a value but it does not help the emission much by increasing the thickness a great deal

Simulation for field emission images of micrometer-long SWCNTs

The electron distribution of open-ended single-walled carbon nanotubes with chirality indexes (7,0) and (5,5) in the field emission conditions was calculated via a multi-scaled algorithm. The field emission images were produced numerically. It was found that the emission patterns change with the applied macroscopic field. Especially, the symmetry of the emission pattern of the (7,0) carbon nanotube is breaking in the lower field but the breaking is less obvious in the higher field. The enlargement factor increases with the applied macroscopic field.Comment: 8 pages, 4 figure