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Geometry dependence of the electrostatic and thermal response of a carbon nanotube during field emission

机译：碳纳米管在场发射过程中的静电和热响应的几何依赖性

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摘要

In this paper we present an analysis to simulate heating within an isolated carbon nanotube (CNT) attached to an etched tungsten tip during field emission of an electron beam. The length, radius, wall thickness and shape of the tip (closed with a hemispherical shape or open and flat) of the CNT and its separation distance from the flat surface are considered as variables. Using a finite element method, we predict the field enhancement, emission current and temperature of the CNT as a function of these parameters. The electrostatic and transient thermal analyses are integrated with the field-emission models based on the Fowler-Nordheim approximation and heating/cooling due to emitting energetic electrons (the Nottingham effect). These simulations suggest that the main mechanism responsible for heating of the CNT is Joule heating, which is significantly larger than the Nottingham effect. Results also indicate that the electrostatic characteristics of CNTs are very sensitive to the considered parameters whereas the transient thermal response is only a function of the CNT radius and wall thickness. Further, the thermal response of the CNT is independent of its geometry, meaning that, as long as a given set of geometrical conditions are present that result in a given emission current, the maximum temperature a CNT attains will be the same.
机译：在本文中，我们提出了一种分析，以模拟在电子束的场发射过程中附着在蚀刻的钨尖端上的孤立碳纳米管（CNT）内的加热。 CNT的尖端的长度，半径，壁厚和形状（以半球形封闭或敞开且平坦）及其与平坦表面的分离距离被视为变量。使用有限元方法，我们根据这些参数预测了碳纳米管的场增强，发射电流和温度。静电和瞬态热分析与基于Fowler-Nordheim近似以及由于发射高能电子而引起的加热/冷却（诺丁汉效应）的场发射模型集成在一起。这些模拟表明，负责加热CNT的主要机理是焦耳加热，它远大于诺丁汉效应。结果还表明，CNT的静电特性对所考虑的参数非常敏感，而瞬态热响应仅是CNT半径和壁厚的函数。此外，CNT的热响应与其几何形状无关，这意味着，只要存在导致给定发射电流的给定几何条件集，CNT所达到的最高温度将相同。

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