Sanchez Jaime A, Mengüç M Pinar
Department of Mechanical Engineering, University of Kentucky, Lexington, KY 40506-0108, USA.
Nanotechnology. 2008 Feb 20;19(7):075702. doi: 10.1088/0957-4484/19/7/075702. Epub 2008 Jan 31.
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.
在本文中，我们进行了一项分析，以模拟在电子束场发射过程中，附着在蚀刻钨尖上的孤立碳纳米管（CNT）内部的加热情况。碳纳米管的长度、半径、壁厚以及尖端的形状（半球形封闭或开放且平坦）及其与平面的分离距离被视为变量。使用有限元方法，我们预测了碳纳米管的场增强、发射电流和温度作为这些参数的函数。静电分析和瞬态热分析与基于福勒 - 诺德海姆近似的场发射模型以及由于发射高能电子导致的加热/冷却（诺丁汉效应）相结合。这些模拟表明，碳纳米管加热的主要机制是焦耳热，其远大于诺丁汉效应。结果还表明，碳纳米管的静电特性对所考虑的参数非常敏感，而瞬态热响应仅取决于碳纳米管的半径和壁厚。此外，碳纳米管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一组特定几何条件，碳纳米管达到的最高温度将是相同的。
