Space Charge Effect in the Field Emission.doc

Space Charge Effect in the Field Emission Author: Pei Yi Director: professor Zhang Gengmin Department of electronics Abstract: Space charge is very important in thermionic emission, and can be calculated in child-langmuir equation. However, there is no similar equation for field emission. Space charge cannot be ignored when there is a high electric field. This article uses FEM method to discuss space charge effect in one array field emission model and two tip field emission models. Some work done by BEM and Monte Carlo methods is also listed. The article also discusses the field-enhancement factor in three Models. 场发射中的空间电荷效应 信息科学学院电子学系4年级本科生：裴轶 （学号 指导老师：张耿民 摘要： 空间电荷在热发射中十分重要， 并且已经有了child-langmuir公式近似计算，但在场发射中还没有类似公式。在电场很高时，空间电荷效应非常明显，不能被忽略。 本文主要应用有限元方法讨论了一种阵列场发射和两种针尖场发射的模型， 分析了空间电荷对场发射的影响。同时一些用电荷密度法和蒙特卡罗方法虚所作的工作也列出，并且讨论了三种模型的场增强因子。 1 INTRODUCTION (1) The difference between thermal emission and field emission Child analyzed the electron flow from a parallel cathode surface of a thermionic vacuum tube. Langmuir extended the analysis to the cylindrical case. In these analyses, the field was assumed to be zero at or near the cathode surface. In the case of thermal emission, the assumption that the virtual cathode is near the face of cathode is reasonable. We often use Child-Langmuir equation to calculate the current flow. J= (1) We can see more clearly from the distribution of potential in figure 1. figure 1：Distribution of potential in three situation The blue line denotes the situation of no space charge; the red line represents the situation of low-density space charge effect; and the black one is in the situation of strong space charge effect. However, for field emission, Eq. (1) is not applicable. We cannot presume that the electrical field on the surface is zero. It is high electrical field that leads to the possibility of field emission. We have to find other ways to discuss field emission. (2) Basic concept of space charge