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1、Space Charge Effect in the Field EmissionAuthor: Pei YiDirector: professor Zhang GengminDepartment of electronicsAbstract: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 ca
2、nnot 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
3、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:00007065)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 emissi
4、on and field emissionChild 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. 1 In the case of thermal emission, the assump
5、tion that the virtual cathode is near the face of cathode is reasonable 2. We often use Child-Langmuir equation to calculate the current flow.2 T 1 bJ =.,V 3/2 J= AE 2 e e9兀 m d2 aWe can see more clearly from the distribution of potential in figure 1.figure 1: Distribution of potential in three situ
6、ationThe 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 fie
7、ld 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 effect in field emissionWhen the electrical field applied to the cathode is low, the space charge effect is n
8、ot evident, and we always use Fowler-Nordheim equation.1.54 x 10 -6 E 2 一EE1/2J = exp-6.83 x 107 v(3.39 x 10 -4 )E 12(e2 E / E)EEThe current flow increases and the space charge effect becomes more and more evident when a higher voltage is applied to the anode for the desired cathode filed.Space char
9、ge effect can be separated by volume space charge effect and discrete space charge effect. When we turn to volume space charge effect, we only consider effect of space charge in the distribution of Poisson field. In fact, since the coulomb interaction between electrons in electron bundle is random,
10、there is also a discrete space charge effect. It should be calculated by statistics means, and a common way is to use Monte Carlo Method.(3) Some studies on the space charge effect in field emission.Some individuals studied the space charge effect, and made a few progresses. However, there are still
11、 many problems to be solved.In the studies of volume space charge effect, many people focused on one dimension. 3,4 The results obtained by these methods are far from the real situation. By a careful examination, we found that authors did not take the field-enhancement factor into consideration. In
12、field emission, field-enhancement factor is determined by the shape of field emitter. If only one dimension is considered, the enhancement factor cannot be gotten, and the result obtained is wrong. Someone also used models of three dimensions, but the analysis has something unreasonable 5. There are
13、 still some calculations 6, using models different from what we used in practice work.In study of the discrete space charge effect, professor Tang Tiantong simulated the motion of electron between two flat surfaces 7 . Researchers in Southeast University simulated space charge effect in beam forming
14、 region 8. They both used Monte Carlo method. However, those studies were not for field-emission system.2. Models(1) Model of nanowire 9The model of nanowire is very important since its shape directly determines the field-enhancement factor, which is denoted by P .(I) Definition of field-enhancement
15、 factor:In geometrical configurations resembling a parallel-plate capacitor, the macroscopic field F is defined by the following equation:Where V is the voltage applied across a gap of thickness d. F means the electric field close to the emitting surface (within 1-2 nm of the surface atoms) and dete
16、rmines the current flow of the field-emitted electrons tunnel. F is sometimes called the barrier field and often thousands of times larger than FM . The ration is defined as field-enhancement factor.P = F (4)FM(II) Cause of field-enhancement factors:Various physics causes of the field-enhancement factor exist, but the simplest one is the conducting nanowire on the emitter surface. Image
