de Assis Thiago A, Dall'Agnol Fernando F
Instituto de Física, Universidade Federal da Bahia, Campus Universitário da Federação, Rua Barão de Jeremoabo s/n, 40170-115, Salvador, BA, Brazil.
J Phys Condens Matter. 2018 May 16;30(19):195301. doi: 10.1088/1361-648X/aaba9f. Epub 2018 Apr 17.
Numerical simulations are important when assessing the many characteristics of field emission related phenomena. In small simulation domains, the electrostatic effect from the boundaries is known to influence the calculated apex field enhancement factor (FEF) of the emitter, but no established dependence has been reported at present. In this work, we report the dependence of the lateral size, L, and the height, H, of the simulation domain on the apex-FEF of a single conducting ellipsoidal emitter. Firstly, we analyze the error, ε, in the calculation of the apex-FEF as a function of H and L. Importantly, our results show that the effects of H and L on ε are scale invariant, allowing one to predict ε for ratios L/h and H/h, where h is the height of the emitter. Next, we analyze the fractional change of the apex-FEF, δ, from a single emitter, [Formula: see text], and a pair, [Formula: see text]. We show that small relative errors in [Formula: see text] (i.e. [Formula: see text]), due to the finite domain size, are sufficient to alter the functional dependence [Formula: see text], where c is the distance from the emitters in the pair. We show that [Formula: see text] obeys a recently proposed power law decay (Forbes 2016 J. Appl. Phys. 120 054302), at sufficiently large distances in the limit of infinite domain size ([Formula: see text], say), which is not observed when using a long time established exponential decay (Bonard et al 2001 Adv. Mater. 13 184) or a more sophisticated fitting formula proposed recently by Harris et al (2015 AIP Adv. 5 087182). We show that the inverse-third power law functional dependence is respected for various systems like infinity arrays and small clusters of emitters with different shapes. Thus, [Formula: see text], with m = 3, is suggested to be a universal signature of the charge-blunting effect in small clusters or arrays, at sufficient large distances between emitters with any shape. These results improve the physical understanding of the field electron emission theory to accurately characterize emitters in small clusters or arrays.
在评估场发射相关现象的诸多特性时，数值模拟非常重要。在小的模拟域中，已知边界的静电效应会影响发射器计算出的顶点场增强因子（FEF），但目前尚未报道有确定的相关性。在这项工作中，我们报告了模拟域的横向尺寸L和高度H对单个导电椭球形发射器的顶点FEF的依赖性。首先，我们分析顶点FEF计算中的误差ε作为H和L的函数。重要的是，我们的结果表明H和L对ε的影响是尺度不变的，这使得人们能够预测L/h和H/h比值下的ε，其中h是发射器的高度。接下来，我们分析单个发射器[公式：见原文]和一对发射器[公式：见原文]的顶点FEF的分数变化δ。我们表明，由于有限域尺寸导致的[公式：见原文]中的小相对误差（即[公式：见原文]）足以改变函数依赖性[公式：见原文]，其中c是一对发射器之间的距离。我们表明，在无限域尺寸的极限（例如[公式：见原文]）下足够大的距离处，[公式：见原文]服从最近提出的幂律衰减（福布斯2016年《应用物理学杂志》120 054302），而在使用长期确立的指数衰减（博纳尔等人2001年《先进材料》13 184）或哈里斯等人最近提出的更复杂的拟合公式（2015年《美国物理联合会进展》5 087182）时未观察到这种情况。我们表明，对于各种系统，如无限阵列和不同形状发射器的小簇，反三次幂律函数依赖性都成立。因此，建议m = 3时的[公式：见原文]是小簇或阵列中电荷钝化效应的通用特征，在任意形状发射器之间足够大的距离处。这些结果增进了对场电子发射理论的物理理解，以便准确表征小簇或阵列中的发射器。
