Theoretical analysis of field electron emission must consider many parameters, one of the most critical being the field enhancement factor (FEF). In a single tip form, the FEF can vary several orders of magnitude and depends only on the system geometry, when the gap length between the emitter and counter-electrode is much greater than the height of the emitter. In this work, we determine very accurate analytical expressions for the FEF of five emitters with various shapes, which are often considered in the literature: Ellipsoidal, Hemisphere-on-Cylindrical post, Hemisphere-on-Orthogonal cone, Paraboloidal, and Hyperboloidal. We map the FEF as a function of the aspect ratio with an error smaller than 2% to serve as a quick reference database. Additionally, we calculate the electric field distribution over the emitters, which can give an insight into the effective notional emission area and the influence of the emitter’s base.

中文翻译：

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确定数值精度高的各种场电子发射器的场增强因子

场电子发射的理论分析必须考虑许多参数，其中最关键的一个是场增强因子（FEF）。当发射极和反电极之间的间隙长度远大于发射极的高度时，FEF可以单尖端形式变化几个数量级，并且仅取决于系统几何形状。在这项工作中，我们确定了五个形状各异的发射器的FEF的非常精确的解析表达式，这些表达式在文献中经常被考虑：椭圆形，圆柱半球，正交圆锥半球，抛物面和双曲面。我们将FEF映射为纵横比的函数，误差小于2％，以用作快速参考数据库。此外，我们计算了发射器上的电场分布，