Large area field electron emitters, typically consisting of several thousands of nanotips, pose a major challenge since numerical modeling requires enormous computational resources. We propose a hybrid approach where the local electrostatic field enhancement parameters of an individual emitter are determined numerically while electrostatic shielding and anode-proximity effects are incorporated using recent analytical advances. The hybrid model is tested numerically on an ordered arrangement of emitters and then applied to recent experimental results on randomly distributed gold nanocones. Using the current-voltage data of two samples with vastly different emitter densities but having similar nanocone sizes, we show that an appropriate modeling of the emitter apex together with the analytical results on shielding and anode-proximity effects leads to consistent results for the apex radius of curvature. In both cases, the I − V data are approximately reproduced for R a ≃ 9 nm. Importantly, it is found that anode-proximity plays a significant role in counter-balancing electrostatic shielding, and ignoring this effect results in the requirement of a much smaller value of R a.

中文翻译：

---

大面积场发射器建模的混合方法

大面积场电子发射器通常由数千个纳米尖端组成，这是一项重大挑战，因为数值建模需要大量的计算资源。我们提出了一种混合方法，其中单个发射器的局部静电场增强参数是通过数值确定的，同时使用最新的分析进展将静电屏蔽和阳极接近效应结合起来。该混合模型在发射器的有序排列上进行了数值测试，然后应用于最近关于随机分布的金纳米锥的实验结果。使用发射极密度大不相同但纳米锥尺寸相似的两个样品的电流-电压数据，我们表明，发射器顶点的适当建模以及屏蔽和阳极邻近效应的分析结果会导致顶点曲率半径的结果一致。在这两种情况下，I - V 数据在 R a ≃ 9 nm 时近似再现。重要的是，发现阳极邻近在平衡静电屏蔽中起着重要作用，忽略这种影响会导致需要更小的 R a 值。