Electrostatic shielding is an important consideration for large area field emitters (LAFEs) and results in a distribution of field enhancement factors even when the constituent emitters are identical. Ideally, the mean and variance together with the nature of the distribution should characterize a LAFE. In practice, however, it is generally characterized by an effective field enhancement factor obtained from a linear fit to a Fowler–Nordheim plot of the $\mathrm{I}-\mathrm{V}$ data. An alternate characterization is proposed here based on the observation that for a dense packing of emitters, shielding is large and LAFE emission occurs largely from the periphery, while well separated emitter tips show a more uniform or two-dimensional emission. This observation naturally leads to the question of the existence of an emission dimension, $D_e$, for characterizing LAFEs. We show here that the number of patches of size $L_P$ in the ON-state (above average emission) scales as $N(L_P)\sim L_P^{-D_e}$ in a given LAFE. The exponent $D_e$ is found to depend on the applied field (or voltage) and approaches $D_e=2$ asymptotically.

中文翻译：

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大面积场发射器的缩放和发射尺寸

静电屏蔽是大面积场发射器 (LAFE) 的重要考虑因素，即使组成发射器相同，也会导致场增强因子的分布。理想情况下，均值和方差以及分布的性质应该是 LAFE 的特征。然而，在实践中，它的特征通常是通过对 Fowler-Nordheim 图的线性拟合获得的有效场增强因子。$\mathrm{一世}-\mathrm{伏}$数据。基于以下观察，这里提出了另一种表征，即对于发射器的密集封装，屏蔽很大并且 LAFE 发射主要发生在外围，而分离良好的发射器尖端显示出更均匀或二维的发射。这种观察自然会引出发射维度是否存在的问题，$D_{\mathrm{电子}}$，用于表征 LAFE。我们在这里展示了大小补丁的数量${升}_{磷}$ 在 ON 状态（高于平均发射）比例为 $N({升}_{磷})～{升}_{磷}^{-D_{\mathrm{电子}}}$在给定的 LAFE 中。指数$D_{\mathrm{电子}}$ 发现取决于施加的场（或电压）和方法 $D_{\mathrm{电子}}=2$ 渐近地。