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arXiv 1605.03473cond-mat.mes-hall
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小型场致发射体阵列/簇的物理静电学

Physical electrostatics of small field emitter arrays/clusters

Richard G. Forbes

摘要:

本文提高了理解静电对小型场发射阵列的尖端场增强因子(AFEF)的影响。使用“发射极板电位浮动球”(FSEPP)模型,重新审视了三个简单的系统相同的柱状发射器的静电和数学。对于隔离发射极,注意到各种方法。只需要考虑球电荷和(分离发射体)镜像电荷的影响。对于2发射系统,公式被发现为“电荷钝化”和“邻场”的影响,为广泛的间隔和“足够紧密的间隔”的发射器。相互电荷钝化总是占主导地位,具有相关的(负的)部分AFEF变化δ_two。对于足够小的发射极间距c,|δ 2|变化为1/c;对于大间距,|δ 2|下降为1/c^3。在三发射极线阵中,存在差分电荷钝化效应和差分邻场效应,但前者占主导地位,并导致“暴露”的外发射极的AFEF(γ_0)高于中心发射极(γ_1)。对于大间距和足够小的间距,找到了曝光比γ =γ_0/γ_1的公式。孤立辐射源的FSEPP模型的精度约为30%。线电荷模型(LCM)是一种替代方案,但最近LCM模型的一个明显的困难。阵列静电学的更好描述可能涉及开发从拉普拉斯方程的精确数值解导出的AFEF的良好拟合方程,也许具有由FSEPP模型结果定性引导的方程形式。在现有的拟合公式中,AFEF的减少随着c的增加呈指数下降,这与FSEPP模型公式不同。FSEPP模型可能会提供一个有用的指导,定性行为的小型场发射体集群大于那些调查。

英文摘要:

This paper improves understanding of electrostatic influences on apex field enhancement factors (AFEFs) for small field emitter arrays. Using the "floating sphere at emitter-plate potential" (FSEPP) model, it re-examines the electrostatics and mathematics of three simple systems of identical post-like emitters. For the isolated emitter, various approaches are noted. On need consider only the effects of sphere charges and (for separated emitters) image charges. For the 2-emitter system, formulas are found for "charge-blunting" and "neighbour-field" effects, for widely spaced and "sufficiently closely spaced" emitters. Mutual charge-blunting is always dominant, with a related (negative) fractional AFEF-change δ_two. For sufficiently small emitter spacing c, |δ_two| varies as 1/c; for large spacing, |δ_two| decreases as 1/c^3. In a 3-emitter linear array, differential charge-blunting and differential neighbor-field effects occur, but the former are dominant, and cause the "exposed" outer emitters to have higher AFEF (γ_0) than the central emitter (γ_1). Formulas are found for the exposure ratio Ξ=γ_0/γ_1, for large and for sufficiently small separations. The FSEPP model for an isolated emitter has accuracy around 30%. Line-charge models (LCMs) are an alternative, but an apparent difficulty with recent LCM models is identified. Better descriptions of array electrostatics may involve developing good fitting equations for AFEFs derived from accurate numerical solution of Laplace's equation, perhaps with equation form(s) guided qualitatively by FSEPP-model results. In existing fitting formulas, the AFEF-reduction decreases exponentially as c increases, which differs from FSEPP-model formulas. FSEPP models might provide a useful guide to the qualitative behaviour of small field emitter clusters larger than those investigated.

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