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首页> 外文期刊>Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures >Thin-slab model for field electron emission
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Thin-slab model for field electron emission

机译：场电子发射的薄板模型

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The elementary Fowler–Nordheim-type (FN-type) equation is often used to describe cold field electron emission (CFE) from carbon nanotubes (CNTs) including closed single-walled CNTs of small apex radius. FN-type equations were originally derived to describe CFE from the conduction band of a bulk metal with a flat surface and use a “flat thick-slab” potential-energy model. This article identifies many theoretical difficulties with using FN-type equations to describe CFE from CNTs. The most serious arise because a closed CNT apex is one-atom thick and can be sharply curved. This article explores a flat thin-slab model for CFE and derives an emission current equation. The model is parametrized using graphene data. The main conclusions are that (a) the occupied parts of electronic subbands probably do not overlap so CFE would come from a single subband; (b) an electron at the Fermi level has large momentum and kinetic energy parallel to the slab surface; (c) a clear conceptual distinction must be made between local thermodynamic work function (Φ) and the zero-field height of the tunneling barrier for a Fermi-level electron; (d) for the thin-slab model, this zero-field barrier height is equal (at 0 K) to Φ+ξf, where ξf is the occupied width of the subband at 0 K; and (e) the emission onset field, for a current density of 1000 A/m2, is estimated as around 9 Vm. The relevance of these conclusions to emission from closed single-walled CNTs is considered. The predicted onset field for a thin-slab model is significantly higher than that predicted by the elementary FN-type equation (around 3.5 Vm), so attempts should be made to measure onset field accurately for CFE from closed CNTs. In practice, with closed CNTs, it might be more favorable for emission to occur from quasiatomic-n-n or quasimolecular localized states rather than a subband; in this case, the question of how these states are supplied arises. More generally, this work draws attention to the need, with thin emitters, to consider issues relating to how the direction of electron motion prior to emission affects the mechanism of emission and the emission probability.
机译：基本的Fowler-Nordheim型（FN型）方程通常用于描述碳纳米管（CNT）的冷场电子发射（CFE），这些碳纳米管包括具有小顶点半径的封闭单壁CNT。最初使用FN型方程式来描述具有平坦表面的块状金属的导带中的CFE，并使用“平坦厚板”势能模型。本文指出了使用FN型方程式描述CNT中CFE的许多理论困难。最严重的出现是因为封闭的CNT顶点只有一个原子的厚度，并且可以急剧弯曲。本文探讨了CFE的扁平薄板模型，并推导了发射电流方程。使用石墨烯数据对模型进行参数化。主要结论是：（a）电子子带的占用部分可能不会重叠，因此CFE将来自单个子带； （b）费米能级的电子具有平行于平板表面的大动量和动能； （c）在费米能级电子的局部热力学功函数（Φ）和隧穿势垒的零场高度之间必须有明确的概念区别； （d）对于薄板模型，该零场势垒高度等于（在0 K时）等于Φ+ξf，其中ξf是在0 K时子带的占用宽度； （e）对于1000 A / m2的电流密度，发射起始场估计约为9 V / nm。考虑了这些结论与封闭单壁碳纳米管排放的相关性。薄板模型的预计起始场明显高于基本FN型方程式的预测场（约3.5 V / nm），因此应尝试从封闭的CNT准确测量CFE的起始场。在实践中，对于封闭的CNT，从准原子n-n或准分子局部状态而不是子带发生发射可能会更有利。在这种情况下，出现了如何提供这些状态的问题。更一般而言，这项工作引起了人们的注意，对于薄发射器，需要考虑与发射前电子运动方向如何影响发射机理和发射概率有关的问题。

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