Abstract When the radius of curvature R of an electron emitter is below 5 nm existing theories of field emission from curved surfaces fail because they assume a constant supply of electrons which is a characteristic only of planar surface emitters. In a previous work of ours we proved that the eigenfuctions of a rotationally symmetric parabolic emitter-the common shape of present nanoscopic emitters- are Whittaker functions and exhibit strong localization. In this paper we calculate the transmitted current density of such an emitter as a function of angle of emission θ and R. The angular dependence of the emitted current density is not very different from that of the classical model of a hemisphere on a post. However, when use is made of the parabolic image potential it is observed that the emission falls significantly. Finally, strongly non-linear Fowler-Nordheim plots are obtained. The significance of this is discussed.

中文翻译：

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纳米抛物面发射器的场发射

摘要 当电子发射器的曲率半径 R 小于 5 nm 时，现有的曲面场发射理论将失败，因为它们假定电子源是恒定的，而这只是平面发射器的特性。在我们之前的工作中，我们证明了旋转对称抛物线发射器的特征函数——目前纳米级发射器的常见形状——是 Whittaker 函数并且表现出很强的局部化。在本文中，我们将这种发射器的透射电流密度计算为发射角 θ 和 R 的函数。发射电流密度的角度依赖性与柱子上半球的经典模型的角度依赖性没有很大不同。然而，当使用抛物线图像势时，观察到发射显着下降。最后，获得了强非线性 Fowler-Nordheim 图。讨论了这一点的重要性。