An ab initio approximation for the modified Paschen's curve for breakdown in microscale electrode gaps

D. Go, R. Tirumala
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Abstract

Summary form only given. Over the past decade, the nature of breakdown in microscale electrode gaps has begun receiving significant attention both because of the potential impact breakdown could have on MEMS devices and as the development of plasma devices trends to smaller and smaller scales. It has been shown that the traditional description of breakdown called Paschen's curve holds true for larger electrode gaps, in the range of approximately 3-15 u m, breakdown deviates significantly from this form. It is now generally accepted that electron field emission is the physical mechanism that causes this deviation to form the so-called modified Paschen's curve. While a simple mathematical formulation exists for Paschen's curve, there is no simple formulation for modified Paschen's curve. A form that includes the effect of ion-enhanced field emission has been previously suggested, but this form relies heavily on a fitting factor. In this work, the underlying physics and parameters of the fitting factor are investigated to formulate an ab initio form of the modified Paschen's curve. This formulation includes the factors of the Fowler-Nordheim equation, and an electrostatics approximation for the impact an ion approaching the cathode has on the electric field. The implications of this approximation, how well it compares to experimental data, and how it may be used for parameteric design are all discussed.
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微尺度电极间隙击穿的修正Paschen曲线的从头近似
只提供摘要形式。在过去的十年中,微尺度电极间隙击穿的性质已经开始受到极大的关注,因为击穿可能对MEMS器件产生潜在的影响,并且随着等离子体器件的发展趋势越来越小。研究表明,传统的称为Paschen曲线的击穿描述适用于较大的电极间隙,在大约3-15 μ m的范围内,击穿明显偏离这种形式。现在普遍认为,电子场发射是导致这种偏差形成所谓修正Paschen曲线的物理机制。对于Paschen曲线,存在一个简单的数学公式,但对于修改后的Paschen曲线,没有一个简单的公式。一种包含离子增强场发射效应的形式已经被提出,但是这种形式在很大程度上依赖于一个拟合因子。在这项工作中,研究了拟合因子的基本物理特性和参数,以制定修改的Paschen曲线的从头开始形式。该公式包括Fowler-Nordheim方程的因素,以及接近阴极的离子对电场的影响的静电近似。讨论了这种近似的含义,它与实验数据的比较,以及如何将其用于参数化设计。
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