The work function may affect the physical, electrical, and chemical behavior of surfaces, making it important for numerous applications and phenomena, including field emission, gas breakdown, and nanotechnology. Despite this importance, studies examining the impact of surface roughness on the work function have only examined the amplitude and not the period of the waviness, which becomes increasingly important with reduced device size. This paper extends these previous scanning Kelvin probe (SKP)-based mathematical models for predicting the work function of a metallic surface with surface waviness by explicitly including the period. For a given ratio of surface roughness amplitude to the distance from the SKP to the center of the waviness, increasing the period or reducing the SKP step distance reduced the surface’s effective work function. In the limit of infinite period (or low SKP step size) and low surface roughness amplitude, the work function approached that expected with a concomitant reduction in the gap distance with no surface roughness. The effective surface work function approaches zero and may become negative as the SKP tip approaches the surface, suggesting the importance in these corrections for nanoscale measurements. As the SKP step size approaches the surface roughness period, the effective work function becomes infinitely large. Implications of these results on gas breakdown, field emission, and nanoscale device design will be discussed.

中文翻译：

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功函数上表面波纹度的理论评估

功函数可能会影响表面的物理，电气和化学行为，因此对于众多应用和现象（包括场发射，气体击穿和纳米技术）来说非常重要。尽管具有这种重要性，但研究表面粗糙度对功函数的影响的研究仅研究了振幅，而不是起伏的周期，随着器件尺寸的减小，起伏变得越来越重要。本文扩展了这些以前的基于扫描开尔文探针（SKP）的数学模型，用于通过明确包括周期来预测具有表面波纹度的金属表面的功函数。对于给定的表面粗糙度振幅与从SKP到波纹中心的距离的比率，增加周期或减小SKP步距会降低表面的有效功。在无限周期（或低SKP步长）和低表面粗糙度幅度的限制下，功函数接近预期值，同时间隙距离减小而没有表面粗糙度。有效的表面功函数接近零，并且随着SKP尖端接近表面而可能变为负值，这表明在这些校正中对纳米级测量非常重要。随着SKP步长接近表面粗糙度周期，有效功函数将变得无限大。将讨论这些结果对气体击穿，场发射和纳米级器件设计的影响。有效的表面功函数接近零，并且随着SKP尖端接近表面而可能变为负值，这表明在这些校正中对纳米级测量非常重要。随着SKP步长接近表面粗糙度周期，有效功函数将变得无限大。将讨论这些结果对气体击穿，场发射和纳米级器件设计的影响。有效的表面功函数接近零，并且随着SKP尖端接近表面而可能变为负值，这表明在这些校正中对纳米级测量非常重要。随着SKP步长接近表面粗糙度周期，有效功函数将变得无限大。将讨论这些结果对气体击穿，场发射和纳米级器件设计的影响。