Theoretical assessment of surface waviness on work function

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.