Calculations of Work Function as a Function of Surface Roughness Period and Shape

Abstract

Because of its importance in surface electrical, chemical, and physical behavior, characterizing work function is paramount in nanotechnology and microscale gas breakdown. A sensitivity analysis of microscale gas breakdown theory demonstrated that work function (WF) and field enhancement played the largest role in influencing gas breakdown voltage when field emission dominated breakdown [1]. The WF used in these theories is typically for a flat surface; however, really electrodes may exhibit surface roughness that causes variations in WF. Previous theoretical studies using a scanning Kelvin probe (SKP)-based mathematical model demonstrated that the measured WF for a surface with sinusoidal surface roughness may differ from the WF for a perfectly smooth surface [2]. However, this model never explicitly addressed the periodicity of the surface roughness, which may become important for very small devices where the SKP step size may be on the order of the surface roughness period or, for breakdown experiments, the periodicity may influence the effective WF near the discharge area. Extending the theory to explicitly consider triangular defects and sine-squared defects shows that the period and constant presence of surface roughness, rather than the precise surface roughness topology, drives WF behavior. Potential applications of the model, such as incorporating it into a universal theory or particle simulations for gas breakdown [3] and further examining nanoscale devices will be discussed.