Transitions in Electron Emission and Gas Breakdown from Nanoscale to Microscale

The miniaturization of electronic devices requires a deeper understanding of electron emission and gas breakdown dynamics at nano- and microscales. Micro- and nanoelectromechanical systems (MEMS and NEMS, respectively) for sensing and scanning, microplasma applications, and directed energy devices require an accurate characterization of electron emission behavior for accurate predictions of device behavior. While breakdown has historically been predicted by Paschen’s law—driven by Townsend avalanche processes—this fails as gap distance decreases to the point where field emission (FE) become relevant. Further decreasing gap distance makes electron emission space-charge-limited as defined by the Child- Langmuir law (CSCL) at vacuum, the Mott-Gurney law (MG) if collisions contribute, or quantum space charge behavior (QSCL) at nanoscales when Schrodinger’s wave equation must be used to consider single particle effects. This study nondimensionalizes the governing equations defining these underlying phenomena to identify transition points between them and understand the underlying physics dominating the emission behavior in these regimes to aid device design and experimental setup. A sample case theorizes a nexus occurring between all emission mechanisms at a pressure of approximately 1780 Torr, a gap distance of 62 nm, and an applied voltage of 6 V. Additionally, we discuss the implications of work function and surface roughness on these behaviors.