Electron Emission and Gas Breakdown from Schrodinger’s Equation to Paschen’s Law

Historically, gas breakdown has been predicted by Paschen’s law; however, deviations from Paschen’s law characterized by the absence of a minimum breakdown voltage arise due to field emission. Recently derived universal, closed form equations predict breakdown voltage from field emission to the classical Paschen’s law for gap distances above the electron mean free path and below the transition to streamer discharge (A. M. Loveless and A. L. Garner, Phys. Plasmas, 24, 113522 (2017).). Continuing reduction in devices sizes motivates assessing the impact of gap size and device pressure for submicroscale gaps. This study extends the previous theory by defining common scaling parameters to derive universal relationships for the transition from field emission to the Child-Langmuir law and from the Child-Langmuir law to Schrodinger’s equation as we reduce gap distance. We report the resulting gap sizes corresponding to each transition up to the classical, universal Paschen’s law as a function of pressure. The implications of these transitions and implications of nanoscale features on this behavior will be discussed.