Incorporating collisions and resistance into the transition from field emission to the space charge regime regime

In electron emission, emission current increases with surface electric field and causes a buildup in space charge that limits the surface electric field, eventually resulting in a transition from the Fowler-Nordheim (FN) equation to the Child-Langmuir (CL) law at vacuum. Coupling single-particle motion to Poisson’s equation and the conservation of energy, one finds universal curves showing this transition from FN to CL (Y. Y. Lau, Y. Liu, and R. K. Parker, Phys. Plasmas 1, 2082 (1994)). One may also model the transition from CL to Mott-Gurney (MG) at non-vacuum pressures by incorporating electron mobility into a fluid model (M. S. Benilov Plasma Sources Sci. Technol. 18, 014005 (2009).). This presentation combines these approaches to predict the transitions from FN to CL and MG, deriving the condition for a new triple point where the asymptotic equations for FN to CL and CL to MG intersect. This presents the impact of leakage and gap distance on vacuum electronics and the transition to microscale breakdown dynamics, driven by FN. We assess dissipation by introducing an external resistor on these asymptotes and the triple point. The implications on the sensitivity of these transitions on device physics will be discussed.