Fundamental properties of field emission-driven direct current microdischarges

Abstract

For half a century, it has been known that the onset of field emission in direct current microdischarges with gap sizes less than 10 μm can lead to breakdown at applied voltages far less than predicted by Paschen's law. It is still unclear how field emission affects other fundamental plasma properties at this scale. In this work, a one-dimensional fluid model is used to predict basic scaling laws for fundamental properties including ion density, electric field due to space charge, and current-voltage relations in the pre-breakdown regime. Computational results are compared with approximate analytic solutions. It is shown that field emission provides an abundance of cathode electrons, which in turn create large ion concentrations through ionizing collisions well before Paschen's criterion for breakdown is met. Breakdown due to ion-enhanced field emission occurs when the electric field due to space charge becomes comparable to the applied electric field. Simple scaling analysis of the 1D Poisson equation demonstrates that an ion density of n+ ≈ 0.1VAε0/qd2 is necessary to significantly distort the electric field. Defining breakdown in terms of this critical ion density leads analytically to a simple, effective secondary emission coefficient γ′ of the same mathematical form initially suggested by Boyle and Kisliuk [Phys. Rev. 97, 255 (1955)].