Theoretical study of scaling law for electron kinetics in field emission-driven microplasmas in the pre-breakdown regime

For microplasmas with a characteristic length less than 10 microns, field emission can be an important process that affects Townsend pre-breakdown regime. In this regime the electron kinetics fail to scale with the reduced electric field E/p (or E/N) due to some population of the electrons behaving ballistically or near-ballistically. This non-collisionality has been considered in a pseudo-analytical expression for the electron energy distribution (EED) that shows that the EED scales with three independent parameters -- pd (collisionality), V (voltage drop across gap) and E/p. As a result the reaction rate coefficients also scale with these parameters. The model is validated using 1D particle-in-cell/Monte Carlo collision (PIC/MCC) simulations. The theory provides new scaling in pre-breakdown field emission-driven microplasmas, and a relatively simple model for identifying operating conditions for plasma chemical processes, encouraging new ideas for controlling plasma chemistry at microscales.