Unification of Gas Breakdown and Electron Emission

The miniaturization of technologies requires a deeper understanding of gas breakdown and electron emission at micro- and nanoscales. Previous work [A. M. Loveless and A. L. Garner, Phys. Plasmas, 24, 113522 (2017).] analytically unified Paschen’s law (PL) for Townsend avalanche with field emission (FE) to show continuous reduction in breakdown voltage with decreasing gap size. Another study [G. Meng, et al., Phys. Plasmas, 25, 082116 (2018).] demonstrated this behavior experimentally and derived an analytic solution with a linear relationship between breakdown voltage and gap size in the field emission-Townsend regime. Further reductions in gap size result in the transitions to space-charge limited emission (SCLE). This paper assesses the transitions between FE and the Mott-Gurney (MG) law for collisional SCLE, MG to the Child-Langmuir (CL) law for vacuum SCLE, and CL to quantum scales with Schrödinger’s equation. These derivations yield a triple point, where FE, MG, and CL predict a common breakdown voltage at a specific gap size and pressure. The implications of these transitions will be discussed.