Device miniaturization increases the importance of understanding and predicting gas breakdown and electrical discharge thresholds. At gap sizes on the order of ten microns at atmospheric pressure, field emission drives breakdown rather than Townsend avalanche. While numerical and analytical models can demonstrate this transition, a quantitative understanding of the relative importance of each parameter remains unclear. Starting from a universal model for gas breakdown across the field emission and Townsend avalanche regimes [A. M. Loveless and A. L. Garner, Phys. Plasmas 24, 113522 (2017)], this paper applies the concept of error propagation from ionizing radiation measurements to determine the relative impact of each factor on the predicted breakdown voltage. For limits of both large and small products of the dimensionless ionization coefficient, α¯, and gap distance, d¯, the electrode work function has the largest relative effect on the predicted breakdown voltages with a deviation of 50% in the work function resulting in an uncertainty in the calculated breakdown voltage of ∼84% for both α¯d¯≫1 and α¯d¯≪1. This quantifies the significance of nonuniformities in material surfaces and changes in the surface structure during multiple electric field applications and help predict the breakdown voltage for small gaps, motivating better electrode characterization both initially and during repeated operation.

Field emitters and microplasmas often use series resistors to mitigate the rapid increase in current density that reduces device stability. This paper investigates the impact of external resistance on the transition of electron emission mechanism as a function of applied voltage V app , gap distance D, and electron mobility μ. For low μ (high gas pressure), the circuit transitions from Fowler-Nordheim (FN) to space charge limited emission by Mott-Gurney (MG) and Child-Langmuir (CL) before reaching Ohm's law (OL). At higher μ, a triple point arises where the asymptotic solutions for FN, MG, and CL intersect. This triple point is uniquely defined by D, μ, or gap voltage V g while also defining a specific gap impedance Z tp . When R ≤ Z tp , the electron emission transitions from FN to MG to CL to OL with increasing V app while MG and CL are bypassed at higher R. For a given R, increasing the applied voltage or emission current causes the gap to appear as a short.INDEX TERMS Electron emission, plasma devices, space-charge effect.

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