<p>Dielectric breakdown in gases is an important criterion for device reliability when designing various electronic devices such as sensors, medical plasma jets and fusion applications. As devices become smaller and more compact, microscale gap distances need to be considered and Paschen’s law, which dictates typical breakdown behavior when electron avalanche dominates, fails. The stronger electric fields for microscale gaps induce field emission, which generates additional electrons that further enhance the electric field at the cathode and the resulting secondary emission to reduce breakdown voltages below those predicted by Paschen’s law. Field emission is governed by the Fowler-Nordheim equation, which mathematically describes the quantum tunneling that occurs. Many studies have examined breakdown voltage in the Paschen’s and field emission regimes but recent theories have unified the two regimes for DC gas breakdown at microscale gaps [A. L. Garner, A. M. Loveless, J. N. Dahal, and A. Venkattraman (2020)]. However, although microwave and RF fields are used in many microelectronics systems and microplasmas, they have been less studied. This thesis derives a breakdown condition that unifies avalanche and field emission for RF fields. The derivation includes analysis of potential secondary emission representations for AC fields. The breakdown condition is then benchmarked to simulations that accounts for both avalanche and field emission for user-defined AC fields.</p> <p>We use a modified version of XPDP1, which is a one-dimensional in space and three-dimensional in velocity (1D/3v) particle-in-cell (PIC) code that incorporates field emission. The resulting breakdown depends on several parameters, most notably gap size d, pressure p and frequency f. We determine breakdown voltages in terms of d and pd scalings for 1-10 𝜇m gap distances, 10-1000 GHz frequencies, and 180-760 Torr pressures. Additional scalings that were studied include the work function, field enhancement factor, secondary emission, and ionization coefficients. PIC demonstrated that the breakdown voltage varied linearly with gap distance up to ~4 𝜇m from DC to 10 GHz for a secondary electron emission coefficient 𝛾𝑆𝐸=0.05. For DC fields, the breakdown voltage decreases with increasing gap distance; the breakdown voltage increases with increasing frequency, approaching linearly with increasing gap distance.</p>