Electric field enhancement due to a saw-tooth asperity in a channel and implications on microscale gas breakdown

The electric field enhancement due to an isolated saw-tooth asperity in an infinite channel is considered with the goal of providing some inputs to the choice of field enhancement factors used to describe microscale gas breakdown. The Schwarz-Christoffel transformation is used to map the interior of the channel to the upper half of the transformed plane. The expression for the electric field in the transformed plane is then used to determine the electric field distribution in the channel as well as field enhancement near the asperity. The effective field enhancement factor is determined and its dependence on operating and geometrical parameters is studied. While the effective field enhancement factor depends only weakly on the height of the asperity in comparison to the channel, it is influenced significantly by the base angles of the asperity. Due to the strong dependence of field emission current density on electric field, the effective field enhancement factor (β_eff) is shown to vary rapidly with the applied electric field irrespective of the geometrical parameters. This variation is included in the analysis of microscale gas breakdown and compared with results obtained using a constant β_eff as is done traditionally. Even though results for a varying β_eff may be approximately reproduced using an equivalent constant β_eff independent of E-field, it might be important for a range of operating conditions. This is confirmed by extracting β_eff from experimental data for breakdown in argon microgaps with plane-parallel cathodes and comparing its dependence on the E-field. While the use of two-dimensional asperities is shown to be a minor disadvantage of the proposed approach in its current form, it can potentially help in developing predictive capabilities as opposed to treating β_eff as a curve-fitting parameter.