A New Universal Gas Breakdown Theory for Classical Length Scales

While Paschen’s law is commonly used to predict breakdown voltage, it fails at microscale gaps when field emission becomes important. Accurate breakdown voltage predictions at microscale are even more important as electronic device dimensions decrease. Developing analytic models to accurately predict breakdown at microscale is vital for understanding the underlying physics occurring within the system and to either prevent or produce a discharge, depending on the application. We first take a pre-existing breakdown model coupling field emission and Townsend breakdown and perform a matched asymptotic analysis to obtain analytic equations for breakdown voltage in argon at atmospheric pressure. Next, we extend this model to generalize for gas and further explore the independent contributions of field emission and Townsend discharge. Finally, we present analytic expressions for breakdown voltage valid for any gas at any pressure, and discuss the modified Paschen minimum at microscale. The presented models agree well with numerical simulations and experimental data when using the field enhancement factor as a fitting parameter. The work presented in this thesis is a first step in unifying gas breakdown across length scales and breakdown mechanisms. Future work will aim to incorporate other breakdown mechanisms, such as quantum effects and space charge, to provide a more complete unified model for gas breakdown