Effect of microscale gas discharges on thermo-field emission current

It has been shown that cold field emission can be an important electron source in microscale discharges. However, if the cathode is heated to a high temperature, thermal emission is initiated, which impacts microscale discharge formation. In both cold and thermal conditions, ionization in the discharge can create sufficient space charge to impact the emission current. In this work, we use a two-fluid plasma model to evaluate the impact of thermal emission on microscale discharge properties. We solve for the electron and ion concentrations between the electrodes, accounting for electron-impact ionization, and self-consistently solve Poisson's equation for the voltage. We incorporate two thermal emission models - the `low field' Schottky emission, and the `high field' thermo-field emission model - in order to accurately predict thermal emission in the microdischarge under different conditions. We evaluate the effect of electron impact ionization on the thermal emission in a microdischarge and find that since there is net positive space charge near the cathode, emission current increases. Furthermore, this ion enhancement increases if either the applied voltage or the cathode temperature is increased. The enhanced emission causes gaseous breakdown to occur at significantly lower voltages than predicted by the classic Paschen's curve or the more recent modified Paschen's curve that also accounts for cold field emission.