Modelling of a low-pressure argon breakdown in combined fields

This paper reports the results of the detailed theoretical and Simulation study of the dependence of the breakdown voltage on the product of the gas pressure and the electrode separation (pd) under the simultaneous application of radio-frequency (rf) and dc fields. Calculations were performed by using a one-dimensional particle-in-cell/Monte Carlo collision code with three velocity components with a new secondary emission model. Our simulation results show that in combined discharges during breakdown an ambiguity region of the left-hand branch of the breakdown curve appears not only by increasing the rf voltage but also by decreasing it. In other words, with lowering of the pressure, the rf voltage first decreases and passes through an inflection point and a minimum on the breakdown curve and then it grows and approaches the turning point on the breakdown curve. In addition, simulation results are also compared with the theoretical predictions based on the phenomenological method. Analytical expressions for the rf breakdown voltage with a superimposed weak dc electric field corresponding to the minimum, to,the inflection point and to the turning point on the breakdown curve have been derived.