Two-dimensional model of a capacitively coupled rf discharge and comparisons with experiments in the Gaseous Electronics Conference reference reactor

We present results from a two-dimensional (2D) numerical fluid model of rf discharges in conditions close to recently published measurements of the spatial distribution of plasma density in the Gaseous Electronic Conference reference cell. The discharge is in pure argon at pressures in the 100 mtorr range, frequency 13.56 MHz, and rf voltage amplitudes on the order of 100 V. The model is based on solutions of the continuity, momentum (drift-diffusion), and energy equations for the electrons, continuity, and drift-diffusion equation for positive ions, coupled with the Poisson equation. The results of the model are qualitatively and quantitatively in good agreement with the experiments. The model predicts a maximum of plasma density off axis, as in the experiment. The ion current density on the electrode is also nonuniform, and increases radially in the conditions of the experiments. The effects of the rf voltage, pressure, and reactor geometry (electrode dimensions, gap length, guard rings, etc.) on the plasma properties and on the uniformity of the ion current on the powered electrode are also discussed. It is shown that the existence of a maximum of plasma density in the radial direction, in the conditions of the experiment, is due to the small value of the electrode spacing. The results show that the harmonic content of the discharge current is also geometry dependent. The comparisons show that 2D, three-moment fluid models can accurately describe the discharge and the effects of the chamber geometry on the plasma properties for pressure above the limit where collisionless electron heating does not play a significant role.