A self-consistent hybrid model of a dual frequency sheath: Ion energy and angular distributions

Abstract

This paper presents a self-consistent hybrid model including the fluid model which can describe the characteristics of collisional sheaths driven by dual radio-frequency (DF) sources and Monte Carlo (MC) method which can determine the ion energy and angular distributions incident onto the dual rf powered electrode. The charge-exchange collisions between ions and neutrals are included in the MC model in which a self-consistent instantaneous electric field obtained from the fluid model is adopted. In the simulation, the driven method we used is either the current-driven method or the voltage-driven method. In the current-driven method, the rf current sources are assumed to apply to an electrode, which is the so-called the equivalent circuit model and is used to self-consistently determine the relationship between the instantaneous sheath potential and the sheath thickness. In the voltage-driven method, however, the rf voltage sources are assumed to apply to an electrode. The dual rf sheath potential, sheath thickness, ion flux, ion energy distributions (IEDs), and ion angular distributions (IADs) are calculated for different parameters. The numerical solutions show that some external parameters such as the bias frequency and power of the lower-frequency source as well as gas pressure are crucial for determining the structure of collisional dual rf sheaths and the IEDs. The shapes of the IADs, however, are determined mainly by the gas pressure. Furthermore, it is found that the results from the different driven methods behave in the same way although there are some differences in some quantities.