Simulation of Dual Frequency Capacitive Sheath over a Concave Electrode in Low Pressure

A self-consistent two-dimensional (2D) collisionless fluid model is developed to simulate the characteristics of a dual frequency capacitive sheath over an electrode with a cylindrical hole. The model consists of 2D time-dependent fluid equations coupled with Poisson's equation, in which the low-frequency (LF) and high-frequency current sources are applied to an electrode. Thus, the so-called equivalent circuit model coupling with the fluid equations will be able to self-consistently determine the relationship between the instantaneous voltage on the powered electrode and the sheath thickness. The time-averaged potential, electric field, ion density in the sheath and ion energy distributions at the bottom of the hole are calculated and compared for different LF frequencies. The results show that the LF frequency is crucial for determining the sheath structure. The existence of the cylindrical hole on the electrode obviously affects the sheath profile in the parallel to the electrode and makes the sheath profile tend to adapt the contours of the electrode, which is the plasma molding effect.