Keywords:
capacitively coupled plasma discharge under RF and DC voltage in 2D cylindrical system.
The capacitively coupled plasma (CCP) is one of the most common types of industrial plasma sources. These plasma discharges typically take place between metal electrodes in a reaction chamber and are driven by a radio frequency (RF) or direct current (DC) power supply. The plasma is sustained by ohmic heating in the main body and stochastic heating through the capacitive sheath.
This example demonstrates the generation of a capacitively coupled plasma inside an axially symmetric reaction chamber with a 50 mm radius and 50 mm length. The top and side walls are grounded at zero potential. A target located at the bottom of the chamber is connected to a 60 MHz AC voltage source at 200 V. There is a small gap of 5 mm between the target and the grounded wall. The chamber is filled with a background gas of Argon at about 0.005 Torr \(\left(2.0 \times 10^{20} \ \text{m}^{-3}\right)\). An initial spatially averaged electron density of \(5 \times 10^{11} \ \text{m}^{-3}\) is seeded to start the discharge. Note that the particle position (and hence density) is chosen in such a way that the density increases as R increases. Therefore, the initial density is less than \(5 \times 10^{11} \ \text{m}^{-3}\) for small values of R and greater than \(5 \times 10^{11} \ \text{m}^{-3}\) for larger values of R.
This simulation can be performed with a VSimPD license.
The Capacitively Coupled Plasma 2D example is accessed from within VSimComposer by the following actions:
The basic variables of this problem should now be alterable via the text boxes in the left pane of the Setup Window, as shown in figure Fig. 453.
The self-consistent electric field is solved from Poisson’s equation by an electrostatic solver in cylindrical coordinates. Time-dependent Dirichlet boundary conditions are used to set up the boundaries of electric fields around the reaction chamber walls.
The plasma is simulated with macroparticles which are moved using the Boris pusher in cylindrical coordinates. Various types of elastic and inelastic collisions of the particles are calculated.
The Setup Window has various parameters available for easy manipulation including the density of the argon background gas (DENSITY_Ar), the voltage (VOLTAGE), and the frequency (FREQ).
Once finished with the problem setup, continue as follows:
After performing the above actions, continue as follows:
To plot the potential:
With a time-step of \(10^{-11}\) seconds, running this simulation for the default 200 time-steps will only capture part of the first oscillation. With the frequency set to \(6\times 10^7\) Hz, the oscillation period is \(1.667\times 10^{-8}\) seconds, which corresponds to 1,667 time-steps. To see the approximate steady-state behavior of this example, set the number of time-steps to 10,000 or more and restart or re-run the simulation. When running in parallel on 4 processors, this should take approximately two hours to complete.
After \(5\times 10^{-8}\) seconds, or 500 dumps, the plasma sheath starts to exhibit oscillating steady-state behavior. To view the behavior of the oscillating plasma sheath, take the following steps:
-0.0005
, then select “Fix Maximum” and set the Maximum to 0.0005
(or experiment with minimum and maximum values for best results) and click OKAfter 250 time-steps, the plasma density should appear as shown in Fig. 456. The green areas at approximately zero charge density denote the quasi-neutral plasma bulk, while the red areas (positive charge density) denote the non-neutral plasma sheath.
To view the plasma sheath potential profile, take the following steps:
The electric potential as well as the axial potential profile should now be visible as shown in Fig. 457. Move the slider to the right to see how the plasma sheath potential oscillates in time.