1D Capacitive Plasma Chamber (capacitivelyCoupledPlasma1DT.pre)

Keywords:

CCP discharge, secondary emission, elastic collision, excitation, ionization.

Problem description

The capacitively coupled plasma (CCP) is one of the most common types of industrial plasma sources. The discharges usually take place between metal electrodes in a reaction chamber and are driven by a radio-frequency (RF) or DC power supply. The plasma is sustained by ohmic heating in the main body and stochastic heating through a capacitive sheath.

This example demonstrates the generation of a capacitively coupled plasma inside two parallel conducting plates separated by 0.05 m. A background Ar neutral gas at approximately 6 mTorr \(\left(2.0 \times 10^{20} \ m^{-3}\right)\) is filled between the electrodes. The right electrode is grounded, while the left one is connected to a voltage source of 200 V at 60 MHz.

This simulation can be performed with a VSimPD license.

Opening the Simulation

The 1D Capacitively Coupled Plasma Discharge example is accessed from within VSimComposer by the following actions:

  • Select the NewFrom Example… menu item in the File menu.
  • In the resulting Examples window, expand the VSim for Plasma Discharges option.
  • Expand the Capacitively Coupled Plasmas (text-based setup) option.
  • Select “1D Capacitive Plasma Chamber (text-based setup)” and press the Choose button.
  • In the resulting dialog, create a New Folder if desired, and press the Save button to create a copy of this example.

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 Fig. 468.

image 1

Fig. 468 Setup Window for the 1D Capacitively Coupled Plasma Discharge example.

The time step DT should sufficiently resolve the plasma frequency and collision frequency. The default time step used in this example is TIMESTEP_FACTOR * (0.1 / Plasma frequency) to ensure stability. The initial primary electrons are gradually loaded into the simulation domain over a period of LOADSTEPS timesteps, which has a default value of 5000.

Input File Features

The self-consistent electric field is solved from Poisson’s equation by the 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 represented by macroparticles which are moved using the Boris pusher in cylindrical coordinates. Various types of elastic and inelastic collisions of the particles are calculated.

Running the simulation

After performing the above actions, continue as follows:

  • Proceed to the Run Window by pressing the Run button in the left column of buttons.
  • To run the file, click on the Run button in the upper left corner of the Logs and Output Files pane. You will see the output of the run in this pane. The run has completed when you see the output, “Engine completed successfully.” This is shown in the window Fig. 469 below.
image 1

Fig. 469 The Run Window at the end of execution.

Visualizing the results

After performing the above actions, continue as follows:

  • Proceed to the Visualize Window by pressing the Visualize button in the left column of buttons.

The ion, primary electron, and secondary electron particle number histories can be shown as in Fig. 470 as follows:

  • From the “Data View” option, select “History”
  • Set the Location of Graphs 2 and 3 to Window 1
  • Set Graph 4 to secondaries with color Green

After around 10ns (2000 time steps), the numbers of ions, primaries, and secondary electrons are each increasing. The simulation converges as the number of secondary electrons approaches a constant, indicating a steady state plasma. At 20ns, when this example ends, the simulation has not yet reached steady state.

image 1

Fig. 470 Visualization of number histories of ion, primary electron and secondary electron macroparticles for around 4000 steps or 20 nanoseconds.

Further Experiments

Vorpal allows one to set up collision interactions with considerable flexibility. The collisions involved in this example are electron-neutral collisions that produce ionization and ohmic heating. As a further experiment, ion-neutral collisions, such as elastic scattering and charge exchange, can also be added to the simulation.

This example uses sample cross-section files (sampleElasticCrossSection.dat, sampleExcitationCrossSection.dat, and sampleIonizationCrossSection.dat) for the neutral argon gas. While the data in these cross-section files is not necessarily physically correct, these files can easily be modified by users to make use of more accurate scattering datasets (EEDL, LXcat, etc.) VSim can directly import scattering data from the LXcat database, which contains cross section data for around one hundred different materials. As another further experiment, the background argon gas and its cross section data can be replaced with other materials in the LXcat database. This enables one to easily switch the background gas in a CCP simulation.

The format of a user-defined cross-sectional data file (e.g. the sample cross-section files used in this example), is formatted as follows:

  • Line 1: Process specifier as a capitalized text string, either ELASTIC, EXCITATION or IONIZATION.
  • Line 2: Threshold, the minimum energy in eV needed for this process to occur, as a float
  • Line 3: Number of table entries, as an integer
  • Lines 4 - end: A two-column table in which the first column is the collision energy in eV, and the second column is the cross-section in square meters.

As an example, the cross-sectional data file sampleElasticCrossSection.dat is shown below:

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
ELASTIC
0.000
7
0.000 0.00e-20
10.50 16.7e-20
25.00 7.75e-20
40.00 4.45e-20
70.00 2.25e-20
100.0 1.50e-20
150.0 1.00e-20

Users may import data from other sources as text files with this format, enabling precision control over the collision processes used in their model.