VizGlow Application Note
Simulation of Coupled Plasma, Electromagnetic Wave and Gas Flow
Physics in an Inductively Coupled Discharge
This note discusses the modeling of a flow-through Inductively Coupled Plasma (ICP) reactor
with the VizGlow Plasma Modeling Software Package and provides an example of tightly
coupled multi-physics simulations with the software. Discharge physics including multitemperature, multi-species transport, and finite-rate plasma chemistry effects are coupled toelectromagnetic wave phenomena driven by inductive coils, and a bulk fluid flow through an
inlet/outlet configuration.
The geometry and mesh for theplasma discharge simulation are shown in Figure 1. The
axisymmetric discharge comprises a dielectric tube of 10 cm inner diameter that is closed on
the left with flow inlet along the axis (inlet diameter 1 cm) and an open inlet on the right. The
axial length of the discharge is 20 cm. The dielectric tube thickness is 5 mm. Four coils areplace just outside the dielectric window
and are driven by radio-frequency (RF)currents to generate non-equilibrium
plasma within the tube. The RF coilfrequency is 13.56 MHz and the coilsdeliver a total of 300 W into the plasma.
The first set of two coils on the left
indicated by “coil1” are driven at acurrent phase lag of 180ocompared to thesecond set of coils “coil2”. Furthermore
the “coil2” is driven with 50% greater
current than “coil1”, i.e. at any instance
Figure 1: Geometry and computational mesh for
Jcoil2 = -1.5 Jcoil1, where J is the coil current.
Inductively Coupled Plasma (ICP) discharge.
The radiation from the coils is confined on
the outside by caging the discharge within a conductive boundary. A 100 sccm pure argon gas
flow enters through the inlet boundary and exits from the outflow boundary where a 100mTorr pressure is imposed.

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The above class of flow-through plasma discharges are encountered in applications such
remote-plasma materials processing reactors and in plasma abatement of contaminants from asemiconductor process reactor.
The computational mesh contains a total of 11,530 cells, and is divided into 5 physical subdomains: the coilcage, which houses coil pairs coil1 and coil2, an annular dielectric window andthe plasma sub-domain that represents the region where the plasma is generated. VizGlow
gives the user complete flexibility in choosing the type of mesh (triangles, quadrilaterals, or a
mix of both in two-dimensional problems). The plasma subdomain is meshed with a purerectangular mesh while the outer coilcage is meshed with triangles.
The ICP plasma is modeled using the quasi-neutral approximation; although VizGlow
provides self-consistent plasma modeling option that is used to simulate other classes ofplasma discharges (see other VizGlow Application Notes for examples).For ICP discharges, whichproduce relatively high charge densities, the plasma sheaths are typically thin and the quasineutral formulation provides is a reasonable approximation. The advantage of the quasineutral approximation is the large simulation time-steps and relatively low computational cost.
The RF-driven coils generate an electromagnetic (EM) wave in the domain which is modelingusing the frequency domain option; a time-domain EM wave option is also available in theVizGlow software. The gas flow is solved with the compressible Navier-Stokes solver that is also
an option in the VizGlow software package.
The coupled model is solved to a steady-state which takes about 500 microseconds in“electron time”. Figure 2 shows theconvergence of the solution to asteady-state as judged by monitoring
important plasma variables (e.g.
potential, charge species density,radical densities, etc.) at specificlocations “trace points” in the
discharge volume. More than one
location is often required to judge
convergence. Note that this “tracepoint”
checkforsimulation
convergence is the safest approach tojudge
convergence.
Other
Figure 2: Transient profiles of important plasma
convergence tests such as monitoring
parameters at a volume “trace point” in the dischargeof volume-averaged variables arethat shows convergence of solution to a steady state.
known to trigger premature (false)

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www.esgeetech.com| VizGlow version 1.8 (Feb 2012)steady-states much earlier in thesimulation.The problem was solved on asingle 2.66 GHz Intel® processor in ~ 4hours of wall clock time.
The real and imaginary components ofthe EM wave field phasors are shown in
Figure 3. The 180o phase difference
between the two sets of RF coil currents isreflected in the wave structure shown in
the figure.
Since the problem isaxisymmetric, the coils drive a pureazimuthally polarized wave in the domain(i.e. only the azimuthal component of thewave field is non-zero). The wave fieldmagnitude on axis is zero for thispolarization as shown in the figure.

Imaginary component of EM wave field

Real component of EM wave field

Figure 3: Imaginary (top panel) and real (bottompanel) components of EM wave field phasors infrequency domain.

The top panel of Figure 4 shows the EM wave power deposited into the plasma (electrons)
as a consequence of electron Joule heating determined by the EM wave field and the induced
plasma currents. The wave power deposition is concentrated near the coils, adjacent to thedielectric tube wall with a peak
power density of 1.3e6 W/m3. This
EM wave power absorbed in plasma
localized power deposition is aconsequence of the plasma skindepth effect. Note that the power
deposition is greater for the secondset of “coil2” since the RF currents
through this set of coils is greaterthan for set “coil1”. The bottom
panel of Figure 4 shows theelectron density in the discharge.
The peak electron density of ~6e17
m-3 is localized on axis below thecoil set “coil2”. Note that location
Electron densityof peak electron density does notcorrespond to the location of peakFigure 4: EM wave power deposition into plasma (topEM wave power deposition. This ispanel) and the electron density (bottom panel).
a consequence of non-local effects

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at low pressures.
Argon metastable radical density

Finally, the argon metastable radicaldensity contours are shown in the top
panel of Figure 5. The radicals areproduced with the much lower thresholdenergy than the charged species andhence significant densities of theseradicals are observed under both sets ofcoils, the density below the second coilset “coil2” being higher.
The peakmetastable radical density shown isGas flow velocity (magnitude)~2e17 m-3. The magnitude of the gas
flow velocity is shown in the bottom
Figure 5: Argon metastable radical density (toppanel of Figure 5. The gas velocities arepanel) and the gas flow speed (bottom panel) in thehighest at flow inlet nozzle location on
reactor.
axis and have a maximum velocity of 66
m/s. The flow expands and moves to towards the outflow boundary at much lower velocities.
The plasma structure is largely unaffected by these flow velocities. For the imposed flow rateof the 100 sccm the flow velocities remain subsonic, although supersonic choked flow
conditions are often encountered for high flow rates. For such higher flow conditions
significant flow-induced modifications to the plasma structure, especially the neutral species,
can occur because of flow.
In summary, the VizGlow Plasma Modeling Software Package provides a wide range ofphysical models and options that allows one to simulate complex coupled phenomena that areencountered in most plasma discharges. The VizGlow Plasma Modeling Software Package ispart of the Overviz framework suite which provides an intuitive interface to set-up a project tobe solved using VizGlow, manipulate multiple projects for parametric studies. VizGlow isprovably fast, robust, and easy-to-use software and currently a leading industrial plasma
simulation tool.
For further information on this application note or details about the VizGlow and other software
packages you may contact us at
Esgee Technologies Inc.
14, North PeakAustin, Texas 78746, USA
info@esgeetech.com
www.esgeetech.com

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