overview of vizglow non-equilibrium plasma simulation software
TRANSCRIPT
December 2014
Overview of VizGlow Non-Equilibrium Plasma Simulation Software
1301 S. Capital of Texas Highway Suite B-122 Austin, Texas 78746
www.esgeetech.com
Contact : [email protected]
Esgee Technologies, Inc. Company background
Located in Austin, Texas, USA Core competencies:
Development of computational simulation tools for multi-physics engineering problems
Modeling and simulation services: work with customers to define problem, setup model with simulation tools, calibration of models for customer specific problems, custom development
Training and support to clients using software tools
2
Esgee Technologies, Inc. Products Overview
OverViz Simulation Suite
Product Philosophy : Provide physics-based, comprehensive, robust, user-friendly, simulation software that delivers deep, domain-specific, analysis, prediction, and optimization capability to customers
Software Packages:
VizGlow Non-equilibrium plasma discharge simulations
VizArc Thermal (arc) plasma simulations
Supporting Modules:
VizFlow Navier-Stokes compressible fluid flow simulations
VizEM Electromagnetics (High-Freq., Low-Freq., DC) simulations
VizGrain Particle-based gas flow physics, hybrid plasma simulations
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VizGlow A comprehensive solution for plasma
simulations
Industry Segments Served by VizGlow
Semiconductor Equipment Makers Semiconductor IC Manufacturers Solar Cell Manufacturers Flat Panel Display Manufacturers Automotive Aerospace systems Electrical device manufacturers
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Applications of Plasma Discharges Areas where VizGlow can be used
Thin film etching / deposition Lighting and display Gas stream processing Aerodynamic flow control Chemical processing Combustion ignition / stabilization Biomedical (sterilization, surgery)
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Plasmas Simulated with VizGlow
Capacitively Coupled Plasmas (CCP)
Inductively Coupled Plasmas (ICP)
ICP with Gas flow physics Wave physics (microwave plasmas)
Plasma Discharge Types: Capacitively Coupled Plasmas (CCP) Inductively Coupled Plasmas (ICP) Microwave Plasmas (MWP) Direct Current (DC) Plasmas Atmospheric Pressure Plasmas (APP) Microdischarges (MD)
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Physics representations in VizGlow
Gas Flow Physics
Gas Chemistry
Surface Chemistry
External Circuit Dynamics
Wave Physics (ICP coils/Microwave)
Magnetic Field Effects
Non-equilibrium Plasma
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OverViz Simulation Suite Development Timeline
The development of the OverViz suite that includes VizGlow is pursued on an aggressive timeline guided by internal roadmaps and customer priorities
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2014 2011 2012 2013 2010 2009
v1.5 v1.6 v1.7 v1.8 v1.9 v2.0
Current VizGlow feature list 10
Physics Plasma formulation:
Self-consistent / Quasineutral
Multi-species / multi-temperature
Drift-diffusion transport for all species / full momentum for ions
Finite rate gas-phase and surface chemistry
Coupling to electromagnetic waves EM wave frequency domain / EM wave time-domain
Coupling to compressible fluid flow physics
Coupling to particle physics
Photoionization model
Range of applicability: ~ few mTorr to 15 atm. (proven with examples)
Numerical Approach Hybrid unstructured mixed mesh representation of geometry
Modern, robust, and scalable solver technology
Fully parallel enabled (scalability to 100’s of processors demonstrated)
VizGlow Governing Equations Description: Governing equations for the plasma model in VizGlow are summarized for self-consistent and quasi-neutral cases
11
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Summary: Plasma fluid model equations Self-consistent model
Electrostatic potential
Species density
Drift-diffusion (transport)
Ion momentum
Electron energy
Bulk energy
0
c
r
gkk
k KkGft
n,...,1,
kkkkkkknDnUn
iiiiiiiiiii upEneZuuut
eeeeee Squpet
e
bulkbulkbulk SQt
e
13
Summary: Plasma fluid model equations Quasi-neutral model
Ambipolar electric field
Ion and neutral species density
Drift-diffusion (transport)
Electron density (quasi-neutrality constraint)
Electron energy
Bulk energy
ekKkGft
ngkk
k
,,...,1,
kkkkkkknDnUn
eeeeee Squpet
e
bulkbulkbulk SQt
e
i
iie nZn
kkkk
kkkk
nZ
nDZ
E
amb ambE
i
iie Z
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Fluid model: self-consistent and quasi-neutral formulations
Self-consistent Poisson equation is solved to find the electrostatic potential
(Gauss’ law) :
Quasi-neutral Ion density equations are solved, and electron density
recovered with the quasi-neutrality constraint:
Ambipolar potential equation is solved:
0
c
r
ionsk
kkenZn
charged
charged
amb
kkkk
kkkk
nZ
nDZ
E
ambE
Choosing between self-consistent and quasi-neutral formulations
Self-consistent Quasi-neutral
CCP Yes -
ICP Yes Yes
ICP+RF bias Yes -
MWP Yes Yes
MWP+RF bias Yes -
DC Yes -
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Self-consistent Required when there is a sheath that needs to be resolved (CCP, RF bias, DC) More difficult to solve numerically (Adds numerical stiffness to the system)
Quasi-neutral Can be used when the plasma density is high, and the sheaths are very thin
(ICP, MWP) Easier to solve numerically compared to self-consistent formulation
(Numerically less stiff; allows for larger time-steps)
VizEM Governing Equations Description: Governing equations for the electromagnetics models in VizEM are summarized for time-domain, frequency domain and magnetostatics cases
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Faraday’s law of Induction:
Ampere’s law:
Gauss’ law:
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Electromagnetics: Maxwell’s equations
t
B=E
-
t
Dj=H
Gauss’ law for magnetic fields:
cD
0 B
Hμ=B
Magnetic induction:
Eε=D
Electric displacement:
EM vector potential equation in time domain
A=B
Electric and Magnetic fields in terms of vector and scalar potential:
Coulomb gauge:
t
AE
MS E+E=E
0 A
Vector potential equation:
tjA
t
A
11 2
2
2
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EM vector potential equation in frequency domain
tieAtA ~
)(
Magnetic vector potential defined as complex phasor:
Vector potential equation in frequency domain:
tiejtj ~
)(
ext
22~~
~~
jAωσiωμεA
imagreal~~~AiA=A
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Vector potential equation for static cases (Magnetostatics)
Modify magnetic induction expression to allow for materials having non-zero magnetization (permanent magnets):
Vector potential equation:
)(ext
2 MjA
)( MHμ=B
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VizFlow Governing Equations Description: Governing equations for the compressible Navier-Stokes equation solver
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Compressible Navier-Stokes Equations
S+x
G=
x
F+
dt
Ud
j
j
j
j
t
i
e
uU
jt
ij
j
p)u+e(
p+uρu
ρu
=F
jiji
ji
qu
=G
0
jjbt
b
uf+s
f=Si
0
iit uu+γρ
p=e
2
1
1 jj
x
Tκ=q
k
kij
i
j
j
iji
x
uμδ
x
u+
x
uμ=τ
3
2
Equation:
Constitutive relationships:
VizFlow provides a variety of optional features Viscous (NS) vs. Inviscid (Euler) equation solvers Time-dependent vs. Steady-state etc.
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VizGlow Chemistry Database Description: Library of chemical reaction mechanisms accompanying VizGlow
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VizGlow is accompanied by a growing database of chemical reaction mechanisms
Pure Noble Gases Ar, He
Simple Molecular Gases H2, N2, O2, Cl
Noble Gas + Other Gas Mixtures Ar+O2, Ar+H2, Ar+Ti (representational)
Semiconductor process gases CxFy series, HBr, CF4+O2+He, SiH4+N2, NH3
Air N2+O2 (air)
Plasma combustion CH4+air, CH4+air+Exhaust Gas Recirculation
Neutral combustion GRI Mech 3.0
Mechanisms available with standard release:
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In additional to mechanisms in the standard release, a variety of more mechanisms are made available to customers based on special arrangement
Esgee also work regularly with customers for mechanism development projects that cater to special customer needs.
Example Simulation of a magnetron CCP reactor for benchmarking accuracy of VizGlow simulation Description: This example provides a benchmark of the accuracy of VizGlow simulations for CCP plasmas with low and high-frequency RF excitation.
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Experimental System
CCP reactor configuration (Hayashi, et al., 2002): • 200 mm wafer • all runs at 40 mTorr • 2 sets of runs: 100 MHz and 13.56 MHz • no magnetic field for 100 MHz cases, about 100 G magnetic field for 13.56 MHz cases (Sekine, et al., 1986)
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Experimental data reported in paper (Hayashi et al., 2002)
Experimental data for density taken at 2 cm above wafer
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Reactor and operating conditions Simulation with Magnetic field effects: • 200 mm wafer • all runs at 40 mTorr • 2 sets of runs: 100 MHz (no mag. field) and 13.56 MHz (80 G uniform mag. field + 0 G runs for comparison) • no wave effects or stochastic heating effects considered • all cases run in rf power control mode
B = 80 gauss
(for 13.56 MHz cases)
wafer (conductor)
focus ring (eps = 3.75)
power supply (symmetric sinusoidal)
100 pF
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Comparison of experimental data with simulations (including effect of B-field)
• Overall all results are in excellent agreement with experimental data
1.E+10
1.E+11
1.E+12
0 1 2 3 4 5
Ele
ctr
on
De
ns
ity (
#/c
m3
)
Cathode Power Density (W/cm2)
13.56 MHz (expt.)
100 MHz (sim.)
13.56 MHz (sim.)
13.56 MHz, B=80 G (sim.)
100 MHz (expt.)
1.E+10
1.E+11
1.E+12
0 200 400 600 800 1,000 1,200
Ele
ctr
on
Den
sit
y (
#/c
m3)
Cathode (wafer) DC bias voltage (V) (negative)
100 MHz (expt.)
13.56 MHz (expt.)
100 MHz (sim.)
13.56 MHz (sim.)
13.56 MHz, B=80 G (sim.)
(density at centerline 2 cm above wafer) (density at centerline 2 cm above wafer)
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• Edge peaked profile with peak position moving increasingly towards
the centerline at higher powers
Results Summary: Effect of power on electron density for 100 MHz cases
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Results Summary: Ion Energy Distribution Functions for 600 W cases
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Example Simulation of Inductively Coupled Plasma (ICP) in HBr for metal/poly-Si etch Description: This example demonstrates the capability of VizGlow for simulation of Inductively Coupled Plasma (ICP) reactors used in semiconductor manufacture. The ability of VizGlow for the simulation of large reactive chemistry problems relevant to etch/deposition processes is highlighted.
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ICP reactor geometry and mesh for VizGlow simulations
11191 cells in gas/plasma domain
plasma
coils cage
dielectric window
wafer folder
wafer holder edge ring
focus ring
wafer
Pure HBr flow inlet (400 sccm)
Flow outlet (5 mTorr = 0.666 Pa)
axis
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Cases studied: 2 coil ICP reactor
-- pure HBr plasma -- 400 sccm flow rate -- 5 mTorr pump-port pressure -- 600 W and 1000 W power at 13.56 MHz
Chemistry: HBr chemistry -- 15 Species: e, Br+, Br2+, HBr+, H+, H2+, Br-, Br, Br2, Br*, Br2*, H, H2, H*, HBr -- 51 gas reactions; simple quench surface chemistry
Approach: Coupled physics -- Frequency-Domain Electromagnetic solver for coil power -- Quasi-neutral reactive plasma -- Compressible fluid flow
ICP etch reactor simulation conditions
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Pump out
(5 mTorr)
Flow Inlet
(78 mTorr)
Pressure
max = 377 m/s
(Mach No. = 2.9)
Flow speed
Gas temperature (Min=117 K)
ICP etch reactor simulation results: Flow physics
Flow streamlines
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Pump out
(5 mTorr)
ICP power absorption
ICP etch reactor simulation results: Coil driven electromagnetics
Aq (imaginary)
Aq (real)
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ICP etch reactor simulation results: Plasma species properties
E temperature E density Br+ density
Br density H density HBr density
H
Br*
ICP etch reactor simulation results: Species fluxes to wafer surface
Br2+
Br
Br+
H+
HBr+
H2+
H2
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Example Simulation of Capacitively Coupled Plasma (CCP) in CF4 for dielectric etch with fluid flow effects Description: This example demonstrates the capability of VizGlow for simulation of Capacitively Coupled Plasma (CCP) reactors used in semiconductor manufacture. The ability of VizGlow for the simulation of large reactive chemistry problems relevant to etch/deposition processes with fluid flow effects is highlighted.
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plasma
dielectric window
wafer folder
wafer holder
edge ring focus ring
wafer
powered
electrode
boundary
7276 cells in gas/plasma domain
CCP reactor geometry and mesh for VizGlow simulations
Flow inlet
(center inlet)
Flow inlet
(edge inlet)
Outflow
41
CCP reactor demo simulations: -- pure CF4 plasma -- 20 mTorr pressure -- 800 W set point CCP power at 100 MHz and 1000 pF block
Chemistry: pure CF4 chemistry -- 12 Species: e, F+, CF3+, CF2+, CF+, F-, C, F, CF3, CF2, CF, CF4 -- 47 gas reactions; simple quench surface chemistry
CCP etch reactor simulation conditions
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Coupled plasma-flow simulation approach
Run flow simulation (no plasma) to steady state
Run coupled plasma-flow model
Initial flow solution provides a good initial guess for coupled simulation
Plasma model is self-consistent which is a suitable choice for CCP simulations
Results confirm that plasma heating and electrostatic forcing of the flow is negligible at 20 mTorr- hence coupling is actually one-way: the plasma is affected by the flow
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CCP etch reactor simulation: Flow physics
For given inner (center) to outer (edge) area ratio of 1:2
For mass flow ratio 2:1, velocity ratio should be 4:1 -> confirmed
Analysis assumes incompressible flow –reasonable in this case (although flow solution algorithm makes no assumptions about the density)
Velocity (m/s) Area (m2)
Flow inlet (center)
3.7 0.045
Flow inlet (edge)
0.95 0.093
2:1
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Cycle averaged potential and electron properties 800 W power at 100 MHz, 20 mTorr pump port pressure, Flow rate 400 sccm
45
46
Cycle averaged positive and negative ion densities 800 W power at 100 MHz, 20 mTorr pump port pressure, Flow rate 400 sccm
46
47
Cycle averaged radical densities 800 W power at 100 MHz, 20 mTorr pump port pressure, Flow rate 400 sccm
47
48
Flux of ions and radicals to wafer 800 W power at 100 MHz, 20 mTorr pump port pressure, Flow rate 400 sccm
F+
CF+
CF2+
CF3+
F
CF3
CF2
CF3
48
Example Parallel CCP simulations using VizGlow Description: This example demonstrates the new parallel computing capability of VizGlow. VizGlow is currently the only plasma simulation software tool capable of accurate and scalable parallel simulations. The example demonstrates the significant improvements now possible with VizGlow parallel computing. Nearly order-of-magnitude speedup is now possible on a 12 core desktop machine. Much faster speedups are possible with larger cluster machines, for example, depending on the size and complexity of the problem being solved.
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VizGlow Parallel features
Can reliably solve any (CCP) problem that VizGlow (serial) can solve Solves plasma equations in parallel on multiple physical subdomains Ability to support multiple circuits connected to different boundaries Supports mixed unstructured meshes- all formats that are read by
VizGlow (serial) are supported in parallel as well
Can deliver speed improvement for problems ranging from small (~5,000 mesh cells) to moderate (~30,000 mesh cells) and large sizes (> 100,000 mesh cells)
No additional input parameters required to setup a problem in VizGlow for Parallel solution Optional parameters can be used to improve parallel performance
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Geometry and mesh
wafer
Cell count: focusRing = 58 gas = 7,276 showerheadBlock = 3,038 showerheadInner = 1,024 showerheadOuter = 954 wafer = 176 waferHolder = 1,751 waferHolderEdge = 1,227 ------------------------------- Total: = 15,504 -------------------------------
gas
showerheadInner showerheadOuter
showerheadBlock
waferHolder
waferHolderEdge
focusRing
wafer waferHolder
gas
waferHolderEdge
focusRing
51
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Mesh partitions for parallel run
Mesh partitioned for 12 processor run
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0
20
40
60
80
100
120
1 2 3 4 5 6 7 8 9 10 11 12
Number of cores
Wall c
lock t
ime (
min
)
Parallel performance (Strong scaling)
Timing run details 50 cycles (100 MHz), CF4 plasma chemistry (11 species, 47 reactions) Dual hex core (12 cores total) workstation running CentOS 5.5 x86_64 (linux kernel 2.6.18)
~7 times faster
~ 2 weeks total CPU time
~ 2 days total CPU time
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1
2
3
4
5
6
7
8
9
10
11
12
1 2 3 4 5 6 7 8 9 10 11 12
Ideal scaling
Actual scaling
Number of cores
Spe
ed
up
Parallel results 12 processors, avg. electron density contours
No influence of parallel mesh partitions on results, and results are identical to serial case
54
Example Extended Microwave Plasma Source. Self-consistent model of plasma + EM wave
55
Extended microwave plasma source: Introduction
Example of microwave generated extended high density plasma source*
http://www.ipf.uni-stuttgart.de/gruppen/pte/duoplasmaline.html
Plasma Excited by Surface Electromagnetic Waves
Metal Electrode
(to be coated)
Microwave TEM mode
Plasma
Coaxial WaveGuide
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-V
Extended microwave plasma source: Geometry / Mesh
100 mm
100 mm
400 mm
100 mm
-V
Plasma (36026 cells)
WaveGuide (3404 cells)
Microwave Inlet
Ground (Metal)
Sheath Mesh (min mesh size ~ 0.1 mm)
Interior Mesh (max mesh size ~ 1 mm)
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Ref: Kousaka, Xu and Umehara, JJAP 44(33), (2005)
Extended microwave plasma source: Simulation Conditions
System: Reactor Chamber described by Kousaka, Xu and Umehara, JJAP 44(33), (2005)
Microwave Power: 500W
DC bias: -500V
Frequency: 2.45 GHz
Pressure: 13 Pa (100 mTorr, 0.13 mbar)
Plasma mode (Self-consistent): Species Density Equations + Ion Momentum + Electrostatic Potential + Electron energy Equation (fluid) + Maxwell (Frequency Domain)
Chemistry Model: Argon plasma
Electron impact reaction using DC-EEDF rate coefficients
Transport models:
Electron transport using DC-EEDF for mobility and diffusion coefficient
Ion momentum equations
58
Extended microwave plasma source: Time Evolution of Electron Density and Microwave Absorbed Power
Electron Number Density (m-3) EM Wave Absorbed Power Density (W/m-3)
59
Extended microwave plasma source: Monitoring of Transient Profiles
Electron Density at Steady State (m-3)
Trace 1 (X=0.05m, Y = 0.15m)
Trace 2 (X=0.05m, Y = 0m)
Trace 3 (X=0.05m, Y = -0.15m)
60
Extended microwave plasma source: Electric Field Components at Different Instants
61
E_Imag (Vm-1)
E_Real (Vm-1)
10 microseconds 50 microseconds 150 microseconds 100 microseconds
Extended microwave plasma source: Correlation of Electron Density and Axial Electric Field Showing the Resonance Effect
10 microseconds 50 microseconds 150 microseconds 100 microseconds
62
Plot of axial variation of electron density (Top Row) and axial component of Electric Field (Bottom Row) showing the enhanced electric field at the under dense – over dense interface due to the “resonance effect”
Extended microwave plasma source: Magnetic Field Components, Poynting Vector and EM Wave Energy Density at Different Instants
63
75 microseconds
150 microseconds
63
Extended microwave plasma source: Selected Plasma Parameters at Steady State
Electron Density (m-3) (log-scale)
Ar+ Density (m-3) (log-scale)
Electron Temperature (K) (log-scale)
Electron Production Rate (m-3s-1) (log-scale)
64
Extended microwave plasma source: Additional Plasma Parameters at Steady State
Electrostatic Potential (V) (linear-scale)
Electrostatic Potential Gradient
Magnitude (V/m) (log-scale)
Electrostatic Joule Heating (W/m3)
(log-scale)
Electromagnetic Joule Heating (W/m3)
(log-scale)
65
Conclusions
• A self consistent model of an extended microwave source with negative DC bias was simulated.
• Dispersion characteristics of surface waves and dependence on electron density and collision frequency was considered.
• Strong enhancement of normal electric field and wave power absorption due to the “resonance effect” was discussed.
• 2D self consistent simulations show this effect and plays a key role in plasma generation and maintenance.
• Transients and steady distribution of various plasma properties was discussed.
66
Example Microwave reactor simulations using VizGlow (Radial line slot antenna reactor)
Reference: L. L. Raja*, S. Mahadevan, P. L. G. Ventzek, and J. Yoshikawa, “Computational modeling study of the radial line slot antenna microwave plasma source with comparison to experiments,” Journal of Vacuum Science and Technology A, Vol. 31, No. 3, 2013, pp. 031304-1-11.
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Example Microwave reactor simulations using VizGlow (Radial line slot antenna reactor)
Reference: L. L. Raja*, S. Mahadevan, P. L. G. Ventzek, and J. Yoshikawa, “Computational modeling study of the radial line slot antenna microwave plasma source with comparison to experiments,” Journal of Vacuum Science and Technology A, Vol. 31, No. 3, 2013, pp. 031304-1-11.
68
Overview of radial line slot antenna simulation conditions
Overview of simulation conditions:
VizGlow (version 1.8beta)
2.45 GHz microwave
Pressure range: 5 mTorr to 180 mTorr
Power range: 700 W to 2000W
Quasi-neutral formulation
Drift-diffusion approximation for ions
Microwave-EEDF based argon plasma chemistry
DC-EEDF based electron transport
Argon plasma
Reference for Expt. data
69
Schematic of experimental system
70
Power effect at 90 mTorr (Electron density)
700 W 1000 W 1500 W 2000 W
Peak density on axis (highly non-local; see next slide on power deposition profile)
Peak density increases with increasing power (upto a point, e.g. 1500 W and 2000 W have nearly the same peak density)
Increasing radial spread of density with increasing power
slots
71
Power effect at 90 mTorr (Electron temperature)
700 W 1000 W 1500 W 2000 W
Electron temperature is relatively insensitive to the power for a fixed pressure
72
Power effect at 90 mTorr (Microwave power density)
700 W 1000 W 1500 W 2000 W
The outer radial slots become increasingly “active” with increasing power (results in increasing radial spread of plasma with increasing power)
73
Pressure effect at 700 W (Electron density)
5 mT
20 mT
50 mT
90 mT
180 mT
Electron density becomes increasingly local with increasing pressure
Peak density increases with increasing pressure for a fixed power
74
Pressure effect at 700 W (Electron temp.)
180 mT
5 mT
20 mT
50 mT
90 mT
Electron temperature is relatively insensitive to the pressure, except for the lowest pressure (5 mTorr)
75
Pressure effect at 700 W (Microwave power den.)
20 mT
180 mT
90 mT
50 mT
5 mT
For low pressures ( 20 mTorr and lower) observe significant penetration of microwave power throughout the reactor. Since densities are low (microwave power deposition observed in regions of below cutoff density)
region where density is
above cutoff
76
Mircrowave power deposition is limited to below cutoff density regions (700 W, 20 mTorr)
Plasma frequency:
Region below cutoff
Electron density Microwave absorbed power
density
Region above cutoff
2/1
0
2
2
1
e
epe
m
nef
202
μwave2
cutoff4
e
mfn e
e
Microwave cutoff density: 316
cutoffμwave m105.7GHz45.2 enf
77
Comparison of VizGlow results to Tian LP data : Effect of varying microwave power
Magnitude and peak densities are in good agreement with experiments (simulation results are systematically lower by about 25 to 50 % compared to expts)
All trends in excellent agreement with experiments
The profile shapes can be improved with improved ion transport model
78
Comparison of VizGlow results to Tian LP data : Effect of varying pressure
Magnitude and peak densities are in good agreement with experiments (simulation results are systematically lower by about 25 to 50 % compared to expts)
All trends in excellent agreement with experiments
5 mTorr results are outlier (we believe this can be improved using low-pressure corrections to the transport formulation. This is being investigated.)
79
Comparison of VizGlow results to Tian LP data : Axial profile of electron parameters
Excellent agreement for axial profile of electron temperature
Peak electron density for simulation is further away from window than the experiments
The nearly linear drop in electron density towards the wafer is captured well by simulations
80
Example Simulation of Three-Dimensional Direct-Current Sputter Deposition of Ti Description: This example demonstrates the capability of VizGlow for simulation of large-scale three-dimensional direct-current discharge for the sputter deposition of Ti metal. The ability of VizGlow for self-consistent, multi-species, multi-temperature discharge simulations with surface-chemistry for sputter etch reactions and the parallel computing capability is highlighted.
81
Three dimensional direct-current discharge geometry and mesh
Symmetry plane
Ti target Direct-current discharge geometry in 3D
exploits symmetry in 2 planes
Hybrid unstructured mesh generated with Gambit™
~160,000 cell with brick and tet cells
FRONT SIDE
82
Gas Chemistry : Ar plasma with Ti
Rxn A B C Activation Energy (ε)
E + Ar -> E + Ar* f(e) 11.56 eV
E + Ar -> 2E + Ar+ f(e) 16.0 eV
E + Ti -> 2E + Ti+ f(e) 6.82 eV
E + Ar* -> 2E + Ar+ f(e) 4.43 eV
Ar* + Ar* -> E + Ar + Ar+ 6.2e-16 0.0 0.0
E + Ar* -> E + Ar f(e) -11.56 eV
Ar* + Ar -> Ar + Ar 2.5e-21 0.0 0.0
Species: E, Ar+, Ar*, Ar, Ti, Ti+
• f(e) indicates reaction rate is tabulated as function of mean electron energy using BOLSIG+
• Otherwise k = A TB exp(-C/ε) in units of molecules-meters-Kelvin
Reactions:
83
Surface Chemistry : Target sputter and wall quench/depositiom
Reactions (Target):
Rxn Sticking
Coeff/Yield
E -> 1.0
Ar* -> Ar 1.0
Ar+ + #Ti(B) -> #Ti +Ar (See graph)
0
0.2
0.4
0.6
0.8
1
0 500 1000 1500 2000Ti
Sp
utt
er
Yie
ld, #
Ar Impact Energy [eV]
Ar->Ti Sputter Yield
Rxn Sticking Coeff
E -> 1.0
Ar* -> Ar 1.0
Ar+ -> Ar 1.0
Ti+ -> Ti(B) 1.0
Ti -> Ti(B) 1.0
Reactions (Wall quench / deposition):
Etch threshold = 25.4 eV
Ar+ Ar
Ti
e
Ti+
target
84
Case studied: -- 3D direct-current discharge -- Argon plasma with Ti species -- 20 mTorr -- 2 kV (negative) at target -- all other surfaces are grounded
Approach: Coupled physics -- Self-consistent plasma discharge model -- Sputter chemistry at target -- quench / deposition chemistry at other surfaces
DC sputter reactor simulation conditions
85
Robust, accurate, and scalable parallel computing is necessary for self-consistent 3D problems
24 processors used for parallel runs
86
Self-consistent potential
Cathode (target) sheath
Anode (substrate) sheath
87
Electron temperature
~ 6 eV in bulk plasma
88
Argon ion and argon metastable densities
89
Sputter product densities : Ti atom and Ti ion species densities
90
Target species fluxes and sputter rates
Ar+ ion flux to target surface
Ar+ ion impact energy to target surface
Ti atom physical sputter etch product flux from target surface
91
Ti deposition on substrate
(Ti+Ti+) total flux to substrate
Ti+ ion flux to substrate (negligible compared to Ti atom flux)
Ti deposition rate at substrate
92
Example Atmospheric pressure Nanosecond pulsed DBD simulations using VizGlow Description: This example demonstrates the ability of VizGlow to be used for high pressure Dielectric Barrier Discharges (DBDs) generated by nanosecond pulses. DBDs have a number of applications including vacuum-chamber free materials processing, chemical processing of gas streams, and plasma actuators for aerodynamic flow control.
93
Pulse DBD Arrangement
Domain size is 2.5 mm x 0.5 mm 0.2 mm wide electrode surrounded by 0.1 mm thick dielectric 1 atmosphere, 300 K Air plasma chemistry with 11 species (E, N2, O2, O, N2+, O2+, N4+,
O4+, O2+N2, O2-, O-) and 21 gas-phase reactions 80,150 cells in mesh
94
Nanosecond Pulse operating parameters
Positive Polarity triangular pulse 3 kV with 4 ns rise and 4 ns fall times Overall simulation time is 10 ns Compare cases with and without photoionization
3 kV
4 ns 8 ns
Applied Voltage
Time
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Importance of photoionization model
3 ns
4 ns
5 ns
6 ns
7 ns
Without Photoionization With photoionization
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Example Simulation of Cold Plasma Applications for Automotive Combustion Ignition Description: This example demonstrates the VizGlow simulation for high pressure cold plasma combustion ignition simulations. Reference: D. Breden, L. L. Raja, C. A. Idicheria, P. M. Najt, and S. Mahadevan, “A numerical study of high-pressure non-equilibrium streamers for combustion ignition application,” Journal of Applied Physics, Vol. 114, 2013, pp. 083302-1-14.
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Introduction
Photo From : University of Southern California Pulsed Power Research Group
http://www.usc.edu/dept/ee/Gundersen/combustion.html
www.etatech.us/Technical-Papers/ECCOS-Advanced-Ignition-System.ppt
Coaxial Geometry (Small gap ~mm)
Corona Geometry (Large Gap ~cm)
Traditional spark (thermal plasma) igniters • Ignition kernel highly localized • Ineffective at igniting lean fuel-air
mixtures
Recent research has focused on utilizing non-equilibrium plasma
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Ref: P. Freen, “Radio Frequency Electrostatic Ignition System Feasibility Demonstration, EISG Final Report,2005
Ref: Shiraishi et al., J. Phys. D: Appl. Phys. 42, (2009), 135208
Advantages • Preferentially heats electrons to high energies • Prevents plasma from transitioning to spark
Nanosecond pulsing for combustion ignition applications
Technique to efficiently ionize atmospheric pressure air
High voltages applied over very short (1-100 ns) duration
Pulse long enough to ionize plasma but shorter than electron recombination time
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Plasma chemistry mechanism for cold plasma igniter simulations
Methane-air plasma chemistry mechanism
Species and pathways relevant to plasma time scale (~10’s ns)
26 Species :
E, O, N2 , O2 , H , N2+ , O2
+ , N4+ , O4
+ , O2+N2 , O2
- , O- , O2(a1) , O2(b1) ,
O2* , N2(A) , N2(B) , N2C , N2(a1), CH4 , CH3 , CH2 , CH4+ , CH3
+ , CH2- , H-
85 Reactions :
1) electron impact, 2) ion-ion, 3) ion-neutral, 4) neutral-neutral
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Coaxial electrode geometry
• 20 degree slice • ~60,000 cells • 27 deg tip
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• 40 kV pulse (square pulse) • 10 atm, Tgas = 700 K • Stoichiometry (molar ratios) Lean : A/F = 40:1 Stochiometric : A/F = 17.2 : 1
One Prong
Eight Prong
Effect of roughness elements selection
Multiple streamers form at prongs Streamers merge into one streamer locally Consider only single roughness element
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Plasma formation dynamics in coaxial electrode igniter
Primary streamer followed by secondary streamer
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Reduced Electric Field
Primary streamer : ~500 Td Secondary streamer : ~200 Td
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Coaxial Electrode Species Yields
4 mm
0.2 mm
Physical Domain Canonical Streamer Domain
Positive Ions Negative Ions Radicals
Lean Stoich Lean Stoich Lean Stoich
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Coaxial Electrode O Radicals
4 mm
0.2 mm Lean
Canonical Streamer Domain
Stoich
Radical Density Transients (LEAN)
9.7 ns
8.8 ns
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Corona Geometry
• 45 degree slice • Inset plasma domain • ~75,000 cells • 115 kV pulse
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Electron density for corona streamer
1 ns 5 ns 10 ns 15 ns 20 ns 25 ns 30 ns
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Corona Geometry Species Yields
4 mm
0.2 mm
Physical Domain Canonical Streamer Domain
Positive Ions Negative Ions Radicals
Lean Stoich Lean Stoich Lean Stoich
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Corona Geometry O Radicals
4 mm
0.2 mm
Lean
Canonical Streamer Domain
Stoich
30 nanoseconds
Radical Density Transients (LEAN)
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Parallel Scale-up 111
Parallel scale-up studies performed for a 80,000 cell problem with the large methane-air chemistry
Excellent scale-up achieved for up to 50 processors. Sub-linear scale-up for up to 200 processors, following which scale-up degrades.
This problem shows nearly 80 times faster CPU times for 140 processors Larger problem sizes will show even better scale-up
Conclusions for cold plasma automotive ignition simulations
Coaxial electrode geometry
Short gap plasma forms in primary and secondary streamer
Peak radical production in secondary streamer
Corona geometry
Long gap plasma produces radicals uniformly
Peak radical production occurs near prong tips
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Example Magnetostatics simulations using VizGlow Description: This example demonstrates the ability of VizGlow to solve magnetostatics problems that is available in VizGlow version 1.9 and later.
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Magnetostatics Example Geometry and mesh for magnetostatics example
Total number of cells: 16784
Cells in case subdomain: 9686
Case
Window
Gas
Central magnet
Side magnets Perfect
conductor
Perfect conductor
S
S N
N S
N
Mesh resolution
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Magnetostatics Example Magnetic induction and magnetic vector potential solutions
B-field Az-field
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Summary Use VizGlow for plasma simulations
Complex geometry representation with
hybrid unstructured meshes
Solve 1-D, 2-D (planar/axisymmetric) and 3-D problems
Modularity and choice in physical model
selections
State-of-the-art numerical solver technology makes VizGlow fast and robust
Constantly evolving based on customer needs
Regularly incorporating advances from internal R&D and published research
Aθ
(Imag)
Aθ
(Real)
ne
Vmagnitude
Example of a coupled physics
simulation with plasma, EM wave and
gas flow effects
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End of presentation
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