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 : info@esgeetech.com

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

3

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

5

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)

7

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

8

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

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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

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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

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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

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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

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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

56

-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)

57

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

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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.

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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.

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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

101

• 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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