37th International Conference on Plasma Science

MINICOURSE Low Temperature Plasma Modeling & Simulation and Applications ~ June 25 (Fri) 14:00-17:00 ~Yuki Sakiyama, Ph.D. (ysaki@berkely.edu) Research Associate Department of Chemical Engineering, University of California, Berkeley

University of California, Berkeley

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Outline1. Problem setting and goals 2. Fluid modeling of atmospheric pressure plasmas 3. Simulation of atmospheric pressure plasmas using COMSOL and MATLAB 4. Plasma chemistry in atmospheric pressure plasmas 5. Neutral gas dynamics in atmospheric pressure plasmas 6. Overview of available codes for simulating low-temperature non-equilibrium plasmas

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1. Problem setting and goals-1 helium RF plasma needle dischargevisible emissionCCD image (cross sectional view)

(Images courtesy of Prof. John Goree)

Predicted emission distribution

Understanding the governing equations and boundary conditions COMSOL and MATLAB Plasma chemistry Gas flow and plasma interaction

dark

bright

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1. Problem setting and goals-2corona-mode (1 mW) glow-mode (100 mW)

Y. Sakiyama and D.B.Graves, J.Phys.D 39 3451 (2006) and J.Phys.D 39 3644 (2006)

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2. Fluid modeling of atmospheric pressure plasmas2.1 Introduction 2.2 Governing equations 2.3 Necessary parameters 2.4 Boundary conditions 2.5 Local field approximation (LFA)

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2.1 Introductionproblem setting species: electrons (e), positive heavy ions (i), neutrals (n) geometry: 1-D parallel plate, gap 2mm external voltage: RF(= 13.56 MHz) gas pressure: 1 atm (= 760 torr), static gas temperature: room temperature

e n

i

Which equations to be solved? What is the physical meaning of the governing equations? What is appropriate boundary conditions? How and where are the necessary parameters obtained?

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2.2 Governing equation-1species continuity equation:n j t + j = R j ,ll

( j = e, i, n)

(eq-1) (eq-2) (eq-3) (eq-4)

drift-diffusion approximation: j = n j j E D j n j ( j = e, i, n) electron energy equation: Poissons equation:5 5 + e ne De = e E Qe-N t 3 3 0 E = q j n j ( j = e, i, n)j

( ne )

from (eq-1)

qjj

n j t

+ q j j = R j ,l = 0j j l

(eq-1) (eq-4')

total mass needs to be conserved!

from (eq-4) 0

n j E = qj t t j

(eq-1) + (eq-4) 0 E + q j j = 0 E + q j j = 0 t t j j total current continuity equation

(eq-5)

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2.2 Governing equation-2species continuity equation:change in time

n j t

+ j = R j ,ll

( j = e, i, n)local creation/loss

(eq-1)

due to motion (convection/diffusion) across the control volume

Reaction term:Rl = k r nl = k r nl nl = k r nl nl nl

n

( k [ s ]) ( k [ m s ]) ( k [ m s ])r r r 1 3 1 6 1

n ( x ) t = n ( x ) ut ( x + x ) t = n ( x + x ) u t

x x x+x

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2.2 Governing equation-3drift-diffusion approximation: j = n j j E D j n j ( j = e, i, n)drift term (motion induced by electric field)

(eq-2)

diffusion term (motion induced by density gradient)

Note: from momentum conservation equation to drift-diffusion approximation

mnu + (mnuu) = qnE p mnmu t = nu = qnE p q kT = nE n mm mm mm mm

(eq-6)(eq-7)

= nE Dn

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2.2 Governing equation-4electron energy equation (EEE):

( ne ) t

5 5 + e ne De = e E Qe-N 3 3 electron heating

(eq-3)

change in time electron energy flux

collisional energy loss

collisional energy loss with background neutral:

Qe-N = l

Elth klr ni ni ni

me el kb k ne ng (Te Tg ) +3 mg e

(eq-8)

inelastic loss (reaction, vibrational excitation)

3 e = kbTe : electron temperature 2 elastic loss with background gas

G.J. M. Hagelaar et al., Plasma Sources Sci. Technol. 14, 722 (2005) R.E. Robson, et al., Rev. Mod. Phys. 77, 1303 (2005)

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2.3 Necessary parameters-1

electron (e) mobility () [m2V1s1] f ()

ions (i) const. f (, T)

neutrals (n) 0

diffusion (D) [m2s1] elastic collision rate coefficient (kel) [m3s1] inelastic collision rate coefficient (kr) [s1, m3s1, m6s1]

f ()

f (T)

f ()

0

0

f ()

f () or f (T)

f () or f (T)

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2.3 Necessary parameters-2: electronscollision cross section (with helium)10-19 -20 -21 -22 -23

[m ]

10 10 10 10

10

-2

10

-1

10 10 10 10 electron energy [eV]

0

1

2

3

10

4

Elastic 3 2S 1 2S 3 2P 1 2P 3SPD 4SPD 5SPD Ionization

Boltzmann equation f e + u f E v f = R( f ) for electrons: t me100

2

(eq-9)

EEDF

EEDF (electron energy distribution function)If EEDF is Maxwellian

10 10 10

-2

Actual EEDF is non-Maxwellian !

-4

-6

0

10

20 30 40 energy [eV]

50

60

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2.3 Necessary parameters-3: electronsparameters for electron (in He, 1 atm, and 300 K)0.5 0.4 1.0

10 10

-12

diffusion mobility

0.8

-14

e [m /sV]

2

0.3 0.2 0.1 0.0 0.12 4 6 8 2 4 6 8 2 4

0.6 0.4 0.2 0.0

[m /s]

elestic collision excitation stepwise ionization2 4 6 8 2 4

De [m /s]

3

10 10 10

-16

k-18

r

2

ionization6 8 2 4

-20

1 10 mean electron energy [eV]

0.1

1 10 mean electron energy [eV]

fitting functions or numerical lookup tables

e = e ( ) , De = De ( )k el = k el ( ) , k r = k r ( )

from electron energy equation

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2.3 Necessary parameters-4: ion mobility1. Experimental data from literature:H.W. Ellis, et al, At. Data Nucl. Data Tables 17, 177 (1976 ) H.W. Ellis, et al., At. Data Nucl. Data Tables 22, 179 (1978) H.W. Ellis, et al., At. Data Nucl. Data Tables 31, 113 (1984) L.A. Viehland, et al., At. Data Nucl. Data Tables 60, 37 (1995)

2. Estimation from theoryi =3.6 103 1 + mg / mi3 p mg ( / a0 )

ion mobility in helium [103 m2/Vs]

[m2 /Vs]Bohr radius

(eq-10)

He+ N+ N2+ N4+ O+ O2+ He2+

1.16 2.19 2.28 1.60 2.25 2.18 1.83

NO+ N2O+ NO2+ H+ H2+ OH+ H2O+

2.15 1.84 1.78 3.39 2.69 2.69 2.28

[atm] [g-mol]

polarizability

Yu.P. Raizer, Gas Discharge Physics, (Springer, Berlin,1997) page 25

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2.3 Necessary parameters-5: diffusion of ionsGER (generalized Einstein relation)H.W. Ellis, et al, At. Data Nucl. Data Tables 17, 177 (1976 )

mi + mg mg ( i E )2 kbTi kbTi Di = = i , Ti = Tg + mm qi 5mi + 3mg kbfrom (eq-7)

(eq-11)

effective heating from electric field

effective ion temperature in He gas100

Ti / Tg

10

N2

+

He1 104 2 4 6 8

+6 8

10 10 electric field [V/m]

5

2

4

6 8

6

2

4

10

7

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2.3 Necessary parameters-6: diffusion of neutralsclassical gas kinetic theorymn + mg 3/ Dn = 1.8583 103 Tg 2 mn mg [atm]

1/ 2

Lennard-Jones radius []

12 p LJ LJ

(eq-12)collision integral [-]

LJ []H He N O H2O N2 2.313 2.576 2.937 2.663 2.591 3.0985

LJ [-] 0.7713 0.6257 0.7298 0.7367 0.888 0.7487 NO O2 H2O2 N2O NO2 O3

LJ []3.099 3.017 3.017 3.202 3.038 3.338

LJ [-] 0.7487 0.7546 0.755 0.8092 0.7981 0.7898

R.B. Bird, et al., Transport Phenomena (Wiley, New York, 2002), page 526 R.J. Kee, et al., Sandia Report SAND86-8246 (1986)

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2.4 Boundary condition-1Boundary conditions for species continuity equationselectrons: e n = ne ions: neutrals:1 4 8kbTe + s e ne E s i ( i n ) (eq-13) me i (eq-14) (eq-15)

8kbTi 1 i n = ni + s i ni E mi 4 8kbTn 1 n n = nn mn 4

switching functions = 1 (E n 0) 0 (E n < 0) 1 (E n < 0) 0 (E n 0) (eq-16)

Ei e e n e n

Ei

s =

G.J.M. Hagelaara, et al., Phys. Rev. E 62, 14521454 (2000) Y.B. Golubovskii, et al, J. Phys. D 35, 751 (2002)

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2.4 Boundary condition-2secondary electron emission coefficient from ions and metastables Ei e e

Ei

~ 0.016 E th 2

(

)

(eq-17)

(semi-empirical formula) secondary electron emission coefficient ( = 5.0 eV)

work function

[eV]Al Fe Ni W Pt 4.25 4.31 4.5 4.54 5.32 He* He+ He2* He2+ N+

0.16 0.23 0.13 0.20 0.15 O+ N2+ O2+ N4+ O4+

0.1 0.09 0.03 0.07 0.03

Yu.P. Raizer, Gas Discharge Physics, (Springer, Berlin,1997) pages 68-71

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2.4 Boundary condition-3Boundary conditions for electron energy equation (EEE)option 1: = const. (0.5 or 1.0 eV) option 2: n = e n w s i ( i n ) i

5 3

inward flux

from secondary electrons (w~5 eV)

(eq-18)

1D RF discharge in helium ( = 320 V)5

m ]

1.2 0.8 0.4 0.0 0.0

electron energy [eV]

-3

ne (BC-1)

ne (BC-2)

4 3 2 1 0 0.0

(BC-2)

[10

17

density

(BC-1)

0.5

1.0 x [mm]

1.5

2.0

0.5

1.0 x [mm]

1.5

2.0

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2.4 Boundary condition-4Boundary conditions for Poissons equationoption 1: = ext at a powered conducting electrode =0 at a grounded conducting electrode option 2: on a dielectric surface

0 E = 0 r Ed + e s d sdtfrom Gausss law

(eq-19) (eq-20)interface (s, s) dielectric gas E x 0 ld

= q j jj

for perfect dielectric:

Ed =

s 0 Ld

Ed

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2.5 Local field approximation (LFA)-1Two options to calculate mean electron energyEEE: LFA: ( ne ) t 5 5 + e ne De = e E Qe-N 3 3 (eq-3)

EEDF (F0)

= 0 3 2 F0 d

= f (E)

a fitting function or lookup table Electron energy dependence of field10

10

18

comparison between EEE and LFA

energy [eV]

[m ] density

Table Fitting

-3

1 0.1

10

17

10

16

ne EEE LFA

ni

nn

He, 1 atm, 300 K0.01 102

10

3

10

4

10

5

10

6

10

7

10

15

0.0

0.5

electric field [V/m]

1.0 x [mm]

1.5

2.0

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2.5 Local field approximation (LFA)-2A problem of the LFA in atmospheric pressure plasmasne E

ne e E

Dene

e e x ( ne ) t

e E = ( ne e E Dene ) E < 0heating rate

electrons are cooled by field!?

EEE:

5 5 + e ne De = e E Qe-N ~ 0 3 3

Not negligibleY. Sakiyama et al., J. Appl. Phys. 101, 073306 (2007) V.R. Soloviev et al., J. Phys. D 42, 15208 (2009)

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3. Simulation using COMSOL and MATLAB3.1 Introduction 3.2 How to set up and run a model in COMSOL 3.3 COMSOL with a MATLAB script 3.4 Example: plasma needle simulation (updated!)

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3.1 IntroductionProblem settingn j t + j = R j ,ll

( j = e, i, n)

(eq-1) (eq-2) (eq-3) (eq-4)

e n

j = n j j E D j n j ( j = e, i, n)

i

5 5 + e ne De = e E Qe-N 3 t 3 ( j = e, i, n) 0 E = q j n jj

( ne )

How to set up and run a model in COMSOL? How to evaluate the simulation results? How to control the current/power, instead of voltage?

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3.2 Setting up and running a model-1General idea about COMSOL Multiphysics A convenient and powerful platform to solve reactive plasma equations: usually sets of coupled, nonlinear PDEs (partial differential equations) with associated initial and boundary conditions Treat charged and neutral species as continuum fluids (fluid model) Use either predefined modules (e.g. convection and diffusion, Helmholtz equation, etc.) or general PDE form Matlab scripts offer more flexible control of COMSOL ( e.g. solving equations sequentially and iteratively)

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3.2 Setting up and running a model-2Before starting to build a model cross section 1. drift-diffusion approximation m >> RF1

solve Boltzmann equation

m: ~1011-1012 [s1] for electrons ~109-1010 [s1] for ions

reaction rate

e, D e

2. electron energy equation (~109) >> RF1

solve plasma equations

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3.2 Setting up and running a model-3Step 1: Input constant parameters and variables Step 2: Draw simulation domain and generate meshes use of symmetry (3D 2D 1D)

Step 3: Add the governing equations and the boundary conditions general PDE mode rather than predefined modules Lagrange quadratic element mostly works finer meshes at electrodes and coarser meshes at the center

Step 4: Select time dependent solver UMFPACK (default linear solver), or PARDISO (memory efficient) Absolute tolerance: 0.0001, Relative tolerance : 0.001

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3.2 Setting up and running a model-4A few more tips before running the simulationInitial conditions: continuity equation: low and uniform density (e.g. ~1012 m3) electron energy equation: low and uniform (e.g. ~1 eV) Poissons equation: linear potential profile between electrodes Periodic steady state: Running for 100-1000 RF cycles Recording transient data of all variables to see the convergence at a fixed point (e.g. at the center)

Run the simulation!

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3.2 Setting up and running a model-5Transient behavior of variables at the center of gap (= 1 mm)2.01.4

Phase-averaged properties after 500 RF cycles5

normalized variables1.5

nn1.2

ne

ni

4

m ]

electron energy [eV]

-3 17

1.0 0.8 0.6 0.4 0.2

1.0

ne0.5

ni

density

[10

3 2

nn

1 0 2.0

0.0

0

100

200

300

400

500

0.0 0.0

0.5

number of RF cycles

1.0 x [mm]

1.5

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3.2 Setting up and running a model-6load of the model number of meshes: ~250 number of DOF: ~4000 60 RF cycles per hour (~5 hours until a steady state) memory usage: ~ 600 MB

computational environment CPU: dual AMD Opteron 250 memory: 12 GB OS: Linux (OpenSuse)

After running the simulationtotal current continuity: jtotal = 0E + q j j = const. t j hi E Di 1022

10

19

metastablesdensity [m ]-3

10

21

density [m ]

metastables1018

-3

10

20

10

17

positive ions

10

19

positive ions1016

10

18

electrons1015

electrons0.4 0.6 0.8 1.0 1017

0.0

0.2

0.0

0.2

0.4

0.6

0.8

1.0

distance from inner electrode [mm]

distance from inner electrode [mm]

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3.4 Plasma needle-11: 1D spherical model< phase-averaged total ionization rate >10 10 ionization rate [m s ]-3 -1 28

1 mm He1000 mW 300 mW 100 mW

27

10 10 10 10 10

26

25

24

23

He (He flow: 2 m/s)0.2 0.4 0.6 0.8 1.0 distance from the inner electrode [mm]Photo: collaborative work with Dr. E.Stoffles in Eindhoven University of Technology

22

0.0

44

3.4 Plasma needle-12: 2D and 1D

10

20

< low power condition >10

21

< high power condition >metastables

10 density [m ]-3

19

metastables density [m ]-3

10

20

10

18

positive ions

10

19

10

17

10 electrons

18

electrons

positive ions

10

16

0.0

0.2

0.4

0.6

0.8

1.0

10

17

0.0

0.2

0.4

0.6

0.8

1.0

distance from inner electrode [mm]

distance from inner electrode [mm]

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3.4 Plasma needle-13: 2D and 1DPower-voltage curve2D axisymetric 1D spherical

Time-averaged densityelectron He2* density [m ]10 10 10 10 1021 20 19 18 1721 20 19 18 17

He* He2+

He+ N2+

20

-3

1D spherical

power [mW]

15 10

density [m ]

10 10 10 10 10

5 0

-3

2D axisymmetric (on the axis)

80

120

160

200

voltage amplitude [V]

0.0

0.2

0.4 0.6 z [mm]

0.8

1.0

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4. Plasma chemistry at atmospheric pressure

4.1 Introduction 4.2 Chemical reactions in fluid model 4.3 Example-1: simplified chemistry model for helium with impurity 4.4 Example-2: plasma chemistry in air 4.5 Tips for simulation with detailed chemistry model (advanced)

47

4.1 Introduction

Mass spectrometry in helium plasma needle discharge

E. Stoffels, et al., Plasma Sources Sci. Technol. 15, 501 (2006)

E. Stoffels et al., IEEE Trans. Plasma Sci., 36, 1441 (2008)

48

4.2 Chemical reactions in fluid models-1Maxwellian? Yes! classical gas kinetic theory transition state theory empiricallyk r = c0T c1 exp( E th / kbT ) (eq-24)

No (= electrons) cross sections for various species and paths

solve Boltzmann equationvarious electron impact reaction rate coefficients

(c1= 0: Arrhenius equation)

e, D e

reaction rate coefficients for neutrals/ions

solve plasma equations

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4.2 Chemical reactions in fluid models-2A + e A* + e A + e A+ + 2e A* + e A+ + 2e A2 + e A + A + 2e A* + A* A+ + A + e A* + B B+ + A + e A+ + e + M A + M A + e A A + B A + B + e A+ + B A + B+ A+ + B + M A + B + M A+B+MC+D+M f() f() f() f() f(Tg) f(Tg) f() f() f(Tg) f(Tg) f(Tg) f(Tg) electron impact excitation electron impact ionization stepwise ionization electron impact dissociation associative ionization Penning ionization electron recombination electron attachment electron detachment charge transfer ion recombination neutral-neutral reaction

f(): rate constant obtained by solving Boltzmann equation

50

4.2 Chemical reactions in fluid models-3Resources for reaction rate coefficient and cross sections data set Cross section data set by A.V. Phelps in JILA (http://jila.colorado.edu/~avp/) Cross sections available in BOLSIG+ GAPHYOR online database (http://gaphyor.lpgp.u-psud.fr/) M. Capitelli, et.al, Plasma kinetics in atmospheric gases (Springer, Berlin, 2000). L.M. Chanin, et al., Phys. Rev. 128, 219 (1962). T. D. Mark, et al., Phys. Rev. A 4, 1445 (1971). H.W. Ellis, et al., At. Data Nucl. Data Tables 22, 179 (1978). C.B. Collins, et al., J. Chem. Phys. 68, 1391 (1978). J.W. Parker, et.al, J. Chem. Phys. 75, 1804 (1981). J.M. Pouvesle, et.al, J. Chem. Phys. 77, 817 (1982). H. Bohringer, et al., Int. J. Mass Spectrom. Ion Phys. 52, 25 (1983). J.M. Pouvesle, J. Chem. Phys. 83, 2836 (1985). F. Emmert, et al., J. Phys. D 21, 667 (1988).

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4.2 Chemical reactions in fluid models-4 H. Matzing, Adv. Chem. Phys. 80, 315 (1991). I.A. Kossyi, et.al, Plasma Sources Sci. Technol. 1, 207 (1992). M.J. Kushner, J. Appl. Phys. 74, 6538 (1993). P.C. Hill, et al., Phys. Rev. A 47, 4837 (1993). T.L. Williams, et al., Mon. Not. R. Astron. Soc. 282, 413 (1996). R. Atkinson, et al., J. Phys. Chem. Ref. Data 26, 1329 (1997). G.S. Voronov, At. Data Nucl. Data Tables 65, 1 (1997). O. Eichwald, et al., J. Appl. Phys. 82, 4781 (1997). H. Tawara, et al., NIFS DATA-51 (1999). V.G. Anicich, J. Phys. Chem. Ref. Data 22, 1469 (1999). S. Rauf, et al., J. Appl. Phys. 88, 3460 (1999). L.W. Sieck, et al., Plasma Chem. Plasma Process. 20, 235 (2000). J.T. Herron, et al., Plasma Chem. Plasma Process. 21, 459 (2001). I Stefanovic et al., Plasma Sources Sci. Technol. 10, 406416 (2001). F. Tochikubo, et al., Jpn. J. Appl. Phys. 41, 844852 (2002). R. Dorai, et al., J. Phys. D 36, 666 (2003). C.D. Pintassilgo et al., J. Phys. D 38, 417430 (2005). K.R. Stalder, et.al, J. Appl. Phys. 99, 093301 (2006). etc. etc. etc

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4.3 Helium plasmas with impurity-1He DBD for material processing OES in helium glow DBD

measured waveform

A. Ricard et al., Surf. Coat. Tech. 112, 1 (1999)

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4.3 Helium plasmas with impurity-2Index R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R12 R13 Reaction He + e He* + e He + e He+ + 2e He* +e He+ + 2e He* + 2He He2* + He He+ + 2He He2+ + He He2 + M 2He + M 2He*+ *

He R1

R2

He+ + R3

e

He* R7 R4 He2* R10 R11 N2+ + e R8 He2+ + e

He2 + e He* + He

+

2He2* He2+ + 2He + e He2 + e He* + N2 N2+ + He + e He2* + N2 N2+ + 2He + e He2+ + N2 N2+ + He2* N2+ + e N2

Y B. Golubovskii, et al.,J. Phys. D 36, 39 (2003) Y. Sakiyama et al., J. Appl. Phys. 101, 073306 (2007)

54

4.3 Helium plasmas with impurity-3Particle density distributions with 0.5ppm N2 (helium RF) Volume-averaged particle density for different impurity level (helium DBD)

T. Martens et al., Appl. Phys. Lett. 92, 041504 (2008) X. Yuan, et al., IEEE Trans. Plasma Sci., 31, 495 (2003)

55

4.4 Plasma chemistry in air-148 species 11 negative particles: e, O, O2, O3, O4, H, OH, NO, N2O, NO2, NO3 16 positive particles: N+, N2+, N3+, N4+, O+, O2+, O4+, NO+, N2O+, NO2+, H+, H2+, H3+, OH+, H2O+, H3O+ 21 neutrals/radicals: N, N*, N2, N2*, N2**, O, O*, O2, O2*, O3, NO, N2O, NO2, NO3, N2O5, H, H2, OH, H2O, HO2, H2O2 630 reactions 21 electron impact excitation/ionization/dissociation 76 electron recombination/attachment 159 charge transfer 245 ion recombination 129 neutral-neutral reactions

56

4.4 Plasma chemistry in air-2Various air DBD devices for biomedicine

Drexel, US

Berkeley, US

Max-Planck, DE

Model description pulse-like plasmas 0D simulation (spatially uniform plasmas) pressure: 1 atm gas temperature: 300 K gas concentration: air with 30% humidity computational time: ~10 hours (Dual Opteron 250, 12GB Mem, comsol3.5a)

n j t

= R j ,ll

on (100 ns)

E = 3106 V/m ne = 1017 m3

1 cycle (100 s)

57

4.4 Plasma chemistry in air-3

time development of species density (in periodic steady state)10 10 100

-1 -2 -3 -4 -5 -6 -7 -8 -9

Ox NxOy

neutrals

positive ions

negative ions

density fraction

10 10 10 10 10 10 10

HxOy Nx+ HxOy + Ox

Ox HxOy-

-

NxOy

-

electron-7 -5

10

-9

10 time [s]

-7

10

-5

10

-9

10 time [s]

-7

10

-5

10

-9

10 time [s]

10

58

4.4 plasma chemistry in air-4phase-averaged species density (in periodic steady state)10 10 100

-1 -2 -3 -4 -5

O3

density fraction

10 10 10 10 10 10

O2 H2 N O OH NO

*

H2O2 HO2

N2O NO2

N2O5

-6 -7 -8

NO3

(charged particle density < 10ppb)

59

4.4 plasma chemistry in air-5Ozone reaction paths 3%: NO + O3 NO2 + O2 4%: O2* + O3 O + 2O2 6%: e + O3 O + O2 + e

74%O + O2 + M O3 + M

6%: O3 + OH HO2 + O2

60

4.4 plasma chemistry in air-6NO reaction paths 4%: N + OH NO + H

41%: NO + O3 NO2 + O2

5%: NO + HO2 NO2 + OH

8%: N* + O2 NO + O*

30%: O + NO2 NO + O2

61

4.4 plasma chemistry in air-7NO2 reaction paths 4%: NO + HO2 NO2 + OH 7%: O + NO2 + M NO3 + M 8%: NO2 + NO3 + M N2O5 + M 29%: O + NO2 NO + O2

40%: NO + O3 NO2 + O2

62

4.4 plasma chemistry in air-8O2 O e, O2* O3 OH N HO2 NO2 O NO3 N2O5 NO N*

63

4.5 Tips for complex chemistry model-1Before starting simulation with hundreds of reactionsn1 1 + 1 = R1 + R12 + K + R1Nr t n2 N 1 2 + 2 = R2 + R2 + K + R2 r t M nNs N 2 + Ns = R1 s + RNs + K + RN r N s t

Ns

highly nonlinear problems (stiff problem)

heavy computation

Nr For example 40 species/700 reactions (air) one-dimensional, RF excitation 12 GB, Dual Opteron 250

wait for a few months until reaching steady state?

64

4.5 Tips for complex chemistry model-2To reduce the computational time1. Sensitivity analysisdn j dt + j = R (klr , t ) = klr nl nl (eq-1 ) (eq-25)

d n R R R t = = + dt klr klr klr t klr dS jl R R S jl = 0 = r + dt kl n j(steady state assumption)

R R n j = r + r kl n j kl (eq-26)

S jl =

n klrsensitivity coefficient

R S jl = n j (jl) matrix

1

R klr

(eq-27)

(l1) matrix

low computational load perturbation around equilibrium state sensitivity dominant reaction pathH. Rabitz et al, Ann. Rev. Phys. Chem. 34, 419 (1983)

65

4.5 Tips for complex chemistry model-3To reduce the computational time2. Reference calculation solve ODEs in several typical conditions (e.g. given ne, )dn j dt + j = R(klr , t ) = klr nl nl (eq-1 )

calculate contribution matrix (normalized reaction rates for each species)species

R11 L R1Ns O M lj = M R N r 1 L R Ns N r normalized

reaction

(eq-28)

medium computational load directly evaluating reaction rate need of finding typical conditions

eliminate unimportant reaction paths (e.g. 1% threshold)

66

5. Neutral gas dynamics5.1 Introduction 5.2 Interaction between neutral gas flow and plasmas 5.3 Example-1: Plasma jet and flow (one-way coupling) 5.4 Example-2: RF plasma needle and flow (two-way coupling)

67

5.1 IntroductionLoughborough, UK

gas: rare gas, air, hydrocarbon power: DC, RF, MicrowaveGreifswald, GE Eindhoven, NL Old Dominion, US

application: etching, thin film deposition, biomedicine

air feed gas plasmas

68

5.2 Plasma-flow interaction-1Assumption: laminar flow, no thermal radiationRe = ud

< Rec (~ 2000 : inside a tube)

Governing equations for neutral gas flow:total mass conservation:

( u ) = 0 T + ucpT = Q ( air u Dair ) = 0 p = RT

(eq-29) (eq-30) (eq-31) (eq-32) (eq-33)

total momentum conservation: ( uui ) = p ( 0 ) g total energy conservation: mass conservation of air: perfect gas law:

(

)

(need compressible N-S equation !)R.B. Bird, et al., Transport Phenomena (Wiley, New York, 2002)

69

5.2 Plasma-flow interaction-2

neutral gas heat and mass transfer model gas temperature gas velocity gas component

momentum transfer energy transfer

plasma fluid model

background gas density mobility and diffusion coefficients for electrons/ions diffusion coefficients for neutrals reaction rate coefficients (including elastic energy loss) flux of species

70

5.2 Plasma-flow interaction-3Momentum transfer from plasmas to neutral gas flowbody force (ion wind): f pls ~ qi ni Efrom ions

(eq-34)E N N i N N

mnu + (mnuu) = qnE p mnmu t f pls = mn jm, j u jj =i , e

(eq-6)

=

m j n j u j q j n j E p j (m j n j u j u j ) t j =i , e

Under typical conditions: qi ni E > qe ne E, kb(neTe ) > othersJ.P. Boeuf et al., J. Appl. Phys. 97, 103307 (2005) C.C. Leiby, Phys. Fluids 10, 1992 (1967) J-S Chang, IEEE Trans. Diel. Electr. Insul. 1, 871 (1994)

71

5.2 Plasma-flow interaction-4Energy transfer from plasmas to neutralheating source: Qpls ~ Qe-N + qi i E + QN-Nelectrons (eq-8) ions

(eq-35)

chemical reactions

Energy transfer between electrons, ions, and neutrals

external electrical power P = qe e E + qi i E (=Joule heating) source terms for EEE source terms for IEE

Se = qe e E Qe-N Qe-ielastic collision

Si = qi i E + Qe-i Qi-N Qi-N ~ qi i E + Qe-i

(~ 0)

Qpls = Qe-N + Qi-N + QN-N = Qe-N + qi i E + Qe-i + QN-Nfrom plasmas to neutral

72

5.2 Plasma-flow interaction-5Assumption: heat/mass transfer from neutral ( < ~103 s) >> RF (external electric field oscillation)

solve time dependent plasma equations for one RF cycle

f pls =

1

RF

RF

0

qi ni Edt ,

Qpls =

1

RF

RF

0

qi ni E dt

solve steady state neutral gas flow equations

73

5.3 Plasma jet-1: introduction

X.Liu and M.Larousi, J. Appl. Phys. 100, 063302 (2006).

Observed ring-shaped emission pattern

M. Teschke et al, IEEE Trans. Plasma Sci. 33, 310 (2005)

N. Merciam-Bourdet et al, J. Phys. D 42, 055207 (2009)

74

5.3 Plasma jet-2: one way coupling He: 7 slpm 7 kV pulse excitation 8 kHz repetitionr N2 He

2D steady state neutral gas flow N2 density distribution

N2 densityc

1D plasma dynamics in cylindrical coordinates (cross sectional view)

r

75

5.3 Plasma jet-3: neutral gas flow0.4

mole fraction of N 2

0.3 0.2 0.1 0.0 0.0

Compressible N-S equation ( u ) = 0

: total mass continuity

N2 u DN2 = 0 : continuity for N2 ( uui ) = p 0.5 1.0 r [mm] 1.5 2.0

(

)

: total momentum continuity

Mole fraction of air20 r [mm] z

N2 rich

10

He channel

0 -20

-10

0

10

20

30

40

50

He rich

76

5.3 Plasma jet-4: plasma dynamicsN2 species: e, He*, He2*, He+, He2+, N2*, N2+

nN2 rate coefficients: from local Boltzmann equation(local field and N2 concentration)

He channel 0

pressure: 1 atm

r

temperature: 300 K solver: COMSOL and Matlab

Fluid model with local field approximation

ni 1 (ri ) + = Si t r r

(mass continuity)

ni i = sgn(qi ) ni i Er Di (drift-diffusion) r 1 (rEr ) = qi ni (Poissons eq. in r-direction) 0 r r i

77

5.3 Plasma jet-5: given electric field

nN2

r

Ez0

r

Given electric field (not self-consistent!) Ez = 3105 V/m 400 ns 0 125 s (8 kHz)reaction rate:

E=

Er + Ez

2

2

Poissons eq.

given

k = f (E)

78

5.3 Plasma jet-6: time evolution of bullet

given electric field

particle density distribution in radial direction

79

5.3 Plasma jet-6: time evolution of bullet

80

5.3 Plasma jet-7: Penning ionization is a keyEz [10 V/m]4 3 2 1 05

0

200

400

time [ns]

600

800

1000

10 10

29

early stage (200 ns)excitation direct ionization Penning ionization

10 10

29

late stage (400 ns)excitation direct ionization Penning stepwise associative

28

28

reaction rate [m s ]

10 10 10 10 10

27

reaction rate [m s ]

-3 -1

-3 -1

10 10 10 10 10

27

26

e He* He He2* N2+

N2 e

26

25

25

24

24

23

23

0.0

0.5

1.0 r [mm]

1.5

2.0

0.0

0.5

1.0 r [mm]

1.5

2.0

81

5.3 Plasma jet-8: for comparison with simulationTime resolution: 1 ns Spatial resolution: ~50 m

inner diameter: 3 mm

amplitude : 7 kV pulse width : 2 s repetition rate : 8 kHz Helium flow: 7 slpm

82

5.3 Plasma jet-9: ionization = emission?6000 5000

+ + B2 u X 2 gOH N2 N2+

3 S , P, D 2 S , PHe He

He O

intensity

4000 3000 2000 1000 0

N2

+

N2

+

He500 600 700

He800

300

400

wavelength [nm]

N2+(B) He*, He2* (40%) kPen He2+ (75%) kchg Emission rate = kem ~ kPen+ kchg (kem >> kPen, kchg) kem N2+(X) kex kem

3SPD

e

2P 2S

Emission rate = kem ~ kex (kem >> kex) ~ kiz (kiz ~ kex)

Effective emission rate = kiz + kPen+ kchg

83

5.3 Plasma jet-10: ring shaped patternY. Sakyiama et al, Appl. Phys. Lett. 96 (2010) 041501

r z 01.0

20 mm

40 mm

integration time for OES: 100 ms (800 bullets)

OES0.8

Model

normalized intensity

0.6 0.4 0.2 0.0 -2

-1

0 r [mm]

1

2

84

5.4 Plasma needle-1: introduction RF(13.56 MHz)-excited gas: He gap distance: 2.5 ~ 4 mm light intensity

0.3 m/s

1.0 m/s

1

2

3

4 radial position

5

6

7

8

1

2

3

4 radial position

5

6

7

5 mm Killing patternJ.Goree, et al, J. Phys. D. 39, 3479 (2006) and IEEE Trans.Plasma Sci. 34, 1317 (2006) (Images courtesy of Prof. John Goree)

85

5.4 Plasma needle-2: two-way couplingNeutral Gas flow He flow ( u ) = 0, ( air u Dair ) = 0 ( uui ) = p + qi ni E T + ucpT = + qi i E + Qel

(mass conservation) (energy conservation)

(momentum conservation)

(

)

air (diffusion) Plasma dynamicsni + i = Si t i = sgn(qi ) ni i E Di ni + ni u ( ne )

(mass conservation) (drift-diffusion)

5 5 + e ne De = e E Q (electron energy) 3 t 3 (Poissons equation) 0 E = qi niY. Sakyiama et al, Plasma Sources Sci. Technol. 18, 025022 (2009).

86

5.4 Plasma needle-3: neutral gas flowHe (1.5 m/s) 1 mm needle N2 (1atm) 2.5 mm z r 5 mm insulator

N2 (1atm)

Unknown variables He/N2 concentration gas pressure

glass plate 5 mm

gas flow velocity (r and z) gas/needle temperature

87

5.4 Plasma needle-4: plasma dynamics

needle 0.85 mm insulator 1.5 mm

1 mm

Unknown variables density: electron, He*, He+,glass plate 2 mm

He2*, He2+, N2+ electron energy electrical potential

88

5.4 Plasma needle-5: gas flow fieldMole fraction of air (log scale) Gas temperature

89

5.4 Plasma needle-6: particle density0.5 0 z [mm]

electrons

1019

He*

-0.5

1018 1017

1018 1016 1018

1017

1016

-1 0.5 0 z [mm]

He2+ 1018

N2+

-0.5

1017 10161017 1.5 2 0 0.5 1 r [mm] 1.5 1016 2

-1

0

0.5

1 r [mm]

90

5.4 Plasma needle-7: ring-shaped emission!Predicted emission intensity0.5

Experimental results by J. Goree et alinsulator needle

e He* He He2* N2+

N2 e He gap: 3 mm

0 z [mm]

He

-0.5

-1 0

0.5

1 r [mm]

1.5 [1023

2 m-3s-1] 1

4 mm

0

0.2

0.4

0.6

0.8

91

5.4 Plasma needle-8: one-way coupling (again)humid air concentration: 2D neutral flow simulation (N-S equation, convection-diffusion) 1D fluid model with detailed chemistry in spherical coordinates on-axis on-axis(1mm gap) Humid air concentration needle Insulator tube

off-axisnair/nHe>10-3 S. mutans

off-axis(2mm gap)

nair/nHe