Modeling of moderate pressure H2/CH4 microwave discharge used for diamond deposition

K. Hassouni, F. Silva, G. Haagelar, X. Duten, G. Lombardi, A. Gicquel(1)

T. A. Grotjohn(2)

M. Capitelli(3)

J. Röpcke(4)

(1)LIMHP, CNRS-UPR 1311, Univeristé Paris 13, 99 Avenue J. B. Clément93430 Villetaneuse, France

(2)Department of Electrial Engineering, Michigan State University, USA East Lansing, USA

(3) Dipartimento di Chimica – IMIP CNR Univeristy of Bari Italy

(4) INP Greifswald

Investigated Device : microwave cavity coupling system + belljar quartz vessel

Usual Experimental Conditions :Feed Gas : H2/CH4 - %CH4 < 5

Pressure : 20-200 TorrInput Power : 0.4-4 kWPower density : 6-100 W/cm3

Flow Rates : 100 - 300 sccm Substrate Temperature : 1000 K - 1300 K

Orders of magnitude :Plasma height 3.5 cm (for 2.45 GHz) Tg > 2000 K - 1011 cm-3 < ne <1013 cm-3

Transport and collisional phenomena in the plasma

Electron heating

Wave-plasma interaction

Electron/heavy species collisions

Energy transfer, ionization, etc...

Heavy species-heavy species collisions

Intermode energy transfer, chemistry

Energy and mass transportConvection, Diffusion

Plasma-surface interaction

Mass and energy transfer

EEDF, <e>

VDF, Tv

ni, i=1-n

Substrate (Ts, cs)

Tg

e + AB

AB(v), AB(r), AB

e

AB+, A, B

Energy and mass transfer

(E,H)

What information do we need ?

I. For a given coupling configuration, What’s the optimal reactor configuration that insures :

1- enhanced density of active species at the growing diamond film, 2- a good thermal stability of the reactor (during up to several weeks )

II. What is the optimal electromagnetic coupling conditions in term of : 1- power2- pressure 2- frequency

process engineering : mass and energy transport, gas phase and surface chemistry

Electrical engineering : resonant electromagnetic modes, wave-plasma interaction

Stro

ngl

y li

nked

Modeling approach

Detailed collisional model in moderate pressure H2 Plasmas* Determination of the main chemical processes and physical phenomena in the reactor.* Set up a satisfactory and useful Physical plasma model

1D transport model of the plasma on the stagnation linefor both H2 and H2/CH4 discharges* Investigate the coupling between Chemistry, Energy Transfer and Transport Phenomena* Determine the behavior of the plasma temperatures and species.

2D Self-consistent model (Only for H2 discharges)

Determine self consistent plasma, electomagnetic field and absorbed power distributions. for axisymmetrical configuration May be used for power deposition optimisation and for scaleup

Detailed Collisional model – H2 (1/2)

I. Vibrational KineticsLarichuta, Celiberto et al.* e- + H2(X,v) ==> e- + H2(X,w) |w-v| < 4

* e- + H2(X,v) ==> e- + H2(B1u,v’) ===> e- + H2(X,w)

* vv relaxation : H2(v) + H2(w) ===> H2(v1) + H2(w 1)

* v-t exchange : H2(v) + H2 (or H) ===> H2(v1) + H2 (or H)

* Dissociation from upper v by heavy species collisions:H2(v) + H2 (or H) ===> 2H + H2 (or H)II. Ground States Kinetics C. D. Scott et al. J. Thermophysics, Vol. 10 1996, p 426* e- + H2(v=4-10) ==> H + H-

* H2+ + H2 ==> H3

+ + H

* Recombination and mutual neutralization of ions

.../..For more detailed description : K. Hassouni, A. Gicquel, M. Capitelli and J. LoureiroPlasma source Science and Technology, 8(3), 494 (1999)

III. Electronically Excited States Kinetics : H2 and HLarichuta, Celiberto et al. H2 : K. Sawada et al. J. Appl. Phys., 78 (5), (1995), p. 2913

H : J. A. Kunc et al., Phys. Fluids, Vol. 30(7), (1987), p. 2255

* e- + H2(v) ==> e- + H2* and e- + H(n) ==> e- + H(m)

* e- + H2 (v) = [H2**]=> H2+ + 2e- and e- + H(n) ==> 2e- + H+

* e- + H2 (v) = [H2**]=> 2H + e-

* H2* + M ==> H2* or 2H

* H(n) + H ==> H(m) + H* M* ==> M*’ + h (M=H or H2)

Optically thick plasma for Lyman radiations M. Glass-Maujean Phys. Rev. Lett., Vol. 62 (2), (1989), p. 144

H(n=2) + H2 ==> H3+ + e- ( = 15-30 A2)

H(n>2) + H2 ==> H3+ + e- - Assumption in this work -

Detailed Collisional model

For more detailed description : K. Hassouni, A. Gicquel, M. Capitelli ad J. LoureiroPlasma source Science and Technology, 8(3), 494 (1999)

Use of the detailed kinetics in the frame of Quasi-homogeneous plasma model

Hom

ogen

eous

Pla

sma

Thi

n B

ound

ary

Lay

er

Subs

trat

e

I n iti a l G u es sE / N , P la s m a c o m p o si t io n , T g

E E D F , R a t e C o n sta n ts , e-s

E le ct r o n B ol tz m a n n E q u a tio nT w o t e r m e x p a n s io n

N e w P la s m a c o m p o s iti o n

S p e ci e s k i n e tic s E q u a tio n s

S p e ci e s a n d e n e r g y L o ss e s a t t h e w a ll

C a lc u la te th e t r a ns p o r t C o e f f i c ie n ts

D a t aM W Pinp , P , t , s, / N

C a lc u la te th e n e w a b s o r b e d M W p o w e r

No

Co r

rect

E/N

acc

o rd

i ng

to (

MW

Pc

- M

WP

i np

)

Y e sT g , E / N , E E D F , V D F a n d S p e c ie s d e n s it i e s

| M W P c - M W Pin p| <

N e w T g

T o ta l E n e r g y E q u a ti o n

Use the effective field assumption => stationary situation

Simulation procedure

EEDFVDF

H2*(n=1-36)

H*(n=1-40)H+, H2

+, H3+, H-, e-

Tg

Quasi-homogenous plasma modelMost significant results : vibrational distribution/

102

0 5 10 15 20 25 3010-3

10-2

10-1

100

101

Den

sité

de

pu

issa

nce

dis

sip

ée (

W/c

m3 )

MWPDav (W/cm3)

Exc. Vib.

Exc. trans-rot.

Dissociation

Exc. Elec. H2

Exc. Elec. H

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.510-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Vibrational quantum

14

13

1211109876543210

MWPDav

= 4.5 W/cm3

MWPDav = 9.0 W/cm

MWPDav

= 15.0 W/cm

MWPDav

= 22.0 W/cm

MWPDav = 30.0 W/cm

VD

F -

(N

v/N

0)

Vibrational energy (eV)

Quasi-homogenous plasma model : most significant results

EEDF behavior and electron impact rate constants

1E-12

1E-10

1E-08

1E-06

1E-04

1E-02

1E+00

0 5 10 15 20 25

Te-l = 19200 K

Te-h = 8500 K

FD

EE

(eV

-3/2)

e(eV)

Bimodal distribution

FDEE Bimodale Te-h = f(Te-l) (univoque)

Energy balance Te-l Te-h

Rate constants only depend on Te-l

We can use a scalar model to describe the electron kinetics

rate constants of Electron-impact process H2 dissociation

1E-221E-211E-201E-191E-181E-171E-161E-151E-141E-131E-121E-111E-101E-9

0 0,5 1 1,5 2 2,5 3 3,5 4

Electron Average Energy (eV)K

d (cm

^3/s)

[H]=0[H]=0.1[H]=0.2[H]=0.3

Quasi-homogenous plasma modelMost significant results

Ionization kinetics & H-atom excited states kinetics

20

10 11 12 13 1410-4

10-2

100

102

104

106

108

Den

sité

(cm

-3)

En (eV)

2 3 4 56

30.0 W/cm3

9.0 W/cm3

Excited state distributioncoupling between excited levels H*H(n=2-3) kinetics do not depend on H(n>3) states

100

MWPDav (W/cm3)10 15 20 25 30 35

10-4

10-3

10-2

10-1

e-+H2 => 2e- + H2+

H2+ + H2 => H3

+ + e-

H(n=2-3) + H2 => H3+ + e-

e-+H => 2e- + H+

ion

isat

ion

rat

e (m

ol. m

-3.s

-1)

Main ionization channel : quenching of H(n=3) and H(n=2) states

Quasi-homogenous plasma modelMost significant results

From full model to simplified model : 9 species [H2,H,H(n=2),H(n=3),H+,H2

+,H3+, e-] /2 energy modes [Tg, eedf]

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0 10 20 30 40

Power density (W/cm^3)

H-a

tom

Rel

ati

ve

den

sity

0 5 10 15 20 25 30 351x10

11

2x1011

3x1011

4x1011

5x1011

6x1011

7x1011

8x1011

9x1011

1x1012

Ele

ctro

n de

nsi

ty (

cm-3)

MWPDav (W/cm3)

Detailed model

Simplified model

Detailed model

Simplified model

2D Self-consistent model for moderate pressure plasma flow

Hassouni, Grotjohn and Gicquel, J. Appl. Phys. (1999)Hagelaar, Hassouni and Gicquel, J. Appl. Phys. (2004)

Plasma simulation

domain

2 Modules

A plasma module simulates the discharge in the low pressure vessel

EM field simulation domain

An electromagnetic module simulates the EM field in the whole cavity

Plasma module2 or 3-temperature thermo-chemically non-equilibrium flow models

Navie-Stockes => Flow velocity

Total energy => Tg

Continuity => species density 0iWinu

i

t

n ii nD

+

Electron energy => Te

H2-vibration mode => Tv

+ div(uehe-eTe) –PEM + Qe-t + Qe-v + Qe- =0Ee

t

+ div(umEv-m-v-mTv-m) + Qv-t - Qe-v + Qv- = 0Ev-m

t

+ div[uihi –t-rT -v-mTv-m –eTe] - PEM + Qrad = 0Et

Coupling nodes

EM module

EM module

tH

E

tE

JH HF 0

HFeffeHF

e mqdtd

m vEv

HFeeHF nq vJ

Electromagnetic moduleA time-domain model where the plasma is considered as a high

frequency conductor

Maxwell Curl equations

plasma model

plasma model

Hassouni, Grotjohn and Gicquel, J. Appl. Phys. (1999)Hagelaar, Hassouni and Gicquel, J. Appl. Phys. (2004)

Momentum equation for the HF component of the electron flow velocity

2D Self-consistent model for moderate pressure plasma flow

Numerical method : Finite Difference Time Domain Method

Ez(

i,j,k

+1/

2)Er(i+1/2,j,k)

E (i,j +

1/2,k)

Hz(

i+1,

j+1/

2,k

)

Hr(i,j+1/2,k+1/2)

H(i+1/2,j,k+1/2)

Ez(

i+1,

j,k

+1/

2)

Er(i+1/2,j+1,k)

t

HErot

0)( Jt

EHrot

0)(

Are naturally satisfied at the grid points

Explicit time integration Leap-Frog shift between E and H, to acheive second order accuracy

2 kinds of boundary conditions are used :Perfect conductor: Et=0 and Hp=0 Nonreflecting boundary condition at the cavity inlet

Staggered grids for the different components of E and H

Only TM modes are considered in this calculation

Define an excitation plane in the computation domain

Te, Tg, ne Grid interpolation

Plasma model12 Transport equations9 espèces -Tg, Tv, <e>

300-400 iterations

Electromagnetic moduleMaxwell Curl equations

HF Momentum equation for electronsE, H, Je-HF, MWPD

15-25 microwave periods

Microwave power densityGrid interpolation

15-20 Iterations

2D Self-consistent modelIteration scheme

Simulation procedure

p, Q-M p

E.Je-HF

Validation of the electromagnetic module

Electric field intensity in the

cavity

Self consistent model without plasma

CST Microwave Studio (Commercial code)

Power density (W.cm-3)

Some results : 600 W – 25 mbarMWPDav=8W/cm-3

Te(K)

20000 K

18 W/cm3

ne(K)

4x1011 cm-3

Tg(K)

2000 K

ne nH Tg

||E||

500 W

800 W

1000 W

Optimal power deposition at 50 mbar

1200 K

600 K

Gas heating is responsible forDischarge regime transition Ignition for maximum E/N

Tg ↗ E/N distribution changes

Very similar to some explenation given for streamer to arc transition

phenomenon

1 ball regime MWPinp↗ Vplasma ↗

thenMWPinp Transition 1B to 2B

2D-self consistent modelFlow effect at high power density

Strong free convection

Inlet

With free convection

Without free convection

1D transport model for H2 plasma flow

•2 Momentum Equations => V=dv/dr|r=0 and u

dudz + 2V +

u

ddz =0 et u

dVdz + V2 -

ddz

dV

dz + =0

•continuity equations for species :

u ddz

Ms

M xsddz

MsM Ds

kTg

dTgdz -

dxsdz + - Ws =0

• 2 energy equations : Tg, Te-l

+e cp-e (u + ue) 23k

d<e>dz

ddz

- 23k e

d<e>dz

-MWPD + Qe-v + Qe-t + Qe-

= 0

Sim

ula

tion

Dom

ain

Substrate

Radial uniformity

2D SC model

1D transport model for H2/CH4 plasma flow

H2/CH4 (Thermal Hydrocraking : C1-2H1-6 species) :

* B. W. Yu and S. L. Girshick, J. Appl. Phys., 75(8), 1994, p. 3914 * C. T. Bowman et al., http://www.me.berkley.edu/gri_mech/Pressure correction on three body recombination reaction

CxHy Charged species kinetics :

Ionization kinetics : e- + CxHy ==> 2e- + CxHy+

•H.Tawara et al., Research Report NIFS-DATA,•Charge transfer kinetics : H3

+ + CxHy ==> H2 + CxHy+1+

* H. Tahara et al., Jpn. J. Appl. Phys., 34.* Dissociative Recombination : CxHy

+ + e- ==> CxHy-1 + H

Lahfaoui et al. J. Chem. Phys., 106 (13)

31 species - 134 reactions model Three reactions Groups

1D transport model for H2 plasma flowSome results

1200

1400

1600

1800

2000

2200

2400

0 1 2 3 4z(cm)

T(K

)

Tg-ModelTv-modelTg-CARSTv-CARS

Substrate Inlet (10 cm)

0,0E+00

2,0E-03

4,0E-03

6,0E-03

8,0E-03

1,0E-02

1,2E-02

0 1 2 3 4z(cm)

H-a

tom

Mol

e F

ract

ion

modelActinometryTALIF

Substrate Inlet (10 cm)

Comparison with experimentsMWPD = 9 W/cm -3 (MWPinp = 600 W and P = 25 mbar)

Conclusion :* Good Agreement on temperatures* H-atom is overestimated in the boundary layer ( 50 %)

1/ 1/ H-atom relative density varies between 1 et 13 % when MWP 9 à 30 W.cm-3

2/ The discharge transitions from a cold non-equilibrium plasma to a thermal plasma

H-atom

Axial profiles of temperature and hydrogen mole fraction

Temperature

Gas

tem

per

atu

re [

K]

Axial position [cm]0 1 2 3 4 5 6 7 8 9 10

1000

1500

2000

2500

3000

3500

(a)

30 W.cm-3

9 W.cm-3

9 W.cm-3

12 W.cm-3

15 W.cm-3

23 W.cm-3

30 W.cm-3

sim

ula

tion

dom

ain

Radiale Uniformity

Substrate

Axial distribution of hydrocarbon species30 W.cm-3 (120 mbar / 2 kW)

CHx C2HyTgmax = 3200 K

1/ C2H2 is the major species (Actually we have H2/C2H2 plasma)2/ Strong density variations in the reacting boundary layer (spatial stiffness)3/ Significant amount of C and C2 species4/ Caution : Interpretation of line of sight measurements outside or inside the discharge ?

5 cm 2.5 cm 25 cm

60 cm

2 cm Tg~3000 K

Tg=600 KTg=300 K

Example : validation of predicted hydrocarbon species densities

TDLAS measurements (INP : Greifswald – J. Ropcke)

Fra

ctio

n m

olai

re

0 5 10 15 20 25 3010

-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Bras optique

C2H4

C2H2

CH4

Position radiale [cm]

CH4

CH3

C2H

2

C2H4

C2H6

C2H6

CH3

Absorption measurements yield :=> CH3 in the dischargeC2H6 outside the dischargeThe model allows to get the spatial distributionand the validation takes place on spatially averaged values

C2H6CH3

C2H2+ :

e-+C2H2 => 2e- + C2H2+

e-+ C2H2+ => C2H + H

CH4 + C2H2+ => C2H3

+ + CH3

C2H3+ :

CH4 + C2H2+ => C2H3

+ + CH3 H3

+ + C2H2 => C2H3+ + H

e-+ C2H3+ => C2H2 + H

C2H5+ :

C2H4 + C2H3+ => C2H5

+ + C2H2 e-+ C2H5

+ => C2H4 + H

1D transport model for H2/CH4 plasma flowComparison with IR absorption measurements

C2H2+ :

e-+C2H2 => 2e- + C2H2+

e-+ C2H2+ => C2H + H

C2H3+ :

H3+ + C2H2 => C2H3

+ + He-+ C2H3

+ => C2H2 + H

C2H5+ :

C2H4 + C2H3+ => C2H5

+ + C2H2 e-+ C2H5

+ => C2H4 + H

Low power density – 9 W/cm-3High power density – 30 W/cm-3

Treatment of more complex discharges ….Sooting discharges for nano and ultranano-crystalline diamond deposition (PAH and soot formation) – undergoing work

Self consistent treatment of pulsed regime – undergoing work

Electron velocity distribution function : anisotropy effect (el exc)

EM field simulation : Resonance region and spatial stiffness

More detailed investigation of the effect of gas heating on the establishment of discharge regimes

Open problems in H/C moderate pressure microwave discharges for carbon films deposition

Soot