modeling of moderate pressure h 2 /ch 4 microwave discharge used for diamond deposition
DESCRIPTION
(1) LIMHP, CNRS-UPR 1311, Univeristé Paris 13, 99 Avenue J. B. Clément 93430 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. - PowerPoint PPT PresentationTRANSCRIPT
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