On the reaction rates in the low pressure
nitrogen discharge
a,b
E. G. Thorsteinsson
and J. T. Gudmundsson
18
(a)
0.8
e
10
7
N+2
6
+
N
16
10
5
4
Te
15
where Eiz is the ionization energy, Eex,i is the threshold energy and
kex,i is the rate coefficient for the i-th excitation process and kiz is the
ionization rate coefficient for single step ionization.
20
10
N
4
10
3
10
Absorbed power [W]
Wall rec. of N( S)
0.8
+
N /n+
Ri/ΣRi
15
10
0.6
0.4
4
N( S) pumped out
10
100
Te [V]
Figure 1: The collisional energy loss versus electron temperature
for the ground state nitrogen molecule N2(X 1Σ+
g , v = 0) and the
ground state nitrogen atom N(4S). The electron energy distribution
is assumed to be Maxwellian-like.
g
5
Ionization
300
345
390
435
480
525
• Relatively good agreement with measured electron temperature and
electron density is shown in figure 3(a).
• The measured dissociation fraction is much lower than the calculated
value despite the excellent agreement with the measured N+ ion fraction.
1
(a)
0
21
10
Ri/ΣRi
Wall rec. of ions
2
Diss. of N2(A)
1
10
N2(X,v=0)
N(S)
19
Pressure [mTorr]
1
(b)
0.8
v=6
N(P)
18
10
100
Pressure [mTorr]
Figure 2: The density of neutral nitrogen species versus discharge
pressure. The absorbed power is 500 W, the gas flowrate is 50 sccm
and the chamber has the dimensions R = 10 cm and L = 10 cm.
• Wall recombination is the dominating loss mechanism for both ions at
low and intermediate pressures, whereas resonant charge transfer and
dissociative recombination are the most important processes at 100
mTorr for the loss of N+ and N+
2 , respectively.
• Although the calculated dissociation fraction is much larger than measurements, the agreement with the other measured plasma parameters
is good.
• Electron impact dissociation and recombination of atoms on the wall
are generally the dominant pathways for the creation and the destruction of neutral atoms, respectively.
0.4
Ioniz. of N(2D)
Wall rec. of N(2D)
4
Ioniz. of N( S)
Acknowledgments
Wall rec. of N(2P)
1
10
100
17
1
• The ions N+ and N+
2 are almost entirely created by electron impact
ionization of their neutral atomic and molecular counterparts.
• Electron impact ionization is important for the destruction of neutral
atoms at low pressure and high power.
Figure 4: The reaction rates for (a) the overall creation and (b)
the overall destruction of neutral nitrogen atoms versus discharge
pressure. Conditions are as in figure 2.
10
• Wall recombination of neutral atoms is responsible for almost all of
their loss, although electron impact ionization accounts for roughly 35
% of the loss at 2000 W.
0.6
Wall rec. of N( S)
Pressure [mTorr]
N2(A)
• Neutral atoms are created mostly by electron impact dissociation of
1Σ+, v > 0)
,
v
=
0)
at
low
power,
by
dissociation
of
N
(X
N2(X 1Σ+
2
g
g
at intermediate power and by wall recombination at high power.
• Wall recombination of the N+ ion is important for the creation of neutral atoms at low pressure and high power.
4
0
N(D)
v=1
10
100
0.2
20
Figure 5: The reaction rates for (a) the overall creation and (b)
the overall destruction of neutral nitrogen atoms versus absorbed
power. Conditions are as in figure 2.
• Electronically and vibrationally excited species become more important with increasing pressure. The density of N2(X 1Σ+
g , v = 1 − 6) is
comparable to the N2(X 1Σ+
g , v = 0) density above 10 mTorr.
Diss. of N (X,v=0)
N(4S) pump
10
Absorbed power [W]
1000
• The discharge is essentially atomic at low pressure but is dominated
by molecular nitrogen at high pressure.
0.4
0
100
Conclusions
Diss. of N2(X,v>0)
0.6
0.2
Ri/ΣRi
• The surface recombination coefficient for atomic nitrogen in assumed
to be 0.07 (Singh et al., 2000a).
• The gas temperature is assumed to have a linear dependence on the
absorbed power, Tg = 0.17 × Pabs + 387 K.
• The density of neutral species versus pressure is shown in figure 2.
The atomic density decreases above 10 mTorr whereas the molecular
density increases monotonically with pressure.
• Vibrationally excited ground state molecules N2(X 1Σ+
g , v > 1) are important at intermediate and high pressure, but negligible at 1 mTorr.
• Density of charged species versus pressure is shown in figure 3(a). The
density of N+ is comparable to the N+
2 density at 1 mTorr, but decreases rapidly with presssure above 10 mTorr.
2
0.2
0.8
Results and discussion
2
Wall rec. of N( D, P)
N/n
2
1
(b)
4
10
1
1000
1
Figure 3: Comparison of the calculations with measurements. (a)
the electron density and # the electron temperature measured
by Singh and Graves (2000b) as a function of discharge pressure.
The absorbed power is 240 W. (b) 2 the fraction of the N+ density
versus the total ion density and # the fractional dissociation measured by Singh and Graves (2000c) as a function of absorbed power
(Pabs ≃ 0.75 × Prf ). The discharge pressure is 30 mTorr. Other
conditions are as in figure 2.
N2
Wall rec. of N+
N+
2
100
Absorbed power [W]
5
Ec [V]
Diss. rec. of
0
(b)
10
Density [m−3]
0.2
1
100
10
6
10
0.4
+
N4
1
0
10
2
Pressure [mTorr]
Fractional concentration
i
Diss. of N (X,v>0)
2
N+3
14
0.6
Diss. of N (A)
3
10
Diss. of N2(X,v=0)
2
10
• In addition to electrons the nitrogen discharge consists of molecular nitrogen in ground state N2(X 1Σ+
g , v = 0), vibrationally excited molecular nitrogen N2(X 1Σ+
g , v = 1 − 6), metastable molecular nitrogen
4S), metastable atomic
N2(A3Σ+
),
atomic
nitrogen
in
ground
state
N(
u
+ and N+.
,
N
nitrogen N(2D) and N(2P), and the positive ions N+, N+
2
3
4
• A comprehensive reaction set has been developed that includes roughly
450 interactions of the discharge species.
• Electrons are assumed to have a Maxwellian-like energy distribution in
the range 1 – 10 V.
• The collisional energy loss per electron-ion pair created is defined as
X
kex,i kel 3me
Ec = Eiz +
Eex,i
+
Te
(1)
kiz
kiz mi
(a)
8
17
Density [m−3]
The global (volume averaged) model
1
9
Ri/ΣRi
Introduction
10
• A global (volume averaged) model is applied to study a low pressure
(1 - 100 mTorr) high density nitrogen discharge in the steady state.
• Based on a previous model of the O2/Ar discharge (Gudmundsson and
Thorsteinsson, 2007)
,
Science Institute, University of Iceland, Reykjavik, Iceland
b
Department of Electrical and Computer Engineering,
University of Iceland, Reykjavik, Iceland
∗
[email protected]
Te [V]
a
a,b,∗
• Neutral atoms are mostly created by electron impact dissociation of
+ on the
N2(X 1Σ+
,
v
>
0)
at
high
pressure
but
by
recombination
of
N
g
wall and dissociation of N2(X 1Σ+
g , v = 0) at low pressure.
• Nearly all neutral atoms are generally lost by recombination on the
wall, with electron impact ionization and pumping of species out of
the chamber being important only at low pressure.
This work was partially supported by the Icelandic Research Fund, the
University of Iceland Research Fund and the Icelandic Research Fund for
Graduate Students.
References
J. T. Gudmundsson and E. G. Thorsteinsson, Plasma Sources Science
and Technology 16, 399 (2007).
H. Singh and D. B. Graves, Journal of Applied Physics 87, 4098 (2000a).
H. Singh, J. W. Coburn and D. B. Graves, Journal of Applied Physics
88, 3748 (2000b).
H. Singh and D. B. Graves, Journal of Applied Physics 88, 3889 (2000c).