Effect of collision induced dissociation reactions in the sheath
on ion energy distributions in capacitively coupled plasma
containing CF4 and H2
Wen-Cong Chen, Xi-Ming Zhu and Yi-Kang Pu
Department of Engineering Physics, Tsinghua University, Beijing 100084, China
Abstract: Ion energy distributions (IEDs) in CF4 and H2 capacitively coupled plasma are investigated by
experimental measurement and theoretical modeling. Continua structures in measured IEDs of CF2+, CF+, C+
and H+ are observed, which are different from charge-transfer-dominant multi-peak structures. A simple model
is introduced to reconstruct IEDs. IEDs predicted by the model are in good agreement with measurements. It’s
found that the continua structures are mainly due to collision induced dissociation (CID) reactions of CF3+ and
H3+ in the sheath.
Keywords: collision induced dissociation, ion energy distribution, capacitively coupled plasma
1. Introduction
2. Measurement
Anisotropic etching of semiconductor materials
during plasma processes is available due to
perpendicular ion bombardments on the substrate.
Ion-neutral reactions in the sheath can greatly
change the energies and fluxes of ions bombarding
the substrate in capacitively coupled plasmas (CCP).
The ion transfers its charge but not its kinetic energy
to the neutral species in charge transfer (CT)
collisions. Therefore the initial velocity of the
secondary ion, which is produced in the sheath, is on
the order of the thermal velocity. Characteristic
multi-peaks in ion energy distributions (IEDs) due to
CT have been observed by different researchers, and
the ion dynamic has been explained.1-2 On the other
hand, certain secondary ions can inherit part of the
kinetic energy of the parent ions in collision induced
dissociation (CID) processes.3 These dissociation
reactions may be responsible for the continua
structures in IEDs measured in CCP containing CF4
and H2.4-5 However, this argument still needs to be
verified.
IEDs on the grounded electrode are measured in a
CF4 capacitive discharge. Details of the setup have
been described in our previous work.7 Briefly, the
plasma is confined between two electrodes by
ceramic and quartz parts, and ion signals are
collected by an energy-resolved mass spectrometer
(Hiden EQP1000) mounted at the center of the
grounded electrode.
In this work, a simple method based on Israel et.
al.’s IED model is used to identify the originals of
ions in IEDs in CCP containing CF4 and H2.6 The
model can predict detail structures of IEDs, and the
results are compared with measurements in CF4 and
H2 discharge.
IEDs in a hydrogen capacitive discharge have been
measured in a similar system by O’Connell.5 IEDs in
H2 presented in this work are taken from Ref.[5] for
comparison with theoretical calculation.
3. Modeling
The simple model of IEDs in a weakly-collisional rf
sheath developed by Israel et al.6 was extended to
Lieberman’s strongly collisional rf sheath in our
previous work.7 The sheath model is limited to highvoltage fast oscillating rf sheath, where the
following assumptions are valid: eVrf>>kTe,
ωpe>>ω>>ωpi. However, the collisional sheath
model are valid only at very high sheath voltage,8
and many input parameters have to be identified.
Instead, an effective field is introduced here to
simplify the calculation of IEDs. The time-averaged
potential profile of the effective field is
  x   cx   , c  0,   0
s
s
.
(1)
Here,  is the sheath dc potential, the ion sheath
s
edge is at x=0, and the potential on the grounded
electrode at x=sm is zero.
The electric field strength is
E  x, t    cx 1 1  cos(t ) 
(2)
.
The ion motion is separated into a time-averaged
part and a fast oscillating one.6-7 The time-averaged
ion velocity arriving at the electrode is obtained
from the energy conservation law. The ion velocity
on the electrode is,
u  x0 , t0   u02  2e Φ  x0   Φ  x   / mi

eE  sm 
mi
sin tarr  
eE  x0 
mi
sin t0 
.(3)
The ion transit time is calculated along the timeaveraged ion trajectory,
Table 2. Ion-neutral reactions in the sheath in H2 discharge
Reactions
1
2
3
4
5
6
7
8
9
H+ + H2 → H + H2+
H2+ + H2 → H3+ + H
H2+ + H2 → H2+ + H2
H2+ + H2 → H+ + H + H2
H2+ + H2 →H2 + H+ + H2
H3+ + H2 → H+ + H2 + H2
H3+ + H2 → H2+ + H + H2
H3+ + H2 → H2 + H+ + H2
H3+ + H2 → H2+ + H + H2
0
Eth /eV
Cross section/ A
2.7
0
0
6
6
11.2
15.5
11.2
15.5
Ref.[9]
Ref.[9]
1.5times of Ref.[9]
Ref.[9]
Ref.[9]
Ref.[9]
Ref.[9]
Ref.[9]
Ref.[9]
Reactions 1-5 and 7-10 in Table 1 are dissociative
charge transfer (DCT) reactions observed in Ref.[3].
Cross sections of CID reactions 11-13 are set half of
the values measured in Ref.[3] for better fitting to
measurement. Constant cross sections are assumed
for symmetric charge transfer (SCT) reaction 6,
fluorine atom transfer (FAT) reaction 14 and DCT
reaction 15. The fluorine atom density is set 1×
1013cm3 for reaction 6.
(4)
Threshold energies and cross sections of reactions in
Table 2 are taken from the review article by Phelps,9
except that the cross section of H2+ symmetric
charge transfer reaction 3 is multiplied by 1.5 for
better fitting as will shown below.
Table 1 and 2 show threshold energies and cross
sections ion-neutral reactions considered here for
CF4 and H2 discharge respectively.
Ion-neutral elastic scattering, secondary electron
emission and ionization in the sheath are not
considered here.
Table 1. Ion-neutral reactions in the sheath in CF4 discharge
Secondary ion fluxes produced from the reactions
are calculated according to the time-averaged energy
of the incident ions, and the oscillating ion velocity
is ignored. Product rate of secondary ion flux by
incident ions with energy E in the space interval dx
at x is
tarr  x0 , t0  
sm
 u
x0
2
0
 2e Φ  x0   Φ  x   / mi
Reactions
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
F+ + CF4 → CF3+ + F + F
F+ + CF4 → CF2+ + F2 + F
F+ + CF4 → CF+ + F2 + F+ F
F+ + CF4 → F+ + CF3 + F
F+ + CF4 → C+ + 2F2 + F
F+ + F →F+ + F
CF3+ + CF4 → CF3+ + F + CF3
CF3+ + CF4 → CF2+ + F2 + CF3
CF3+ + CF4 → CF+ + F + F2 + CF3
CF3+ + CF4 → C+ + 2F2 + CF3
CF3+ + CF4 → CF2+ + F + CF4
CF3+ + CF4 → CF+ + F2 + CF4
CF3+ + CF4 → C+ + F + F2 + CF4
CF2+ + CF4 → CF3+ + CF3
CF2+ + CF4 → F+ + CF3 + CF2

1/ 2
dx  t 0 .
Etha
/eV
Cross section /
10-20m2
0
2.3
5.7
13.1
13.1
0
10.2
18.4
23.4
34.3
35.7
44.6
53.5
0
0
Ref.[3]
Ref.[3]
Ref.[3]
Ref.[3]
Ref.[3]
100b
Ref.[3]
Ref.[3]
Ref.[3]
Ref.[3]
3b
3b
3b
20 b
20 b
a
Threshold energies list are incident ion energy in the laboratory
frame calculated from information in Ref.[3], except for reaction
6, 14 and 15.
b
Energy-independent cross sections are assumed.
c
Energetic products are underlined as in Ref.[3].
d  i  E  nn dx ,
(5)
where Гi is incident ion flux, Ē is the time-averaged
incident ion energy, σis the reaction cross section at
Ē, and nn is the neutral species density.
Initial energy of secondary ion from CT reactions
can be taken as zero with respect to the sheath
voltage, while the produced ions from CID reactions
are energetic. During the calculation of CID
reactions, part of the incident ion energy is used to
overcome the threshold energy and the rest of it is
inherited by products according to their masses. For
example, a CF3+ ion collides with a thermal CF4
molecular with kinetic energy Ei and a CF2+ ion is
produced (reaction 11 in table 1). Thus secondary
CF2+ ion would have initial kinetic energy of 50/69
×(Ei-35.7).
Secondary ions produced from reactions may be
consumed by other reactions on the way to the
electrode. And the possibility for a secondary ion to
impinge on the electrode is exp(-dx/λ), whereλis
the ion mean free path.
Secondary peaks in IEDs of H2+ and H3+ result from
symmetric charge transfer and proton transfer
reactions of H2+ respectively. The double-peak
structure in H3+ IED is mainly form by secondary
ions converted from H2+ ions, since the cross section
of conversion reaction 2 in Table 2 for low energy
H2+ ions is very large.9
IEDs are obtained by summing up the ion fluxes in
the corresponding ion energy intervals.
4. Result and discussion
Good agreements between measured and calculated
IEDs are achieved by adjusting the coefficients c and
νin Eq.(1) as shown in Figure 1 and 2. In the CF4
discharge, the C+ ion signal is so small that C+ IED
measured in a Ar/CF4/O2 CCP discharge is used for
comparison with calculation. The C+ ion energy is
normalized by the sheath dc voltage.
Continua structures in IEDs of CF2+, CF+ and C+ are
mainly form by secondary ions produced from CID
reactions of CF3+, although there are still some peak
structures in the calculated IEDs of CF+ and C+. This
means there may be some reactions that may smooth
the structures and are not included in the model.
However, the center energies of measured continua
structures decrease with decreasing ion mass, which
is reasonable because heavier ions can inherit more
kinetic energy of the incident ion during CID
reactions.
Figure 1. Measured and calculated IEDs in CF4 CCP at
frequency of 40.68 MHz and pressure of 40 mTorr with 40 W
power, except the measured C+ signal in (e) are from a
Ar/CF4/O2 discharge at 40.68 MHz,40 mT and 50W.
CID reactions do not produce energetic fluorine ions,
which is not verified in Ref.[3]. And interestingly,
the secondary fluorine ions are not produced from
symmetric charge transfer reactions, and may be
from CF2+ DCT reactions, which agree with
observation in Ref.[3] and [10] that there is a strong
loss channel of CF2+ in the sheath.
The continua structure in H+ IED is mainly due to
H3+ CID reactions, while CID and DCT reactions of
H2+ and DCT reaction of H3+ also contribute.
Figure 2. Measured (Ref.[5]) and calculated IEDs in H2 CCP at
frequency of 13.56 MHz and pressure of 5 Pa.
Figure 3 shows the relative intensities of ion fluxes
both at the ion sheath boundary and on the electrode.
The results on the electrode from measurement and
model prediction agree well, and the ion flux ratios
at the sheath boundary and on the electrode show a
significant difference from each other.
The H+ flux at the sheath boundary is too small to
observe, while the signal on the electrode is more
than 10 percent of the total ion flux due to strong
dissociations of CF3+ ions in the sheath.
CF3+ ions are converted into smaller ions in the
sheath, and the fluxes of smaller ions increase
dramatically.
with experimental measurement are achieved. It’s
found that collision induced dissociation reactions in
the sheath can dramatically lower the ion mean
energy and change the ion flux ratios on the
substrate in CCP containing CF4 and H2, which may
eventually influence the etching and deposition
process.
6. Acknowledgement
The authors would like to thank Dr. Deborah
O’Connell for sharing her experimental data, and
Prof. Michael Lieberman for his helpful discussions.
This work is supported by National Natural Science
Foundation of China under Grant No 10775087 and
No 10935006.
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Figure 3. Relative intensities of different ions fluxes in (a) H2
and (b) CF4. Both ion fluxes intensities at the ion sheath edge
and on the electrode predicted by the model are presented.
5. Conclusion
IEDs in CF4 and H2 capacitive discharge are
successfully reconstructed and good agreements
[10] R. J. M. M. Snijkers et al., J. Appl. Phys. 79,
8982 (1996).