Numerical Study on Low Pressure Inductively CoupledPlasma Sources for Nanocrystalline Diamond Deposition
Katsuyuki Okada*, Shojiro Komatsu, and Takamasa Ishigaki
Advanced Materials Laboratory, National Institute of Materials Science,
1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan; okada.katsuyuki@nims.go.jp

Numerical study on low pressure inductively coupled plasma (ICP) used for nanocrystalline diamonddeposition has been performed with direct simulation Monte Carlo (DSMC) method and electronMonte Carlo simulation. Spatial distributions of electron density, electron temperature, and plasma
potential are obtained. The electron energy distribution functions (EEDFs) are compared with theexperimental results obtained with a Langmuir probe previously. The EEDFs of an Ar and a CH4/H2
plasma obtained from the simulation agree well with the measured data. The calculated EEDF of aCH4/H2 plasma at 50 mTorr exhibits a hump around 6 eV, which corresponds to a hump around 6 eVin the measured EEDF at the same pressure. It can be attributed to the resonant peak of the vibrational
excitation cross section of CH4 molecule.
1. Introduction
We have applied a low pressure inductively
coupled plasma (ICP) to deposit nanocrystalline
diamond [1]. The sp2/sp3 bondings of thenannocrystalline diamond were evaluated with
Raman spectroscopy [2] and electron energy loss
spectroscopy [3]. Langmuir probe and mass
spectrometric measurements were performed tocharacterize the ICP [4,5]. We obtained plasma
parameters {electron density (Ne), electron
temperature (Te), and plasma potential (Vp)},
electron energy distribution functions (EEDFs),and ion energy distributions (IEDs). For better
understanding of the ICP, we need a theoreticalinvestigation such as modeling or numericalsimulation. Economou et al. [6] used the direct
simulation Monte Carlo (DSMC) method todemonstrate reactive neutral and ion flow in an
ICP reactor. Nanbu et al. [7] also used theelectron Monte Carlo method for obtaining theproduction rate of radicals. Takekida and Nanbu[8] reported the EEDFs of capacitively coupled
Ar plasmas using particle-in-cell/Monte Carlo(PIC/MC) method.
In this study, we report on the numericalsimulation of the ICP used for nanocrystalline
diamond deposition using DSMC method andelectron Monte Carlo simulation. Spatial
distributions of Ne, Te, and Vp are obtained. The
calculated EEDFs are compared with themeasured EEDFs.
2. Experiment and Simulation
The detailed descriptions of low pressure
ICP-CVD system and Langmuir probe
measurement were reported previously [1,4]. To
be brief, a low pressure ICP was generated in a

growth chamber by applying 13.56 MHz rf
powers of 1 kW to a three-turn helical antenna
wound around a quartz tube. An Ar or a CH4/H2(5:75 mixture) plasma was generated at pressures
ranging from 10 to 50 mTorr. A Langmuir probe(Smart Probe; Scientific Systems Inc.) was utilized
to measure plasma parameters and EEDFs.
The procedure of simulation is as follows. Theflow, electromagnetic field, and plasma are
assumed to be axisymmetric. The height of thereactor is 110 mm. A three-turn helical coilwound around a quartz tube with 40 mm indiameter. The calculation was performed withDSMC method and electron Monte Carlosimulation. Collisions of e-H, e-H2, e-CH4, e-CH3,e-CH2, and e-CH are considered in a CH4/H2
plasma.
Surface reactions of radicals play a critical roleindetermining
theconcentrations
anddistributions of ions and radicals in a reactive
plasma such as CH4/H2 plasma. The sticking ofCH3, CH2, and CH radicals on the surface aretaken into consideration in the calculation. The
sticking coefficients of CH4, CH3, and CH2
radicals are refereed to 1.0X10-4, 1.0X10-3, and
3.0X10-2 in the previous reports [9-11].
3. Results and Discussion
Figures 1(a) and 1(b) show the Ne and Te of anAr plasma at 50 mTorr, respectively. The Ne isconcentrated near the rf antenna, and the Te has adoughnut-shape distribution near the rf antenna.
Figure 2(a) and 2(b) show the density of Ar+ andAr*, respectively. While the former has a similar
distribution to the Ne, the latter spreads toward thegrowth chamber.
The Ne and Te of a CH4/H2 plasma at 50 mTorr

are shown in Fig. 3(a) and 3(b), respectively. The
Ne is concentrated near the rf antenna similar tothat of Ar plasma. The Te is high along the quartz
tube, which is different from that of Ar plasma.
The density of H+, CH3+, H*, and CH3* are shownin Fig. 4(a), 4(b), 4(c), and 4(d), respectively.
While the ion distributions are concentrated near
the rf antenna, the radical distributions spread into
the growth chamber. The distributions strongly
depend on each radical.
Figure 5(a) shows the measured EEDF of an
Ar plasma at 50 mTorr (closed circles) and thecalculated one at the same pressure (open circles).
The each EEDF is nearly a straight line, whichmeans that the electron energy has a Maxwelliandistribution. Although the calculated EEDF above
10 eV slightly deviates from a straight line, it isconsistent with the measured EEDF.
Figure 5(b) shows the measured EEDF of aCH4/H2 plasma at 50 mTorr (closed circles) andthe calculated one at the same pressure (opencircles). They are different from the EEDF of an
Ar plasma at the same pressure. There is a humparound 6 eV in both measured and calculated
EEDF. Turner and Hopkins [12] reported theunusual structure of the EEDF. They found a dip
around 4 eV in the EEDF of a N2 plasma, whichis interpreted as the electric absorption of N2
molecule corresponding to the resonant peak of
the vibrational excitation cross section. In the CH4vibrational excitation cross sections, Ȫv(1,3) andȪv(2,4) have a peak around 6 eV [13]. Therefore,
the hump around 6 eV can be attributed to theelectric absorption of CH4 molecule analogous to
the vibrational absorption of 4 eV electrons of theN2 molecule.
The calculated EEDF of a CH4/H2 plasma
agrees well with the measured one. Accordingly,
the unusual structure around 6 eV in thecalculated EEDF can also be attributed to theresonant peak of the vibrational excitation crosssection of CH4 molecule.

FIG. 1(a) Electron density of Ar plasma

FIG. 1(b) Electron temperature of Ar plasma

Acknowledgment
The authors would like to thank Mr. M. Tanakaand T. Takasaki of PEGASUS Software Inc. fortheir useful advice on the calculation.
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FIG. 2(a) Density of Ar+FIG. 2(b) Density of Ar*

FIG. 3(a) Electron density of CH4/H2 plasma

FIG. 3(b) Electron temperature of CH4/H2 plasma

FIG. 4(a) Density of H+

FIG. 4(b) Density of CH3+

FIG. 4(c) Density of H*

FIG. 5(a) The measured EEDF (closed circles) and thecalculated EEDF (open circles) of an Ar plasma at 50mTorr.

FIG. 4(d) Density of CH3*

FIG. 5(b) The measured EEDF (closed circles) and thecalculated EEDF (open circles) of a CH4/H2 plasma at50 mTorr.