22P013-O
Global Model of Inductively coupled CH4/H2 Plasmas
誘導性結合型CH4/H2プラズマのグロ-バルモデル
Takashi Kimura
木村 高志
Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466-8555, Japan
名古屋工業大学 〒466-8555 名古屋市昭和区御器所町
A global model for electropositive plasma is used in order to understand the plasma chemistry in CH4/H2
plasmas assuming the Maxwellian electron energy distribution. Most of CH4 molecules are easily
dissociated, so that the dominant neutral species are hydrogen molecules, CH4 molecules and hydrogenatoms, followed by the hydrocarbons such as C2Hm (m=1,2 and 4). The dominant ions are CH5+, C2H+,C2H3+, C2H5+, and C3H5+ at low hydrogen fractions, whereas the density of H3+ becomes dominant ion
species as hydrogen fraction increases. Some measurable parameters such as electron density and its
temperature are compared with the model results, obtaining reasonably good agreement.

1. Introduction
Theoretical studies of the plasmas inhydrocarbon-based feedstock for the PECVD ofdiamond-like, graphite-like and amorphous
carbon films [1-5] have been reported. The global
model is one of the methods that have been usedin order to treat the physical and chemical
processes in the plasmas. On the other hand, themodels, in which the plasma chemistry andsurface chemistry are combined, have beendeveloped for thin-film deposition and etching
purposes.[4,5] Mantzaris et al [4] combined
plasma chemistry and surface chemistry models
to study the diamond-like-carbon film deposition
process for an rf capacitively coupled CH4
discharge and showed that the surface reaction
can greatly affect on the composition of neutral
radicals in the plasma.
The objectives of this research are toinvestigate the effect of hydrogen addition on
plasma parameters in inductively coupled rf(13.56MHz) CH4/H2 plasmas and to understandthe plasma chemistry of such plasmas using theglobal model.

the chamber. Electrons, which have a Maxwellianenergy distribution with electron temperature Te, arealso assumed to be uniform over the chamber. All
positive ion species, which are assumed to have thesame profile, must satisfy the quasineutrality, ne =n+, where n+ is the sum of the positive ion densities.
The gas temperature in the discharge space isassumed to be 600 K.
The surface processes for hydrogen atoms, CH3,and CH2, are incorporated in the model. The
adsorption and desorption processes, and theadsorbed layer processes, in which the adsorbed
species can react with the atomic hydrogen from theplasma yielding the gas-phase products, are mainly
considered using same parameters [4,5]. The ionsare directly incorporated in the growing film.
Therefore, the sticking coefficient for ions can beassumed to be unity. The incorporation of ions is
considered to occur on the whole surface, whereas
the reactions between the adsorbed layer and theions are not considered in this model.
The equations for each particle and power
balance are then solved by the Runge-Kutta
numerical method to obtain equilibrium.

2. Description of Model
A global model for electropositive plasma isapplied to the CH4/H2 plasmas in a cylindricalchamber of radius R (= 80mm) and length L (=75mm), since the ratio of negative ion to electron
density should be assumed to be very low. 27
neutral species (CHj (j=1-4), C2Hj(j=1-6),
C3Hj(j=1-8), C4Hj(j=7-9), C, C2, H2, H(1s), H(2s),and H(2p)) and 27 charged species (electrons,CHj+(j=1-5),C2Hj+(j=1-6),C3Hj+(j=1-8),C4Hj+(j=7-9),
C+, H+, H2+, and H3+) are considered in the model.
All neutral species are assumed to be uniform over

3. Results and Discussion
In Figs. 1(a)-1(b), the electron density and its
temperature are shown as a function of hydrogen
fraction XH2, together with the experimental results.
The measured and calculated ne gradually decrease
with increasing XH2. On the other hand, themeasured and calculated temperatures slightly
increase with the increase in XH2. Since theionization rates of hydrocarbons by electron impact
are much larger than those of hydrogens, theelectron temperature increases with the decrease in
the density ratio in order to satisfy the balance of

the charged species productions and loss to the wall.
The increase in electron temperature should
contribute to the increase in the collisional energy
loss between electrons and neutral species, such ashydrogens and hydrocarbons, resulting in thedecrease in electron density with increase in XH2
under the same power injected into plasmas.

exp.

model ( p = 25mTorr)

0.5(a)
020406080

100

XH2 (%)
5exp.

model ( p = 25mTorr)

43+2(b)1020406080100

XH2 (%)
Fig. 1 Electron density (a) and its temperature at25mTorr, where the power injected into plasma is140W.

CH4C2H4H1021
Number density (m-3)

CH 5 +
C2 H+ 5H21017+

CH 4 +
C2H+3H3+

CH 3 +
C2 H-3

Electron temperature (eV)

0Number density (m )ne (×1017-3m )1The densities of neutral species calculated at 25mTorr are shown in Fig. 2. Most of CH4 molecules
are easily dissociated, so that the dominant neutralspecies are always hydrogen molecules, CH4molecules and hydrogen atoms, followed by thehydrocarbons such as C2Hm (m=1,2 and 4). The
increase in net production rate is roughly
proportional to the product [CHx] [CHy] of thedensities of light hydrocarbons, resulting in theincrease in densities of C2Hm larger than theincrease in densities of light hydrocarbons.
The positive ion densities calculated at 25mTorr
is shown in Fig. 3. The dominant ions at XH2 lower
than 50% are CH5+, C2H+, C2H3+, C2H5+, and C3H5+,
whereas the density of H3+ increases with theincrease in XH2 and H3+ becomes dominant ion
species at XH2 higher than 60-70%. Most ofdominant hydrocarbon ions except C2H+ are mainly
produced by the reactions between the hydrocarbon
ions and CH4 (or H2), rather than direct ionizationand dissociative ionization processes by theelectron impact.

CH3C2 H2H21015

1014

CH 2C2 H

0204060X H2 (%)

80100Fig. 3 Densities of main charged species calculated
at 25 mTorr, where the power injected into plasma
is 140W.

1020
10191018
1017

1016

0204060
XH2 (%)

80100Fig. 2 Densities of main neutral species calculated
at p = 25 mTorr, where the power injected intoplasma is 140W.

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