Mode transition in dusty micro-plasma driven by pulsed radio-frequency source in C2H2/Ar mixture
School of Science, Qiqihar University, Qiqihar 161006, China
† Corresponding author. E-mail:
lxmjsc98@163.com
1. IntroductionHydrogenated amorphous carbon (
-C:H) thin films deposited by the plasma enhanced chemical vapor deposition (PECVD), is widely used in passivation layers[1] and flat-screen displays.[2] In PECVD, the formation and growth of nanoparticles is a generally recognized problem. It turns out to be harmful in the microelectronics industry,[3,4] whereas in nanoscale materials, it is beneficial.[5] To describe the nanoparticles formation and growth mechanism clearly, Deschenaux et al.[6] studied the radio frequency (RF) acetylene dusty plasma by using mass spectrometry. The mass spectrometry showed that the higher-mass hydrocarbon anions and cations nearly 200 amu is formed from the species comprising 14–15 carbon atoms. In theory research, De Bleecker et al.[7,8] developed a detailed chemical kinetic scheme to reveal the nanoparticle formation mechanisms in RF acetylene plasma. However, their results for negative ions are not in agreement with the experiment by Deschenaux.[6] Thus, Mao et al.[9] extend De Bleecker’s one-dimensional fluid model by adding some new mechanisms for negative ion formation. When comparing with the experiment results,[6,10] a reasonable agreement is received. However, in these studies the thermophoretic force is not taken into account for the constant gas temperature. It has been shown that, thermophoretic force has a great affect on the spatial distribution of nanoparticles,[11] thus the neutral gas energy equation should be considered.
In PECVD, to obtain better uniformity and higher deposition rate, atmospheric pressure RF acetylene discharges is often used. In recent years, microdischarges (MDs) have received extensive attention due to their specific advantages, such as stable non-equilibrium, highly energetic electrons, and different discharge structures characteristics. Thus, they are widely used in materials treatment and modification, microsatellite propellers, and plasma display panels.[12,13] In MDs, the pressure is generally very high while the plate distances are in the range of micrometer and submillimeter, thus the secondary electron emission play a dominant role. However, when the discharge conditions are slightly changed, the stable non-equilibrium plasma is easy to convert to non-uniform discharge. These shortcomings have greatly restricted the application of MDs. But fortunately, the recent studies have indicated that, MDs driven by pulse source instead of the conventional AC discharge can obtain uniform plasma in a larger parameter range.[14] Pulsed discharges have received extensive attention due to their advantages, such as the higher peak current density, electron density and electron generation efficiency, the easier to produce the uniform large area plasma, and the higher nonbalance of the generated plasma.[15–19] Therefore, it is necessary to investigate nanoparticles formation and growth mechanism and pulsed discharge mode in RF acetylene microdischarge.
In this article, we mainly studied the behavior of nanoparticles in C2H2/Ar pulsed radio-frequency MDs plasma, which are generally produced by a series of chemical reactions.[20,21] The fluid model[9] is extended by adding the neutral gas flow and heat transfer equations, thus the role of thermophoretic force on the nanoparticles formation and growth mechanism is presented. The effects of pulse width, repetition frequency on electrons, ions, radicals as well as nano particles densities, electron temperature, plasma uniformity are our mainly concerned. The outline of the paper is presented as follows: Section 2 summarizes the fluid model and the aerosol dynamics model, and analyzes the simulation conditions of those models. In Section 3, the pulsed discharge parameters effects on the plasma property and nanoparticles behavior are carefully investigated, and some brief conclusions are presented in the end of paper.
2. Theoretical model2.1. Fluid modelFluid models solve the continuity equations for each species j including electrons, ions, radicals, neutral gases, and nanoparticles[20,21] in the C2H2/Ar MDs plasma is described by
where
nj is particle density,
Rj represents the source and sink terms. The particle flux terms
![](cpb_26_4_045202/cpb_26_4_045202_ieqn3.gif)
for electrons, ions and radicals are given by
where
μj and
Dj are mobility and diffusion coefficient for particles
j. Since the masses for ions are much larger than that of electrons, the effective electric field is introduced to follow the inertia effects. For nanoparticles, the flux equation is determined by the assuming that the neutral drag force balances with the sum of electrostatic force, ion drag force and thermophoretic force
Here
and
are the density and flux for nanoparticles.
and
are the ion mass and nanoparticle mass, respectively. g is the gravitational acceleration and
the thermal conductivity.
and
are the ion average speed and average thermal velocity.
represents momentum loss frequency and
the Coulomb logarithm. The transport equation is incorporated in each nanoparticle domain of aerosol dynamics model (Subsection 2.2), the nanoparticle between 1.0 nm and 50 nm in diameter is taken into consideration.
The neutral gas temperature
is not taken as a constant, and calculated by
where
![](cpb_26_4_045202/cpb_26_4_045202_ieqn14.gif)
and
![](cpb_26_4_045202/cpb_26_4_045202_ieqn15.gif)
are the density and heat flux vector for neutral gases, respectively.
![](cpb_26_4_045202/cpb_26_4_045202_ieqn16.gif)
represents energy transfer to the neutral species by collisions with other species.
![](cpb_26_4_045202/cpb_26_4_045202_ieqn17.gif)
is the heat capacity at constant volume. The neutral gas velocity
![](cpb_26_4_045202/cpb_26_4_045202_ieqn18.gif)
is described by
where
![](cpb_26_4_045202/cpb_26_4_045202_ieqn19.gif)
and
![](cpb_26_4_045202/cpb_26_4_045202_ieqn20.gif)
are the gas pressure and mass for the neutral gases.
![](cpb_26_4_045202/cpb_26_4_045202_ieqn21.gif)
is the transfer of mass to the neutral gas fluid by collisions with other species.
![](cpb_26_4_045202/cpb_26_4_045202_ieqn22.gif)
is the neutral viscous stress tensor.
To obtain electric fields, Poisson’s equation is coupled with the continuity and momentum equations, make the fluid model self-consistent. Finally, the electrons energy balance equations are solved to determine the electron temperature, while the ion pressure take a little role in the momentum equation, thus the ion temperature is set at a constant of 400 K. The discharge parameters, such as the diffusion constants and mobility as well as the electron collisions (ionization, attachment, and dissociation) coefficients as a function of the average electron energy, are calculated from the electron energy distribution function (EEDF). The EEDF are obtained from the Boltzmann equation in a two-terms approximation. Consequently, the particle density, potential, electron temperature, neutral gas temperature and the other characteristics of plasmas can be described as a function of position, owing to the correlation of each equation.
2.2. Aerosol dynamics modelThe aerosol dynamics model in this article is used to investigated the nanoparticles growth process. In the model, the temporal evolution of the nanoparticles density
in a volume range (
), can be investigated by the general dynamic equation.[22]
where the first term on the right-hand side accounts for the particles formation between two smaller particles owing to the coagulation, while the second term expresses the loss of particles from coagulation with all particles. The third term is the new particles formation, where the formation rate with volume
v0 from nucleation is
![](cpb_26_4_045202/cpb_26_4_045202_ieqn25.gif)
. The factor 1/2 in the first term on the right-hand side is used to avoid collisions counted twice in the integral,
![](cpb_26_4_045202/cpb_26_4_045202_ieqn26.gif)
is the coagulation frequency between interacting particles with volume
u and volume
v. In this computation, the volume domain was divided logarithmically in 38 sections, comprising particles between 1.0 nm and 50 nm in diameter.
The primary large anions of nanoparticles formation in this C2H2/Ar MDs plasma is the C12H
and C12H
, which are produced by successive anion-C2H2 polymerization reactions,
where the larger anions C
![](cpb_26_4_045202/cpb_26_4_045202_ieqn29.gif)
H
![](cpb_26_4_045202/cpb_26_4_045202_ieqn30.gif)
and C
![](cpb_26_4_045202/cpb_26_4_045202_ieqn31.gif)
H
![](cpb_26_4_045202/cpb_26_4_045202_ieqn32.gif)
are primarily formed by C
2H
![](cpb_26_4_045202/cpb_26_4_045202_ieqn33.gif)
and H
2CC
![](cpb_26_4_045202/cpb_26_4_045202_ieqn34.gif)
. To simplify the calculation, two different pathways are all stopped at anions containing 12 carbon atoms in the model, as we couldn’t describe an unlimited number of larger anions (C
![](cpb_26_4_045202/cpb_26_4_045202_ieqn35.gif)
H
![](cpb_26_4_045202/cpb_26_4_045202_ieqn36.gif)
and C
![](cpb_26_4_045202/cpb_26_4_045202_ieqn37.gif)
H
![](cpb_26_4_045202/cpb_26_4_045202_ieqn38.gif)
). The aerosol dynamics model is finally coupled to the fluid model to describe the formation and growth mechanisms of nanoparticles.
2.3. Boundary conditionsIn this work, the RF sources 13.56 MHz is applied to the upper electrode, while the lower electrode is grounded. The boundary conditions for the fluid model specified are as follows:[23] the electron flux at the electrodes is describe by
with the electron reflection coefficient
![](cpb_26_4_045202/cpb_26_4_045202_ieqn39.gif)
, the secondary electron emission coefficients
![](cpb_26_4_045202/cpb_26_4_045202_ieqn40.gif)
. Similar to the electron flux, the negative ion flux
and the positive ion flux gradients at the electrodes
![](cpb_26_4_045202/cpb_26_4_045202_ieqn41.gif)
. The neutral gas velocity gradients at the electrodes
![](cpb_26_4_045202/cpb_26_4_045202_ieqn42.gif)
. The radicals flux at the electrode is
where the sticking probability of radicals
![](cpb_26_4_045202/cpb_26_4_045202_ieqn43.gif)
is given by Ref. [
7].
3. Results and discussionIn this article, we mainly investigated the physical qualities of dusty plasma in pulsed radio-frequency C2H2/Ar MDs, thus the influences of duty ratio, modulation frequency on the electron density, H2CC
density, and nanoparticles density are carefully discussed.
Figure 1 illustrates the variation of electron density at the center of the discharge and the electron flux at the upper electrode, with the duty ratio
, 0.2, 0.3, 0.4, 0.5. As we can be seen, a maximum point for electron density is presented at duty ratio
. That is to say, the electron density increases definitely with the increasing of duty ratio in the range of
, while decreases with the increasing of duty ratio in the range of
. The most likely cause of this phenomenon is that a mode transition appears around the duty ratio
. When the duty ratio is less than 0.3, the discharge is mainly sustained by the sheath capacitance. Although some ionization does produced by the high-energy secondaries, the electron current is very small comparing with the ion current. Therefore, most of the secondary electrons are lost from the discharge before significant ionization occurs, and then sheath oscillation is responsible for sustaining discharge (α regime). However, as the duty ratio increases from 0.3 to 0.5, electron current increases rapidly, which has been shown in Fig. 1(b), and then secondary electrons are responsible for the significant ionization (γ regime). On the other hand, increased the duty ratio tends to reduce the sheath depth, which cause the secondary electrons emitted from the electrodes decrease. Thus, the electron density decreases with the increasing of duty ratio in the range of
.
The negative ion H2CC
density variation with the duty ratio is described in Fig. 2. As is well known in Refs. [9] and [24], 95% of the carbon nanoparticles formation and growth was triggered by the reactive H2CC
precursor. Thus, the duty ratio effects on the H2CC
density should be carefully studied. For the same reason as the changing trend of electron density, we can clearly see that the H2CC
density first increases and then decreases with the increasing of duty ratio, and it is generally at a rather high value (
). This calculation results have once again provided evidence for the existence of the mode transformation (α to γ).
In order to investigate the behavior of nanoparticles clearly, figure 3(a) shows the spatial variation profile of nanoparticle density at the duty ratio
and figure 3(b) shows the nanoparticle density at the center of the discharge at different duty ratio, with the nanoparticle diameter
nm. It can be clearly seen from Fig. 3(a) that, the nanoparticle exhibits a local maximum near the showerhand electrode under the influence of thermal gradient in gas temperature, and keeps much higher value in the bulk plasma, owing to the larger collisions frequency at gas pressure of 600 Torr. In addition, we also can see from Fig. 3(b) that, the nanoparticle density shows a rapid increase in the duty ratio range of 0.1 and 0.3, while a gentle decrease in the range of 0.3 and 0.5. The maximum of nanoparticle density
is appeared at the duty ratio
.
Figure 4 displays the spatial variation profiles of electron density in a pulse period, with the modulation frequencies
, 500 kHz, and 5 MHz while the duty ratio is fixed at a certain value
throughout our calculations. It is clearly seen in Fig. 4 that the electron density responds strongly to the modulation frequency. The electron density increases from approximately
at
MHz to a maximum of approximately
at
. In general the following two main reasons can be used to explain this phenomenon.
(i) The width of sheath becomes broader with the decrease of the modulation frequency, and then the secondary electrons emitted from the electrodes increase. Therefore, the electron density varies significantly with the modulation frequency.
(ii) As the modulation frequency gets lower, the pulse-on time increases,[20] which resulting in larger collisions rate. The collision effect in the sheath region drives the electron density increases.
Thus, we can conclude that adjustments of modulation frequency can be an effective method for electron density increasing.
Figure 5 shows the spatial variation of negative ion H2CC
density in a pulse period, with the modulation frequency presented at three different values. We can see in Fig. 5 that H2CC
density increases from approximately
to a maximum of approximately
with the decreasing of modulation frequency. It can be also seen that, upon changing the modulation frequency, the sheath width increase slightly. This is the reason why the negative ion H2CC
density just increased by two times with the decreasing of modulation frequency, compared with the electron density.
The effect of modulation frequency on the nanoparticle density is also taken into accounted, as shown in Fig. 6. The nanoparticle density has been time averaged in a pulse period, and the nanoparticle diameter is chosen at
nm. We can see in Fig. 6 that the nanoparticle density in the plasma bulk increases with the decreasing of modulation frequency, which brings about a two-fold increase. However, the nanoparticle density near the showerhand electrode is significantly increased from approximately
at
MHz to a maximum of approximately
at
. There are three reasons listed below for this phenomenon.
i) A greater thermal gradient in gas temperature is presented near the showerhand electrode, which make the nanoparticle density exhibits a local maximum near the showerhand electrode.
ii) The sheath width increases greatly with the decreasing of the modulation frequency, which cause the nanoparticle density near the showerhand electrode increase rapidly.
iii) The initial particle H2CC
density of nanoparticle formation increases slightly with the decreasing of the modulation frequency, resulting that the nanoparticle density in bulk plasma region changed less.
4. ConclusionIn conclusion, the effects of pulse parameters on the formation and growth of dust particles are investigated in pulsed radio-frequency microdischarges plasma by using a self-consistent couple of aerosol dynamics model and fluid model. The aerosol dynamics model is used to determine the nanoparticles growth process, and the fluid model is used to determine the nanoparticles formation process and calculate the spatiotemporal evolution of electrons, ions, and neutrals. In the simulation, the neutral gases energy equation is taken into account.
Different from what we have learned in pulsed discharge, a mode transition from electron collision heating (α regime) to secondary electron heating (γ regime) has been found as the duty ratio increases from 0.1 to 0.5, basing on the variation of electron density, H2CC
density and nanoparticles density. When the duty ratio is less than 0.3, comparing with the ion current, the electron current is very small, thus sheath oscillation is responsible for sustaining discharge. As the duty ratio increases, the electron current increases, secondary electrons are sufficient for the significant ionization. The modulation frequency effects on the plasma density are also discussed. By decreasing the modulation frequency, the width of sheath increases, the electron density, H2CC
density and nanoparticles density increase rapidly, especially the nanoparticles density near the showerhand electrode. Furthermore, the results show that the neutral gas temperature gradient has a great effect on the spatial distribution of nanoparticle density.