Microdischarges (MDs) have become the subject of considerable research due to their wide range of possible applications in materials treatment and modification, plasma display panels, radiation sources, microsatellite propellers, and in biomedical and environmental applications.^[1,2] Among those applications, the microdischarges showed unique properties, such as highly energetic electrons, non-equilibrium, and different discharge structure characteristics. A stable non-equilibrium plasma at length scales ranging from μm to mm is the most remarkable advantage of MDs, where the plasma quenching effects usually exist. In order to overcome plasma quenching effects, MDs rely on high gas pressure ranging from 100 Torr (1 Torr = 1.33322 × 10² Pa) to 1 atm (1 atm = 1.01325 × 10⁵ Pa), thus the low breakdown or sustained voltages of a few hundred volts is achieved.^[3] Due to the various technological implications of MDs, high-pressure small-scale plasmas become increasingly important. To this effect, a fundamental understanding of the characteristics of atmospheric pressure plasmas and microplasmas is obviously crucial. By experimental measurements and computer simulations,^[4–8] several attempts have been made to describe the microplasmas in atmospheric capacitively rf discharges. Babayan et al.^[4–6] investigated the atmospheric pressure helium rf microdischarges, which are operated at gas temperatures below 100 °C. The results showed that a high density of reactive species is generated and a stable capacitive discharge is produced, which are suitable for the downstream processing of substrates. Iza et al.^[7,8] demonstrated non-equilibrium characteristics and the highly energetic electrons effects in rf microdischarges. By using DC discharge model, Economou and Radjenovic et al.^[9,10] investigated the breakdown voltage versus pd scaling, and observed that the cathode layer (sheath) classical scaling law does not apply. Lee et al.^[11,12] presented two operating modes, α and γ, in atmospheric pressure capacitive discharges, which depends on the dominant ionization process. In γ discharge, the plasma is sustained by secondary electron emission, while in the α discharge, it is sustained by bulk ionization. They showed that the changes of input power and ultra-high frequency are the major causes for the α–γ mode transition.

The behaviors of inert gases, such as Ar and He, are relatively well understood in MDs, but the reactive gases discharge characteristics, such as the C₂H₂/Ar, SiH₄/Ar, and C₂H₂/Ar/H₂ discharge properties are still elusive so far. First, reactive gases discharges can yield highly polymerized ions, and these hydrocarbon–gas mixtures tend to produce dust particles, which will cause structural voids, dislocations, and film delamination which ultimately lead to malfunctioning devices.^[13,14] Second, reactive gases discharges are widely used in microelectronics manufacturing and photovoltaic cells.^[15,16] Therefore, a detailed investigation of the microplasma species densities, such as electrons, ions, molecules, radicals as well as nanoparticles, together with a comprehensive understanding of their behavior in reactive gases discharge are very necessary. In MDs, with micrometer and submillimeter gaps, the gas pressure is usually very high, thus the secondary electron plays an important role in sustaining the discharge, which is quite different from the low-pressure discharge. Furthermore, the simple parallel-plate configuration instead of the special microhollow electrodes or pin electrodes configurations is found to be sufficient to produce plasma.^[17] In this study, we focus our interest on the influence of pressure, power, and gas flow on the nanoparticle formation and growth mechanisms in a C₂H₂/Ar microplasma, where Ar accounts for the vast majority to generate a stable non-equilibrium plasma. In capacitively coupled MDs, the plasma density can be very high and the large-aperture uniform plasma can be obtained, which can be useful in processing.

The structure of this article is as follows. A description of the fluid model and the aerosol physics model are briefly surveyed in Section 2, and the formation, transport, and growth mechanism for nanoparticles are also elaborated. In Section 3, the MDs parameters effects on the plasma and nanoparticles characteristics are carefully discussed. Finally, a short conclusion is described in Section 4.

In this article, to investigate the behaviors of a nanoparticle in MDs, a 13.56-MHz radio-frequency source with the peak voltage of 100 V is applied to the upper showerhead electrode, and the lower electrode is grounded. In this rf MDs, the plasma is sustained by the secondary electron emission (SEE), where the secondary electron emission coefficient depends on the state of the electrode surface, the kind of particle, the particle energy which impacts on the electrode, and the electrode material. We investigated the effects of different secondary electron emission coefficients on the plasma parameters, and observed that SEE coefficients almost have no special effects on the absolute values of the results. Thus, the SEE coefficient is assumed to be γ_se = 0.1. We set the total input flow rate at F_tot = 400 sccm, with 5% mole fraction of acetylene at 20 sccm. The gas pressure ratio of Ar: C₂H₂=19:1. The ion temperature T_ion = 400 K and the initial electron temperature T_e = 3 eV. The gas distance between two parallel plate electrodes varies from 100 μm to 1000 μm. The gas pressure is in the range of 100 Torr–760 Torr, while the voltage varies from 100 V to 300 V. In this model, the time-step of an RF (13.56 MHz) cycle is set to be 7.4 × 10⁻¹³, and the space-step is 5 × 10⁻⁶ m. To speed up the calculation, the time-step for describing the neutral–neutral chemistry is 100 times larger than the RF cycle, while the dust particles’ time-step is equal to 7.4 × 10⁻⁹.

Figure 1 shows the calculated density of positive ions, electron and negative ions at the centre of the plasma, with the electrode spacing L = 1000 μm. It should be noted that the maximum of electron density is about 4 × 10¹² cm⁻³. Opposed to electron density, Ar⁺ takes a value of about 1 × 10¹⁰ cm⁻³, meaning that the electron density is around two orders of magnitude larger than the Ar⁺ density. This may result from the following two reasons: (i)

Based on Moravej,^[20] the ionization coefficient for argon is cm³/s, meaning that Ar⁺ is only produced by electron impact collisions on Ar above 15.8 eV, while is produced by electron impact collisions on C₂H₂ above 11.4 eV from Ref. [14]. Thus, the ionization coefficient of argon is much smaller than the ionization coefficients of acetylene;

Fig. 1.

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	Fig. 1. The positive ions, negative ions and electron density obtained from our simulation, with V = 100 V, P = 600 Torr, L = 1000 μm.

In acetylene discharges, is presented as an important positive ion, which reaches a concentration of about 2 × 10¹¹ cm⁻³ in the plasma bulk, approximately 20 times larger than the density of Ar⁺. Negative ions H₂CC⁻ and C₂H⁻ are the main precursors for the particle formation, since they can be confined in the discharge region on the concerted action of the electrostatic force, the corresponding peaks are 1 × 10¹² and 5 × 10¹⁰.

The spatial profiles of the electron temperature (T_e), the ionization coefficient (k_r) for Ar, and the dissociative ionization coefficient (k_di) for C₂H₂ are displayed in Fig. 2. As we can see, the electron temperature presents two peaks near the presheath for the electric field effect, but much lower in the plasma bulk around 1.2 eV. In fact, to obtain a stable discharge in microplasmas, a large number of inert gases, such as argon and helium, are required. Thus, the gas pressure ratio of Ar and C₂H₂ is set to 19 in this paper. Since Ar⁺ density is much lower than the density, which has been described in Fig. 2, some comparison between k_r and k_di is made in Fig. 3. We can clearly see that the peak of k_di is five orders of magnitude larger than the maximum value of k_r, which finally leads to density is a factor of 20 higher than Ar⁺ density under the condition of Ar: C₂H₂=19:1. It is worth noticing that the ionization coefficients k_di and k_r keep stable values in the plasma region but increase rapidly in the sheath region for the acceleration of the electric field.

Fig. 2.

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	Fig. 2. The spatial variation profiles of the electron temperature (Te) and the ionization coefficient (kr) for Ar, as well as the dissociative ionization coefficient (kdi) for C2H2, with the settings the same as those in Fig. 1.

Figure 3 shows the spatial profiles of the H₂CC⁻ density generated through the electron impact attachment on C₂H₂ and the corresponding attachment coefficient k_da, effects from different gas pressure, which has been set at 400, 600, and 760 Torr. As we can see, the k_da shows little decrease to the gas pressure while the H₂CC⁻ density increases sharply with the increasing of gas pressure, indicating that the rising amplitude of the background gas density is much larger than the decrease amplitude of the attachment coefficient. With increasing the pressure, the collisions between background gas (C₂H₂) and electrons become more frequent, and more ions are produced. However, more collision frequency existence will finally lead to the decrease in the electron energy and electron temperature, thus the attachment coefficient k_da decreases with the increasing of gas pressure. Moreover, the attachment coefficient exhibits two peaks in the presheaths, but much lower in the bulk plasma; similar distribution has also been observed in the electron temperature. However, the anion H₂CC⁻ mainly locates in the plasma region under the high-voltage electrostatic field.

Fig. 3.

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	Fig. 3. The spatial variation profiles of the negative ion (H2CC−) and the corresponding attachment coefficient kda at different gas pressure, with P = 400, 600, and 760 Torr.

The effect of gas pressure on the nanoparticles’ density n_d is plotted in Fig. 4, with the particle size of 10 nm. It can be clearly seen in Fig. 4 that a local maximum is presented in front of the showerhead electrode, which is due to the fact that the thermophoretic force moves the nanoparticles away from the showerhead electrode to the presheath region where the gradient of the neutral gas temperature is maximum. Compared with our previous studies,^[19] the nanoparticle density in the bulk plasma for MDs is much higher, suggesting that more collisions between background gas and electrons occur due to higher gas pressure, and this leads to the increase of nanoparticles and the shrinking in the sheaths. Therefore, the nanoparticles’ profile has a great difference between atmospheric pressure microdischarges and low pressure radio-frequency discharges. We can also notice from Fig. 4 that the nanoparticle density increases definitely with the increasing of gas pressure, especially in the presheath region. This is responsible for increases in the collision frequency and plasma density, as well as the neutral gas temperature gradient.

Fig. 4.

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	Fig. 4. The spatial variation profiles of the nanoparticle number density nd at different gas pressure, with the settings the same as those in Fig. 3.

Figure 5 shows the spatial profiles of the negative ion density (H₂CC⁻) and the attachment coefficient k_da effects from different electrode spacing, with the gas pressure of 600 Torr. We can see from Fig. 5 that H₂CC⁻ increases with the decreasing of electrode spacing. As is well known, decreasing the electrode spacing tends to expand the sheath to the bulk plasma, and then more secondary electrons can be emitted from the upper and lower electrodes, which leads to the higher plasma density. This result indicates that the electrode spacing has a great effect on the plasma parameters. Evident influences of the electrode spacing on the electron impact collisions can also be seen in Fig. 5. As we can see, the two peaks of k_da appear in the presheath region instead of just increasing with the decreasing of electrode spacing, showing that the electrode spacing can not only change the plasma parameters, but also their distribution.

Fig. 5.

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	Fig. 5. The spatial variation profiles of the negative ion (H2CC−) and the corresponding attachment coefficient kda at different electrode spacing, with L = 300, 500, and 1000 μm.

Figure 6 illustrates the spatial profiles of nanoparticles’ density n_d dependent on the electrode spacing, in which the electrode spacing has been set at 300, 500, and 1000 μm. The nanoparticles’ size is set at D_d = 10 nm, where the nanoparticles can display the coagulation properties. As we can see, a dominant peak of the nanoparticle density is presented near the upper electrode but much lower concentration in the bulk plasma, showing evidently the neutral gas flow effect. Moreover, similar to Fig. 5, the nanoparticle density in this article greatly depends on the electrode spacing. As the electrode spacing decreases from 1000 μm to 300 μm, the particle density increases by nearly two times. This is due to the fact that the important precursor density (H₂CC⁻) of the dust formation increases with the decreasing of electrode spacing, which drives the nanoparticle density increases. These results are quite different from the low pressure rf discharge, since the gas ionization is dominated by the secondary electron emission in the MDs, while the low pressure rf discharge is mainly sustained by the bulk plasma electrons collisions.

Fig. 6.

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	Fig. 6. The spatial variation profiles of the nanoparticle number density nd at different electrode spacing, with the settings the same as those in Fig. 5.

Figure 7 presents the spatial profiles of the negative ion density (H₂CC⁻) and the attachment coefficient k_da, depending on the applied voltage, with the voltage set at 100, 200, and 300 V. It can be seen that, the attachment coefficient k_da and the density of H₂CC⁻ dramatically increases with the increasing of the applied voltage, especially the H₂CC⁻ density increases exponentially. In this article, secondary electron emission is responsible for the electron heating, thus the input voltage and power are mainly dissipated by the secondary electrons. In other words, as the voltage increases, more secondary electrons can be emitted from the electrodes, resulting in an increase in the attachment efficiency and plasma density. Thus, H₂CC⁻ density in the bulk plasma increases deeply with the applied voltage, whereas the attachment coefficient increases slightly. The voltage effect on the nanoparticle density n_d is also investigated, which has been plotted in Fig. 8. Similar to the results of H₂CC⁻ density, the nanoparticle density at the size of 10 nm increases greatly with the increasing of the applied voltage, especially at the peak region, suggesting high gas temperature gradient effect. We can conclude that the applied voltage has a great impact on the plasma density and even the nanoparticles’ formation and growth.

Fig. 7.

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	Fig. 7. The spatial variation profiles of the negative ion (H2CC−) and the corresponding attachment coefficient kda at different applied voltage, with V = 100, 200, and 300 V.

Fig. 8.

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	Fig. 8. The spatial variation profiles of the nanoparticle number density nd at different applied voltage, with the settings the same as those in Fig. 7.

The behavior of nanoparticles in atmosphere microdischarges is carefully investigated by using a self-consistent coupling between an aerosol dynamics model and one-dimensional hydrodynamic model. In these MDs, the neutral flow cannot be ignored since the thermophoresis force has a great impact on the distribution of nanoparticle density. Thus, the flow equation and heat transfer equation for neutral gas are carefully investigated. From the standard model, it was found that the secondary electron emissions play a leading role in sustaining discharge.

In this article, the effects of pressure, electrode spacing, and applied voltage on the plasma density and nanoparticle density were studied. We noticed that increasing the electrode spacing, the H₂CC⁻ density and nanoparticle density decreased instead of increasing, under the influences of secondary electron emissions. However, the pressure has a relatively smaller impact on the nanoparticle density. We have, in particular, discussed the role of applied voltage on the nanoparticle density, particle size of 10 nm. By varying the applied voltage between 100 V and 300 V, the nanoparticle density increased nearly two orders of magnitude. Hence, the applied voltage can be a very important parameter that can strongly influence the nanoparticle properties, even at moderate voltage differences of 100 V or more.