| Citation: |
Xucheng WANG, Shuhan GAO, Yuantao ZHANG. Numerical study on peak current in pulse-modulated radio-frequency discharges with atmospheric helium–oxygen admixtures[J]. Plasma Science and Technology, 2022, 24(8): 085401. DOI: 10.1088/2058-6272/ac67bf
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Atmospheric pressure pulse-modulated radio-frequency (rf) plasmas have drawn growing attention due to their potential in applications. By selecting appropriate modulation parameters, the diffused and large-volume plasma can be generated in the pulse-modulated rf plasma with plenty of reactive oxygen species, which is essential for the biomedical application of helium–oxygen plasmas. In this paper, by means of a fluid model, the formation of the peak current in the first period (PCFP) in a pulse-modulated rf helium–oxygen discharge driven by a sinusoidal voltage is discussed, the existence of a reverse field near the anode caused by the negative and positive charges contributes greatly to the mechanism of PCFP. In the simulation, as oxygen admixture increases, the negative ions of O- and O2- become dominative anions in the sheath region, which can't be driven to the anode very quickly to build a reverse field, thus the PCFP eventually disappears. This study can effectively enhance the understanding of different transportation behavior of heavy negative ions and electrons, and further optimize pulse-modulated rf discharges with helium–oxygen mixtures in various applications.
During the past decades, owing to the wide application fields and lower costs, atmospheric pressure plasmas have been greatly developed [1–5]. Compared with low-pressure plasmas, atmospheric plasmas are easy to apply and do not require expensive vacuum equipment, which is very essential for the application of plasmas in the materials and environments [6, 7]. The atmospheric capacitively coupled radio-frequency (rf) discharges could produce the stable large-volume plasmas in α mode without the dielectric barriers, and high-density active species are generated through the frequent multi-body collisions in the rf plasmas, which is of great significance for the application of plasma biomedical, such as wound healing, tissue regeneration, and so on [8–10]. However, when more energy is coupled into the atmospheric rf plasmas, the transition of discharge from the α mode to the γ mode will be observed, and the hot and constricted plasmas can be generated, together with the increase of the gas temperature, leading to reduced device longevity in industrial applications [11–13]. Therefore, in most applications of atmospheric pressure rf plasmas, it is always desirable to operate discharges in α mode and avoid the transition to γ mode [14, 15].
The application of pulse-modulated technology enables the rf plasma to be only generated during the power-on phase and the mode transition from α mode to γ mode will be delayed. At the same time, by selecting the suitable duty cycle and modulation frequency, the pulse-modulated rf discharges can be further optimized for applications, and the electron density and electron energy still maintain higher while reducing the power consumption [16]. The atmospheric pulse-modulated rf discharges could lead to new discharge characteristics in the range of very high frequency (VHF), even in the range of ultra-high frequency (UHF). During the first period of the pulse-modulated rf discharges in the power-on phase, a very strong peak current can be observed [17]. Plenty of energetic electrons with an energy of more than 50 eV have been produced in the PCFP [18]. When other gases, such as oxygen, are admixed to the discharge gas of helium, a large number of reactive particles could be obtained in the atmospheric pressure rf plasmas. These reactive particles are found to play essential roles in biomedical applications [11, 19]. In the previous study, the optimization of the atmospheric rf discharge of helium–oxygen plasmas at a normal frequency of 13.56 MHz was analyzed using a numerical simulation [20]. However, less attention has been paid to the discharge characteristics of helium–oxygen plasmas under atmospheric pressure when the rf frequency reaches the VHF range, and plenty of energetic electrons produced during the first period by pulse-modulated rf discharge are also critical for the formation of reactive oxygen species. Therefore, the formation mechanism of PCFP in helium–oxygen plasmas should be further understood, and the effects of different oxygen admixtures on PCFP should be discussed.
This work focuses on the generation mechanism of the PCFP in helium–oxygen plasmas produced by pulse-modulated rf discharges. The second section is concerned with the description of the mathematical model used for this study. The third section gives the findings of the mechanism of the PCFP in pulse-modulated rf helium–oxygen discharges, and the effect of oxygen admixture on the PCFP is also investigated in the third part according to the simulation data. In the fourth section, a conclusion is summarized.
A one-dimensional fluid model is applied in this work to investigate the discharge mechanism of atmospheric pulse-modulated rf discharges. The production and destruction of various particles are given by the continuity equations
| ∂Ne, a, i, n∂t+∇·Γe, a, i, n=Se, a, i, n | (1) |
where the indices e, a, i, and n are electrons, negative ions, positive ions, and neutral particles, N is the density of various particles, S refers to the source item of particles, respectively. Γ is the flux of particles calculated by the diffusion-drift approximation, which is expressed as
| Γe, a, i=∓μe, a, iENe, a, i-De, a, i∇Ne, a, i | (2) |
| Γn=-Dn∇Nn | (3) |
where μ and D denote mobility and diffusion coefficients of various particles. Both drift and diffusion are considered for charged species, while only diffusion is taken into account for neutral species. The transportation coefficient of electrons was computed using the Boltzmann equation solver based on the collision cross-section data from the Phelps database in the LXCat website [21]. The mobilities of ions related to oxygen species were given from references [22, 23], and the corresponding diffusion coefficients of ions are calculated from mobility using Einstein relation [24]. The diffusion coefficients of neutral species related to oxygen species were given from reference [25]. The transportation coefficients of helium were mainly obtained from references [26, 27], E
is the electric field in the discharge region, which is calculated by the Poisson equation given as
In this model, the current balance equation shown in equation (4) can be derived by performing the time differentiation on both sides of the Poisson equation [27–29].
| ε0∂E∂t=j0-jg | (4) |
where ε0 represents the vacuum permittivity, j0 and jg are the total current density and the conduction current density. j0 is given by equation (5) and jg is expressed as equation (6).
| j0=ε0ddVdt+1d∫d0jgdx | (5) |
| jg=e(∑iΓi-∑aΓe,a) | (6) |
where d is the electrode spacing, V is the applied voltage given by equation (7), e is the elementary charge. The electron energy conservation equation can accurately calculate the electron temperature, which is expressed in references [26, 29].
In the simulation, the applied voltage is given as a piecewise function, which includes the power-on phase (denoted as Pon) and power-off phase (denoted as Poff) in equation (7), respectively.
| V={V0sin(2πft),t∈PonrV0sin(2πft),t∈Poff} | (7) |
where V0 is the amplitude of the sinusoidal applied voltage fixed as a constant of 200 V during the power-on phase, f is the rf frequency, r refers to the voltage modulation rate (VMR) changing from 0% to 100%, that is the ratio of voltage amplitude between the power-on phase and power-off phase. In this paper, the VMR is fixed as 15% to ensure the stability of the simulation.
As the driving frequency reaches several hundred MHz, the simulation data calculated by the fluid model match the computational data well, obtained from the particle-in-cell Monte Carlo collision (PIC-MCC) model in references [30, 31]. Therefore, the fluid description could still capture the main discharge characteristics with the driving frequency ranging from tens of MHz to hundreds of MHz [32–34]. In the present helium–oxygen plasma model, 17 species and 65 important chemical reactions were considered. The reaction set can be obtained from the previous studies in reference [20], which are mainly from the zero-dimensional simulation at the atmospheric helium–oxygen plasma [35, 36], and by comparing with the experimental results, the reaction set used has been validated in reference [16]. In addition, the simulation results in the previous work based on these species and reactions are consistent with the experimental results [11, 19, 37]. In this work, the model consists of four neutral particles (He, O, O2, and O3), eight charged particles (e, He+,
In the pulse-modulated rf discharge, the PCFP can be observed by rising the excitation frequency to the VHF range, even in the UHF range, which has been discussed in previous studies [40–42]. In the first rf period of the pulse-modulated rf discharge, many energetic electrons could be obtained, essentially attributed to the generation of reverse electric field near the anode. As we know, the continuous rf discharges usually can only produce electrons with medium energy [41], and in the helium–oxygen plasmas, energetic electrons play a crucial role in the generation of reactive oxygen species. In this work, a pulse-modulated rf voltage with an excitation frequency of 500 MHz and a modulation frequency of 6.25 MHz is served as the power source, figure 1 presents the evolution of current density at a sinusoidal voltage amplitude of 200 V, an oxygen admixture of 0.5%, and a duty cycle of 70%. In the first rf period of the power-on phase, a remarkable peak current is generated. The value of the PCFP is 10.1 A cm-2, which is 11.1% greater than those in the rest periods only of 9.1 A cm-2 during the power-on phase. In the rest of the rf periods, the PCFP will not be observed, which shows a different discharge pattern from the usual pulse-modulated rf discharges with the excitation frequency of 13.56 MHz [16, 43, 44].
To better understand the formation mechanism of the PCFP, figure 2 shows the spatial profiles of positive and negative charge densities at different moments. It can be noted that in figures 2 and 3, T1 is the moment when the first rf period starts during the power-on phase, that is, at this moment, the applied voltage is zero and then it begins to grow. T2 and T3 are the moments when the current density reaches the positive peak value in the first and second rf periods during the power-on phase, respectively. As shown in figure 2(a), the distribution of positive and negative charge densities is almost completely symmetrical. According to the previous study [38, 45], the positive ions are mainly
Figure 4(a) shows the profile of electron temperature at the moment when the current density reaches the peak value during the first rf period. It is obvious that the electron temperature near the anode reaches 6 eV. The reverse electric field near the anode shown in figure 3(b) could accelerate the electrons, enhancing the electron energy. These electrons with higher energy contribute to the formation of the PCFP. In addition, the electron flux is given in figure 4(b). As shown in figure 4(b), the electron flux in the anode sheath region is approximately 1019 cm-2s-1, which is much greater than the electron flux of about 1016 cm-2s-1 in the cathode sheath region. Moreover, the flux of electrons in the anode sheath is much larger than that of negative ions, indicating that the reverse electric field formed near the anode is caused by the fast movement of electrons rather than ions to the vicinity of the anode.
Consequently, the formation of the PCFP in helium–oxygen plasmas could be attributed to the following aspects. On one hand, the rf frequency should be increased to the VHF range, so that the voltage or electric field could be greatly enhanced during a very short duration. In this work, driven by a sinusoidal voltage with a voltage amplitude of 200 V and a rf frequency of 500 MHz, the average voltage rising rate of a quarter cycle of the whole period is 400 Vns-1. The gas voltage will rise rapidly and reach its maximum, afterwards it drops sharply and rises conversely, which will drive electrons to sustain between the anode and the bulk plasma region. In addition, the heavier positive and negative ions in the plasma could not respond to the fast changes of the applied electric field at the VHF range and will remain in the bulk plasma region, producing a reverse electric field near the anode. The electrons between the anode and the bulk plasma region could be reheated by the reverse electric field, leading to the formation of the PCFP. This is why the excitation frequency in the simulation is chosen to be a very high-frequency range of 500 MHz.
On the other hand, the presence of a reverse electric field and the initial spatial distribution of the charged species are also key factors for the PCFP generation. As shown in figures 1 and 2, the first rf period is excited at the same frequency as the rest periods, but the peak current is observed only in the first rf period. The reason is that there is a reverse electric field in the first rf period, but not in the rest periods. From the foregoing discussion, driven by the excitation frequency in the VHF range, electrons will accumulate between the anode and the bulk plasma region, causing the density of negative charges near the anode to be larger than the density of positive charges, generating a reverse electric field. This electric field will reheat the electrons and increase the energy of the electrons, which is an essential factor in the formation of a large peak current.
In previous studies, the appropriate modulation parameters such as duty cycle, modulation frequency, and rf frequency can effectively optimize the pulsed-modulation rf discharge to improve the discharge stability and power efficiency [40]. With the growth of the duty cycle, the value of PCFP initially ascents and reaches the maximum, then decreases. Finally, when the duty cycle is 100%, the PCFP cannot be formed, which suggests that the PCFP can only be generated in pulse-modulated discharges. A more detailed analysis of the parameters such as the duty cycle has been explained in simulations of reference [17]. When the rf frequency is fixed as a constant, the value of PCFP will decrease as the modulation frequency increases. Moreover, by increasing the VMR, the rf discharge becomes completely continuous and the value of the PCFP gradually decreases, until the PCFP finally disappears [41].
The admixture of electronegative gas can also seriously influence the formation of the PCFP. Figure 5 presents the evolution of current density when the oxygen admixtures are 0.1% (a), 0.5% (b), 1.0% (c), and 3.5% (d). With the increase of oxygen admixture from 0.1% to 3.5%, the peak current during the first rf period is no longer noticeable, and the PCFP also drops or even disappears. The maximum value of the PCFP is 10.6 A cm-2 and the peak value of the stable current density is 9.0 A cm-2 at the duty cycle of 70% and the oxygen admixture of 0.1%, given in figure 5(a). When the oxygen admixture increases to 0.5%, the maximum value of the PCFP decreases to 10.1 A cm-2 shown in figure 5(b). As the oxygen admixture continues to increase, figure 5(c) presents the value of the PCFP of approximately 9.1 A cm-2 when the oxygen admixture is 1.0%. However, in figure 5(d), when the oxygen admixture increases to 3.5%, the PCFP is not observed, and the maximum value of current during the first rf period is only 5.0 A cm-2.
According to the computational data, figure 6 summarizes in detail the dependence of the value of PCFP on the oxygen admixture, as well as the peak current density in the rest stable rf periods. As shown in figure 6, the maximum value of the PCFP is observed when the oxygen admixture is as large as 0.1%. As the oxygen concentration increases, the value of PCFP and the maximum current density in the rest stable rf periods are both decreasing. Due to the electronegativity of oxygen, the rise of oxygen admixture causes a large number of electrons to be adsorbed by molecular oxygen, and the pulse-modulated rf discharge becomes more electronegative, leading to the decrease of electron density in the discharge region, meanwhile the negative ions of O- and
To give a more detailed description, figure 7 presents the spatial profiles of electric field at the instant when the current density in the first rf period gets to the maximum for various oxygen admixtures. According to the spatial profiles of the electric field in figure 7, the electric field in the bulk plasma region increases with the growth of oxygen concentration, and the thickness of the anodic sheath decreases gradually. When the oxygen admixtures are 0.1%, 0.5%, and 1.0%, the reverse electric fields near the anode are 10.0, 8.6, and 7.8 kVcm-1 from the simulation. This qualitatively indicates that the increase of oxygen concentration can effectively weaken the reverse electric field near the anode. More electrons in the discharge space have been attached by molecular oxygen with the increase of oxygen concentration, thus resulting in a reduction of the density of electrons driven to the vicinity of the anode. As a result, the reverse electric field generated near the anode is eventfully reduced.
As the oxygen admixture reaches 3.5%, the reverse electric field near the anode is no longer observed and the PCFP is not obtained. Figure 8 presents the spatial distribution of the density of main species and electric field at an oxygen admixture of 3.5%, a duty cycle of 70%, and an applied voltage of 200 V. Compared with the distribution of main particles density at the oxygen concentration of 0.1% at the instant of T2, shown in figure 3(b), the densities of electrons and various ions decrease significantly, caused by the addition of electronegative gases [20]. Although the electrons near the anode are still the main component of negative charges, the electrons density is already lower than the positive ions density, and a reverse electric field with the same polarity as that near the cathode cannot be formed. The importance of the reverse electric field for the formation of peak current has been emphasized in the foregoing discussion. Therefore, the PCFP is not observed when the oxygen admixture is 3.5%.
In summary, a fluid model is performed to study the formation of the PCFP in atmospheric pulse-modulated rf discharges with admixture gas of helium and oxygen as the working gas. The numerical data show that when the rf frequency and the modulation frequency are 500 MHz and 6.25 MHz, a PCFP with the value of 10.1 A cm-2 could be observed during the power-on phase of helium–oxygen discharges. When a sinusoidal voltage with a larger excitation frequency even in the range of the UHF, is applied to the admixture gas of helium and oxygen, the electrons are driven to the anode by the applied electric field and stay between the anode and the bulk plasma region, forming a reverse electric field near the anode, the electrons near the anode could be reheated to form the PCFP. However, with the increase in oxygen impurity the negative ions of O- and
This work was supported by National Natural Science Foundation of China (No. 11975142).
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