Electron dynamics and metastable species generation in atmospheric pressure non-equilibrium plasmas controlled by dual LF–RF frequency discharges

1 Introduction

Atmospheric pressure (AP) cold plasmas have extensive applications due to their unique features, such as simple and convenient operation processes, high electron densities, low gas temperatures, and plenty of reactive particles. Particularly, dielectric barrier discharges (DBDs), as a conventional way to generate high-density plasmas with a low temperature at atmospheric pressure, have many applications not only in traditional fields, such as sterilization [1], deactivation of bacteria/virus/cancer cells [2–5], would healing [6], and exhaust gas cleaning [7], but also in emerging areas such as special material surface treatment/modification [8, 9], air-flow control [10] and semiconductor manufacturing [11]. Recently, studies for gas–liquid interface interactions by DBD structures have also provoked great interests [12].

The DBD system usually has a wider parameter range, with the electron density varying in the 10¹⁷–10²⁰ m^-3 regime, depending on discharge modes (diffusive, pattern, or filamentous) and driving methods [13–15]. In a traditional DBD ignition mode often with a single driving source, the driving frequency is increased from kHz [16] to MHz [17]. For the single ∼ kHz driving, the discharge current develops in a pulse-like type, with one or several short pulses per discharge period. The discharge is mainly in a filamentous form, with higher electron densities in significant non-uniformity or lower electron densities in a mild diffusive mode. As the driving frequency increases to MHz, the discharge characteristics become quite different from those of the kHz driving case, typically with better spatial uniformity and higher electron density. Meanwhile, the breakdown voltage under the MHz radio frequency (RF) driving is only about a third of that in the kHz low-frequency (LF) driving condition, which makes the RF DBD very attractive. In spite of the aforementioned advantages of DBD, challenges still remain in the directional parameter optimizing and parameter de-coupling. Especially, for bio-medicine applications, it is tough to make a trade-off between demands of a higher particle density and an acceptable gas temperature [18]. In order to independently control desired plasma parameters, modulation by dual frequencies (DF) and/or tailored voltage has been proposed and demonstrated to modify the power dissipation and electron dynamics, particularly the electron heating process, and thus to achieve the demanded DBD plasma parameters [19, 20]. For instance, Liu et al. adopted a frequency combination of 200 kHz/13.56 MHz to investigate the effect and mechanism of each frequency component on the DF discharge [21]. They demonstrated that the DF excitation provided a higher input power and improved discharge uniformity, with potential applications in plasma-assisted surface processing [22]. On the other hand, F. Massines et al. investigated the influences of amplitude and frequency of applied voltages on DF-excited DBD plasmas in a wide voltage range [23, 24]. Particularly, the influence of LF voltage amplitude on the RF discharge process and the mode transition from α to α-γ were studied [25]. Recently, our results also show that DF and tailored voltage waveform excitation are valid approaches to achieve independent control and optimization over both electron density and gas temperature in AP–DBD systems [26–30]. However, the electron dynamic behaviors and the mechanisms of particle density directional optimization still remain unclear and unresolved in AP non-equilibrium plasma studies.

In this work, we adopt dual-medium frequencies of 50 kHz/5 MHz to study the influence and control of electron dynamics and metastable species generation and thereby provide the plasma density directional optimization strategy and its mechanisms. Moreover, we provide a theoretical explanation for our previous work of plasma density directional optimization [26], namely, the electron density has a substantial increase, but gas temperature has no obvious increase. The paper is organized as follows: a simplified simulation model and its analytic method are described in Section 2. The simulation results are shown and discussed in Section 3. Then, a short summary of the work is given in Section 4.

2 Model description

In order to further understand and describe the complex physical and chemical processes of AP–DBD systems (in particular their electron dynamics), a time-dependent 1D drift–diffusion model with the plasma platform PLASIMO was used in this work, and details about PLASIMO are shown in [21, 30, 31]. In the model, particle transport equations for the electron, ion, and metastable species are solved in drift–diffusion approximation, where the electrical field is given by Poisson’s equation. The energy transport equation is also applied for the electron only with a cold ion assumption. Argon is used as the working gas in this work. Four species, i.e., e (electrons), Ar^*, Ar⁺, and Ar₂⁺, are considered for argon chemical kinetics, with detailed information on related reactions being listed in Table 1. The diffusion coefficient of metastable argon is calculated by the collision integral method [36]. The electron mobility is calculated as a function of the mean electron energy W from the electron energy distribution function (EEDF) by using the Boltzmann solver BOLSIG+ [37], where the chemical reaction rate coefficients involving electrons are also obtained.

TABLE 1. Transport coefficients and associated reactions.

2.1 Governing equations and boundary conditions

In this work, since the area of the electrode is much larger than the discharge gas gap, the drift–diffusion model can simulate the development of the discharge. Four species mentioned previously are mainly considered in this model. The Ar^* is in the 4s excited state, and the lifetime of the 4s excited state of Ar^* is 100–140 ns. In the vicinity of this excited level, there are many semblable levels, and they can transform with each other quickly; hence, we consider these particles as metastable particles. The spatial and temporal distribution of particles is described with the continuity equation:

Here, n_r is the number density of r-th particles, including e, Ar^*, Ar⁺, and Ar₂⁺. S_r is the source term of r-th particles, and it is calculated by

Here, k_i is the reaction coefficient; α_i is the Townsend coefficient; n_r1, n_r2, and n_r3 are the reaction number densities in different equations. The N_r in Eq 1 is the r-th particle flux, and it is described as

Here, i represents Ar⁺ and Ar₂⁺; E is the electric field; μ_e and μ_i are the mobility rates of electron and ions, respectively. The ion mobility rate is the function of the reduced electric field (E/n), and the electron mobility rate is the function of the mean electron energy, which is solved by Boltzmann equation. D_e, D_i, and D_Ar* are the diffusion coefficients of e, ion, and Ar*, respectively, which are calculated by Einstein relation:

Here, e is the elementary charge, T_i is the temperature of the i-th particle, and k_B is the Boltzmann constant. In this work, the electric field is solved by Poisson’s equation:

Here, φ is the electric potential and ε is the dielectric constant. The discharge circuit is calculated by Kirchhoff’s voltage law (KVL):

Here, V_a(t) is the applied voltage, V_d(t) is the dielectric voltage and the loop circuit, and i₁(t) is obtained by the Morrow–Sato equation.

In this model, we assume the positive ion particles are totally recombined when they impact on the cathode dielectric layer, and hence the boundary condition cathode is considered as

Here, $v_{\mathrm{i}}=\sqrt{\frac{8k_{\mathrm{B}}{T}_{\mathrm{i}}}{\pi m_{\mathrm{i}}}}$ is the ion thermal velocity, m_i is the mass of ion, u_n is the normal vector which directs toward the surface of the dielectric layer, and α_i0 is the coefficient which relates to the electric field of the boundary and is expressed as

The secondary electron emission induced by the positive ion impact on the cathode dielectric surface has been considered by

Here, γ is the secondary electron emission coefficient; α_e1 and α_e2 are the coefficients which relate to the electric field of the boundary and are expressed as

The boundary of electron energy is related to the electrons, and hence they have a similar form. Since the generation mechanism of secondary electron emission is fairly complicated in dielectric barrier discharge, we simplify the mean secondary electron energy as 2.5 eV, which is approximately identical to the mean electron energy near the plasma sheath. The boundary of electron energy is simplified as

Here, $v_{\mathrm{e}}=\sqrt{\frac{8k_{\mathrm{B}}{T}_{\mathrm{e}}}{\pi m_{\mathrm{e}}}}$ is the electron thermal velocity, N_ε is the electron energy flux, and n_ε denotes the energy density of the electron.

For the metastable atom, we assume they totally de-excitate to the ground state atoms, and the boundary condition is written as

For the electric field, the dielectric surface can simulate the charge, and the electric flux in the dielectric surface is discontinuous.

Here, D_g is the electric flux in the ground electrode, D_a is the electric flux in the applied excitation electrode, and σ is the surface charge density obtained by

The related species reactions and their associated transport coefficients in this work are shown in Table 1. The sketch of the DBD model in this work is shown in Figure 1.

FIGURE 1. Model sketch of dynamics and energy transport processes in a DBD plasma.

2.2 Discharge conditions and benchmark

We first verify the validity of the model by comparing the numerical and experimental results for similar conditions in single LF or RF DBD. The discharge plasma is generated and sustained in a geometrically symmetric parallel-plate DBD configuration. The dielectric material we adopt is polyethylene terephthalate (PET), whose relative permittivity (dielectric constant) and thickness are ε = 3.4 and d_B = 1 mm, respectively. The gas gap between the two layers is fixed as d_g = 2 mm. The secondary electron emission coefficient of the dielectric material is 0.07. The gas temperature at the dielectric layer boundary is fixed at T_g = 400 K ($\approx$ 0.04 eV). The initial ions and electrons are uniformly distributed in the discharge region with the same density of 10⁷ cm^-3. Additionally, 600 equidistant grids are used to resolve the 1-mm inter-electrode gap, and 2×10⁵ time-steps are applied within an applied voltage cycle to resolve the temporal dynamics of all plasma species.

Figure 2 presents a typical discharge waveform, including applied and discharge current density, driven by a 50 kHz@1.2 kV LF (the upper row) as well as a 5 MHz@0.7 kV RF (the lower row), respectively, and the corresponding spatio-temporal distributions of the electric field and electron density during two discharge periods. The discharge current density is characterized by a short pulse per half cycle in the LF driving case and approximately sinusoidal in the RF case. As the driving frequency increases from ∼kHz to ∼ MHz, both the electric field and the electron density increase gradually, due to the higher electrical oscillation compressing the sheath electron density. Both numerical results of the individual LF or RF discharge presented here are clearly in good agreements with previous numerical and experimental results under the similar condition [24].

FIGURE 2. Time-dependence of the discharge voltage–current characteristic, electric field, and electron density, respectively, in the low-frequency-only discharge of 50 kHz@1.2 kV (A) and in the high-frequency-only discharge of 5 MHz@0.7 kV (B).

3 Results and discussions

This work aimed to understand the impact factors on electron dynamics and metastable species generation in the DF discharge process, and thereby obtain the electron density/temperature control and modulation strategies by dual-frequency (LF-RF) excitation. First, we try to find the DF governance patterns, e.g., the LF-dominant, the DF-comparable, or the HF-dominant, and then focus on the different ratios and corresponding plasma parameters. Thereafter, we analyze electron dynamics and control and optimization mechanisms.

3.1 Governance patterns of DF DBD

The governance pattern of DF discharges can be simply described by the ratio of LF to RF voltage amplitudes with fixed dual frequencies. In this work, with f_L = 50 kHz/f_H = 5 MHz, we gradually vary the LF (50 kHz) voltage from 0 to 1500 V and alter the RF (5 MHz) voltage from 0 to 400 V. Figure 3 presents typical discharge waveforms under various voltage amplitude ratios of LF/RF. For the LF-dominant discharge mode with a ratio of V_LF = 850 V/V_RF = 150 V, as shown in Figure 3A, the discharge current density (red line) oscillates in the high frequency of the RF and is enveloped by a pulse-like waveform during the low-frequency period. When reducing the ratio to V_LF = 700 V/V_RF = 300 V, although the voltage curve (blue line) is still LF-dominant, the discharge current density waveform is in an LF-modulated quasi-sinusoidal oscillation, as shown in Figure 3B. We then call the discharge mode in this case as a DF-comparable mode. The discharge current pattern clearly distinguishes various discharge mechanisms and plasma parameter regimes. Furthermore, lowering the ratio to V_LF = 100 V/V_RF = 400 V, the discharge is then clearly dominated by the RF component, and the discharge current density exhibits a completely high-frequency oscillation, with the discharge characteristic not essentially different from the RF-only driving. Hence, its feature is similar to that of the HF-only discharges.

FIGURE 3. Time-dependence of the applied voltage (blue lines) and discharge current density (red lines) over two low-frequency periods with f_L = 50 kHz and f_H = 5 MHz; the voltage ratios of (A) V_L = 0.85 kV/V_H = 0.15 kV, (B) V_L = 0.7 kV/V_H = 0.3 kV, and (C) V_L = 0.1 kV/V_H = 0.4 kV.

To better understand and distinguish the aforementioned governance patterns, we show in Figure 4 the spatial distributions of feature parameters, including electron/argon ions/metastable ion densities and electron temperature, in the discharge gas gap, which are temporally averaged over an LF period. Obviously, one can see a sheath region near the boundary, characterized by the significant variations of particle densities (n_e, n_Ar+, and n_Ar*). For the LF-dominant discharge, as shown in Figure 4A, the electron density decreases substantially near the boundary to form a sheath. In addition, the LF component dominates the discharge and induces the cathode sheath expansion and decreases the plasma bulk region and the density compared with the DF-comparable mode and the HF-dominant mode, as shown in Figures 4B, C, respectively. This can be explained by the increase in the ion loss due to the drift to the cathode by the strong LF electric field [24]. The electron temperature in the bulk plasma decreases to its bottom level at x = 0.5–1.5 mm, due to the higher electron power absorption in this region. For the single-frequency dielectric barrier discharge, the electron temperature has a strong coupling with electron power absorption, i.e., if the power absorption increases so does the electron temperature. For the dual-frequency discharge, the higher frequency oscillation within a period of low frequency can effectively capture the electron and trap electrons within plasma sheaths. The sheath thickness is similar to that in the RF-only DBD discharge, but the electric field in the sheath region is much stronger. The peaks of particle densities are located at the central region where the electron temperature reaches its minimum.

FIGURE 4. Time-averaged spatial distributions of particle densities and the electron temperature in (A) the LF-dominant mode of V_LF = 0.85 kV/V_RF = 0.15 kV, (B) the DF-comparable mode of V_LF = 0.7 kV/V_RF = 0.3 kV, and (C) the HF-dominant mode of V_LF = 0.1 kV/V_RF = 0.4 kV.

For the DF-comparable mode, as shown in Figure 4B, as the proportion of the HF component increases, all particle densities increase while the electron temperature steeply decreases in the plasma bulk region. The minimum value of electron temperature occurs at the sheath edge due to the enhanced direct ionization and strong RF electric field. Furthermore, the discharge in this mode is characterized by a cathode reduction on both sides of the plasma bulk region, meaning the density of ions is always large enough to cause the RF electron oscillation, which induces a space–charge electric field. For the HF-dominant mode, as shown in Figure 4C, the spatial distributions of time-averaged particle densities and electron temperature are similar to those in the RF-only DBD discharges [41, 42]. Hence, the discussion for features of the HF-dominant mode is also similar to that in the previous RF-only DBD studies.

3.2 Particle generation and distribution in various governance patterns

In Figure 5, we further show the time-averaged particle densities varied with LF and RF voltage amplitudes. In general, it is observed that all time-averaged particle densities are positively proportional to V_RF. For LF voltage, however, although n_e, n_Ar*, and n_Ar+ increase with the increase in V_LF when V_RF = 350 V, they decrease first and then increase with a turning point approximately at V_LF = 200 V when V_RF = 250 V or 300V. The possible reason is due to the uncompensated ion density loss at a low LF component voltage, as shown in Figure 5D. The ratio of electrons and Ar ions shows the Ar ion density has a rapid increase when V_LF>300 V. As V_RF reaches a high level, e.g., at V_RF = 350 V, the RF component is large enough to compensate the ion loss, and hence the particle densities keep increasing with the LF voltage amplitude, and also the ratio of electrons and Ar ions presents a relatively steady increase. The electron density is enhanced by a factor of 4.6 (the ratio of V_RF = 350 V, V_LF = 1400 V, and V_RF = 250 V/V_LF = 100 V) by changing the LF/RF voltage amplitude ratio. Correspondingly, the densities of Ar^* and Ar⁺ densities can be enhanced by a factor of 2.7 and 2.5, respectively.

FIGURE 5. Time-averaged particle densities varied with the low frequency voltage for (A) the electron, (B) the Ar*, and (C) the Ar+, at V_RF = 250, 300, and 350 V, respectively, and (D) the ratio of the maximal density electrons and Ar ions.

To gain a clear picture of the density evolution, the spatial distributions of particle densities developed in two LF periods are shown in Figure 6. In Figure 6A, one can find that for discharges dominantly controlled by LF, the maximum electron density is located near the sheath region. Modulated by the RF component, the electron density in the bulk plasma region maintains a high level, different from the electron density distribution in only LF-driven DBDs. The similar spatial distribution tendency can be observed for n_Ar+. For the distribution of n_Ar+, the maximal value is at ∼400 μm from the instantaneous cathode, near the sheath region. In the LF-dominant mode, n_Ar+ has a similar distribution to only LF-driven DBDs, with one peak in each LF period, but of a higher intensity. The electron-depleted region oscillates with the RF driving. Moreover, even a weak RF component can notably expand the bulk plasma region, causing further ion loss at the instantaneous cathode.

FIGURE 6. Spatial distribution of particle densities in two LF periods, for the LF-dominant mode with V_L = 1300 V/V_H = 350 V (the upper row) and the DF-comparable mode with V_L = 550 V/V_H = 350 V (the lower row), where the electron density is shown in (A, D), the metastable state in (B, E), and the ion in (C, F).

For the DF-comparable mode, the electron is mostly distributed in the plasma bulk region, with a significant electron density decrease near the sheath region, as shown in Figure 6D. In this case, LF-only DBD discharge characteristics completely disappear due to the considerable RF modulation. The Ar* species majorly distributes near the sheath region and is continuously created in the LF period. It is worth noting that all particle densities have a reduction in comparison with the LF-dominant mode. However, electron and argon ion densities only decrease slightly, while the argon metastable density decreases obviously by almost an order of magnitude. This suggests that the LF component mainly affects the metastable particle generation.

3.3 Mechanism discussion under different governance patterns

Figures 7A, B shows the spatio-temporal profiles of the power absorption (P_e,abs = J_e·E) as a function of the RF voltage amplitude in two LF periods with V_RF = 250 V and 350 V, respectively. It is observed that the major power absorption occurs near the plasma bulk region, which mainly results from RF ohmic heating since the power absorption intensity increases with the RF voltage. Thus, electrons can be heated throughout the LF period. To further investigate electron dynamics, the power absorption in five continuous RF periods is shown in Figures 7C, D. One can find that the discharge remains in an α-γ transition mode. In the α-γ transition mode, the plasma is driven by the electron current density and SEE. The power absorption is majorly observed in both the expansion and collapse areas of the sheath and extended into the sheath. As the RF component is enhanced, the plasma sheath is compressed and the power absorption inside the sheath increases obviously. By further increasing the RF component, the discharge then completely enters into the γ-mode (not shown here).

FIGURE 7. Spatio-temporal profile of the power absorption in two LF periods, for (A) V_L = 100 V/V_H = 250 V and (B) V_L = 100 V/V_H = 350 V, respectively. Moreover, (C) and (D) are in five RF periods in the selected regions corresponding to (A) and (B).

When the discharge is dominantly controlled by the LF driving, the power absorption presents a different spatio-temporal profile, as shown in Figures 8A, B. In the figures, we can see that major power absorption occurs near the sheath region, and the major excitation peaks around each LF power maximum, which is quite different from the DF-comparable mode. Increasing the RF component to 350 V, the RF oscillation begins to be apparent, as shown in Figure 8B. To show the process more clearly, the power absorption in five continuous RF periods is plotted in Figures 8C, D. In the figures, one can find an asymmetric structure of the electron power absorption. For the instantaneous cathode side, the electron power absorption occurs near the sheath region; for the instantaneous anode side, a weaker power absorption occurs at both expansion and collapse regions of the sheath. Furthermore, by increasing the RF component, the power absorption is enhanced at both sides and gets extended to the bulk plasma region from the instantaneous anode, which suggests that more secondary electrons are trapped by the enhanced RF electric field.

FIGURE 8. Spatio-temporal profiles of the power absorption in two low-frequency periods, for (A) V_L = 1300 V/V_H = 250 V and (B) V_L = 1300 V/V_H = 350 V, respectively. And, (C, D) are five RF period enlargements in the selected region corresponding to (A, B), respectively.

Furthermore, we investigate the influence of the DF discharge on the plasma parameters. Fast Fourier transform (FFT) of the discharge current and their associated power spectra for different discharge modes is carried out and shown in Figure 9. As a rapid and effective method to analyze non-linear phenomena, we and other groups have also applied FFT in previous studies [23, 26]. From the frequency spectrum (0–25 MHz) shown in Figure 9A, one can see that, for the discharge dominantly controlled by the LF component, apart from the fundamental frequencies of ω_L = 50 kHz and ω_H = 5 MHz, the third RF harmonic (3ω_H = 15 MHz) and sum + beat of the LF and the second RF harmonic (2ω_H + ω_L and 2ω_H - ω_L), as well as side-bands, are also excited. Nevertheless, the second RF harmonic (2ω_H) itself is too weak to be observed. These components are related to the RF amplitude modulated by the LF and reveal the frequency interaction in the discharge process by DF driving [23]. Clearly, the maximum of the power spectrum density (PSD) occurs at the fundamental RF frequency. Nevertheless, PSD at high harmonics is also substantial, as shown in Figure 9C. These results suggest that the excited high harmonics also significantly contribute to the high electron density generation.

FIGURE 9. Typical fast Fourier transform (FFT) spectra and power spectral densities of the dual-DBD discharge current in the LF-dominant mode with V_L = 1300 V/V_H = 350 V, (A, C) and the DF-comparable mode with V_L = 550 V/V_H = 350 V, (B, D).

By weakening the LF component, the discharge achieves the DF-comparable mode. In this regime, the second RF harmonic structure is quite different from the LF-dominant mode. As shown in Figure 9B, not only the associated sum and beat frequencies, 2ω_H + ω_L and 2ω_H - ω_L, respectively, but also the second RF harmonic, 2ω_H, are all clearly excited. Moreover, the third RF harmonic, 3ω_H, is also strengthened. In the corresponding PSD shown in Figure 9D, one can find that the second RF harmonic and the LF fundamental are comparable, and other high harmonics are also more intensive than those in the LF-dominant case.

The FFT amplitudes of the discharge current as a function of LF and RF voltage amplitudes are presented in Figure 10, including some major excitation spectral lines, such as the fundamentals (ω_L and ω_H), the second RF harmonic (2ω_H), associated beat (2ω_H - ω_L) and sum (2ω_H + ω_L), and the third RF harmonic (3ω_H). As shown in Figure 10A, V_LF varies from 500 V to 1500 V, with a fixed V_RF = 350 V, and one can observe that as the LF component increases, the amplitudes of the LF-related components, namely, ω_L, 2ω_H - ω_L, and 2ω_H + ω_L, also have an obvious increase. However, the RF component and its frequency doubling are substantially suppressed by enhancing the LF component. On the other hand, as shown in Figure 10B, V_RF varies from 0 to 400 V, with a fixed V_LF = 150 V. In the figure, one can see that, for V_RF = 0, the discharge does not occur due to the excessively low input power. As the RF component, i.e., the fundamental, increases, its second harmonic and associated sum and beat components with the fundamental LF also increase, while the fundamental LF component is suppressed substantially. Meanwhile, the third RF harmonic is also suppressed. Combining these results with those in Figure 5, we find that, in the electron density modulation, restraining the high harmonic and increasing the sum and beat components can be an effective mechanism to obtain the desired electron density.

FIGURE 10. FFT components of the fundamentals (LF and RF), the second harmonic with their sum and beat, and the third harmonics in (A) the LF-dominant mode and (B) the DF-comparable mode.

4 Conclusion

In this work, we report the influence of dual-frequency (LF and RF) modulation on the electron dynamics and metastable species generation in AP DBD argon plasmas under different governance patterns described by the ratio of LF to RF as well as the balance between ion loss and creation. The study focuses on the AP DBD discharge excited by a hybrid voltage source of a 50 kHz LF plus a 5 MHz RF based on a 1D fluid model in the drift–diffusion approximation. The main conclusions of this work are listed as follow:

■ It is found that the DF discharge exists in two distinct modes depending on the LF voltage amplitude. With a 2-mm discharge gas gap and a fixed RF component, the electron density at first decreases and then increases with the increase in the LF voltage amplitude.

■ When the discharge is dominantly controlled by the LF, the ion drift to the instantaneous cathode is independent of the RF component, and more electrons are generated both in the bulk and sheath regions. Moreover, the LF component induces a significant ion loss at the instantaneous cathode, which gets more significant as the RF component increases.

■ By FFT of the current and PSD of the discharge, one can find that in the discharge driven by DF, a typical three-wave interaction can be observed. The amplitude of high RF harmonics and associated sum and beat components varies with DF discharge patterns. In the plasma density modulation, the sum and beat components of the second RF harmonic with the LF can be an effective mechanism for density enhancement.

Data availability statement

The raw data supporting the conclusion of this article will be made available by the authors, without undue reservation.

Author contributions

All authors listed have made a substantial, direct, and intellectual contribution to the work and approved it for publication.

Funding

This work was supported by the National Natural Science Foundation of China Grant No. 51907040, the Key Laboratory of Engineering Dielectrics and Its Application (Harbin University of Science and Technology), and Ministry of Education Grant No. KFM202108.

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s note

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References