Romain Magnan

Gerjan Hagelaar

Mohamed Chaker

Françoise Massines

Atmospheric pressure dual RF-LF frequency discharge: Influence of LF voltage amplitude on the RF discharge behavior

Keywords: dielectric barrier discharge (DBD), atmospheric pressure plasma, dual frequency

This work is a contribution to a better understanding of dual frequency discharge at atmospheric pressure. Based on experiments and numerical modeling, it is focused on radio frequency (5 MHz)low frequency (50 kHz) plane/plane dielectric barrier discharge in a Penning mixture (Ar-NH3). The discharge is in the α-RF mode, biased by a LF voltage having an amplitude ranging from 0 to 1300 V.

When the LF amplitude increases, there is a threshold (around 600 V for a 2 mm gap) from which the light intensity (experiment) and the ionization level (modelling) drastically increase. In this work the physics of the RF-LF DBD below and above this threshold is studied. Depending on the respective RF and LF polarity, the net voltage applied to the gas is alternatively enhanced or reduced which induces an increase or a decrease of the ionization level. In all cases the ion drift to the cathode due to the LF voltage results in an ion loss and a production of secondary electrons. For a LF voltage amplitude lower than 600 V, the ions loss to the cathode is higher than the ions creation related to the secondary electrons.

The consequence is a decrease of the plasma density. This density oscillates at a frequency equal to 2LF: it is maximum each time the LF voltage amplitude is equal to 0 and minimum when the LF voltage amplitude is maximum. For a LF voltage amplitude higher than 600 V, when the LF and RF polarity are the same, the secondary electrons emission is high enough to counterbalance the ion loss, to enhance the bulk ionization and the discharge becomes a γ-RF. The gas voltage is controlled by the dielectric

Introduction

The Dielectric Barrier Discharge (DBD) is an easy and robust solution to generate low temperature discharges. DBDs have many applications including polymer treatment [START_REF] Massines | A comparison of polypropylene-surface treatment by filamentary, homogeneous and glow discharges in helium at atmospheric pressure[END_REF], ozone generation [START_REF] Kogelschatz | Dielectric Barrier Discharge : Their History, Discharge Physic, and Industrial Applications[END_REF], air flow control [START_REF] Dong | Experimental study of a DBD surface discharge for the active control of subsonic airflow[END_REF], plasma medicine [START_REF] Gelker | Permeabilization of human stratum corneum and full-thickness skin samples by a direct dielectric barrier discharge[END_REF]. High quality thin films like water barrier [START_REF] Brunet | Tailored Waveform of Dielectric Barrier Discharge to Control Composite Thin Film Morphology[END_REF][6] [START_REF] Ghimire | Improvement of wettability and absorbancy of textile using atmospheric pressure dielectric barrier discharge[END_REF][8] [START_REF] Profili | Nebulization of Nanocolloidal Suspensions for the Growth of Nanocomposite Coatings in Dielectric Barrier Discharges[END_REF] or antireflective and passivating film for photovoltaic cells [START_REF] Bazinette | Influence of the Discharge Mode on the Optical and Passivation Properties of SiNx:H Deposited by PECVD at Atmospheric Pressure[END_REF] [START_REF] Vallade | A-SiNx:H antireflective and passivation layer deposited by atmospheric pressure plasma[END_REF] [START_REF] Bazinette | Atmospheric Pressure Radio-Frequency DBD Deposition of Dense Silicon Dioxide Thin Film[END_REF][13] are synthesized using diffuse, streamer-free, linear DBD, easy to scale up for in-line production in conditions similar to corona treatment. One of the key issues for applications is the low power of diffuse DBD which often limits the precursor decomposition and the thin film growth rate. Rising the excitation frequency from kilohertz to megahertz is a solution to sharply increase the DBD power level and thus to reduce the processing time [START_REF] Massines | Hydrogenated Silicon Nitride SiNx:H Deposited by Dielectric Barrier Discharge for Photovoltaics[END_REF] [START_REF] Bazinette | Optical emission spectroscopy of glow, Townsend-like and radiofrequency DBDs in an Ar/NH3mixture[END_REF]. The radio frequency DBD (RF-DBD) generates a high electron density of about 10 11-12 /cm 3 , with a high mean power injected in the plasma of 10 W/cm 3 . The breakdown voltage of the RF-DBD is one third of that of the low frequency DBD (LF-DBD) [START_REF] Bazinette | Identification of the different diffuse dielectric barrier discharges obtained between 50kHz to 9MHz in Ar/NH3 at atmospheric pressure[END_REF], which makes the RF-DBD easier to operate. In the α-RF mode, the discharge is sustained by the electrons generated in the gas bulk and the dielectric is not necessary to ensure the discharge stability. However, the highest power values are reached in the γ mode where the discharge is sustained by cathode electron emission.

In this case, a DBD configuration is required to achieve a diffuse discharge [START_REF] Shi | Plasma stability control using dielectric barriers in radio-frequency atmospheric pressure glow discharges[END_REF] [START_REF] Shi | Mode transition in radio-frequency atmospheric argon discharges with and without dielectric barriers[END_REF]. Another specific feature of RF plasmas is that the ions cannot oscillate in the RF electric field. Using an additional low frequency voltage provides a way of extracting the ions from the bulk and to control their flux to the wall.

Dual frequency (DF) excitation was previously investigated in low pressure plasmas to independently control the plasma generation and the ion flux on the surface i.e. the electron heating and A c c e p t e d M a n u s c r i p t the ion acceleration across the sheath [START_REF] Schulze | Optimization of the electrical asymmetry effect in dual-frequency capacitively coupled radio frequency discharges: Experiment, simulation, and model[END_REF][19] [START_REF] Donkó | PIC simulations of the separate control of ion flux and energy in CCRF discharges via the electrical asymmetry effect[END_REF] [START_REF] Kitajima | Functional separation of biasing and sustaining voltages in two-frequency capacitively coupled plasma Functional separation of biasing and sustaining voltages in two-frequency capacitively coupled plasma[END_REF]. At atmospheric pressure, the collision rate is large and the previous investigations were focused on the DF influence on the electron energy distribution function (EEDF), as well as on the control of the electron density and of the ion flux to the wall, and on the ionization mode [START_REF] Zhang | Electron heating and mode transition in dual frequency atmospheric pressure argon dielectric barrier discharge Electron heating and mode transition in dual frequency atmospheric pressure argon dielectric barrier discharge[END_REF][23] [START_REF] Gans | The challenge of revealing and tailoring the dynamics of radio-frequency plasmas[END_REF] [START_REF] Waskoenig | Nonlinear frequency coupling in dual radio-frequency driven atmospheric pressure plasmas[END_REF]. Most studies were focused on the use of high frequencies (HF) in MHz range, for both excitation frequencies. However, some works combine kHz and MHz [START_REF] Zhou | Nonequilibrium atmospheric pressure plasma jet using a combination of 50 kHz/2 MHz dual-frequency power sources[END_REF][27] [START_REF] Massines | RF-LF dual frequency uniform dielectric barrier discharge for thin film processing[END_REF] frequencies. In [START_REF] Liu | Atmospheric-pressure diffuse dielectric barrier discharges in Ar/O2gas mixture using 200 kHz/13[END_REF][30], Liu et al superimpose a RF voltage to a LF-DBD to modulate the electric field, which improves the uniformity of the discharge and increases the input power.

RF voltage leads to a low electron temperature, ion trapping in the plasma bulk and more power transferred to elastic collisions, which enhances gas heating due to vibrational excitation especially in case of nitrogen [START_REF] Bruggeman | Foundations of atmospheric pressure nonequilibrium plasmas[END_REF] [START_REF] Berchtikou | Thermometry in noble gas dielectric barrier discharges at atmospheric pressure using optical emission spectroscopy[END_REF]. The low frequency could influence the ion flux to the wall, increase the secondary electron emission and the electron temperature while the high frequency ensures a large plasma density with a higher ionization rate at the sheath edge. Applying a dual frequency modifies the power dissipation and the electron heating mechanism. In a DF plasma (14 MHz-2 MHz) at atmospheric pressure, increasing the voltage amplitude of the LF component induces the transition from the α mode to the γ mode [START_REF] Zhang | Electron heating and mode transition in dual frequency atmospheric pressure argon dielectric barrier discharge Electron heating and mode transition in dual frequency atmospheric pressure argon dielectric barrier discharge[END_REF]. Observations show a change in the ionization mechanism from wave riding to cathode secondary emission associated to an increase of the electron temperature.

In this work, the discharge initially operates in the α mode at 5 MHz RF frequency. The discharge physics modifications of the RF-DBD induced by the increase of the LF voltage amplitude are investigated using both experiments and 1D-simulation. This study is carried out in an Ar/NH3 Penning mixture and focuses on the light emission, the plasma ionization dynamics and the species density within the gas gap. The chosen LF frequency is 50 kHz because previous work [START_REF] Bazinette | in preparation[END_REF] carried out in the same discharge configuration we have found that the coupling between RF and LF frequencies is maximum for a LF of 50 kHz. kHz with a voltage amplitude varying from 0 to 1300 V.

Model description

The discharge is simulated using a 1D self-consistent fluid model, based on a general 2D plasma code previously used for other discharges and described in [START_REF] Hagelaar | Model of an inductively coupled negative ion source : I . General model description[END_REF] [START_REF] Gregorio | Nanosecondpulsed dielectric barrier discharges in Kr / Cl 2 for production of ultraviolet radiation[END_REF], which was adapted to the DBD geometry in 1D Cartesian space. This model solves the electron, ion and metastable continuity and momentum transfer equations coupled to Poisson's equation. The energy equation is also solved for the electrons. The model provides the space and time variations of the electric field and the densities of electrons, Ar + and Ar2 + ions, and Ar metastables.

Equations and boundary conditions

The equations for electrons are:

𝜕𝑛 𝑒 𝜕𝑡 + ∇. (𝜞 𝑒 ) = 𝑆 𝑒 (1)
𝜞 𝑒 = -𝜇 𝑒 𝑛 𝑒 𝑬 -𝐷 𝑒 ∇𝑛 𝑒 (2)
The equations for ions are:

𝜕𝑛 𝑖 𝜕𝑡 + ∇. (𝜞 𝑖 ) = 𝑆 𝑖 (3)
𝜞 𝑖 = 𝜇 𝑖 𝑛 𝑖 𝑬 -𝐷 𝑖 ∇𝑛 𝑖 ( 4
)
where n is the particle density, 𝜞 is the particle flux, S is the particle source term due to chemical processes occurring in the plasma, 𝑬 is the electric field, 𝜇 and 𝐷 are the mobility and the diffusion coefficient, respectively. The equations for the metastable atoms are similar to those for electrons and ions except that their mobility is zero. The electric field is obtained from the electrostatic potential solved from the Poisson equation:

A c c e p t e d M a n u s c r i p t 𝜀 0 𝛻𝑬 = -𝜀 0 𝛻 2 𝜙 = -𝑒𝑛 𝑒 + ∑ 𝑞 𝑖 𝑖 𝑛 𝑖 [START_REF] Brunet | Tailored Waveform of Dielectric Barrier Discharge to Control Composite Thin Film Morphology[END_REF] where 𝜀 0 is the permittivity of free space, 𝜙 is the electrostatic potential, 𝑒 is the elementary charge and 𝑞 𝑖 is the ion particle charge. The summation runs over all ion species.

The equation of energy is solved for electrons:

3 2 𝜕(𝑛 𝑒 𝑘 𝐵 𝑇 𝑒 ) 𝜕𝑡 + 5 2 ∇ • (𝚪 𝑒 𝑘 𝐵 𝑇 𝑒 -𝑛 𝑒 𝐷 𝑒 𝑘 𝐵 ∇𝑇 𝑒 ) = -𝑒𝚪 𝑒 • 𝑬 -𝐶 (6)
where 𝑘 𝐵 is the Boltzmann constant, 𝑇 𝑒 is the electron temperature, and C is the density of the net power lost in collisions and plasma-chemical processes. Here, the electron temperature is an effective temperature defined as 2/3 of the electron mean energy, because the electrons are not Maxwellian. This electron temperature is used to obtain the electron mobility, the electron diffusion coefficient and the rate coefficients of all electron-induced processes included in the source terms S and C, from look-up tables obtained from the electron Boltzmann solver BOLSIG+ [36] [37].

Boundary conditions are imposed on the particle fluxes at the walls:

𝚪 𝑒 ⋅ 𝐧 = 𝑛 𝑒 𝑣 𝑤,𝑒 -∑ 𝛾 𝑖 𝑛 𝑖 𝑖 𝑣 𝑤,𝑖 (7)
𝚪 𝑖 ⋅ 𝐧 = 𝑛 𝑖 𝑣 𝑤,𝑖 (8)
where n is the normal vector pointing toward the wall and 𝑣 𝑤 is an effective velocity at the wall. These boundary conditions take into account the secondary electrons emission following ion and metastable impact on the walls with a secondary emission coefficient set to 0.05. A similar boundary condition is used for the electron energy flux at the wall. For more information about these boundary conditions we refer the reader to [START_REF] Hagelaar | Model of an inductively coupled negative ion source : I . General model description[END_REF].

As a boundary condition for the Poisson's equation, sinusoidal RF and/or LF voltages are imposed at the electrodes. The voltage drop across the dielectrics is self-consistently calculated, taking into account their permittivity and the accumulated surface charge obtained by time-integration of the electron and ion wall fluxes, as in [START_REF] Gregorio | Nanosecondpulsed dielectric barrier discharges in Kr / Cl 2 for production of ultraviolet radiation[END_REF]. Each dielectric is 1 mm thick with a relative permittivity of 9.

A c c e p t e d M a n u s c r i p t

The list of the considered plasma chemical reactions and their rate coefficients are detailed in Table 1. To simplify the results analysis, Penning ionization of NH3 is considered without adding NH3 and NH3 + , but considering the creation of Ar + from Ar metastables using a reaction coefficient corresponding to 200 ppm of NH3 in Ar. Thus the species considered in the kinetic description are electrons, Ar + and Ar2 + ions and Ar*. The species Ar* includes all the excited argon states, including the metastable states and the radiative resonant states.

Table 1. Model kinetic reactions and rate coefficients

Reaction 3 represents the radiative losses taking into account all the excited states, the coefficient corresponds to the trapping rate for the radiative reaction. This coefficient was initially taken as 5x10 5 s -1 in agreement with [START_REF] Balcon | Numerical model of an argon atmospheric pressure RF discharge[END_REF] but, as discussed in section 3.2, we found that it should be increased up to 1.5x10 6 s -1 to achieve a good agreement between numerical and experimental results. 2) e + Ar2 + → Ar* + Ar 7.35 x 10 -14 x Te -0.67 m 3 s -1 [START_REF] Mehr | Electron-temperature dependence of electron-ion recombination in Argon[END_REF] 3) Ar* → Ar 1.5 x 10 6 s -1

4) e + Ar* → e + Ar 2 x 10 -13 m 3 s -1 A c c e p t e d M a n u s c r i p t

Validation of the model

To be suitable for the dual frequency DBD, the model should properly describe both RF and LF-DBD. This was verified by comparing numerical and experimental results for a 5 MHz DBD and a 50 kHz DBD obtained at 350 V and 1 kV respectively. To further confirm the validity of the model, the experimental and numerical density of Ar 3 P2 metastable atoms were compared for RF and LF discharges. The Ar 3 P2 density was measured by laser absorption spectroscopy. In the model, Ar* includes all the excited state of Ar. To calculate the Ar 3 P2 density from the modeling Ar* density, we assume that the four first excited level of Ar are the most occupied. These four excited levels are 3 P2, 1 P1, 3 P0 and 3 P1. They are in equilibrium and the distribution on each level is proportional to (2J+1) [START_REF] Carbone | Electron impact transfer rates between metastable and resonant states of argon investigated by laser pumpprobe technique[END_REF][52] [START_REF] Carbone | Determination of electron-impact transfer rate coefficients between argon 1s 2 and 1s 3 states by laser pump -probe technique[END_REF]. Thus the Ar 3 P2 density is equal to the modeling Ar* density multiplied by 5/(5+3+1+3) =5/12. In the case of the RF discharge, for a frequency of 5 MHz and a voltage amplitude of 350 V, the rate coefficient of reaction 3 (Table 1) was increased in order to reduce both metastable density and power in such a way to obtain similar experimental and numerical results (Table 2). Then, using the same coefficient, experimental and numerical results were compared in the case of the 50 kHz DBD for 1 and 2 mm gap. As presented in Table 2, both experiments and model predictions agree within a factor lower than 2, which is acceptable. A c c e p t e d M a n u s c r i p t

Influence of the LF voltage amplitude on RF discharge

The aim of this work is to understand the influence of the LF voltage amplitude on the behavior of a dual frequency RF-LF DBD. For this purpose, the LF voltage amplitude applied at a constant power RF discharge is first varied over a range spanning from 0 to 1300 V, which is wide enough to determine the different discharge modes. Then, we focus on each mode to understand the discharge behavior. 3.5 between 600 and 1000 V before getting again independent of the LF voltage above 1000 V. This behavior allows to identify two modes: mode 1, below 600 V and mode 2, above 1000 V. For mode 1, the mean intensity decreases above 250 V, while for mode two that seems to be reached at 750 V, the intensity decreases beyond 900 V. The difference between the mean and the maximum of the light intensity is associated with the discharge dissymmetry at the RF scale. As an example, previous work has shown that the RF discharge could turn off during part of the RF cycle, which reduces the mean discharge power but not the maximum value [START_REF] Bazinette | in preparation[END_REF].

Similar behavior is observed with the results of numerical modeling for the DF discharge in the same conditions as for experiments, i.e. a 5 MHz RF voltage amplitude of 350 V and a LF voltage amplitude ranging from 0 to 1300 V. As illustrated by the mean electron and ion densities shown in Figure 4, a steep variation is observed between 600 and 1000 V. The electron density is enhanced by a factor of 2 and that of ion by a factor of 3. Below 600 V, the densities decrease like the mean light intensity showing that the discharge weakens. Above 600 V, the density of electrons and ions increase.

Both experimental and numerical results indicate the presence of a transition in the discharge behavior at some LF voltage amplitude: mode 1 below 600 V and mode 2 above 600 V. In the following, our aim is to understand the differences between these modes. For this purpose, results obtained for discharge either in mode 1 or in mode 2 are discussed in detail. The voltages for each of these discharge are provided in Table 3. The RF-DBD corresponding to the same RF voltage (5 MHz, 350 V) is used as a reference. The low frequency is 50 kHz and the voltage amplitude is 400 V for the mode 1 and 1 kV for mode 2. A c c e p t e d M a n u s c r i p t Among the 10 reactions considered in the collisional-radiative model, only seven play a significant role (Table 4). The electrons and Ar + ions are mostly created by Penning ionization (reaction 9) with a contribution of direct ionization (reaction 6) increasing from ̴ 0 for mode 1 to 15% for mode 2. This latter reaction involves electrons with more than 15.8 eV i.e. a large electric field. Ionization produces Ar + that is very efficiently converted in Ar2 + by the 3 body reaction 10. Subsequent ion loss due to dissociative recombination is small, only 5% for mode 1 and 10% for mode 2. However, it is important to note that a large part of these ions (99% for mode 1 and 83.5% for mode 2) are produced via reaction 9, which mimicks Penning ionization of NH3, so that in reality they would not be argon ions at all but rather NH3 + ions. The ions loss due to dissociative recombination is rather low, 5 and 10% for mode 1 and mode 2 respectively. Both ions and electrons are mainly loss at the walls. Whatever the discharge regime is, the metastable atoms are mainly created from the ground-state level of Ar by electron collisions (reaction 1) while their losses are due to Penning ionization (12%) and to reaction 3 (88%). The mean and maximum densities of electrons, ions and metastable atoms is reported in Table 5 for the two DF modes and compared to those of the classical RF discharge. For a given mode, all species show a similar behavior. The difference between a RF and a DF mode 1 discharge is a decrease of all the species densities. The variation is less than a factor 2. From RF to DF mode 2 the densities increases. The maximum of the electron and ion density increase by a factor of 4 and the metastable density by a factor of 18 while the mean density of the electron and ion slightly increase and the metastable density increases by a factor of 3.

To summarize, the contribution of the different reactions of Table 1 are similar for the RF and the DF mode 1 discharges, while for the DF mode 2 discharge, direct ionization is more important even if Penning ionization remains dominant. The ionization of the metastable states is always low. In DF mode 1, the discharge is weakened by the increase of the losses to the wall (or drift to the cathode), which lowers the densities of the species in contrast with DF mode 2 in which the discharge strengthens by the increase of these densities.

Spatially-resolved results across the gas gap, averaged over a LF cycle, are presented in Figure The RF, DF mode 1 and 2 discharges are characterized by a cathode fall on each side of the plasma bulk showing that the density of ions is always large enough to make the RF electron oscillation induce a space-charge electric field. The three discharges are RF discharges. The maximum of the electron temperature is similar in these three cases (3.3 to 3.5 eV) and is located within the sheath, close to the cathode. Compared to the RF-DBD, in DF mode 1, the low LF voltage amplitude induces the cathode sheath expansion and decreases the plasma bulk and the density. This is explained by the increase of the ion loss due to the drift to the cathode by the LF electric field. It results in a decrease of the ion density and in a decrease of the electric field due to the electron RF oscillation. As compared to an RF discharge, the electron temperature remains high in a larger zone and the area where electrons, ions and metastable atoms are created is broader, their density decreases because of the enhanced loss to the cathode. The plasma bulk density is also reduced and the discharge weakens.

In DF mode 2 where the LF voltage amplitude is higher, all densities increase, the electron temperature (Te) steeply decreases in the bulk. The Te minimum value is at the sheath edge because of the high direct ionization in this area. The cathode fall thickness is similar to that in the RF discharge but with a stronger field and the formation of a negative glow. The higher LF voltage amplitude yields the increase of ionization over a wider zone and the plasma bulk further reduces as compared to the RF-

A c c e p t e d M a n u s c r i p t

DBD. The maximum electron and ion density is observed where Te reaches its minimum value that is half of that of the other modes, i.e. about 1 eV compared to 2 eV.

To summarize, applying a LF voltage reduces the average ion density in comparison with that of the RF discharge. This modifies the electric field distribution, but does not change the chemical kinetics. All species have their density reduced. At high LF voltage amplitude, the ion density increases and the cathode fall length shrinks while direct ionization mainly occurs at the edge of the cathode fall.

The next step is to determine when the variation of the densities species and the electric field occur. This is the aim of the following paragraph where experimental (Figure 6) and numerical results are presented with space and time resolution (Figure 7). Figures 6a and6d show the space-resolved light intensity (Fig. 6a) as well as the voltage and current density (Fig. 6d) as a function of time for the RF discharge. Clearly both emission and current density are uniform at the LF scale. The maximum emission occurs in the plasma bulk. This emission is mainly due to the continuum which is related to the electron density. Thus, an emission localized in the gas bulk could be related to a high electron density. This feature is characteristic of an α-RF discharge at atmospheric pressure [START_REF] Bazinette | Optical emission spectroscopy of glow, Townsend-like and radiofrequency DBDs in an Ar/NH3mixture[END_REF]. For a DF discharge in mode 1 (Figure 6b), the maximum emission always takes place in the bulk showing that the discharge mode is the same as that of the RF and is an α-RF.

However, the LF modulates this α-RF discharge. Both light emission and current are time modulated with an increase from 2.5 to 5 µs i.e. in the region where the LF voltage amplitude is weak. The maximum of the light emission and the current occur before Va = 0 V, but due to the capacitive configuration of the DBD reactor, the voltage applied to the gas, Vg, is equal to 0 before Va [START_REF] Massines | Glow and Townsend dielectric barrier discharge in various atmosphere[END_REF]. Ion drift is proportional to Vg and not to Va and these observations show that lower is the LF voltage amplitude applied to the gas, higher is the discharge power and the ionization. In other words, lower is the ion extraction from the gas bulk higher is the discharge power. The ion loss is the reason why light intensity at low LF voltage amplitude in DF mode 1 is always lower than the RF discharge.

For a LF voltage amplitude of 1000 V, when the discharge is in DF mode 2 (Figure 6c), the light intensity gets larger than for the RF discharge. The discharge behavior depends on the LF voltage A c c e p t e d M a n u s c r i p t polarity. When LF voltage is positive, from 1 to 5 µs, the light intensity is larger in the middle of the gap with a modulation similar to that of the DF mode 1, reaching a maximum around 2.5 µs which is expected to correspond to Vg = 0 V. When LF voltage is negative, from 5 and 10 µs, the variation of the light intensity over the half cycle is larger. The maximum of the emission is significantly stronger and the maximum are not in the middle of the gap but shifted closer to the electrodes. These maxima last for about 1.5 µs and they are correlated with a current maximum increase. In an atmospheric pressure RF discharge, the localization of the light close to the electrode is attributed to a γ mode [START_REF] Shi | Mode transition in radio-frequency atmospheric argon discharges with and without dielectric barriers[END_REF]. In a γ-RF discharge, a large part of the seed electrons are cathode secondary electrons. As they are accelerated by the cathode fall, they have enough energy to make direct ionization which is in agreement with the increase of the direct ionization (Table 4) and the field and charge distribution shown in Figure 5c.

The model enables the understanding of the observations just reported. The gas voltage, the electric field and the electron and metastable densities across the gap are shown in Figure 7 for the RF discharge and the two DF discharge modes. The results are presented on a half cycle i.e. 10 µs as it was the case for the experimental results. Time 0 ns corresponds to the maximum LF applied voltage and 10 µs to its minimum.

RF-DBD DF-DBD (mode 1)

DF-DBD (mode 2) As shown in Figure 7j, in absence of LF voltage, the metastable density is maximum at about 300 µm from the cathode, at the sheath edge. The electron density maximum occurs within the plasma bulk, where the electric field is weak. Due to the RF voltage, the electrons oscillate over a distance 500 µm from the dielectric surface. As the LF voltage amplitude increases, the gas voltage is modified as well as the electric field, hence the electron and metastable densities. In the DF-DBD mode 1, these parameters behave similarly to those of the RF-DBD. In agreement with the experiments, the electron A c c e p t e d M a n u s c r i p t density remains maximum within the bulk (Figure 7h), which shows that the discharge still behaves like an α-RF discharge. A consequence of the LF voltage is that half of the time ionization takes place farther from the cathode because of the modulation of the sheath thickness by the LF component. The sheath length expands from about 500 µm to 900 µm on the side of the electrode biased with a negative LF voltage. This expansion of the sheath is explained by a lower ion density due to the higher ion loss at the cathode. Due to the RF voltage, the electron depleted zone always oscillate at the RF scale with an amplitude of 500 µm. For a high LF voltage amplitude, i.e. in the DF mode 2, ionization is clearly higher than in the case of the RF discharge. In comparison with the RF-DBD, the electric field maximum as well as the electron and metastable densities are enhanced by factors of 3, 4 and 20, respectively. The electric field maximum is achieved when Vg is maximum while the peak of the densities occurs later and is located at the sheath edge. The electric field and the densities are high only over a short period of time around 3 µs as compared to the 10 µs of the half cycle. This behavior is in very good agreement with the phase-resolved emission spectroscopy and it is similar to the characteristics of a typical DBD with a current pulse associated to a gas voltage drop stopping the ionization. This is confirmed by comparing the results with the space and time-resolved electrical field and electron and metastable densities of a 50 kHz, 1 kV, LF discharge. The maximum and the depletion zone are very similar

a) b) c) A c c e p t e d M a n u s c r i p t d) e) f) g) h) i) j) k) l)
showing that there is a common ionization mechanism. In the glow DBD, ion bombardment at the cathode is the main source of secondary electrons. One can therefore conclude that the high amplitude of the LF voltage is associated with a large secondary electron emission from the cathode, when the LF and RF polarities are the same. When they are out of phase, LF makes the ions drift toward the RF anode but the secondary electrons cannot ionize the gas due to the RF voltage. This is illustrated in Figure 9 that presents the metastable density over 3 RF cycles when Vg is maximum. Clearly, the metastable density only increases during half of the RF cycle. Comparing Figure 8b (LF discharge) and Figure 7i (mode 2 of DF discharge) clearly shows that RF always plays a dominant role, allowing a large increase of the electron density in the gas bulk from 10 10 to several 10 11 /cm 3 . This comparison also illustrates why the γ-RF mode generated by the dual frequency is diffuse: the density of electrons remains always large, a condition favoring the achievement of a diffuse discharge. 1,1x10 18 1,6x10 18 2,1x10 18 2,6x10 18 3,2x10 18 3,7x10 18 4,2x10 18 Ar* density (m -3 )

Page 22 of 32 AUTHOR SUBMITTED MANUSCRIPT -PSST-103305.R1

A c c e p t e d M a n u s c r i p t LF over part of the half cycle. The electron production rate oscillates at twice the RF frequency. In Figure 10 b andc, these variations are compared to the gas voltage.

For DF mode 1, the maximum electron production is observed when the LF voltage applied (VLF) is zero, as for the metastable atom density shown in Figure 7k. This supports the previous explanation provided, i.e. when VLF = 0 V, the ions are no more extracted from the sheath, their density is higher, the cathode sheath is thinner, and the electric field and the electron temperature reach higher values, which results in a larger ionization rate. The electron production rate value reaches 4.4x10 22 m - 3 , which is slightly lower than for the RF-DBD even when VLF = 0 V, because ions lifetime is larger than the RF cycle. The production rate decreases to 2.3x10 22 m -3 when the LF voltage reaches its maximum because the extraction at the cathode is maximum.

In DF mode 2, the ionization rate is low during the first part of the cycle. It is similar to that observed for the RF discharge and the DF-DBD discharge in mode 1. From a gas voltage of about 500 V, the ionization rate increases and Vg is maximum right after that. This is the behavior of a low frequency DBD: when the ionization increases, the solid dielectrics are charged and the gas voltage decreases. The γ-mode occurs about 1/5 of the LF cycle. The maximum of the metastable atom density (Figure 7l) is reached when the production of electron is maximum (Figure 10c).

For each RF cycle, the oscillation of discharge characteristics at the RF scale is due to the alternation between additive and subtractive amplitude of the LF and RF components. The oscillation amplitude of the ionization rate at the RF scale is minimum when the LF voltage is zero, as clearly observed in Figure 10c. For DF mode 2, the ionization rate reaches its minimum right after VLF minimum and is equal to that of DF mode 1.

Both DF modes 1 and 2 show a peak of electron production, but their origin are quite different.

For DF mode 1, the peak is observed when the VLF is zero because of ion extraction from the gas is reduced. For DF mode 2, the peak starts when Vg is maximum and its amplitude is 50 times higher, indicating a new ionization mechanism occurs. A larger contribution of direct ionization from 0 to 15% takes place together with a larger ion drift to the cathode, hence a higher secondary emission when the polarities of RF and LF are identical.

A c c e p t e d M a n u s c r i p t 24

For the two DF-DBD modes, the sheath can be seen as the superposition of RF and LF sheaths.

The "LF sheath" is defined by the ion density: higher is this density shorter the sheath is. The "RF sheath" thickness oscillates with the RF voltage. This oscillation amplitude stays the same but its spatial position is defined by the "LF sheath". Both the ion flux to the wall and the secondary electron flux increase with the LF voltage amplitude and their maximum take place simultaneously. Secondary emission could also be due to metastable. However, the flux of metastable atoms is negligible as compared to that of ions.

Conclusion

The effect of the LF voltage amplitude on an α-RF-DBD of constant power is studied through 1D-simulation and experiments. Both numerical and experimental results point out two distinct discharge modes which depends on the VLF amplitude. For a 2 mm gap and a 350 V, 5 MHz RF discharge, the transition is observed for LF voltage amplitude between 600 V and 1000 V. For VLF A c c e p t e d M a n u s c r i p t lower than 600 V, the DF is an α-RF, for higher VLF, around the maximum of the gas voltage, the α-RF discharge becomes a γ-RF for about 3 µs each half cycle of VLF.

Whatever its value, VLF drifts ions to the LF cathode and secondary electrons are produced when the RF and LF cathode are the same electrode. These electrons are multiplied in the gas bulk according to an amplification rate that depends on the voltage applied to the gas. This voltage is equal to the sum of LF and RF voltage minus the voltage applied to the dielectric, Vds. In a RF discharge, Vds is negligible, in a DF discharge it increases with the drift of the bulk charge to the electrodes i.e. VLF amplitude. On one hand, VLF induces a loss of ions at the LF cathode, on the other hand, these ions produce secondary electrons which are multiplied by the RF discharge. The discharge regime depends on the equilibrium between the loss and the creation of the ions.

For low VLF, the secondary ionization is low and the discharge physics is controlled by the ion loss. The gas bulk ion density and thus electron density decrease when VLF increases. The RF plasma density is lower than that of the RF discharge. The flux of ion at the cathode depends on the instantaneous VLF amplitude, higher it is, higher is the loss and larger is the cathode sheath.

Consequently, during a LF cycle the plasma density oscillates. It is maximum when VLF = 0 V and minimum when VLF is maximum. For an LF voltage amplitude equal to 1000 V, the voltage applied to the gas reach values high enough to enhance the secondary ionization to such a point that the physics of the discharge depends on the secondary electrons multiplication at the sheath edge. The γ mode is observed. γ and α mode alternate at the RF frequency and the discharge is a dielectric barrier controlled discharge. The stability of this γ mode is explained by the rather low increase of the electron density compared to the -mode and by the fact that the duration of the -mode is only 1/5 of LF cycle (figure 10c) which limits overheating.

The DF discharge with a high LF voltage amplitude is promising for PECVD because of the high densities of electrons and metastables which should ensure an efficient dissociation of the thin film precursors with a homogeneous discharge and because of the ion flux to the surface which should be efficient to densify the coating. In order to complete this study, the next work in progress is focusing on the transition between these modes, the importance of the secondary electron emission coefficient and the influence of the RF voltage amplitude.

Figure 1 .

 1 Figure 1. (a) Schematic drawing of the discharge cell and (b) voltage applied between

Figure 2 Figure 2 .

 22 Figure 2 presents the calculated time variations of the current density, the voltage applied to the

Figure 2b presents the

  Figure 2b presents the results for the LF-DBD. In agreement with the literature, one current

4. 1 Figure 3 .

 13 Figure 3. Mean and maximum of the light

Figure 4 .

 4 Figure 4. Mean density of electrons and ions

5 .Figure 5 .

 55 Figure 5. Electron temperature, direct ionization and mean density profiles of the electron, ion

Figure 6 Figure 6 .

 66 Figure6shows the space and time variation of the light intensity over a LF half cycle. Pictures

Figure 7 .

 7 Figure 7. Simulated Space and time variation of the gas voltage (a-c) and spatio-temporal

A c c e p t eFigure 8 .Figure 9 .Figure 10 .

 8910 Figure 8. Space and time distribution of the (a) electric field, (b) electron density and (c)

Figure 10a compares the

  Figure 10a compares the electron production of the RF discharge and the two discharge modes

Figure 11 .

 11 Figure 11. Ion flux to the wall and secondary electron emission flux for: (a) RF-DBD, (b) DF-

A c c e p

  t e d M a n u s c r i p t A c c e p t e d M a n u s c r i p t A c c e p t e d M a n u s c r i p t A c c e p t e d M a n u s c r i p t

Table 2 . Comparison of experiment and modeling of Ar metastable density for various discharge conditions

 2

	Gap Conditions	Ar metastable density		Ref
			Experiment	Modeling
			Ar 3 P2	Ar 3 P2 = Ar* x 5/12
	1mm	50 kHz	Max	Max	[54]
		1000 V	2.5 x 10 10 cm -3	2.6 x 10 10 cm -3

Table 3 . Voltages used in the experimental and numerical studies for mode 1 and mode 2 DF-DBD

 3

	RF 5 MHz DF-DBD mode 1 5 MHz RF-DBD DF-DBD mode 2 5 MHz A c c e p t e d M VRF 350 V 350 V 350 V a n u s c r i p t LF VLF 0 0 50 kHz 400 V 50 kHz 1000 V

Comparison of the different discharge modes

  Before to consider space and time-resolved results, the relative contributions of the different reactions considered in the model (Table4) are presented.

Table 4 . Relative contributions of the most important reactions of Table 1 to the creation and loss of electrons, Ar + and Ar2 + ions and metastable atoms for the different discharge modes.

 4

		RF	DF mode 1	DF mode 2
	Electron
	Direct ionization (reaction 6)	0%	0.2%	15%
	Penning ionization (9)	95%	95%	80%
	Recombination of Ar2 + (2)	-7%	-5%	-10%
	Ar + Ion	RF	DF mode 1	DF mode 2
	Direct ionisation (6)	0%	0.2%	16%
	Penning ionization (9)	99%	99%	83.50%
	Stepwise ionisation (5)	0%	0%	0.2%
	Ion conversion Ar + ->Ar2 + (10) -100%	-100%	-100%
	Ar2 + Ion	RF	DF mode 1	DF mode 2
	Conversion Ar + -> Ar2 + (10) 100%	100%	99.80%
	Metastable ionisation (5)	0%	0%	0.2%
	Recombination of Ar2 + (2)	-7%	-5%	-10%
	Metastables	RF	DF mode 1	DF mode 2
	Direct excitation (1)	99%	99.5%	98.50%
	Penning ionization (9) -12%	-12%	-12%
	Desexcitation (3) -88%	-88%	-88%

Table 5 . Mean and max of electron, ion and metastable atoms densities for the 3 discharge modes.

 5

	RF	DF mode 1	DF mode 2