On the influence of electrode surfaces on the plasma chemistry of a capacitive chlorine discharge

One-dimensional particle-in-cell/Monte Carlo collisional simulations are performed on capacitive chlorine discharges with 2.54 cm gap rf driven by a sinusoidal with voltage amplitude of 222 V at driving frequency of 13.56 MHz. The properties of the discharge, the reaction rates for creation and loss of a few key species, the electron energy probability function, and the primary electron power absorption processes are explored as the gas pressure and the inclusion of secondary electron emission processes in the discharge model is varied. Five cases are investigated, including and neglecting electron, ion, and fast neutrals induced secondary electron emission. The negative ion Cl− is almost entirely created by dissociative attachment and lost through ion-ion recombination, and therefore the capacitive chlorine discharge is recombination dominated.


Introduction
The capacitively coupled discharge typically consists of two parallel metallic electrodes, where one is the powered electrode, connected to a rf voltage or current source, while the other is grounded.A few centimeter gap is maintained between the electrodes into which a neutral gas is injected, and depending on the voltage amplitude and frequency, breakdown occurs and a discharge forms.Typically, the gas pressure varies between 0.1 and 100 Pa, but it can be as high as atmospheric pressure, the driving voltage is a few hundred volts and the driving frequency is in the range 10 5 to 10 8 Hz.Because of the high driving voltages, ions are accelerated up to hundreds of volts before they bombard the electrodes.For most Original Content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.practical applications in etching and deposition the feedstock is a molecular gas, such as chlorine.A discharge in chlorine or chlorine mixtures is applied for etching processes in integrated circuit fabrication, to etch poly-silicon, aluminum, and compound semiconductors [1,2], in particular when highly anisotropic etching is desired [3][4][5].The etch processes are driven by the flux of Cl atoms onto the substrate, and bombardment by Cl + 2 and Cl + ions, that are produced largely by electron impact on the chlorine molecule.Both Cl atoms and Cl 2 molecules are effective etchants but Cl atoms have 2-3 times higher etch yields than the Cl 2 molecule [6].
Electron impact processes play a fundamental role in these discharges.The electrons can be created through ionization in the plasma volume, referred to as primary electrons, and due to emission from the electrode surfaces due to particle bombardment, referred to as secondary electrons.The bombardment of the electrodes by positive ions and electrons generates the secondary electrons which are accelerated across the sheath to high energies.These electrons have therefore a great influence on the discharge properties [7].Both primary and secondary electrons play important roles by ionizing the neutral species and in generating the reactive Cl radicals, mainly by electron impact dissociation of the Cl 2 molecules, and dissociative attachment.For the Cl 2 molecule all electron impact excitation processes appear to be dissociative.Electron detachment processes from Cl − by electrons, chlorine atoms, and chlorine molecules, all have an energy threshold and are not very effective (see e.g.discussion by Huang and Gudmundsson [8]).
Particle-in-cell Monte Carlo collision (PIC/MCC) simulations can be applied to determine the electron heating mechanism, the energy distribution functions for electrons and ions, self-consistently, for the capacitive discharge and therefore give a deeper insight into the plasma discharge phenomena and surface processes.In early studies PIC/MCC simulations were applied to simulate the capacitively coupled chlorine discharge to study the discharge structure dependence on the pressure and applied voltage [9,10].Furthermore, the particlein-cell/dynamic Monte Carlo approach was used to study the spatiotemporal electron dynamics in the capacitive chlorine discharge [11,12].However, these simulations lacked in number of species and had limited reaction sets.For instance, Cl + ions and corresponding reactions and electron impact dissociation processes, which can have a significant role in the discharge, and the etching process, were neglected [9,12].In later studies the oopd1 (object-oriented plasma device for one dimension) simulation code based on the PIC/MCC method has been used to simulate the chlorine discharge with more involved chemistry.This included studying the gas pressure influence on the species and plasma properties such as electron power absorption of a voltage driven single frequency capacitive chlorine discharge [8,13], and more recently, tailored voltage waveform effects on a voltage driven dual frequency capacitive chlorine discharge [14].
A volume averaged global model study of a high density chlorine discharge evaluated and compared the reaction rates for the various reactions in the pressure range 0.13-13.3Pa [15].It was shown that the electronegativity increases rapidly with decreasing dissociation fraction since the Cl − ions are created entirely by dissociative electron attachment and are lost almost entirely through mutual neutralization with Cl + 2 and Cl + ions.However, the capacitive chlorine discharge is typically not very dissociated [16] and the electronegativity therefore can be expected to be high.
To understand the particle balance process and creation and loss of species like Cl radicals and Cl + 2 ions in a capacitive chlorine discharge, a detailed analysis of the dominant reactions for each species is required.Here, 1D PIC/MCC oopd1 code [17,18] simulations are applied to explore the role of secondary electrons, emitted from the electrode surfaces, on the plasma chemistry, the discharge operation and discharge properties, in the presence of secondary electron emission.This includes a comprehensive and detailed investigation of the chemical reactions, species energy and densities, and plasma characteristics.The reaction set and the cross sections used for this study are discussed in section 2. The results, the electron energy and electronegativity, the particle creation and loss, and the species power absorption, are discussed in section 3. A summary and conclusion are given in section 4.

The PIC/MCC method and the chlorine model
The one-dimensional object-oriented PIC/MCC code oopd1 [7,[17][18][19] is applied to explore a capacitively coupled chlorine discharge.The chlorine plasma discharge is located between two parallel, planar electrodes with the left electrode connected to a sinusoidal voltage source and the right electrode grounded.The feedstock gas is composed of the Cl 2 molecule which has low (near zero) threshold for dissociative attachment and low dissociation energy (2.5 eV), while the electron affinity is high (2.45 eV).The Cl atom has electron affinity of 3.61 eV.The current PIC/MCC model for the chlorine discharge constitutes the ground state molecule Cl 2 (X 1 ∑ + g ,v = 0), the ground state atom Cl( 2 P u ), the negative ion Cl − ( 1 S g ), and the positive ions Cl + ( 3 P g ) and Cl + 2 ( 2 Π g ).In the simulations the charged particles; electrons, Cl + 2 , Cl + , and Cl − ions, are tracked at all energies.The neutral species densities are much higher than the densities of the charged particles and therefore the neutrals are only treated kinetically if their energy reaches a preset threshold value of 1 eV.Neutrals with energy lower than this threshold energy are treated as background species.Note that fast neutrals can be created in dissociation processes, charge transfer, and fragmentation.Fast neutrals can be both Cl atoms and Cl 2 molecules.The Cl 2 molecules are assumed to have fixed density and temperature, maintained uniformly in space and assumed to have a Maxwellian velocity distribution at the gas temperature (here T n = 26 mV).The chlorine atoms, with energy below the threshold, are treated as time-and space-evolving fluid.
The reactions taken into account and the cross sections are described in detail elsewhere [8].However, for this current study, the electron impact excitation cross sections for the Cl 2 molecule, that eventually lead to dissociation, originally calculated by Rescigno [20], are updated with more recently calculated cross sections by Hamilton et al [21].The two cross section sets are compared in figure 1.We note that there are some slight differences between the two cross section sets.How those differences influence the discharge properties will be discussed below.
In the PIC method computer particles are tracked.Each computer particle represents a cluster of 10 6 − 10 9 real particles (e.g.electrons, ions or neutrals).For each computer particle, the oopd1 code tracks the 1D displacement in the axial (x) direction and 3D velocity space (v x , v y , and v z ) based on a leap-frog integration scheme.The stability and accuracy of the explicit leap-frog method is maintained through fulfilling the conditions ω pe ∆t ⩽ 0.2 and ∆x ⩽ λ De , where ∆t is the time-step, ω pe = (e 2 n e /ϵ 0 m e ) 1/2 is the electron plasma frequency, ∆x is the grid spacing and λ De ≡ (ϵ 0 T e /en e ) 1/2 is the electron Debye length.All particle interactions are treated based on the null-collision scheme in the Monte Carlo method [22].The accuracy of the null collision method is ensured by keeping the time-step ∆t short enough so that the probability of more than one collision per particle per time-step is low.A time-step is chosen such that ν max ∆t ≪ 1, where ν max is the maximum collision frequency within the discharge.This last constraint is usually the most important at higher operating pressure when determining ∆t.The time-step for this current study was chosen ∆t = 1.8437 × 10 −11 s.
Earlier, the simulation results based on the chlorine discharge model were compared with experimental measurements of the electron density, plasma impedance, and phase angle found in the literature for validation [8].The experimentally measured electron density by Ono et al [23] was found to be roughly twice as high as the simulation results when secondary electron emission is neglected.However, when the secondary electron emission yield due to ion bombardment is set 0.3 the measured electron density was found to be comparable to the simulation results.The simulation results were also compared to the measured phase angle and plasma impedance by Bose et al [24,25] and very good agreement was observed.
Here, the electrons, depending on their origin, are split into two separate particle groups.The electrons that are created by electron impact ionization of the chlorine atoms and molecules in the discharge bulk are referred to as primary electrons.Electrons can also be emitted from surfaces upon particle impact.Here, the electrons emitted from the electrodes, the secondary electrons, are tracked as separate species.We apply energy-dependent secondary electron emission yield for both ion-induced electron emission γ see,i (E i ) and ground state atom-induced electron emission γ see,n (E n ) from the electrode surfaces.We use the fit to the secondary electron emission yield for a clean surface bombarded by argon ions and argon neutrals, incident on various metal surfaces versus particle energy, given by Phelps and Petrović [26] and Phelps et al [27].This is the same approach as taken when modelling low-pressure capacitive argon discharges [28,29] and has more recently been used when exploring a capacitive argon discharge in the intermediate pressure regime [7].Here, for the ion induced secondary electron emission yield, we use the fits made for argon ions bombarding metal surface for both Cl + and Cl + 2 ions bombarding the electrodes.Similarly, for the fast neutral Cl and Cl 2 bombarding the electrodes we use the fits for fast argon neutrals in the ground state.This assumption is made due to lack of data for chlorine.Keep in mind that the secondary electron emission yield depends on the work function of the electrode surface and the ionization potential of the bombarding ion among other parameters, so argon may not be a good representative of chlorine.As the ionization potential of argon is higher than that for chlorine the ion induced secondary electron emission yield may be overestimated using this fit.The ions are accelerated across the sheath and collide with the solid surface, inducing secondary electron emission.Typically, in the early PIC/MCC chlorine studies only the ion-induced secondary electron emission was taken into account, often assuming a constant secondary electron emission yield.This approach is represented by a rather large ion induced secondary electron yield of γ see,i = 0.5 for comparison.We also include electron-induced secondary electrons, implemented using the empirical Vaughan's formula describing electron-induced secondary electron yield that depends on the electron impact energy and incident angle γ e (E e , θ) [30,31], as described by Gopinath et al [32].Note that the empirical Vaughan's model allows for the electroninduced secondary electron emission yield to be above unity if the incident electron energy is above certain energy, i.e. tens of volts for most metal and dielectric materials.Here, the electron induced secondary electron emission is incorporated using the modified Vaughan approach as described by Wen et al [33].This also implies that we additionally incorporate a 3% elastic reflection component and 7% inelastic back-scattered component [33], where the fitting parameters are based on the experimental data of Baglin et al [34] and Kirby et al [35,36].A total of five cases with no or varying secondary electron emission process included in the discharge model are explored for a range of pressures.A summary showing all the cases explored, with incremental contribution of secondary electron emission processes, is given in table 1.The most realistic case that best describes the chlorine discharge is Case IV.
It is a challenge to simulate molecular gases as the dissociation processes and the processes that involve charged particles, occur on widely different timescales.To resolve this issue we take a hybrid approach, and apply a global model [15,37] to determine the dissociation fraction within the discharge, beforehand.Note that global models neglect spatial variations in the plasma parameters as well as the kinetics of the discharge and the acceleration of ions towards surfaces is significantly smaller than that expected in a capacitively coupled discharge.Therefore, a higher fraction of the absorbed power will be dissipated in electron heating in the global model calculation which may lead to overestimation of the Cl atom density.The absorbed power calculated by the PIC/MCC simulation for a given pressure and gap size becomes an input parameter for the global model calculations, iteratively.This gives the partial pressures for Cl 2 molecules and Cl atoms that are used to set the composition of the neutral background gas in the PIC/MCC simulation.These values are listed in table 2. As the pressure rises, there is a corresponding increase in absorbed power.Consequently, the Cl atom fraction exhibits an upward trend with increasing pressure.For this study the applied voltage is kept fixed for all cases and as the pressure is increased the absorbed power increases and the electron density increases.The increased electron density with increased pressure in turn increases the dissociation.The calculated partial pressures and their dependence on pressure and power are in general agreement with the experimentally determined values which are found to be a few percent or less at low power in capacitive discharges [16] and inductively coupled discharges [38] and increase with increased power and decrease with increased pressure in capacitive [23] and inductive discharges [38][39][40].
In the simulation the chlorine atoms are treated as timeand space-evolving diffusing fluid as discussed elsewhere [7,19].All neutral fluid species are assumed to have a Maxwellian velocity distribution at 26 meV.Along with the charged particles, the Cl fluid densities were evolved selfconsistently in time, due to diffusion, collisions, and interactions with the electrodes.The feedstock gas molecules are regarded as a fixed fluid which is uniformly distributed between the electrodes.The diffusion fluid, represents a low density, reactive neutral Cl atoms, that are assumed to diffuse only against the fixed fluid.However, ground state chlorine atoms and molecules with energies exceeding E ground thr = 1 V, were followed as PIC species.For the heavy particles we use a sub-cycling, and the heavy particles are advanced every 16 electron time steps.

Results and discussion
The one-dimensional particle-in-cell/Monte Carlo collisional (PIC/MCC) simulations are performed on a capacitive chlorine discharge with 2.54 cm gap driven by a sinusoidal.The pressure was varied in the range 2-50 Pa while the driving frequency and the voltage amlitude were kept fixed at 13.56 MHz and 222 V, respectively.

Electron energy and electronegativity
Figure 2 shows the electron density, the Cl − density, and the electronegativity in the discharge center (α 0 ) versus pressure for the varying secondary electron emission processes included in the discharge model.For all the cases, with no or varying secondary electron emission processes, the electron density (figure 2(a)) increases with increased gas pressure.There is only a slight difference between using the older electron impact excitation cross sections (old, Case I) and using the more recently calculated cross sections (new, Case II) at 2 Pa and the pressures above 35 Pa.In addition, when a large ion induced secondary electron emission yield is assumed (here γ see,i = 0.5, Case V), the electron density is higher than for all the other cases (see figure 2(a)).The center Cl − density is shown versus pressure in figure 2(b).The Cl − density also increases as the pressure is increased.For pressures of 30 Pa and lower updating the electron impact excitation cross sections has very small impact on the electron density or the negative ion density, which can be seen by comparing Cases I and II, both with γ i = 0. But, for pressures above 35 Pa, the impact of the change in the electron excitation cross sections from the ones calculated by Rescigno [20] (old, Case I) to the more recent calculations of Hamilton et al [21] (new, Case II), is notable, however it is small.For all the cases, with increasing pressure the electronegativity in the discharge center α 0 increases before it stabilizes at a relatively constant level, albeit with fluctuations as seen in figure 2(c).This is because for pressures above about 10 Pa both the electron and the Cl − ion densities increase with increased pressure at similar rate for all pressures.Keep in mind that Case IV is the most realistic case.Adding secondary electron emission to the discharge model drastically increases the electron density at all pressures, which leads to the lower electronegativity.Therefore, in the case of large ion induced secondary electron yield (γ see,i = 0.5, Case V), the electronegativity is lower than for the other cases.Thus, secondary electron emission from the electrodes leads to a reduction in electronegativity, which is especially noticeable at higher pressures (see figure 2(c)).
The primary electron temperature at the discharge center is plotted versus pressure in figure 3, while the secondary electron emission processes are varied.We see that incrementally adding secondary electron emission decreases the primary electron temperature.For high ion induced secondary electron emission yield γ see,i = 0.5 the primary electron temperature is lower than for the other cases and increases with increased pressure for pressures above 10 Pa.The average electron energy is determined by the particle balance.Increased electron density decreases the electron temperature and also when the number of hot secondary electrons is increased the average energy of the primary electrons must decrease.
Figure 4 depicts the electron energy probability function (EEPF) for the primary electrons at the center of the discharge and averaged over the 0-1 mm region next to the electrode (the sheath region) across various pressures and secondary emission models (Cases I-V).For all pressures, a distinct Druyvesteyn-like distribution is evident at the lower energies, accompanied by a high-energy tail.Notably, at 2 Pa, when γ see,i = 0.5, the high-energy tail representing highenergy electrons is most prominent in comparison to other secondary emission cases, while neglecting secondary electron emission the tail is significantly weaker (see figure 4(a1)).This trend is consistent in the EEPF within the sheath region.However, for cases with higher secondary emissions (Cases IV and V), the EEPF is depleted at lower energies and decreases more rapidly compared to the other cases (see figure 4(a2)).At pressure of 10 Pa, for Case V, where γ see,i = 0.5, the EEPF decreases faster at the lower energies compared to the other cases, observed both in the discharge center and within the sheath regions.However, examining the tails of the distributions reveals that at higher energies, the EEPF is larger for cases that include secondary electron emission.Consequently, among these cases, γ see,i = 0.5 exhibits the highest EEPF, as depicted in figures 4(b1) and (b2).With an increase in pressure to 25 Pa, similar to 10 Pa, the EEPF at the discharge center decreases sharply at lower energy and have energy tail at higher energies where cases include secondary electron emission exhibit higher EEPF (see figure 4(c1)).Similarly, within the sheath region, the EEPF demonstrates an increase for all energy levels.It should be noted that in Cases III and IV, there is a significant decrease in the EEPF at 80 eV as illustrated in figure 4(c2).At 50 Pa, the EEPF at the discharge center exhibits a depletion below 40 eV for all cases, except in the instance of γ see,i = 0.5 (Case V), where it drops around 50 eV and no high-energy tail is noted at this pressure as seen in figure 4(d1).Conversely, within the sheath region, the EEPF increases for all energy levels.There is a noticeable yet small divergence in the EEPF at lower energies, which becomes more pronounced at high-energy tails (above 30 eV), indicating that models with higher secondary emission elevate the EEPF at higher energy (see figure 4(d2)).Examining the EEPF distribution at the discharge center, it is evident that as the pressure rises, there is a reduction in the EEPF, aligning with the observed decrease in electron temperature at the discharge center (see figure 3).In addition, when secondary electron emission is included in the model, the primary electron temperature is reduced.This behaviour is consistent with findings reported earlier for the capacitive chlorine discharge [8,41] as well as the capacitive argon discharge [7,42].

Particle balance process
To study how the secondary electron emission influences the creation and loss of the various species, the dominant reactions responsible for generation and loss of a few important species is shown for three different pressures in figures 5-8.For the analysis we selected gas pressures of 2 Pa, 10 Pa, and 50 Pa, while also considering varying the completeness of the secondary electron emission processes.The relative contribution of various processes to the creation and loss of the chlorine molecular ion Cl + 2 are shown in figures 5(a) and (b), respectively.When the secondary electron emission is neglected almost all the ionization to form Cl + 2 is due to electron impact ionization by the primary electrons as seen in figure 5(a).As the secondary electron emission is taken into account electron impact ionization by secondary electrons comes into play.When we use high constant ion induced secondary electron emission yield the contribution of secondary electrons to the ionization is as high as 40%.We also note that there is always some contribution to the creation of Cl + 2 from charge transfer Cl + + Cl 2 −→ Cl + Cl + 2 , and the relative contribution increases with increased secondary electron emission from the electrodes as well as increased pressure.At the lower pressures of 2 Pa and 10 Pa, the Cl + 2 ions are almost entirely lost as they bombard the electrodes.With increasing pressure to 50 Pa the role of ion-ion mutual recombination increases (see figure 5(b)) and is roughly 40% for the cases where the secondary electron emission is neglected at 50 Pa, and about 50% for the Case IV.
The creation of the negative ion Cl − is almost entirely due to dissociative attachment and as the secondary electron emission processes are added to the discharge model, some, but small contribution, is due to secondary electrons, as seen in figure 6(a).The dominating loss processes for the negative ion Cl − are shown in figure 6(b).At 50 Pa almost all the negative ions are lost through ion-ion mutual neutralization Cl − + Cl + 2 , while as the pressure is lowered associative detachment by the Cl atom and detachment by the Cl 2 molecule play an increasing role, with over 50% contribution at 2 Pa.The capacitive chlorine discharge is recombination dominated at pressures above 10 Pa, while detachment by the Cl atom has some impact at lower pressures.
As discussed in the introduction the etch process is driven by the flux of Cl atoms, as the Cl atoms have 2-3 times higher etch yields than the Cl 2 molecule [6].The relative contributions of the processes that lead to the creation of Cl atoms are shown in figure 7(a).The dominating process is electron impact dissociation by the primary electrons, and there is a very small contribution from dissociative attachment by the primary electrons.With increasing secondary electron emission, electron impact dissociation by the secondary electrons plays a bigger role, but has less than 25% contribution even for the high ion induced yield of γ i = 0.5.Dissociative attachment always has rather small contribution.The main loss process for the Cl atoms is flux to the electrodes, but electron impact ionization, associative detachment, and charge transfer have much smaller roles, as seen in figure 7(b).The role of these latter processes increases with increasing pressure, in particular for the electron impact ionization at 50 Pa.At 2 Pa pressure, the primary method of generating atomic Cl + ions when secondary electron emission is ignored, is through dissociation ionization of Cl 2 .However, when secondary electron emission is taken into account, dissociation ionization through the secondary electron in generating atomic Cl + ions becomes particularly pronounced, with its contribution exceeding 50% in Case V.As the pressure rises to 10 Pa, the primary mechanism for generating Cl + ions shifts towards charge transfer between Cl 2 + and Cl (Cl + 2 + Cl → Cl 2 + Cl + ).However, when considering secondary electron emission, dissociation ionization reactions become more significant, contributing approximately 40% (for Cases III and IV) and 70% (for Case V) respectively.It is important to note that the contribution of electron impact ionization of Cl atoms at 10 Pa increases compared to 2 Pa.At 50 Pa, Cl + is primarily created through electron impact ionization of atoms.Similarly to lower pressures, when secondary electron emission is considered, electron impact dissociative ionization of Cl 2 also plays a role, albeit to a lesser extent than at lower pressures.For Case V, the dissociative ionization reactions are the dominant processes for Cl + generation (figure 8(a)).The main loss process for Cl + at the lower pressures is flux to the electrodes.As the pressure is increased to 50 Pa, the dominant loss process shifts towards charge transfer (figure 8(b)).

The spatial variation of the reaction rates
We will now explore the spatial variation of the reaction rates for the creation loss of a few selected species at 10 Pa.We only look at Case IV, which has the most realistic description of the secondary electron emission processes.The spatial variation of the reaction rates for the creation of Cl + 2 ions and the loss of Cl + 2 ions through volume processes is shown in figure 9.As discussed earlier electron impact ionization by the primary electrons is the dominating process for the creation of Cl + 2 ions.We see that there is a small peak at the plasma-sheath interface, while the reaction rates are flat within the electronegative core as seen in figure 9(a).The reaction rate for electron impact ionization by the secondary electrons shows the same trend but is roughly an order of magnitude smaller and charge transfer has only slightly higher contribution within the electronegative core.The reaction rates for the volume Cl + 2 ion loss processes are shown in figure 9(b).Recall from the discussion in section 3.2 that most of the Cl + 2 ions are lost as flux to the electrodes see figure 5(b).The ion-ion mutual neutralization of Cl − and Cl + 2 ions is the dominant Cl + 2 ion volume loss process, while charge transfer has slightly lower contribution.Dissociative recombination e + Cl + 2 and fragmentation have a much smaller contribution.All of these reactions occur mainly within the electronegative core.
The reaction rates for the generation and loss of Cl − ions are shown in figure 10. Figure 10(a) shows that dissociative attachment of the chlorine molecule by primary and secondary electrons are the main Cl − production mechanisms.The primary electrons contribute almost two orders of magnitude more than the secondary electrons.Also, we note that polar dissociation has orders of magnitude smaller contribution.The spatial variation of the Cl − loss processes is shown in figure 10(b).The chlorine discharge is ion-ion recombination dominated as the ion-ion neutralization between Cl − and Cl + 2 within the electronegative core is the dominant loss process for Cl − .This is followed by associative detachment by Cl atoms and smaller contribution from detachment by the Cl 2 molecules, ion-ion neutralization between Cl − and Cl + , and finally detachment by the electrons.We note that the detachment by the Cl 2 molecule occurs primarily in the plasmasheath region and decreases to a minimum at the discharge center.
Figure 11(a) shows the time averaged reaction rates for the Cl generation.The dominant reaction among all processes is primary electron impact dissociation which occurs mainly within the plasma bulk but has a small peak at the plasmasheath interface.Electron impact dissociative attachment also shows some contribution as do various ion-ion mutual neutralization processes.As shown in figure 7(b) the dominant loss process for the Cl atoms is flux to the walls.We explore the spatial variation of the volume loss processes in figure 11(b).The main volume loss process for Cl is the charge transfer to form Cl + followed by associative detachment by the Cl atom.

Power absorption
The time-averaged power absorption by the various charged species at pressures of 2 Pa, 10 Pa, and 50 Pa, while considering different secondary electron emission processes in the discharge model is shown in figure 12.It shows the power absorption J • E for each individual charged species divided by the total power absorption by all the charged species.For both Cases I and II, where secondary emission is neglected, roughly 76% of the power is absorbed by the Cl + 2 ions at 2 Pa.With increased pressure, this fraction diminishes to around 57% and 31% at 10 Pa and 50 Pa, respectively.Similar to the Cl + 2 ion, the power absorption by the Cl + ion decreases with increased pressure from 8% at 2 Pa to 1% at 50 Pa.Conversely, the power absorption by Cl − is minimal, being <1% at 2 Pa.Nevertheless, with increasing gas pressure, its power absorption rises to 9% at 50 Pa.For Cases I and II, where only primary electrons are present, the electron power absorption is 15% at 2 Pa.This value rises to 39% at 10 Pa and approximately 58% at 50 Pa.
Case III which includes energy dependent secondary electron emission caused by ion and heavy atoms bombardment of the electrodes, and Case IV, which in addition includes electron induced secondary electron emission, have very similar power absorption proportions across all pressures.At 2 Pa, the Cl + 2 ion has the highest absorption fraction of 75% (Case III) and 78% (Case IV).As the pressure is increased, this fraction diminishes to 57% at 10 Pa and further reduces to 31% at 50 Pa.The power absorption fraction for Cl + is in the range from 4% (Case III) and 8% (Case IV) at 2 Pa to 2.6% at 50 Pa.The Cl − power absorption fraction for Cases III and IV is similar to Cases I and II at 2 Pa and 10 Pa or <1% and 2% at 2 Pa and 10 Pa, respectively.However, this fraction increases to 6% with increased pressure.As the pressure increases, the primary (secondary) electron power absorption fraction for Cases III and IV increases (decreases) from 13% (3% (Case III) and 4.5% (Case IV)) at 2 Pa to 36% (3%) at 10 Pa, and 55% (2%) at 50 Pa.
For Case V, where only constant secondary electron emission induced by ion bombardment of the electrodes γ i = 0.5 is considered, the power absorption by Cl + ions and secondary electrons is higher than for the other cases assuming secondary electron emission.The power absorption fraction for Cl − is <1%, 2%, and 4% at 2 Pa, 10 Pa, and 50 Pa, respectively.Cl + 2 has the highest power absorption fraction with around 65% at 2 Pa, which reduces with increased pressure to 55% and 38% at 10 Pa and 50 Pa, respectively.The primary electron power absorption fraction increases from 6.5% at 2 Pa to 13% at 10 Pa and 35% at 50 Pa.The secondary electrons have power absorption fraction of 19% at 2 Pa, which slightly increases to 19.6% at 10 Pa and decreases to 16% at 50 Pa.Note that the power absorption fraction by secondary electrons at 2 Pa and 10 Pa is higher than for the primary electrons.
The spatio-temporal behavior of the electron power absorption in the sheath region is shown in figure 13 for the case when the secondary electrons are neglected (Case II).For this case only primary electrons are present and the electron power absorption is highest near each sheath edge and at phases corresponding to when the sheath is most rapidly expanding into the bulk.For each of the graphs, the abscissa covers the sheath region from the powered electrode on the left hand side and 4.2 mm into the discharge gap.The ordinate covers the full rf cycle.We see that the electron power absorption is mainly due to the oscillating sheath expansion into the bulk (red shading) and some of this power absorption is cancelled over an rf period by the oscillating sheath contraction (dark blue shading), indicating α-mode.We also note that a significant power absorption (red and yellow areas) and somewhat smaller power loss (dark blue areas) are also evident in the plasma bulk region as seen clearly in figures 13(a) for 2 Pa.The electron power absorption structure appears to be more complicated at 50 Pa, but there is still a significant electron power absorption within the plasma bulk.This behaviour in the electron power absorption indicates a hybrid power absorption mechanism that consists of drift ambipolar pressure heating (DA-mode) which is originated mainly from the electron density gradient, and stochastic heating or sheath oscillation (α-mode).This heating mechanism is identical to what has been observed in capacitively coupled oxygen discharge operated pressure below about 3 Pa [43,44], chlorine discharge operated up to 50 Pa [13], and CF 4 discharge operated at around 80 Pa [45].
Figure 14 shows the spatio-temporal behavior of the electron power absorption in the sheath region for the most realistic case, when secondary electron emission due to ion, electron, and neutral bombardment of the electrodes is included in the discharge model (Case IV).The figure shows the electron power absorption for both the primary electrons (left column) and the secondary electrons (right column).We note that there is power absorption by the primary electrons due to the expanding and contracting sheath, as well as near the maximum of the sheath width (yellow shading), while for the secondary electrons there is power absorption within the sheaths at phases corresponding to maximum sheath width, maximum sheath voltage, and minimum rf current, as can be seen in figures 14(a2), (b2) and (c2).This indicates that secondary electron emission from the electrodes is an important electron power absorption mechanism as the emitted electrons are accelerated across the sheath.

Summary
We applied the one dimensional object-oriented PIC/MCC code oopd1 to study a 2.54 cm gap, capacitive coupled chlorine discharge driven by a sinusoidal at 13.56 MHz with voltage amplitude of 222 V.The discharge model included various secondary electron emission processes while the pressure was varied in the range from 2 to 50 Pa.Five cases were studied (table 1), including and neglecting energy and incident angle dependent secondary electron emission yield due to electron bombardment, and constant or energy dependent secondary electron emission due to ion and atom bombardment of the electrodes.For all cases, the electron and the Cl − ion density increase with increased gas pressure.The electronegativity in the discharge center (α 0 ) initially increases and then stays almost constant with further increasing the pressure.Adding secondary electron emission to the discharge model increases the electron density leading to lower electronegativity.In addition, we investigated how secondary electron emission and gas pressure influence the generation and loss of different species, including the Cl + 2 ion, the negative Cl − ion, and the Cl atom.The negative ion Cl − is solely created through dissociative attachment.At 50 Pa, all negative ions are lost through mutual neutralization, and as pressure decreases, associative detachment by the Cl atom and the Cl 2 molecule play an increasing role.The capacitive chlorine discharge is recombination dominated for pressures above 10 Pa.The study reveals that secondary electron emission decreases the power absorption (J • E) fraction by primary electrons, Cl + 2 ions and Cl − ions, while increasing the power absorption fraction by Cl + ions.Moreover, the power absorption fraction by Cl − ions and primary electrons increases with increasing pressure, while it decreases for Cl + 2 ions, Cl + ions, and secondary electrons.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).

Figure 1 .
Figure 1.Comparison of the electron impact excitation cross sections from the ground state Cl 2 (X 1 Σg + ) molecule into the dissociative Π states.The dashed lines show the cross sections calculated by Rescigno [20] (old) and the solid lines show the cross sections calculated by Hamilton et al [21] (new).

Figure 2 .
Figure 2. The time-averaged (a) center electron densities, (b) center Cl − ion densities, and (c) the center electronegativity (α 0 ) versus pressure for varying secondary emission processes included in the discharge model.

Figure 3 .
Figure 3.The time-averaged primary electron temperature at the discharge center versus pressure for varying secondary emission processes included in the discharge model.

Figure 4 .
Figure 4.The electron energy probability function (EEPF) for the primary electrons including and excluding the various secondary electron emission processes at (a) 2 Pa, (b) 10 Pa, (c) 25 Pa, and (d) 50 Pa (1) at the discharge center and (2) within the sheath region of a capacitively coupled chlorine discharge with a discharge gap of 2.54 cm driven by a sinusoidal with the voltage amplitude of 222 V at driving frequency of 13.56 MHz.

Figure 5 .
Figure 5.The relative contributions to the (a) creation and (b) loss of the molecular ion Cl + 2 .A capacitive chlorine discharge with 2.54 cm gap driven by a sinusoidal with a voltage amplitude of 222 V at driving frequency of 13.56 MHz.

Figure 6 .
Figure 6.The relative contributions to the (a) creation and (b) loss of the ion Cl − .A capacitive discharge with 2.54 cm gap driven by a sinusoidal with a voltage amplitude of 222 V at driving frequency of 13.56 MHz.

Figure 7 .
Figure 7.The relative contributions to the (a) creation and (b) loss of the Cl atom.A capacitive chlorine discharge with 2.54 cm gap driven by a sinusoidal with a voltage amplitude of 222 V at driving frequency of 13.56 MHz.

Figure 8 .
Figure 8.The relative contributions to the (a) creation and (b) loss of the ion Cl + .A capacitive chlorine discharge with 2.54 cm gap driven by a sinusoidal with a voltage amplitude of 222 V at driving frequency of 13.56 MHz.

Figure 9 .
Figure 9.The spatial variation of the reaction rates for the (a) creation of Cl + 2 ions and (b) loss of Cl + 2 ions.A capacitive chlorine discharge with 2.54 cm gap driven by a sinusoidal with a voltage amplitude of 222 V at driving frequency of 13.56 MHz at 10 Pa for Case IV.

Figure 10 .
Figure 10.The spatial variation of the reaction rates for the (a) creation of Cl − ions and (b) loss of Cl − ions.A capacitive chlorine discharge with 2.54 cm gap driven by a sinusoidal with a voltage amplitude of 222 V at driving frequency of 13.56 MHz at 10 Pa for Case IV.

Figure 11 .
Figure 11.The spatial variation of the reaction rates for the (a) creation of Cl atoms and (b) loss of Cl atoms.A capacitive chlorine discharge with 2.54 cm gap driven by a sinusoidal with a voltage amplitude of 222 V at driving frequency of 13.56 MHz at 10 Pa for Case IV.

Figure 12 .
Figure12.The time-averaged power absorption fractions of primary and secondary electrons, Cl + 2 , Cl + , and Cl − ions assuming various secondary electron emission conditions at varying pressures for a capacitive chlorine discharge at with 2.54 cm gap driven by a sinusoidal with a voltage amplitude of 222 V at driving frequency of 13.56 MHz.

Figure 13 .
Figure 13.The spatial-temporal behavior of the electron power absorption in the sheath region at (a) 2 Pa, (b) 10 Pa, and (c) 50 Pa when the secondary electron emission is neglected (Case (II)).For a capacitive chlorine discharge with 2.54 cm gap driven by a sinusoidal with a voltage amplitude of 222 V at driving frequency of 13.56 MHz.

Figure 14 .
Figure 14.The spatial-temporal behavior of the electron power absorption in the sheath region at (a) 2 Pa, (b) 10 Pa, and (c) 50 Pa when the most realistic secondary electron emission model is assumed (Case IV).The left column shows the primary electron power absorption and the right column the secondary electron power absorption.For a capacitive chlorine discharge with 2.54 cm gap driven by a sinusoidal with a voltage amplitude of 222 V at driving frequency of 13.56 MHz.

Table 1 .
Overview of the secondary electron emission yields used for the five cases explored.In Cases I and II the secondary electron emission processes are neglected.Case III assumes only neutral and ion induced energy dependent secondary electron emission yield and Case IV has in addition electron induced secondary electron emission.Case V assumes only a constant ion induced secondary electron emission yield.

Table 2 .
The composition of the thermal background neutrals used in the PIC/MCC simulations.The partial pressure is determined by global (volume averaged) model calculations.