Ion dynamics in capacitively coupled argon-xenon discharges
M. Klich, S. Wilczek, J. F. J. Janssen, R. P. Brinkmann, T. Mussenbrock, J. Trieschmann
IIon dynamics in capacitively coupled argon-xenondischarges
M. Klich , S. Wilczek , J. F. J. Janssen , R. P. Brinkmann , T.Mussenbrock , J. Trieschmann Department of Electrical Engineering and Information Science, Ruhr UniversityBochum, D-44780, Bochum, Germany PlasmaMatters B.V., De Groene Loper 19, 5600 MB Eindhoven, The Netherlands Electrodynamics and Physical Electronics Group, Brandenburg University ofTechnology Cottbus-Senftenberg, Siemens-Halske-Ring 14, 03046 Cottbus, Germany
Abstract.
An argon-xenon (Ar/Xe) plasma is used as a model system for complexplasmas. Based on this system, symmetric low-pressure capacitively coupled radio-frequency discharges are examined utilizing Particle-In-Cell/Monte Carlo Collisions(PIC/MCC) simulations. In addition to the simulation, an analytical energy balancemodel fed with the simulation data is applied to analyze the findings further. Thiswork focuses on investigating the ion dynamics in a plasma with two ion species anda gas mixture as background. By varying the gas composition and driving voltage ofthe single-frequency discharge, fundamental mechanics of the discharge, such as theevolution of the plasma density and the energy dispersion, are discussed. Thereby,close attention is paid to these measures’ influence on the ion energy distributionfunctions at the electrode surfaces. The results show that both the gas compositionand the driving voltage can significantly impact the ion dynamics. The mixing ratioof argon to xenon allows for shifting the distribution function for one ion species fromcollisionless to collision dominated. The mixing ratio serves as a control parameterfor the ion flux and the impingement energy of ions at the surfaces. Additionally, asynergy effect between the ionization of argon and the ionization of xenon is found anddiscussed.
1. Introduction
Radio-frequency capacitively coupled plasmas (RF-CCPs) operated at low-pressures area core part of modern technology [1–3]. Especially for semiconductor fabrication, plasmaprocesses like ion-assisted etching [4, 5] and ion implantation [6–8] are key technologies.Plasma tools help to achieve an integration depth of only a few nanometers [9–11]. Onemajor challenge of these processes is to control the energy and flux of impinging ionson the wafer separately [1–3, 12–16].Techniques using multiple driving frequencies, such as voltage waveform tailoring[12], succeed to independently control the plasma generation and the ion bombardmentenergy [17, 18]. The plasmas investigated in these studies are predominantly argonplasmas [13, 16, 19]. However, industrially relevant etching plasmas consist of rather a r X i v : . [ phy s i c s . p l a s m - ph ] F e b on dynamics in Ar/Xe CCPs /H [20–22] or SF /O [23, 24]. For these plasmas, theinterplay of several charged and neutral heavy species impacts the ion dynamics. Theion dynamics in the plasma eventually determine how ions reach the walls. Here, boththe quantitative (e.g., how many ions reach the target/substrate?) and the qualitativeperspective (e.g., how are the ions affected by collisions?) need to be considered.Researching complex plasma chemistry in RF-CCPs is a tedious task. Experimentalstudies show that the ion energy distribution functions (IEDFs) at the electrodesbecome rather complicated [25–29]. Commonly used tools such as the retarding fieldanalyzer filter the incident ions by energy and do not differentiate between the ionspecies [25, 29, 30]. There is recent and ongoing work to utilize ion mass spectrometryto overcome these issues [31]. Nevertheless, this technique is currently not widelyapplied as a diagnostic tool to analyze plasmas. Therefore, theoretical studies andsimulations are necessary to help to interpret and to understand the measured data.However, the inherently complex chemistry renders a complete simulation cumbersome.The commonly used kinetic Particle-In-Cell/Monte Carlo collisions (PIC/MCC) methodtypically avoids complex chemistry mainly due to lack of cross section data (althoughconceptually possible). The reasoning is to keep the number of species and superparticlestraceable [32]. Otherwise, the computational load of PIC/MCC simulation would notbe feasible.Combining complex discharge chemistry with the multi-frequency approachesmentioned above makes a detailed assessment of ion dynamics’ features too cumbersometo conduct collectively. Hence, we decide to investigate the fundamental principles ofa discharge with two ion species for this study. The mixture of the noble gases argonand xenon has some history of being an adequate model for complex chemistry. In low-pressure plasmas, the plasma chemistry of noble gases becomes relatively simple [35,36].Therefore, studies on ion acoustic waves [33,34] and a generalized Bohm criterion [35–37]depicted this mixture as a simple example for a multi-ion discharge. Recent studies byKim et al. [38] and Adrian et al. [39] contributed to those discussions using or referringto Ar/Xe plasmas.Apart from being a model system, there are some academic applications of Ar/Xeplasmas (e.g., as trace gas for mass spectrometry [40, 41], for the diagnostics of theelectron temperature [42], or in halide lamp simulations [43]). Furthermore, the mixturehas had great success as the illuminant [44] or as part of the illuminant mixture [32,45,46]of plasma display panels (PDPs). This historical background causes both gases tobe relatively well researched. This fact entails many valuable data for theory andsimulation.This work aims to add to the existing studies conducted for various gas mixtures[47–50], investigating their intrinsic mixture dynamics. This knowledge will eventuallyenable the adaptation of the known means of plasma control to the complex dischargesof industrial relevance. In contrast to the existing studies, our work is focused on theimpact of the gas mixture composition on the ion dynamics. We will show that the gascomposition is a suitable control parameter for the ion dynamics (e.g., the impingement on dynamics in Ar/Xe CCPs
2. Methods and models
The first particle simulations were introduced in the 1940s [51], and the PIC/MCCscheme was developed in the 1960s [52]. Since then, the PIC/MCC method becamea commonly used tool to self-consistently simulate low-pressure plasmas [32, 52, 53].Despite having the disadvantage of a substantial computational load, its most significantadvantage is the statistical representation of distribution functions in phase-space,allowing the method to capture non-local dynamics [53, 54].For this work, a benchmarked PIC/MCC implementation called yapic1D [56] isused to generate the results. The original code is modified to include two backgroundgases and multiple ion species. Aside from that, diagnostics for the energy balancemodel mentioned above is added to the original code.This simulation setup is taken to be fully geometrically symmetric (compareWilczek et al. for details [54]). 1d3v electrostatic simulations are executed using aCartesian grid with 800 grid cells representing an electrode gap of 25 mm. The resultingcell size ∆ x meets the requirement to resolve the Debye length λ D [52, 54, 56]. Similarly,the single harmonic driving frequency f RF “ .
56 MHz is sampled with 3000 points perRF period. The time step ∆ t is sufficiently small to fulfill the requirement regarding theelectron plasma frequency ω pe [52, 54, 56]. Several other studies mention the influenceof the number of superparticles on the statistics and the plasma density [56–58]. Forthis work, we did not include individual weighting for different particle species. To havean acceptable resolution for each ion species at all values of the xenon fraction x Xe , wesimulated about 800.000 super-electrons for each case. The advantage of this choice isthat an average of 3000 converged RF-cycles provides satisfactory results.The ideal gas law defines the neutral species’ total density, and the neutral fraction x i is varied. Thereby, the gas pressure p gas is kept constant at 3 Pa, and the gastemperature T gas at 300 K. First, we choose the amplitude of the RF voltage V RF to be on dynamics in Ar/Xe CCPs reaction process name ε thr [eV] data source1 e ´ + Ar Ñ e ´ + Ar elastic scattering - Phelps2 e ´ + Ar Ñ e ´ + Ar ˚ electronic excitation 11.5 Phelps3 e ´ + Ar Ñ ´ + Ar ` ionization 15.8 Phelps4 e ´ + Xe Ñ e ´ + Xe elastic scattering - Phelps5 e ´ + Xe Ñ e ´ + Xe ˚ electronic excitation 8.32 Phelps6 e ´ + Xe Ñ ´ + Xe ` ionization 12.12 Phelps7 Ar ` + Ar Ñ Ar ` + Ar isotropic scattering - Phelps8 Ar ` + Ar Ñ Ar + Ar ` resonant charge exchange - Phelps9 Ar ` + Xe Ñ Ar ` + Xe isotropic scattering - LJ pot10 Xe ` + Xe Ñ Xe ` + Xe isotropic scattering - Phelps11 Xe ` + Xe Ñ Xe + Xe ` resonant charge exchange - Phelps12 Xe ` + Ar Ñ Xe ` + Ar isotropic scattering - Viehland Table 1.
Plasma chemistry and collision processes considered in the simulation.Meaning of the data sources: “Phelps” refers to the cross section data found initiallyin the JILA database [59] and now distributed by the LXCat project [60–62]. “LJ pot”refers to a cross section obtained based on a phenomenological Lennard-Jones potentialas described by Laricchiuta et al. [63]. “Viehland” marks a cross section calculatedfrom an interaction potential given by Viehland et al. [67]. Details of the calculationscan be found in section 2.3.
100 V. Later in section 3.3, we discuss the implications of a voltage variation between100 V and 1000 V on the ion dynamics. All the parameters presented in this section aretypical for baseline studies of RF-CCPs [14–16, 54, 56].
For PIC simulations to provide a realistic representation of the particle distributionfunctions and physics in a low-pressure discharge, collisions need to be considered. Themethod of choice is the Monte Carlo collision technique [52–54] that is combined witha so-called null collision scheme [54–56]. Both techniques require the knowledge ofmomentum transfer cross sections.The chemistry set for argon and xenon is in line with the work of Gu (cid:19) mundsson etal. [35,36]. All reactions can be seen in detail in table 1. In contrast to Gu (cid:19) mundsson etal., we decide to take advantage of the commonly used and acknowledged [19, 54, 56, 68]cross section data obtained by Phelps. The data was initially distributed via the JILAdatabase [59] and is now available at the LXCat project website [60–62]. Phelpscombines the cross sections for all electronically excited states into one “effectiveexcitation” cross section. This effective excitation reduces the total number of reactionsand the numerical load.The second difference compared to Gu (cid:19) mundsson et al. is our treatment of themissing cross section data for Ar ` /Xe and Xe ` /Ar. Both conclude to neglect chargetransfer collisions between argon and xenon due to it being a non-resonant process that on dynamics in Ar/Xe CCPs On an elementary level of theory, all cross sections are based on an interaction potentialbetween the colliding particles. If the literature does not provide a cross section, apossible solution is to make it the modeler’s task to develop an interaction potential bymaking several assumptions. A classic example of this is the Langevin capture crosssection [72] used in studies to make up for unknown cross sections [73]. Despite theLangevin cross section’s advantages, a complete implementation is numerically extensiveand leads to anisotropic scattering [74, 75]. The cross sections given by Phelps are akind of momentum transfer cross sections [59]. There, the scattering angles are foundin an isotropic manner [52]. Hence, it is questionable to apply anisotropic scattering fortwo collisions while the other collisions are treated isotropically. We perceive anotherapproach to be more suitable for this work.The approach used in this work is based on Laricchiuta et al. [63], who use aphenomenological potential to describe a two-body interaction given by V ij p x q “ (cid:15) p,ij « mn ij p x ij q ´ m ˆ x ij ˙ n ij p x ij q ´ n ij p x ij q n ij p x ij q ´ m ˆ x ij ˙ m ff , (1)where the standard exponents of the Lennard Jones potential, 12 and 6, are replacedby n p x ij q and m . Depending on the type of interaction, m is either 4 for neutral-ioninteractions or 6 for neutral-neutral interactions. In this work, the potential is appliedto neutral-ion interactions only. Hence, m is always equal to 4. The dimensionlesscoordinate x “ r { r m,ij depends on the parameterized position of the potential well on dynamics in Ar/Xe CCPs Figure 1.
Cross sections for the electron and ion collisions used in this work. a) showsthe cross section of collision processes from electrons with argon neutrals. b) showsthe cross sections of collision processes from electrons with xenon neutrals. c) showscross sections of the collisions of Ar + ions. d) shows cross sections of the collisionsof Xe + ions. The data source and a detailed description of each process are foundin table 1. Abbreviations used in the legend: ela = elastic collision electron/neutral, exc = electronic excitation electron/neutral, ion = electron impact ionization, iso =isotropic scattering ion/neutral as defined by [59], back = backscattering ion/neutralas defined by [59]. r p,ij . The potential itself is scaled by the parameterized potential well depth (cid:15) p,ij . Bothparameterizations are empirical approximations that depend on atomic properties likethe polarizability. More details related to the exact empirical formulas can be found inLaricchiuta et al. [63], Cambi et al. [64], Cappelletti et al. [66], and Aquilanti et al. [65].Two additional steps are required to obtain the cross section. The first step iscalculating the scattering angle, χ ij according to χ ij p (cid:15) ij , b q “ π ´ b ż r d rr b ´ b r ´ V p r q (cid:15) ij (2) on dynamics in Ar/Xe CCPs (cid:15) ij the kinetic energy in the center of mass frame, b the impact parameter, r thedistance between the particles, and r the distance of closest approach. The scatteringangles are calculated using a program that is based on Colonna et al. [71]. The secondstep is calculating the cross section σ ij σ p l q ij p (cid:15) ij q “ π ż “ ´ cos l χ ij p (cid:15) ij , b q ‰ b d b, (3)with l an integer that indicates which type of cross section is calculated. In this work, weused l “
1, which corresponds to the momentum transfer cross section. The cross sectionis integrated based on an algorithm developed by Viehland [70]. Finally, the scatteringangle corresponding to the obtained momentum transfer cross sections is consistentlytaken to be isotropic in our simulations.
The conservation of energy is one of the central continuity equations of physics and soknowing how the energy disperses into a system is key to understanding the process. Interms of low-temperature plasma physics, a frequently used model as given by Liebermanand Lichtenberg [1] for a geometrically symmetric situation reads: S abs “ n s u B ε tot “ B ε tot “ e Γ B p ε e ` ε c ` ε i q . (4) S abs denotes the total energy flux into the system, n s the plasma density at the sheathedge, u B denotes the Bohm velocity, Γ B is the ion flux at the Bohm point, and ε tot is thetotal energy loss in eV. The last transformation in equation (4) shows that the energyloss per electron-ion pair created may be split into an energy loss due to electrons hittingthe bounding surface ( ε e ), an energy loss due to collisions ( ε c ), and an energy loss dueto ions impinging at the bounding surface ( ε i ). The loss terms ε e and ε i describe anaveraged energy loss of the system per lost particle (neglecting particle reflections). Thethird term ε c is treated differently. It represents the collisional losses per newly createdelectron/ion pair.Previous work [76] has shown that an adaptation of equation (4) gives insight intothe system’s electron dynamics by calculating all necessary terms from a PIC/MCCsimulation. An essential insight is that, due to flux conservation, the Bohm flux Γ B canbe exchanged by the electron flux Γ e , el or the ion flux Γ i , el at the electrode.In detail, the energy conversion through collisions ε c consists of an electron ε c , e and an ion contribution ε c , i . For low-pressure plasmas, it is argued that the energy lossdue to ion collisions ε c , i is often negligible [1]. However, a PIC/MCC study by Jianget al. [77] showed that ε c , i can significantly impact the energy balance of low-pressureplasmas.Using both insights, we evolve equation (4) into an energy balance model for two on dynamics in Ar/Xe CCPs Figure 2.
The trend of the plasma density while varying the background gascomposition. a) shows the development of the time and space averaged total iondensity. b) shows the fraction of Xe + ions in the discharge. (conditions: p gas “ l gap “
25 mm, V RF “
100 V, f RF “ .
56 MHz) ion species, here explicitly given for our case of an Ar/Xe mixture: S abs , tot “ S abs , e ` S abs , Ar ` ` S abs , Xe ` , (5) S abs , e “ p Γ e ε e ` Γ Ar ` ε c , e , Ar ` Γ Xe ` ε c , e , Xe q , (6) S abs , Ar ` “ Ar ` p ε i , Ar ` ` ε is , Ar ` ` ε cx , Ar ` q , (7) S abs , Xe ` “ Xe ` p ε i , Xe ` ` ε is , Xe ` ` ε cx , Xe ` q . (8)For this and more complex systems, it is useful to split the total energy flux S abs , tot into aseparate term for each species. This separation is done in equation (5). Besides, we splitthe collisional losses to the background gas for ions, ε c , i , into two terms. One representsthe losses due to charge exchange collisions for Ar + ions ( ε cx , Ar ` ) and Xe + ions ( ε cx , Xe ` ).The other term gives the losses caused by the remaining isotropic scattering. It separatesthe isotropic losses for Ar + ions ( ε is , Ar ` ), and Xe + ions ( ε is , Xe ` ). This distinction isbased on the nomenclature of Phelps [59] and will prove useful for understanding theion dynamics.The terms for the electron flux (Γ e ), the Ar + ion flux (Γ Ar ` ) and the Xe + ion flux(Γ Xe ` ) in this model are obtained from the PIC/MCC simulation at the surface of theelectrodes.
3. Results and Discussion
Initially, the influence of the gas composition on the discharge is investigated by varyingthe Ar/Xe density ratio. Figure 2 a) shows the total ion density n i , tot as a function of on dynamics in Ar/Xe CCPs x Xe or the argon gas fraction x Ar , respectively. Here, the totalion density n i , tot is defined as the sum of the spatially and temporally averaged numberdensities of Ar + and Xe + ions. The gas fractions of argon and xenon are defined bythe ratio of the respective species density and the total gas density. In analogy to thisdefinition, we define an ion fraction, e.g., the fraction of Xe + ions x Xe ` , as the ratioof the number density of Xe + ions and the total ion density n i , tot . Figure 2 b) depictsthis Xe + ion ratio as a function of the xenon gas fraction x Xe or argon gas fraction x Ar ,respectively.When varying the gas mixture from pure argon to pure xenon by successivelyincreasing the xenon fraction x Xe , the plasma density rises significantly over about oneorder of magnitude (fig. 2 a)). The ratio of Xe + ions (fig. 2 b)) reveals that even smalladmixtures of xenon to an argon gas produce a high amount of Xe + ions. A xenonfraction of x Xe « .
15 is already sufficient for Xe + ions to become the dominant ionspecies. Xenon admixtures of about 30 percent ( x Xe “ .
3) produce a strongly Xe + dominated discharge ( x Xe ` Á . + ions in the discharge as a function of the gas composition show non-linearrelations. Hereby, the trend of figure 2 a) approximates a compressed parabola whilstthe trend of 2 b) resembles the function of the square root. In the following, the overalldominance of Xe + ions will be examined and explained in more detail. The difference inthe ionization energies gives a basic explanation of the observed behavior. The ionizationthreshold for xenon ( ε thr , i , Xe “ .
12 eV) is much smaller than the threshold for argon( ε thr , i , Ar “ . σ i , Xe is about one order of magnitude bigger than the corresponding cross section σ i , Ar for argon (comp. fig. 1 a) and b)). As a result, Xe + ions are prevalent, even for lowxenon admixtures, and dominate the discharge for a wide mixture range. This resultagrees with previous works [48, 50] that, for different mixtures, have shown at least onedominant ion species for a wide range of admixtures.The influence of the gas composition also directly manifests in a variation of theIEDFs for both ion species. The plots of figure 3 show IEDFs for both Ar + and Xe + ions at the electrode surface. The energy, plotted on the abscissa, is given in eV. Theordinate shows the IEDF normed on the respective ion flux Γ i , s at the electrode. Eachrow of figure 3 represents results for both ion species and the same case. The cases aredistinguished by the xenon fraction x Xe as indicated. Here, the plots in the right columnshow IEDFs of Ar + ions, and the results for Xe + ions are shown in the right column.In section 2.2, we argue that the charge exchange between Ar + /Xe and Xe + /Ar,respectively, is a non-resonant process and a three-body collision. We conclude that thisprocess is negligible. As a result, a variation of the gas composition changes the ions’probability to perform charge exchange collisions. Therefore, Ar + ions, for high argonfractions x Ar , show an IEDF clearly dominated by collisions. This IEDF becomes acollisionless distribution for small argon admixtures to a xenon background (fig. 3 left).The IEDF of Xe + ions shows a similar trend except that Xe + ions have a less distinct on dynamics in Ar/Xe CCPs Figure 3.
Ion energy distribution function (IEDF) at the electrode for differentcompositions of the background gas. The left column shows distribution functionsfor Ar + ions. The corresponding distributions for Xe + ions are on the right side of theplot. (conditions: p gas “ l gap “
25 mm, V RF “
100 V, f RF “ .
56 MHz) on dynamics in Ar/Xe CCPs Figure 4.
Evaluation of the energy balance equations (eq. (5) - (8)) for variousgas compositions. All parameters have been calculated by means of a PIC/MCCsimulation. (conditions: p gas “ l gap “
25 mm, V RF “
100 V, f RF “ .
56 MHz) bimodal behaviour for the cases with high argon fraction. This difference is explainedby the scaling of the width of the bimodal peak being proportional to a m ´ [2, 28].Besides, an argon fraction x Ar of 0.2 and 0.3 or, vice versa, a xenon fraction x Xe of 0.2 and0.3 creates an intermediate or hybrid regime. A significant number of ions experiencesthe discharge as being collision dominated, while the remaining ions cross the sheathcollisionlessly. In figure 3, the described regime is visible for argon at x Xe “ . x Xe “ .
8. Several distinct peaks are visible at low energies that stem fromcharge exchange collisions, and at high energies, the characteristic collisionless bimodalpeak is clearly established. In these cases, particularly, the scaling of the bimodal peakwidth can be observed. For both cases, Xe + ions establish a bimodal peak narrowerthan the bimodal peak formed by Ar + ions. For a fundamental understanding of the energy distribution within the system, theenergy balance model resembled by eqs. (5) - (8) may be used, as shown in figure4. We calculate all parameters and properties by means of a PIC/MCC simulationaveraged over 3000 RF periods. The plot shows two bars for each of the chosen gascompositions. The grey bar on the left-hand side represents the total absorbed energyflux S abs , tot . The colored bars on the right-hand side resolve the different channels ofenergy dissemination in detail. The colors blue (electron energy lost at the electrode on dynamics in Ar/Xe CCPs ε e ), red (averaged energy consumption per e/Ar + -pair ε c , e , Ar ), and green (averagedenergy consumption per e/Xe + -pair ε c , e , Xe ) represent the right-hand side of equation(6). The right-hand side of equation (7) is depicted in pink (Ar + ion energy loss atthe electrode ε i , Ar ` ), cyan (energy loss by isotropic scattering ε is , Ar ` ), and purple(energy loss by backscattering ε cx , Ar ` ). The remaining colors olive (Xe + ion energyloss at the electrode ε i , Xe ` ), brown (energy loss by isotropic scattering ε is , Xe ` ),and orange (energy loss by backscattering ε cx , Xe ` ) visualize the right-hand-side ofequation (8).At first, it is noticeable that figure 4 shows a roughly square-root-shaped increaseof the absorbed energy flux density S abs as a function of the xenon fraction x Xe . Thistrend is a consequence of the boundary conditions in combination with the variedgas composition. The PIC/MCC simulations considered in this work use a single-frequency voltage source as a boundary condition for calculating the electric field. Theenergy flux density is calculated self-consistently according to the plasma state. At lowxenon fractions x Xe , xenon neutrals and Xe + ions successively provide additional lossmechanisms, and the energy consumption increases rapidly. Whereas at higher xenonfractions, xenon already dominates the discharge, and the energy consumption slowlysaturates. Lieberman and Lichtenberg present the scaling law n s S abs [1]. In section3.1, we discussed that the trend of the plasma density n i , tot as a function of the xenonfraction x Xe (comp. fig. 2 a)) is approximated by a parabola. Combined with thesquare-root-shaped trend of the absorbed energy flux density S abs as a function of thexenon fraction x Xe , we see the resulting trend of n i , tot and S abs match the anticipatedscaling.The results calculated for pure argon ( x Xe “ .
0) and pure xenon ( x Xe “ . « . « . ε cx , Ar ` -purple- or ε cx , Xe ` -orange-, resp.) make up for a significantamount of the transferred energy.Both the individual energy transfers of each particle species and the exact resolutionof specific loss channels will in the following prove useful to understand and analyze thedischarge. To make the results comparable, we decide to switch the representation of theenergy flux density S abs from absolute units to relative units (comp. fig. 5). Thereby, on dynamics in Ar/Xe CCPs Figure 5.
The energy balance equations (5) - (8) applied for the background gasvariation. All properties are calculated from a PIC simulation and referred to the totalabsorbed energy flux S abs , tot . All plots show the right-hand side of their correspondingequation in relative units. a) represents equation (5), b) equation (6), c) equation(7) and d) equation (8). (conditions: p gas “ l gap “
25 mm, V RF “
100 V, f RF “ .
56 MHz) we refer to the energy fluxes of each case individually with respect to the total energyflux S abs , tot .Figure 5 shows a rearrangement of the data of figure 4 in the relative representationexplained before. Each of the subplots a) to d) respectively present the right-hand sideof equations (5) to (8). The abscissa of all plots mark energy flux densities in relativeunits, and the ordinates are in units of the gas fractions ( x Xe or x Ar , resp.). The colorschemes for figures 5 b), c), and d) are similar to the ones used in figure 4. Figure 5 a)introduces a new color scheme for the total energy fluxes absorbed by electrons (brightblue), Ar + ions (fuchsia), and Xe + ions (lime green). on dynamics in Ar/Xe CCPs + ions are for a wide rangeof mixtures the dominant ion species. Second, for constant gas pressure, collisionalfeatures of the IEDF depend on the gas composition, and even a collisional/collisionlesshybrid regime can be reached. Both observations are confirmed and explained by theenergy balance. Figure 5 a) shows that for a xenon fraction x Xe between 0.15 and 0.2,Ar + ions and Xe + ions absorb an equal amount of energy (30 % of S abs or « ).Simultaneously, the production of Xe + ions is more effective than the production ofAr + ions. This increased effectiveness is due to the lower ionization energy of xenon( ε thr , Xe “ .
12 eV) compared to argon’s ionization energy ( ε thr , Ar “ . x Xe “ .
2) serves as the best examplefor this finding. There are, with a Xe + ion fraction x Xe ` « . + ions than Ar + ions inside the discharge. Nevertheless, more energy per electron-ion pairis consumed to produce Ar + ions (red) than for the generation of Xe + ions (green) (fig.5 b)). This finding is explained by the lower excitation and ionization levels of xenoncompared to argon. Simultaneously, these lower excitation and ionization levels openup new loss channels for the electrons inside the system. Raising the xenon fraction x Xe yields more and more electrons that are not energetic enough to participate in inelasticprocesses in an argon discharge. Thus, the averaged electron energy ε e drops when goingfrom an argon discharge to a xenon discharge. The decreasing loss term ε e (blue) infigure 5 b) hints at the average electron energy of the system and gives evidence of thisexplanation. All in all, this shows that the production of Xe + ions fills an unoccupiedenergetic niche where numerous low energetic electrons can participate. Therefore, asignificant production of Xe + ions is observed even for low xenon fractions x Xe and Xe + ions are the dominant ion species for the majority of the possible Ar/Xe mixtures.The trends observed in the IEDFs (fig. 3) and the conclusions drawn from thisobservation are confirmed by the energy balance as well (fig. 5 c) and d)). Looking atthe losses due to charge exchange collisions ε cx , i for both Ar + ions (fig. 5 c), purple)and Xe + ions (fig. 5 d), orange), it becomes apparent that the collisional featuresare switched between Ar + and Xe + ions when going towards more argon, or xenonrespectively, dominated gas mixtures. The losses due to charge exchange for Ar + ions ε cx , Ar ` monotonically fall as a function of the xenon fraction x Xe (fig. 5 c), purple) whilethe corresponding term for Xe + ions ε cx , Xe ` monotonically raises, when displayed as thesame relation (fig. 5 d), orange). The slight difference in the trends is explained bythe dominance of the Xe + ions in the discharge. While the density of Xe + ions rapidlyincreases, when adding small amounts of xenon to an argon background (comp. fig.2 a)), the density of Ar + ions vanishes as fast among the dominant Xe + ions. Hence,there are not enough Ar + ions present in discharges dominated by Xe + ions, so that thelosses of Ar + ions in total cannot significantly contribute to the energy absorbed by thedischarge (fig. 5 a), fuchsia).In addition to this, the mean energy of Xe + ions at the electrode ε i , Xe ` shows avery different trend than all the collisional quantities (fig. in 5 d), olive). Instead ofmonotonically rising with the xenon fraction x Xe as the corresponding Ar + term does on dynamics in Ar/Xe CCPs x Ar (comp. fig. 5 c), pink), the Xe + curve shows amaximum at x Xe “ .
4. This maximum is closely connected to the dominance of Xe + ions. At 40 percent xenon admixture ( x Xe “ . + ions already make up for about90 percent of the ions in the discharge (fig. 2 a)). At the same time, argon is thedominant background rendering Xe + ions more or less incapable of doing a relevantamount of charge exchange collisions. This lack of charge exchange collisions is seen inthe IEDF of Xe + ions, that even for a xenon fraction x Xe “ . x Xe , thenumber density n Xe ` and the flux density Γ Xe ` are lower and fewer Xe + ions reach theelectrode. This decrease results in a lower energy loss. For higher xenon fractions x Xe ,the charge transfer collision of Xe/Xe + becomes more and more probable. This trendmanifests in the IEDFs (fig. 3, right) and the trend of the loss term for charge exchange ε cx , Xe ` (fig. 5 d), orange). Thus, the energy loss of Xe + ions to the surface finally dropsbecause the energy gets dissipated more strongly to the neutral gas via charge exchangecollisions.The minimum of the total energy flux density absorbed by electrons S abs , e (fig. 5 a),bright blue) has a similar explanation. For a xenon fraction x Xe “ .
5, electrons absorbthe lowest amount of energy. Under these conditions, Xe + ions make up for almost allthe ions in the discharge. Figure 2 b) shows that for a xenon fraction x Xe “ . + ion fraction x Xe ` is approximately 0.9. At the same time, xenon atoms make upfor just 50 percent of the background gas. The amount of collisions with argon or xenonparticles respectively is, as argued before, significantly reduced compared to mixtureswith a high amount of either of the gases. Thus, for xenon fractions x Xe ă .
5, theproduction of Ar + ions causes electrons to absorb and invest more energy. For xenonfraction x Xe ą .
5, collisions with xenon neutrals become successively more probable,and the production of Xe + ions consumes more energy (comp. fig. 5 b), green) withoutsignificantly changing the discharge conditions any more (comp. fig. 2).Additionally, figure 3 shows that x Xe “ . x Xe ă . + ionsis visibly affected by collisions and vice versa for higher xenon fraction ( x Xe ą . In terms of our simulation, a raised driving voltage equals, if all other parameters (gascomposition, pressure, etc.) are kept constant, raising energy input to the system.Figure 6 a) shows a semi-logarithmic representation of the time and space averagedtotal plasma density n i , tot as a function of the gas fractions ( x Xe or x Ar , resp.). Thedifferent colors differentiate the data for different RF amplitudes (black = 100 V, red =250 V, blue = 500 V, green = 1 kV). The black curve shows the same data as figure 2 a).Due to the aforementioned higher input energy, the plasma density is raised in general on dynamics in Ar/Xe CCPs Figure 6.
The trend of the plasma density while varying the background gascomposition and driving voltage. a) shows the development of the time and spaceaveraged total ion density. b) shows the relative fraction of Xe + ions in the discharge.(conditions: p gas “ l gap “
25 mm, f RF “ .
56 MHz) while the several curves’ general trend is kept. Independent of the driving voltage,argon discharges have a significantly lower plasma density than xenon discharges, andthe transition while varying the gas composition shows the same non-linear trend. Insections 3.1 and 3.2, we discuss that in this context, non-linear means parabolic.Apart from this, a varied driving voltage alters the dominance of Xe + ions. Figure6 b) shows a similar plot to figure 2 b). The Xe + ion fraction is presented as a functionof the gas fraction ( x Xe or x Ar , resp.). The colors have the same meanings as in figure 6a), and the black curve was also presented before (see fig. 2 b)). Figure 6 b) shows that,for a fixed xenon fraction x Xe , a raised voltage reduces the fraction of Xe + ions x Xe ` present in the discharge. The case for x Xe “ . + ions x Xe ` drops from approximately 0.7 to roughly 0.6.Once again, the energy balance (fig. 7) explains the discharge mechanisms governinghow an increased driving voltage raises the plasma density. Similar to figure 5, termson the right-hand side of the energy balance equations (5) - (8) are shown in relativeunits and as a function of the gas fractions ( x Xe or x Ar , resp.). In contrast to figure 5,each panel of figure 7 represents just one term of the respective equation’s right-handside. The different curves represent data for different driving voltages V RF , ranging from V RF “
100 V to V RF “ S abs , e ) in bright blue. Figure7 b) depicts the total energy flux density absorbed by Ar + ions ( S abs , Ar ` ) in fuchsia, andfigure 7 c) presents the total energy flux density absorbed by Xe + ions ( S abs , Xe ` ) in limegreen. Together figures 7 a) - c) show the right-hand side of equation (5). Therefore, on dynamics in Ar/Xe CCPs Figure 7.
The energy balance equations (5) - (8) applied for both the variation ofthe background gas and the driving voltage V RF . All properties are calculated from aPIC simulation and referred to the total absorbed energy flux S abs , tot . All plots showone term on the right-hand side of their corresponding equation in relative units. a)shows the electron’s part S abs , e of eq. (5). a ) - a ) show the three terms of equation(6) and add up to the respective curve of a). b) represents the Ar + ions’ part S abs , Ar ` of equation (5). b ) - b ) present the three terms of equation (7) and sum up to therespective curve of b). c) shows the Xe + ions’ part S abs , Xe ` of equation (5). c ) - c )depict the three terms of equation (8), and their addition gives the respective curve ofc). (conditions: p gas “ l gap “
25 mm, f RF “ .
56 MHz) on dynamics in Ar/Xe CCPs S abs , tot , resp.). Vertically the details of each particle species’ powerabsorption are presented. Figures 7 a ) - a ) each show one term of the right-hand sideof equation (6). The average energy loss of electrons at the electrodes ε e is shown infigure 7 a ) in blue. The averaged amount of energy needed to create an electron/Ar + ion pair ( ε c , e , Ar ) is found in panel a ) in red, and the related term for electron/Xe + ionpairs ( ε c , e , Xe ) is depicted in panel a ) in green. The individual terms of the right-handside of equation (7) are shown in figures 7 b ) - b ). They reveal the details of the Ar + ion dynamics by presenting the average energy loss by Ar + ions at the electrodes ( ε i , Ar ` ,fig. 7 b ), pink), the energy loss of Ar + ions caused by isotropic scattering ( ε is , Ar ` , fig.7 b ), cyan), and the energy loss of Ar + ions due to backscattering ( ε cx , Ar ` , fig. 7 b ),purple). Similarly, figures 7 c ) - c ) show the right-hand side of equation (8). Theyunravel the details of the Xe + ion dynamics by showing the average impingement energyof Xe + ions at the electrodes ( ε i , Xe ` , fig. 7 c ), olive), the energy lost by Xe + ions inisotropic scattering collisions ( ε is,Xe ` , fig. 7 c ), brown), and the energy lost by Xe + ionin backscattering collisions ( ε cx,Xe ` , fig. 7 c ), orange). Vertically, the sum of the datain the subscript labeled panels gives the curves of the non-subscript labeled one (e.g.,panels a ) - a ) sum-up to panel a)).In general, it is apparent that a raised driving voltage reduces the ratio of energycoupled to the electrons (fig. 7 a)) and raises the fraction absorbed by both Ar + andXe + ions (fig. 7 b) or fig. 7 c), resp.). The increased energy consumption into the ioncontribution mainly consists of two parts. First, a raised driving voltage V RF increasesthe voltage drop across the boundary sheaths, and ions gain higher impingement energiesafter crossing the sheath collisionlessly. This is shown in figure 7 b ) for Ar + ions andin figure 7 c ) for Xe + ions. Second, an increased energy gain for the ions inside thesheath goes along with an increased energy loss caused by charge exchange collisions.The corresponding terms ε cx , Ar ` for Ar + ions (fig. 7 b )) and ε cx , Xe ` for Xe + ions (fig.7 c )) support this hypothesis. Furthermore, the cross sections for charge exchangedominate the ones for isotropic scattering at high energies (comp. fig. 1 c) and d)).Correspondingly, the already low energy losses by Ar + ions ( ε is , Ar ` , fig. 7 b )) and Xe + ions ( ε is , Xe ` , fig. 7 c )) caused by isotropic scattering decrease due to the increaseddriving voltage V RF . The maximum of figure 7 c ) was discussed in section 3.2. Theenergy-efficient production of Xe + ions already creates a high amount of Xe + ions forsmall xenon fractions x Xe . Thus, there are optimal parameters for Xe + ions to bombardthe surface with the least collisional loss ( x Xe “ . V RF “
100 V, sec. 3.2). Theaforementioned enhanced role of backscattering and decreased influence of isotropicscattering causes the optimal parameters for higher driving voltages V RF to shift tohigher xenon fractions x Xe (e.g., X Xe “ . V RF “ )).In terms of ion production, the previous assessment shows that the higher thedriving voltage is set, the smaller the fraction of the energy consumed for creating newelectron/ion pairs becomes. Furthermore, the maximal amount of energy consumed forcreating Xe + ions in a pure xenon background ( x Xe “ .
0, fig. 7 a )) is always lower than on dynamics in Ar/Xe CCPs Figure 8.
The trend of the ion densities while varying the background gas compositionand driving voltage. a) shows the development of the time and space averaged Ar + ion density. b) shows the development of the time and space averaged Xe + ion density.(conditions: p gas “ l gap “
25 mm, f RF “ .
56 MHz) the corresponding maximum for Ar + ions in a pure argon background ( x Ar “ .
0, fig. 7a )). As argued before, this finding correlates with the fact that the threshold energiesof all inelastic processes involving xenon are significantly lower than those involvingargon. This observation additionally reveals why Xe + ions dominate the discharge formost conditions. It becomes best visible by comparing the pure argon case ( x Xe “ . )) with the pure xenon case ( x Xe “ .
0, fig. 7 a )) for a driving voltage of1 kV. Here, roughly eight percent of the total energy flux density is used to producean electron/Ar + ion pair (fig. 7 a )). For the corresponding pure xenon case, only fivepercent of the total energy is used to produce an electron/Xe + ion pair (fig. 7 a )).Simultaneously, the xenon case’s plasma density is more than one order of magnitudehigher than in the argon case (comp. fig. 6 a)).Since the production of Xe + ions remains more effective for all applied drivingvoltages, there has to be another reason why the dominance of Xe + ions is reduced. Aclose examination of figures 7 a ) and 8 explains the observed. Both panels of figure8 are similar in structure to figure 6 a), but show the individual ion densities ( n Ar ` infig. 8 a) or n Xe ` in fig. 8 b), resp.) as a function of the gas fraction ( x Xe or x Ar , resp.).The different colors again mark different values of the driving voltage V RF , and the colorscheme is the same as in figure 6 a). The trend of the Ar + ion density in figure 8 a)already reveals the underlying process responsible for the decreased dominance of Xe + ions. Even for the base case ( V RF “
100 V), the maximum of the density of Ar + ions isfound for a xenon fraction x Xe “ . x Xe “ . + ions (comp. fig. 8). This maximum is shifted by a raised drivingvoltage to a xenon admixture of 30 percent ( x Xe “ .
3, fig. 8 a)). Recalling figure 6 a), it on dynamics in Ar/Xe CCPs + ions is higher than in a discharge without xenon admixture. This effect affects theAr + ions for low voltages as long as most neutrals are argon atoms. A raised drivingvoltage shifts the maximum of the Ar + ion density and the benefits of this synergy effectto higher xenon fractions.For Xe + ions, on the other hand, this synergy effect cannot be observed (fig. 8 b)).This observation is due to the higher ionization energy of argon. Figure 7 a ) helps tounderstand this observation by showing the energy lost by electrons at the electrodes ε e . The general trend of the curves for ε e is a reduction by a raised driving voltage (fig.7 a )). An equivalent conclusion is that energy is dissipated more efficiently inside thevolume of the discharge. In terms of our non-equilibrium low-pressure discharge, thereare just two ways for electrons to lose energy. Either they interact inelastically with thebackground or transfer their energy to the surface by arriving at the electrodes. The firstoption was discussed before (fig. 7 a ) and a )), and the second option is discussed here.Both processes similarly respond to the increased driving voltage, which means that ahigher driving voltage increases the ion production efficiency. Simultaneously, the energydissemination efficiency is increased the more xenon is added to the background gas. Insection 3.1, we discuss that an increased amount of xenon atoms in the discharge provideslower energetic electrons with the opportunity to get involved in inelastic processescompared to a discharge with lower or no xenon addition (see fig. 5 d)). In figure 7 a ),the same trend is observed for all depicted driving voltages. As a function of the xenonfraction x Xe , the energy lost by electrons at the electrode ε e is monotonically falling.Vice versa, argon has higher thresholds for inelastic processes, especially ionization, thanxenon (comp. tab. 1). Thus, adding argon to a xenon background cannot produce ahigher electron density that would cause more ionization of xenon. The synergy effectdoes not take place for Xe + ions that benefit from additional ionization of argon.Figures 9 and 10 show, similar to figure 3, IEDFs normalized to the respectiveparticle flux densities at the electrode surface. The difference between figure 9 and 10is in the gas composition (fig. 9: x Xe “ .
1, fig. 10 x Xe “ . + ions in the left column panels and IEDFs for Xe + ions in the right one.The difference between each figure’s four rows is the altered amplitude of the RF voltage V RF given on each panel’s top. Panels of the same row share the same voltage.The figures show that for the IEDF, a raised driving voltage, first of all, meansthat the averaged sheath voltage x φ s y increases. This increase manifests in the widthof the characteristic collisionless single bimodal peak. Its width scales with V RF and a x φ s p t qy { x s p t qy [28, 78]. Kawamura et al. [28] give the averaged sheath width x s p t qy in on dynamics in Ar/Xe CCPs Figure 9.
Ion energy distribution function (IEDF) at the electrode for different drivingvoltages. The left column shows distribution functions for Ar + ions. The correspondingdistributions for Xe + ions are on the right side of the plot. (conditions: p gas “ x Xe “ . l gap “
25 mm, f RF “ .
56 MHz) terms of the collisionless Child-Langmuir law: x s p t qy “ ˆ em i ˙ { ˆ ε x j i p t qy ˙ x φ s p t qy { (9)with e the elementary charge, m i the ion mass, ε the vacuum permitivity, and x j i p t qy theaveraged ion current inside the sheath. For argon, the increased bimodal peak’s widthis found in figure 10 (left) and for xenon in figure 9 (right). From top ( V RF “
100 V) to on dynamics in Ar/Xe CCPs Figure 10.
Ion energy distribution function (IEDF) at the electrode for differentdriving voltages. The left column shows distribution functions for Ar + ions. Thecorresponding distributions for Xe + ions are on the right side of the plot. (conditions: p gas “ x Xe “ . l gap “
25 mm, f RF “ .
56 MHz) bottom ( V RF “ + ions: fig. 10 left, Xe + ions: fig. 9 right).At the same time, a higher driving voltage at a constant pressure produces higherenergetic ions. Higher kinetic energy enlarges the mean free path of those ions sincethe mean free path is energy-dependent [2] and the collision cross sections fall at highenergies (see fig. 1). Thus, the distance between the peaks in the low energetic part ofthe IEDFs that are connected to charge exchange collisions is increased with the driving on dynamics in Ar/Xe CCPs V RF “
500 Vand V RF “ + (fig. 9) and Xe + ions (fig. 10). Here,charge exchange collisions are responsible for the appearance of the low energetic peak.Section 3.1 discusses that low energetic peaks vanish for Ar + ions when the xenonfraction x Xe is raised and vice versa. For a second or third bimodal peak to establish,two requirements have to be met. First, ions have to be able to react to the sheathelectric field. Second, there has to be some sort of hybrid regime that we discussedin section 3.1. Combining these requirements also means that only charge exchangecollisions that happen clearly above the averaged sheath position can establish anadditional bimodal structure. Under these conditions, the slow ions produced throughcharge exchange experience the sheath’s modulation that eventually determines theirimpingement energy. A charge exchange collision inside the sheath during the collapsingphase causes the ions to gain slightly lower impingement energy than a charge exchangeduring the expanding sheath phase.According to Lieberman and Lichtenberg [1], there is a weak dependency betweenthe average position of the sheath edge and the voltage amplitude ( s m V { ). Thus,it is more likely for the collisional structures of IEDFs at higher voltages to showbimodal structures. The IEDFs of Xe + ions at a xenon fraction x Xe “ . V RF “
100 V, the resultsclearly show a single bimodal peak and several non-bimodal charge exchange peaks. For V RF “
250 V, the main bimodal peak is centered around «
110 eV, and at least oneadditional bimodal peak around 87 eV is visible. At 500 V, the IEDF has at least fourbimodal peaks (centered around «
130 eV, «
170 eV, «
180 eV, and «
210 eV). The casefor V RF “ «
190 eV, «
260 eV, «
325 eV, and «
410 eV). For that case, solely charge exchange collisions thattake place deep inside the boundary sheath and close to the electrode do not show anysign of bimodal features.The hybrid regime of the IEDFs itself is also influenced by a raised driving voltage V RF . For a voltage amplitude V RF “
250 V, a slightly higher voltage than that of thebase case, the hybrid regime appears for lower admixtures of xenon (fig. 9) or argon,respectively (fig. 10). Here, the broadening and amplification effects of a raised drivingvoltage prevail. Thus, the hybrid regime establishes earlier than for lower voltages.The IEDFs for even higher driving voltages (see V RF “
500 V and V RF “ + (fig. 9) and Xe + ions (fig.10) are damped compared to the lowest energetic peaks. This trend arises from the factthat the cross section for charge exchange collisions for high energies drops much slowerthan the cross sections for isotropic scattering (comp. fig. 1 c) and d)). Therefore, on dynamics in Ar/Xe CCPs
4. Conclusion
The objective of this work was to investigate the ion dynamics of plasmas containing twoion species. This investigation was conducted by simulating a low-pressure capacitivelycoupled plasma with a mixture of argon and xenon as the background gas. The overallresult is that the gas composition serves as a means to control the collisionality ofthe ion species and thus the ion dynamics. Section 3.1 shows that the gas composition(more specifically the argon fraction x Ar or xenon fraction x Xe , respectively) significantlyaffects the discharge, especially the ion dynamics. The effect on the discharge resemblesa parabolic function of the plasma density and the xenon fraction x Xe (comp. fig. 2).A complete energy balance that we self-consistently calculate based on a PIC/MCCsimulation helps understand this effect. Inelastic processes in xenon (e.g., ionizationwith ε i , Xe “ .
12 eV) have significantly lower energetic thresholds. Thus, electronsdistribute their energy more efficiently when the xenon fraction x Xe is raised. We showthat especially the ionization process in xenon is energetically more favorable than inargon. This disparity leads to Xe + ions being the dominant ion species for a broad rangeof xenon fractions x Xe .For the ion dynamics, we present that the gas composition controls the collisionalcharacteristics of the IEDF. Between argon and xenon, only non-resonant charge transfercollisions are possible. Three-body collisions do not occur in relevant amounts in thelow-pressure regime. Therefore, a varied xenon fraction x Xe shifts the multiple lowenergetic peaks (characteristic for charge exchange and a collision dominated regime)from argon (most pronounced at x Xe “
0, fig. 3 left) to xenon (most pronounced at x Xe “
1, fig. 3 right). Additionally, a collisional/collisionless hybrid regime is present forspecific gas fractions. Some ions experience the discharge within this hybrid regime ascollision dominated while others traverse the boundary sheath without collisions. Theanalysis of the energy balance helps to understand these effects as well. It reveals thatcharge exchange is, even at low-pressures, a relevant energy loss process for ions. Araised xenon fraction x Xe depletes (Ar + ions) or contributes to (Xe + ions) this processfor the respective ions (fig. 5). Thus, the addition of xenon increases (Ar + ions) ordecreases (Xe + ions) the impingement energies of the respective ions. Furthermore,the energy balance reveals optimal parameters for the impingement energy of ions inthis mixture. In this context, optimal refers to overall minimal collisional losses for theions, thus desirable conditions for processes (e.g., ion-assisted etching). For x Xe “ . V RF attenuates the dominance of the Xe + ions(sec. 3.3). The reason for this observation is a synergy effect. The argon’s ionization on dynamics in Ar/Xe CCPs + but not Xe + . Furthermore, it is presentedthat the increased driving voltage V RF intensifies structures (e.g., broadens the width ofbimodal peaks) and further complicates the IEDFs (e.g., by creating multiple bimodalpeaks). The energy dependence of the cross section for charge exchange causes thehybrid regime to shift to different mixing ratios when solely varying the driving voltage.Both observations are supported by the analysis of the energy balance too. Overall,the energy balance has proven to be a practical and impactful diagnostic. The resultsof section 3.3 show that the gas composition controls the ion dynamics over a widerange of driving voltages. However, the effect of varied gas compositions is not entirelyindependent of the driving voltage.Future work based on this study will develop in two directions. On the one hand,the model system Ar/Xe needs to be left behind. The presented basic principles haveto be investigated in more complex and process relevant gas mixtures like Ar/CF orCF /H . The energy balance model can be adapted to and should be tested for thesegas mixtures. On the other hand, based on this work’s findings, the influence of acombination of multi-frequency discharges and a varied gas composition on the iondynamics should be investigated. For example, a multi-frequency approach could beused to optimize the ion production, which at V RF “
100 V was found to be optimal fora xenon fraction x Xe “ .
4, further.Another open research question is: How does the addition of secondary electronemission and realistic surface coefficients alter the ion dynamics? The argon ionization’ssynergy effect, especially, could be significantly affected when secondary electrons causean amplification of the ionization process. To our best knowledge, there are no publishedexperimental results that analyze the influence of the gas mixture on the IEDFs. Norare there studies that experimentally report about the hybrid regime or the synergyeffect within the ionization of argon. All of these studies would be crucial to validateour findings and simulation.
Acknowledgments
This work was supported by the German Research Foundation (DFG) via CollaborativeResearch Centre CRC 1316 (Project ID: 327886311), Transregio TRR87 (Project-ID:138690629), and project MU 2332/6-1.
ORCID IDs
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