A Linear Microwave Plasma Source Using a Circular Waveguide Filled

applied sciences

Article A Linear Microwave Plasma Source Using a Circular Waveguide Filled with a Relatively High-Permittivity Dielectric: Comparison with a Conventional Quasi-Coaxial Line Waveguide

Ju-Hong Cha, Sang-Woo Kim and Ho-Jun Lee *

Department of Electrical Engineering, Pusan National University, Busan 46241, Korea; [email protected] (J.-H.C.); [email protected] (S.-W.K.) * Correspondence: [email protected]

Abstract: For a conventional linear microwave plasma source (LMPS) with a quasi-coaxial line transverse electromagnetic (TEM) waveguide, a linearly extended plasma is sustained by the surface wave outside the tube. Due to the characteristics of the quasi-coaxial line MPS, it is easy to generate a uniform plasma with radially omnidirectional surfaces, but it is difﬁcult to maximize the electron density in a curved selected region. For the purpose of concentrating the plasma density in the deposition area, a novel LMPS which is suitable for curved structure deposition has been developed

and compared with the conventional LMPS. As the shape of a circular waveguide, it is ﬁlled with relatively high-permittivity dielectric instead of a quasi-coaxial line waveguide. Microwave power at

Citation: Cha, J.-H.; Kim, S.-W.; Lee, 2.45 GHz is transferred to the plasma through the continuous cylindrical-slotted line antenna, and H.-J. A Linear Microwave Plasma the radiated electric ﬁeld in the radial direction is made almost parallel to the tangential plane of Source Using a Circular Waveguide the window surface. This research includes the advanced 3D numerical analysis and compares the Filled with a Relatively results with the experiment. It shows that the electron density in the deposition area is higher than High-Permittivity Dielectric: that of the conventional quasi-coaxial line plasma MPS. Comparison with a Conventional Quasi-Coaxial Line Waveguide. Appl. Keywords: microwave plasma; linear microwave plasma source; three-dimensional plasma ﬂuid Sci. 2021, 11, 5358. https://doi.org/ simulation 10.3390/app11125358

Academic Editor: Mohammed Koubiti 1. Introduction Microwave plasma sources (MPSs) are driven by applied frequencies of 1–100 GHz and Received: 8 May 2021 lead to electron heating and excitation of a discharge from the electromagnetic waves that Accepted: 3 June 2021 Published: 9 June 2021 either penetrate the plasma or exist along the surface [1,2]. With weakly ionized MPS used for material processing, waves are important to transfer energy from the excited surface of

Publisher’s Note: MDPI stays neutral the waveguiding structure to the bulk plasma, where the wave energy is absorbed [3]. The with regard to jurisdictional claims in main element of the MPS, for material processing, is the microwave-to-plasma applicator published maps and institutional affil- because it determines the structure of the electromagnetic field in the plasma as well as iations. the absorption energy efficiency of plasma [4]. The structure of the electromagnetic field in plasma is determined by the correlation of the internal plasma parameters (electron density, plasma frequency, etc.) and the external source parameters (waveguide structure, size of source, frequency, etc.). The energy absorption efficiency of MPS is determined by the wave penetration depth in the plasma, wave field strength at the plasma surface, and Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. waveguiding structure. This article is an open access article Among the MPS for material processing, the sources generally have a form in which distributed under the terms and waves propagate along the transmission lines. The plasma is generated by the waves conditions of the Creative Commons emitted from the dielectric surface which replaces a part of the waveguiding structure. Attribution (CC BY) license (https:// Depending on the size and structure of the dielectric surface, plasma sources using the creativecommons.org/licenses/by/ transmission line field can be classified in the following ways: (i) plasma is a part of 4.0/). the waveguiding structure (transmission line applicators) and (ii) plasma is sustained

Appl. Sci. 2021, 11, 5358. https://doi.org/10.3390/app11125358 https://www.mdpi.com/journal/applsci Appl. Sci. 2021, 11, x FOR PEER REVIEW 2 of 20

Appl. Sci. 2021, 11, 5358 transmission line field can be classified in the following ways: (i) plasma is a part of2 the of 20 waveguiding structure (transmission line applicators) and (ii) plasma is sustained by the field leaking out of the structure (antenna applicators) [5]. For the transmission line applicator,by the field the leaking cross section out of theof structurethe plasma–dielectric (antenna applicators) contact is [5wide,]. For whereas the transmission for the antennaline applicator, applicator, the the cross plasma–dielectric section of the plasma–dielectric contact cross section contact is narrow. is wide, So, whereas in the for case the ofantenna antenna applicator, applicator, the the plasma–dielectric process stability is contact high since cross the section wave ispropagation narrow. So, mode in the and case theof resonant antenna applicator,cavity in the the waveguiding process stability structure is high are since less theaffected wave by propagation plasma generation. mode and Hence,the resonant in material cavity processing, in the waveguiding which requires structure stable areplasma less affectedoperation, by antenna plasma applicator generation. typeHence, MPSs in are material preferred. processing, which requires stable plasma operation, antenna applicator typeAmong MPSs arethe preferred.antenna apllicator type MPS, LMPSs are mainly used for large area processingAmong [6]. theErstwhile antenna LMPS apllicator models type [7] MPS,were LMPSseither in are the mainly form of used discharge for large tubes area placedprocessing inside [ 6the]. Erstwhileguiding structure LMPS models or in th [7]e wereform eitherof discharge in the formtubes of across discharge the wide tubes waveguideplaced inside wall the parallel guiding to structurethe electric or field in the [8,9]. form However, of discharge in terms tubes of across productivity the wide improvementwaveguide walland large parallel area to material the electric processing, field [8 ,the9]. shape However, of the in discharge terms of tubes productivity inside theimprovement guiding structure and large is not area suited material for the processing, application, the so shapethe shape of the of the discharge discharge tubes outside inside thethe guiding guiding structure structure is is notdemanded. suited for A the SW application, sustained sosource the shape called of the the duo-plasma discharge outside line source,the guiding which structureuses the quasi-coaxial is demanded. line A TEM SW sustained wave mode, source was calledinvented the according duo-plasma to the line shapesource, of the which discharge uses the outside quasi-coaxial the tube linewith TEM a waveguiding wave mode, structure was invented [10,11]. according Due to the to highthe shapescalability of the with discharge a large outside processing the tube area with [12,13], a waveguiding duo-plasma structure line source [10, 11has]. Duebeen to appliedthe high to scalabilitymany plasma with enhanced a large processing chemical vapor area [ 12deposition,13], duo-plasma (PECVD) line processes source hassuch been as hardapplied coating, to many thin plasmafilm, synt enhancedhesis of chemicalgraphene, vapor and display deposition panels, (PECVD) which processes require a such large as area,hard an coating, operation thin pressure film, synthesis of 0.2~3Torr, of graphene, and high and speed display processes panels, [14–17]. which require a large area,In anthe operation quasi-coaxial pressure line ofTEM 0.2~3 wave Torr, mode, and highthe isotropically speed processes emitted [14– transverse17]. wave field fromIn the the quasi-coaxial inner conductor line TEM is perpendicular wave mode, theto the isotropically tangential emitted plane of transverse the window wave field from the inner conductor is perpendicular to the tangential plane of the window surface in all radial directions, and the dielectric surface in all radial directions is exposed surface in all radial directions, and the dielectric surface in all radial directions is exposed to interact with the plasma generation. Therefore, it is easy to generate a uniform plasma to interact with the plasma generation. Therefore, it is easy to generate a uniform plasma in in the radially omnidirectional plasma–dielectric window surfaces. However, it is difficult the radially omnidirectional plasma–dielectric window surfaces. However, it is difficult to to maximize the process productivity by concentrating the plasma density in a one- maximize the process productivity by concentrating the plasma density in a one-directional directional selected deposition region. In this study, for the purpose of concentrating the selected deposition region. In this study, for the purpose of concentrating the plasma plasma density in the selective area, a cylindrical slotted LMPS that had a high electron density in the selective area, a cylindrical slotted LMPS that had a high electron density in density in a specific deposition region was proposed and was compared with the quasi- a specific deposition region was proposed and was compared with the quasi-coaxial LMPS. coaxial LMPS. The shape of the discharge outside the guiding structure [18–20], The shape of the discharge outside the guiding structure [18–20], cylindrical-slotted LMPS cylindrical-slotted LMPS was excited by feeding power in the circular TE11 mode. was excited by feeding power in the circular TE11 mode.

2.2. Plasma Plasma Source Source Overview Overview

BothBoth quasi-coaxial quasi-coaxial line line TEM TEM and and circular circular TE11 TE LMPS11 LMPSss were were fabricated fabricated to compare to compare the characteristicsthe characteristics of plasma of plasma generation generation accordin accordingg to the waveguiding to the waveguiding structure structure and the and wave the fieldwave direction. field direction. The circular The circular TE11 wave TE11 modewave was mode compared was compared with quasi-coaxial with quasi-coaxial line TEM line mode,TEM mode,as shown as shown in Figure in Figure 1. In1 the. In thefigure, figure, the thedashed dashed and and straight straight lines lines represent represent the the magneticmagnetic and and electric electric fields, fields, respectively. respectively.

FigureFigure 1. 1.FieldField lines lines at atradial radial cross-section cross-section for forquasi-coaxial quasi-coaxial TEM TEM and and circular circular TE11 TE waveguiding11 waveguiding structure. (a) Quasi-coaxial TEM linear MWP and (b) circular TE11 waveguiding structure. structure. (a) Quasi-coaxial TEM linear MWP and (b) circular TE11 waveguiding structure.

In the circular waveguide, with the diameter determined, the wave frequency must exceed the cut-off frequency of propagation. Among the lower order modes of circular waveguides, there are the TE11 and TE01 wave modes, in which the transverse electric ﬁeld Appl. Sci. 2021, 11, x FOR PEER REVIEW 3 of 20

Appl. Sci. 2021, 11, 5358 In the circular waveguide, with the diameter determined, the wave frequency must3 of 20 exceed the cut-off frequency of propagation. Among the lower order modes of circular waveguides, there are the TE11 and TE01 wave modes, in which the transverse electric field direction is formed parallel to the quartz window surface. In the circular waveguide of direction is formed parallel to the quartz window surface. In the circular waveguide of the the same specification, the cut-off frequency of TE01 is twice more than that of the TE11 same speciﬁcation, the cut-off frequency of TE01 is twice more than that of the TE11 wave wave mode. Therefore, it is easier to use the TE11 mode with a lower cut-off frequency mode. Therefore, it is easier to use the TE11 mode with a lower cut-off frequency when the whenfrequency the frequency is ﬁxed at is 2.45 fixed GHz at 2.45 and GH thez waveguide and the waveguide radius is lowradius [1]. is low [1].

3.3. Experiment Experiment Experiment SetupSetup BasedBased onon thethe correlations correlations with with the plasmathe plas characteristicsma characteristics [21], the geometry[21], the parametersgeometry parametersfor the waveguiding for the waveguiding structure were structure set to improve were theset powerto improve transfer the efﬁciency power fromtransfer the efficiencywave generator from the to thewave plasma generator region. to In the the pl quasi-coaxialasma region. line In TEMthe quasi-coaxial waveguiding line structure, TEM waveguidingmicrowave power structure, was deliveredmicrowave through power awas TE/TEM delivered coupler through which a wasTE/TEM bent atcoupler 90◦, as whichshown was in Figurebent at2 a.90°, as shown in Figure 2a.

FigureFigure 2. 2. SchematicSchematic diagram diagram of of microwave microwave plasma plasma source. source. (a ()a )Quasi-coaxial Quasi-coaxial TEM TEM linear linear MWP MWP and and

(b(b) )circular circular TE TE1111 waveguidingwaveguiding structure. structure.

ToTo maximize maximize the the power power transfer transfer ratio ratio when when converting converting from from a arectangular rectangular TE TE10 10to toa quasi-coaxiala quasi-coaxial line line TEM TEM waveguiding waveguiding structure, structure, a rod-shaped a rod-shaped antenna antenna was wasplaced placed in the in fieldthe fieldconcentration concentration region. region. The Therod-shaped rod-shaped antenna antenna was was made made of ofcopper copper as as an an inner inner conductor.conductor. The The diameter diameter of ofthe the inner inner conductor conductor was was 9 mm, 9 mm, and andthe axial the axial length length was 600 was mm.600 mm.The microwave The microwave propagated propagated mainly mainly in the space in the between space between the inner the rod inner and rod the andquartz the tube.quartz The tube. space The between space between the inner the innerconductor conductor and andthe thequartz quartz tube tube was was filled filled with with atmosphericatmospheric pressure pressure for for the the device device cooling cooling by by the the flow flow of of compressed compressed air air [10]. [10]. Inside Inside the the plasmaplasma chamber, chamber, quartz quartz window window was was placed placed to to separate separate the the field field generator generator and and plasma plasma excitation region which is filled with argon gas at low pressure. The quartz window excitation region which is filled with argon gas at low pressure. The quartz window 𝜖 = 4e r was= 4 designedwas designed with an with inner an diameter inner diameter of 32 mm, of 32 a mm,thickness a thickness of 2 mm, of and 2 mm, a total and length a total oflength 550 mm of 550 in mmthe axial in the direction. axial direction. The compressive The compressive strength strength of the ofquartz the quartz window window was 2 2 117,000was 117,000 kg/cm kg/cm2, the Young, the Youngmodulus modulus was 73,900 was kg/mm 73,9002 kg/mm, and the, tensile and the strength tensile was strength 510 2 kg/cmwas 5102, which kg/cm could, which sustain could sustainthe mechanical the mechanical load loadwithout without deformation deformation in in the the correspondingcorresponding axial axial length. length. The The plasma plasma was was ignited ignited by by the the excitation excitation of of a a discharge discharge from from thethe electromagnetic electromagnetic waves waves that that penetrate penetrate or or exist exist along along the the quartz quartz window window surface. surface. The propagation wave mode was converted from the rectangular TE10 wave mode The propagation wave mode was converted from the rectangular TE10 wave mode to to the circular TE11 wave mode as shown in Figure2b. In the circular TE 11 waveguiding the circular TE11 wave mode as shown in Figure 2b. In the circular TE11 waveguiding structure, microwave power was transferred to the plasma through the continuous cylin- structure, microwave power was transferred to the plasma through the continuous drical slot antenna along the wave propagation direction. The circular waveguide was cylindrical slot antenna along the wave propagation direction. The circular waveguide made of copper material with an inner diameter of 30 mm and a thickness of 1 mm. In the was made of copper material with an inner diameter of 30 mm and a thickness of 1 mm. cylindrical slotted waveguiding structure, the cut surface of the circular TE11 waveguide In the cylindrical slotted waveguiding structure, the cut surface of the circular TE11 was cut to a radial thickness of 10 mm along with an axial length of 500 mm from the waveguide was cut to a radial thickness of 10 mm along with an axial length of 500 mm entrance of the plasma chamber to the end of the continuous axis. The quartz window from the entrance of the plasma chamber to the end of the continuous axis. The quartz and plasma generation process were set to be the same as in Figure2a. When the inner diameter of the circular waveguide was 30 mm and was filled with free space material characteristics, the cut-off frequency in the circular waveguide was approximately 5.9 GHz. For the circular waveguide of 30 mm diameter, it was necessary to lower the cut-off fre- Appl. Sci. 2021, 11, x FOR PEER REVIEW 4 of 20

window and plasma generation process were set to be the same as in Figure 2a. When the inner diameter of the circular waveguide was 30 mm and was filled with free space material characteristics, the cut-off frequency in the circular waveguide was Appl. Sci. 2021, 11, 5358 approximately 5.9 GHz. For the circular waveguide of 30 mm diameter, it was necessary4 of 20 to lower the cut-off frequency below 2.45 GHz for the wave propagation in the applied frequency. Accordingly, a rod type (diameter = 30 mm, 𝜖 =9) alumina was inserted insidequency the below circular 2.45 GHzwaveguiding for the wave structure, propagation and the in thecut-off applied frequency frequency. was Accordingly, reduced to a third of 5.9 GHz. rod type (diameter = 30 mm, er = 9) alumina was inserted inside the circular waveguiding structure,To compare and the the cut-off source frequency characteristics, was reduced experiments to a third were of 5.9conducted GHz. under 500mTorr Ar plasmaTo compare condition the source where characteristics, 0.6 kW microwave experiments power were was conductedapplied. The under experimental 500 mTorr systemAr plasma used condition for this wherestudy 0.6is shown kW microwave in Figure power3. Continuous was applied. wave The (CW) experimental power at 2.45 sys- GHztem used was fortransmitted this study from is shown a magnetron in Figure3 .(ASTEX Continuous MKS wave Fl20608-3kW (CW) power Mag at Head, 2.45 GHz ASTEX was Smarttransmitted Match from Fl20606-3kW) a magnetron to (ASTEXthe waveguide MKS Fl20608-3kW mode converter Mag by Head, a rectangular ASTEX Smart TE10 Match wave modeFl20606-3kW) through to the the WR340 waveguide waveguide. mode converter The power by asupply rectangular (MKS TE Smart10 wave Power mode generator through Fl20160-1-3kW)the WR340 waveguide. was connected The power to a three-phas supply (MKSe line Smart and outputted Power generator 300–3000Fl20160-1-3kW W. As shown) inwas Figure connected 3, the to microwave a three-phase transmission line and outputted line from 300–3000 the generator W. As shownto the plasma in Figure includes3, the mi- a WR340crowave 3-Stub transmission tuner, dummy line from load the generator(Fl20164), to and the circulator plasma includes (AX3161) a WR340 as the 3-Stub product tuner, of Nationaldummy loadElectronics. (Fl20164), and circulator (AX3161) as the product of National Electronics.

Figure 3.3. Schematic of thethe experimentalexperimental systemsystem showingshowing thethe microwavemicrowave couplingcoupling arrangement.arrangement. (a) Quasi-coaxialQuasi-coaxial TEMTEM linear MWPMWP andand ((b)) circularcircular TETE1111 waveguiding structure.

In the the circular circular TE 11 LMPS,LMPS, the the microwave microwave transmission transmission line from from the power generator to the waveguide mode converter was same as that of thethe quasi-coaxialquasi-coaxial waveguidingwaveguiding structure, as shown in Figure3 3.. InIn thethe circularcircular waveguidingwaveguiding structure,structure, WR340WR340 twistedtwisted waveguide was used to set the electric fieldfield in the required direction because the plasma interacting surface typically faced the depositiondeposition region, and the waveguidingwaveguiding structure was changed from a rectangular WR340 waveguide to a circularcircular waveguidingwaveguiding structure through a homemade rectangular to a circular waveguidewaveguide converter.converter. For thethe experimentexperiment with with the the linear linear MWP MWP source, source, a cylindrical a cylindrical chamber chamber with a diameter with a of 500 mm and a height of 150 mm was fabricated, as shown in Figure4a,b. The microwave diameter of 500 mm and a height of 150 mm was fabricated, as shown in Figure 4a,b. The power was designed to propagate along the straight line in the quartz tube. To increase microwave power was designed to propagate along the straight line in the quartz tube. the spatial uniformity of the gas flow, a showerhead type gas inlet structure was used, To increase the spatial uniformity of the gas flow, a showerhead type gas inlet structure which was located opposite to the deposition region, 40 mm away from the quartz window was used, which was located opposite to the deposition region, 40 mm away from the surface. The images of the plasma generated near the window surface were taken, as quartz window surface. The images of the plasma generated near the window surface shown in Figure4b. It represents the images of the MWP plasma optical emission patterns were taken, as shown in Figure 4b. It represents the images of the MWP plasma optical along the linear direction from the front side and right side views. The mounting position emission patterns along the linear direction from the front side and right side views. The of the camera in the plasma chamber is shown in Figure4b as the front and side views. The equipment used to record the shape of plasma was a cylindrical camera (model: Microsoft Life Cam Studio) suitable for the rounded type chamber flange. The brightness of the emitted light was slightly distorted because the plasma shape was captured by a camera equipped with a neutral density(ND) filter (product of HORUSBENNU, 49 mm), which was used to reduce the brightness to 1/400. Appl. Sci. 2021, 11, x FOR PEER REVIEW 5 of 20

Appl. Sci. 2021, 11, x FOR PEER REVIEW 5 of 20

mounting position of the camera in the plasma chamber is shown in Figure 4b as the front andmounting side views. position The of equipmentthe camera usedin the toplasma record chamber the shape is shown of plasma in Figure was 4ba cylindricalas the front cameraand side (model: views. Microsoft The equipment Life Cam used Studio) to reco suitablerd the for shape the rounded of plasma type was chamber a cylindrical flange. Thecamera brightness (model: of Microsoft the emitted Life light Cam was Studio) slight suitablely distorted for the because rounded the type plasma chamber shape flange. was

Appl. Sci. 2021, 11, 5358 capturedThe brightness by a ofcamera the emitted equipped light waswith slight a lyne distortedutral density(ND) because the filter plasma (product shape5 of was 20of HORUSBENNU,captured by a 49camera mm), whichequipped was usedwith to a reduce neutral the density(ND)brightness to 1/400.filter (product of HORUSBENNU, 49 mm), which was used to reduce the brightness to 1/400.

Figure 4. Front (a) and top (b) views of the experimental and diagnostic setup diagram. FigureFigure 4. 4.Front Front ( a(a)) and and top top ( b(b)) views views of of the the experimental experimental and and diagnostic diagnostic setup setup diagram. diagram. Figure 5 shows the plasma diagnostics using a homemade single Langmuir probe(LP)FigureFigure 5in shows 5the shows deposition the plasmathe plasmaregion. diagnostics Thediagnostic depo usingsitions ausing homemade process a homemade is single usually Langmuir carriedsingle probe(LP) outLangmuir 20–25 inmmprobe(LP) the away deposition infrom the region.depositionthe window The region. deposition surface. The processHence,deposition isthe usually processdiagnosis carried is usually was out performed 20–25carried mm out in away20–25 the fromdepositionmm theaway window areafrom at surface. thefive window points Hence, (20–25surface. the diagnosis mm Hence, away was thefrom performed diagnosis the window in was the surface) depositionperformed at area20in mm the at ﬁveintervalsdeposition points from (20–25 area the at mm center, five away points as from shown (20–25 the in window Figuremm away surface)5. The from tip at of 20the the mm window LP intervals was surface) made from of theat a 100µm center,20 mm asdiameterintervals shown tungsten infrom Figure the wire5center,. The (10 tipas mm shown of in the length), LPin Figure was wh madeich 5. Thewas of atipdesigned 100 of theµm toLP diameter satisfy was made the tungsten collisionless of a 100µm wire (10thindiameter mm sheath in length),tungsten condition which wire [22]. was(10 mm designed in length), to satisfy which the was collisionless designed thin to satisfy sheath the condition collisionless [22]. thin sheath condition [22].

FigureFigure 5.5. DiagnosticDiagnostic setupsetup inin thethe depositiondeposition region.region. Figure 5. Diagnostic setup in the deposition region. TheThe electronelectron energyenergy distributiondistribution functionfunction (EEDF)(EEDF) waswas obtainedobtained byby calculatingcalculating thethe secondsecondThe derivativederivative electron of energyof the the measured distributionmeasured I–V curveI–V function curv [23,24e (EEDF)].[23,24]. The second was The obtained derivativesecond derivativeby of calculating the measured of thethe 00 ” currentmeasuredsecond withderivative current respect withof to thethe respect probemeasured biasto the voltage, I–V probe curv Ibiase ,e was[23,24]. voltage, proportional The 𝐼 , secondwas to proportional the derivative electron energy toof thethe f ( ) ” g ( ) = 1/2 f ( ) probabilityelectronmeasured energy functioncurrent probability with (EEPF) respect efunctionε , whichto the (EEPF) wasprobe related 𝑓bias(𝜀) , to voltage,which the EEDF was 𝐼 , aswasrelatede proportionalε toε the eEEDFε .to The theas electron density/ is calculated by integrating the EEDF, and the electron temperature was 𝑔electron(𝜀) =𝜀 energy𝑓(𝜀) .probability The electron function density (EEPF) is calculated 𝑓(𝜀), whichby integrating was related the toEEDF, the EEDFand the as measured/ as an effective electron temperature T , which corresponds to a mean electron electron𝑔(𝜀) =𝜀 temperature𝑓(𝜀). The was electron measured density as isan calculated effectivee f f electronby integrating temperature the EEDF, 𝑇 ,and which the energy from the integrals of the EEDF [23,24]. correspondselectron temperature to a mean waselectron measured energy asfr oman theeffective integrals electron of the temperatureEEDF [23,24]. 𝑇 , which corresponds to a mean electron energy from the integrals of the EEDF [23,24]. 4. Simulation 4.1. Simulation Methods Conventionally, analyses of long linear microwave sources reveal limitations to solving the transmission model self-consistently [25–27]. Self-consistency requires that the wave ﬁeld and continuity equations be solved simultaneously to account for the effects of the plasma radial and axial inhomogeneities. The plasma spatial inhomogeneity can be calculated by using numerical methods [28–34]. Based on numerical methods, in this study, a ﬂuid plasma simulation model(using COMSOL Multiphysics) in the 3-D domain was presented to solve the plasma and wave equations self-consistently [35]. The spatially self-consistent description of the transmis- Appl. Sci. 2021, 11, x FOR PEER REVIEW 6 of 20

4. Simulation 4.1. Simulation Methods Conventionally, analyses of long linear microwave sources reveal limitations to solving the transmission model self-consistently [25–27]. Self-consistency requires that the wave field and continuity equations be solved simultaneously to account for the effects of the plasma radial and axial inhomogeneities. The plasma spatial inhomogeneity can be calculated by using numerical methods [28–34]. Appl. Sci. 2021, 11, 5358 Based on numerical methods, in this study, a fluid plasma simulation model(using6 of 20 COMSOL Multiphysics) in the 3-D domain was presented to solve the plasma and wave equations self-consistently [35]. The spatially self-consistent description of the transmission line could be achieved because the plasma fluid simulation could solve the wavesion and line plasma could beequations achieved simultaneously because the plasma in 3-D fluid space. simulation The correlation could solve between the wavethe plasmaand plasma generation, equations longitudinal simultaneously power inabsorption, 3-D space. Theand correlationsustaining betweenthe electric the plasmafield generatedgeneration, from longitudinal electromagnetic power waves absorption, could and be calculated. sustaining the electric field generated from electromagneticIn Figure 6, the waves simulation could begeometry calculated. was designed in the same way as in the Figure 2 (experiment).In Figure 6The, the height simulation and the geometry diameter was of designed the chamber in the were same designed way as in the the sameFigure as 2 the(experiment). experiment. The The parts height of andthe power the diameter applicat ofor the and chamber structures were in designedthe simulation the same were as designed,the experiment. as shown The in partsthe upper of the parts power or applicatorpanels of andthe figure. structures In the in thecase simulation of the quasi- were designed, as shown in the upper parts or panels of the figure. In the case of the quasi-coaxial coaxial TEM LMPS, shown in Figure 6a, wave excitation was applied at one side (power TEM LMPS, shown in Figure6a, wave excitation was applied at one side (power feeding feeding port) of the WR340 waveguide structure as the rectangular TE10 mode. The port) of the WR340 waveguide structure as the rectangular TE10 mode. The rectangular rectangular TE10 wave was converted to a quasi-coaxial TEM mode through a rod-shaped TE wave was converted to a quasi-coaxial TEM mode through a rod-shaped antenna at antenna10 at the location 34⁄ ×λ (λ : WR340 guide wavelength, 14.36 cm in 2.45 the location 3/4 × λ (λ : WR340 guide wavelength, 14.36 cm in 2.45 GHz) away GHz) away from the powerwr340 inputwr340 port where the electric field was maximized. On the from the power input port where the electric field was maximized. On the other hand, in other hand, in the circular TE11 mode, shown in Figure 6b, the WR340 waveguide and the the circular TE mode, shown in Figure6b, the WR340 waveguide and the converter of converter of the rectangular11 to circular waveguiding structure was omitted to reduce the the rectangular to circular waveguiding structure was omitted to reduce the computational computational loads. As the wave mode was conserved from the rectangular TE10 to the loads. As the wave mode was conserved from the rectangular TE10 to the circular TE11 [1], circular TE11 [1], the power applicator was designed to be simplified by applying a the power applicator was designed to be simplified by applying a cylindrical TE11 wave cylindrical TE11 wave power directly to one side of the cylindrical alumina surface (power power directly to one side of the cylindrical alumina surface (power feeding port), as feedingshown port), in Figure as shown6b. In thein Figure electromagnetic 6b. In the waveelectromagnetic model in COMSOL wave model Multiphysics in COMSOL [ 35 ], Multiphysicspower application [35], power method application could be method selected could so that be theselected input so power that the of input the active power port of is thefully active deposited port is fully on the deposited conductive on materialthe conductive [36]. In material both the [36]. cases In of both this the study, cases this of power this study,application this power model application was selected model to reduce was theselected calculation to reduce time. the 500 calculation mTorr Ar plasmatime. 500 with mTorr2.45 GHzAr plasma and 0.6 kWwith microwave 2.45 GHz power and was0.6 applied.kW microwave The background power gaswas temperature applied. The was backgroundset to 300 K,gas and temperature the neutral was gas set density to 300 was K, and assumed the neutral to be uniformgas density and was was assumed calculated to underbe uniform the assumption and was calculated of an ideal under gas. The the velocityassumption of the of electron an ideal was gas. assumed The velocity to have of a theMaxwellian electron was distribution. assumed to have a Maxwellian distribution.

FigureFigure 6. 6.GeometryGeometry of ofMWP MWP 3-D 3-D simulation simulation (a ()a quasi-coaxial) quasi-coaxial TEM TEM linear linear MWP MWP and and (b (b) )circular circular TE11 TEwaveguiding11 waveguiding structure. structure.

TableTable 1 1lists lists the the Ar Ar chemical chemical reaction reaction set set used used in in the the simulation. simulation. In In this this simulation, simulation, + electrons,electrons, Ar Ar+ ions,ions, and and Ar Ar** (first (ﬁrst Ar Ar metastable metastable species) species) were were considered considered [37–40]. [37–40 ].In In particular, the reaction set containing the Ar excited states and step-ionization was selected to increase the accuracy of the calculations in the pressure regime [36–42]. The cross sections are given for the charged particle reaction sets, and the rate coefﬁcients are given for the reactions of quenching and ionization by atomic collisions. Appl. Sci. 2021, 11, 5358 7 of 20

f Table 1. Selected reaction for Argon discharges (∆ε: threshold energy, σc: cross-section, k : rate coefﬁcient (m3/s)) [38–41].

f Reaction Formula Type ∆ε (eV) σc,k e + Ar → e + Ar Elastic scattering - [38] e + Ar → e + Ar* Excitation 11.55 [38] e + Ar* → e + e + Ar+ Step-ionization 4.16 [39] e + Ar → e + e + Ar+ Direct-ionization 15.76 [38] Ar + Ar+ → Ar + Ar+ Scattering - [40] Ar + Ar+ → Ar + Ar+ Charge exchange - [40] e + Ar* → e + Ar Quenching - [41] Ar + Ar* → Ar + Ar Quenching - [41] Ar* + Ar* → e + Ar+ + Ar Ionization - [41]

4.2. The Computational Mesh & Geometry To generate the 3-D meshes based on the advancing-front method (AFM) meshing algorithm, tetrahedral meshes were used for the discretization in 3-D geometry models. The mesh in the quasi-coaxial TEM model consists of approximately 8.7 × 105 elements and 5 the mesh in the circular TE11 model consists of approximately 7.5 × 10 domain elements. The meshes used in these models were set ﬁner (0.1~1.2 mm) near the quartz window surface than those in the rest of the discharge chamber (10 mm in maximum).

4.3. Governing Equations The 3-D simulation model in this work coupled two physical models, namely the electromagnetic ﬁeld and plasma models. The continuous 2.45 GHz electromagnetic wave ﬁeld (sinusoidal) was considered time-harmonic with amplitude E [34]. The frequency analysis calculated the sinusoidal response for one period and deduced average rms loads. It applied those to the transients in the plasma model with boundary conditions depending on the time t.

4.3.1. The Electromagnetic Field Model The electric field in the microwave model satisfied the following equation deduced from the Maxwell’s equations. The wave equation for this case assumed that the time variation of the electric and magnetic field components was harmonic and the medium was non-magnetic [43].

−1 2 ∇ × [µr (∇ × E)] − ω ε0εr − jωσ ) E = 0 (1)

This Helmholtz equation for the electric field was solved simultaneously in the waveguiding structure and in the plasma chamber. Here, E denotes the electric field(HF field), k is √ 0 the wave number in free space (k0 = ω µ0ε0), ω is the angular frequency (2π× 2.45 GHz), −12 ε0 and µ0 are the free space permittivity 8.854 × 10 [F/m] and free space permeability −7 2 (4π × 10 N/A ), j is imaginary unit, σ is conductivity, respectively. εr is the relative permittivity depending on the property of the materials. As the material property, the q relative permittivity of the quartz window is εr = 4. The alumina used in TE11 mode had al co a relative permittivity of εr = 9, the relative permittivity of copper is εr = 1, the relative air p permittivity of air is εr = 1, and the relative permittivity of plasma is expressed as εr in the following equations. 2 p ωpe εr = 1 − , (2) ω(ω − iven) Appl. Sci. 2021, 11, 5358 8 of 20

s 2 neq ωpe = , (3) meε0

where q is the elementary charge and me is the mass of an electron. ωpe denotes the plasma frequency that depends on the electron density ne, and the ven is the electron-neutral collision frequency for momentum transfer [44].

tot ven = kAr(ε)·nAr (4)

ven is expressed as a function of mean electron energy ε and the number of neutral tot particles densities [34,45]. The expression ki is the total collision rate of neutral species i. By calculating the mean electron energy (ε) with a Maxwell distribution function and substituting it into the ﬁrst moment Boltzmann equation, σp (plasma conductivity) can be obtained as a function of the plasma parameter.

2 neq σp = (5) me(ven + jω)

The unmagnetized plasma conductivity σp is expressed as a function of ne, ven, and ω. The conductivity of copper is 6 × 107 S/m. Both quartz and air are set to non-conductive q air materials (σq = σair = 0) and non-magnetic materials (µr = µr = 1). For non-magnetized p high frequency plasmas, the relative permeability µr = 1. The density of the abosrbed power from the electromagnetic is calculated as in the following equation [1,46–49].

1 Q = Re(σE·E∗) (6) h 2

Qh [44] is the density of the absorbed microwave power, Re denotes the real part of the corresponding expression, and E∗ is the complex conjugate of E.

4.3.2. Plasma Model Normally, it is known that the gas flow and the temperature highly affect the spatial spreading of neutral gases [43]. However, in this model, the neutral fluid velocity was set to 0 and the neutral gas temperature was set to 300 K to simplify the model in the 3-D domain. Hence, the equations used in this simulation and the terms related to the neutral fluid velocity were omitted. ∂ (n ) + ∇·Γ = R (7) ∂t e e e Γe = − µe·E )ne−(De·∇ne) (8)

q kBTe µe= , De= (9) meνen meνen The continuity equation for the electron density is given as above. Here, E denotes the electric ﬁeld(DC ﬁeld), ne is the electron density and Re is electron production rate. In this simulation, the mobility of electrons was calculated as a function of the electron energy by using BOLSIG+ [50], and the diffusivity was determined from Einstein’s relation. In this model, the electron mobility used to calculate the electron transport properties was taken from the electron impact reactions set to ven. Here, µe is the electron mobility, and De is the electron diffusivity [49–53].

∂ (n ) + ∇·Γ + E·Γ = S +Q /q (10) ∂t ε ε e en h Γε = − µε·E )nε − ∇(Dεnε) (11) 5 µ =( )µ , D =µ T (12) ε 3 e ε ε e Appl. Sci. 2021, 11, 5358 9 of 20

The conservation equation for the electron energy density is given by the aforementioned equations, where, nε is the electron energy density, Sen is the energy loss/gain from the collisions, and Qh is the heat source for plasma model absorbed from the electromagnetic wave power. In addition, Te is the electron temperature, µε is the electron energy mobility, and Dε is the electron energy diffusivity [51–54]. Both µε and Dε are calculated from the electron mobility µe, using the Einstein relation.

∂ ρ (w ) = ∇·j + R (13) ∂t k k k

jk = ρwkvk (14)

∇ωk vk = Dk − zkµkE (15) ωk As aforementioned, for non-electron species (neutral, excited species, and ions), the equation is solved for the mass fraction of each species. This is the simplified form of the Maxwell-Stefan equation, which makes it computationally less expensive in solving the transport equations. Here, wk is the mass fraction of the kth species, jk is the diffusive flux vector, and Rk is the rate coefficient for species k. The rate coefficients of electron-heavy particle reactions are calculated from the cross-section of the corresponding reaction σ as a mean value [34]. In addition, ρ is the density of the mixture, vk is the diffusion velocity 2 for species k, Dk is the diffusion coefficient (diffusion coefficient of Ar: DAr is 0.01 m /s, ∗ + which is same for Ar and Ar ), zk is the charge number of species k, and µk is the mobility for species k [55–59]. E = −∇V, ∇ e0erE = ρ (16)

N ! ρ = q ∑ zknk − ne (17) k=1 As aforementioned, the electrostatic field can be calculated using Poisson’s equation. The space charge density, ρ, is computed based on the plasma chemistry (electron density and ion density) [35]. V is the electric potential and nk is the number density of species k. The boundary conditions of the waveguiding structure power input ports were used to supply electromagnetic waves (input power) in the active ports. At metallic boundaries, the perfect electric conductor (PEC) boundary condition was used, except for the copper material region where the antenna rod was in the quasi-coaxial MWP and the cylindrical guiding structure was in the circular guiding structure MWP. The PEC boundary condition sets the tangential component of the electric field to 0 [35]. The wall boundary condition used to calculate the transport equation was the inhomogeneous Neumann boundary condition. The value of the normal flux to the boundary is described by following equation [34]:

n·Γk = (1/4)· γknkvk, (18)

where n denotes the unit vector normal to the boundary and vk is the velocity magnitude (thermal velocity for neutrals and Bohm velocity for ions), nk is the density of the k species, and γk is the sticking coefficient. In this study, the sticking coefficient of each species at the wall boundary was set to 1. The wall boundary condition [60] in the electron energy equation, which is the homogeneous Neumann condition, were used to set the normal flux of the energy density to 0. The electron energy settings in the metallic material wall boundary conditions were set to 0, the electron reflection coefficient at the wall was set to 0, and the walls in contact with the plasma were set to have a ground potential (V = 0). In most cases, when calculating the microwave plasma by using the numerical methods, numerical problems arose with regions where ne (electron density) values were close to ncr (critical density). To avoid this, COMSOL Multiphysics provides a method using a “Doppler broadening parameter” which allows for convergence [49]. However, in this Appl. Sci. 2021, 11, x FOR PEER REVIEW 10 of 20

to 0. The electron energy settings in the metallic material wall boundary conditions were set to 0, the electron reflection coefficient at the wall was set to 0, and the walls in contact with the plasma were set to have a ground potential (V = 0). In most cases, when calculating the microwave plasma by using the numerical methods, numerical problems arose with regions where 𝑛 (electron density) values Appl. Sci. 2021, 11, 5358 10 of 20 were close to 𝑛 (critical density). To avoid this, COMSOL Multiphysics provides a method using a “Doppler broadening parameter” which allows for convergence [49]. However, in this model, the use of this method was limited to prevent the deterioration model,of the computational the use of this accuracy. method was limited to prevent the deterioration of the computational accuracy. 5. Results and Discussion 5. ResultsNormally, and Discussion the generation of optical emission is associated with the Ar* excitation stateNormally, species, which the generation means electron of optical heating emission occurs. is associatedThe electron with heating the Ar* mechanism excitation is statebased species, on the whichelectric means field profiles, electron and heating in th occurs.is study, The the electron wave field heating was mechanismfed by a wave is basedlauncher on from the electric the end field of the profiles, tube. In and the linea in thisr MWP, study, which the wave applied field power was to fed one by side a wave port, launcherelectron fromdensity the attenuation end of the tube.appeared In the along linear the MWP, linear which axis due applied to the power difference to one in side the port,power electron absorption density along attenuation the wave appeared propagation along di therection, linear axiswhich due could to the result difference in a specific in the powerelectron absorption density distribution. along the wave Moreover, propagation if the direction,reflection whichof the couldwaves result was inmade a specific at the electronopposite density boundary, distribution. the formation Moreover, of a standing if the wave reflection occurred. of the A wavesstanding was wave made formed at the in oppositethe antenna boundary, structure the and formation made inhomogeneous of a standing wave line occurred.strengths Aofstanding an electric wave field, formed which incaused the antenna a spatial structure difference and in made the plasma inhomogeneous power absorption line strengths along ofthe an axial electric direction. field, which causedFigure a spatial 7 shows difference that the in themicrowave plasma power power absorption is applied alongfrom thethe axialleft side direction. in the front viewFigure and the7 shows right side that in the the microwave side view. power For TE is11 appliedwave mode, from as the shown left side in Figure in the front7a, the viewbrightness and the of right the emitted side in thelight side is view.higher For at TEthe11 beginningwave mode, of wave as shown propagation, in Figure 7anda, the the brightnessfaint pattern of thebecomes emitted clearer light istowards higher the at the end. beginning From Figure of wave 7b, propagation,we see that from and the right- faint patternside view becomes the optical clearer emission towards pattern the end. can From be observed Figure7b, more we see clearly. that fromIn the the quasi-coaxial right-side viewline TEM the optical wave emissionmode, the pattern same optical can be observedemission pattern more clearly. and the In decrease the quasi-coaxial in brightness line TEMalong wave the axial mode, directions the same are optical observed emission as in pattern the TE and11 mode. the decrease On the inother brightness hand, emitted along thelight axial pattern directions in the are TEM observed structure as in was the different TE11 mode. in the On theintensity other hand,of the emittedemitted lightlight patternbrightness in the along TEM the structure axial line was and different the wavelength in the intensity of the ofemitted the emitted light wave light brightnesspattern. In alongthe TEM the structure, axial line emitted and the light wavelength brightness of theconc emittedentrated light at the wave beginning pattern. of Inthe the axial TEM line structure,was relatively emitted lesser light and brightness was evenly concentrated distributed, atas theshown beginning in Figure of 7c. the The axial wavelength line was relatively lesser and was evenly distributed, as shown in Figure7c. The wavelength of the of the emitted light pattern was longer than that of the TE11 mode. The half wavelength emitted light pattern was longer than that of the TE mode. The half wavelength observed observed on the optical emission pattern was measured11 to be 23 mm in TE11 and 47 mm onin theTEM. optical emission pattern was measured to be 23 mm in TE11 and 47 mm in TEM.

Figure 7. Images of MWP plasma optical emission patterns of Ar circular TE11 waveguiding Figure 7. Images of MWP plasma optical emission patterns of Ar circular TE11 waveguiding structure. structure. (a) Front view, (b) right side view, quasi-coaxial TEM, (c) front view, and (d) right side (a) Front view, (b) right side view, quasi-coaxial TEM, (c) front view, and (d) right side view. view. Figures8–10 show the simulation results of the spatial proﬁles of the electric ﬁeld, electronFigures density, 8–10 and show electron the simulation temperature, results respectively, of the spatial for eachprofiles source of the along electric the axialfield, andelectron radial density, directions. and Figure electron8b showstemperature, that the respectively, coordinate direction for each issource based along on the the center axial of the waveguide, and the X-axis is directed perpendicular (radial direction, θ = 0◦) from the waveguide to the plasma column; the Y-axis (radial direction, θ = 90◦) is the direction of the height, and the Z-axis is the wave propagation direction (axial direction) in the waveguiding structure. Appl.Appl. Sci.Sci. 20212021,, 1111,, xx FORFOR PEERPEER REVIEWREVIEW 1111 ofof 2020

andand radialradial directions.directions. FigureFigure 8b8b showsshows thatthat thethe coordinatecoordinate directiondirection isis basedbased onon thethe centercenter ofof thethe waveguide,waveguide, andand thethe X-axisX-axis isis directeddirected perpendicularperpendicular (radial(radial direction,direction, θθ == 0°)0°) fromfrom thethe waveguidewaveguide toto thethe plasmaplasma column;column; thethe Y-axisY-axis (radial(radial direction,direction, θθ == 90°)90°) isis thethe directiondirection ofof thethe height,height, andand thethe Z-axisZ-axis isis thethe wavewave prpropagationopagation directiondirection (axial(axial direction)direction) inin thethe waveguidingwaveguiding structure.structure. |𝑬| 𝐸 +𝐸+𝐸 InIn FigureFigure 8,8, thethe E-fieldE-field profileprofile (norm(norm |𝑬| (E-field(E-field amplitude,amplitude, 𝐸 +𝐸 +𝐸 )))) isis calculatedcalculated inin thethe 3-D3-D domain.domain. InIn FigureFigure 8,8, atat TEMTEM wavewave mode,mode, thethe directiondirection ofof thethe radiallyradially emittedemitted wavewave electricelectric fieldfield isis perpendicularperpendicular toto thethe tangentialtangential planeplane ofof thethe quartzquartz windowwindow surface in the XY plane. In the radial direction, the electric field strength was maximum Appl. Sci. 2021, 11, 5358 surface in the XY plane. In the radial direction, the electric field strength was maximum11 of 20 atat thethe coppercopper antennaantenna surfacesurface (inner(inner conductor)conductor) andand decreaseddecreased asas itit waswas emittedemitted inin allall directionsdirections ofof plasma–dielectricplasma–dielectric contactcontact windowwindow surfacessurfaces [10].[10].

q 2 2 2 Figure 8. Electric ﬁeld norm ||E𝐸||(E-ﬁeld amplitude, E𝐸x++𝐸Ey++𝐸Ez) simulation results. (a) TEM mode of quasi-coaxial FigureFigure 8.8. ElectricElectric fieldfield normnorm |𝐸| (E-field(E-field amplitude,amplitude, 𝐸 +𝐸+𝐸)) simulationsimulation results.results. ((aa)) TEMTEM modemode ofof quasi-coaxialquasi-coaxial linear MWP and (b) circular TE11 mode waveguiding structure MWP. linearlinear MWPMWP andand ((bb)) circularcircular TETE1111 modemode waveguidingwaveguiding structurestructure MWP.MWP.

Appl. FigureSci.Figure 2021 9. ,9. 11 ElectronElectron, x FOR PEER density density REVIEW profileprofile proﬁle at at 500 500 mTorr mTorr MWP. MWP. ((aa))) TEMTEMTEM modemodemode ofofof quasi-coaxialquasi-coaxialquasi-coaxial linearlinearlinear MWPMWPMWP andandand (((bb))) circularcircularcircular TETETE121111 of 20 11 modemode waveguiding waveguiding structure structure MWP. MWP.

Figure 10.10. Electron temperaturetemperature at 500500 [mTorr][mTorr] MWP.MWP.( a(a)) TEM TEM mode mode of of quasi-coaxial quasi-coaxial linearlinear MWPMWP ((bb)) circular circular TE TE1111 modemode waveguidingwaveguiding structurestructure MWP.MWP. q In Figure8, the E-field profile (norm |E| (E-field amplitude, E2 + E2 + E2)) is cal- On the other hand, in the TE11 mode, the electric field radiated locallyx y in thez radial culateddirection in from the 3-Dthe continuous domain. In line Figure slot8 ,antenna, at TEM and wave the mode, radially the radiated direction electric of the field radially was emittedparallel to wave the electrictangential field plane is perpendicular of the quartz to window the tangential surface. plane In the of radial the quartz direction, window the electric field strength was maximal at the dielectric surface (alumina), which contacted a slot surface of the cylindrical waveguiding structure and it decreased with radial emission. In the standing waveform, the half-wavelength of the propagating quasi-coaxial line TEM mode through the coaxial line was approximately 48 mm. In the TE11 mode, the half wavelength of the wave propagating through the dielectric was 22 mm, which was approximately 2.1 times smaller. The calculated wavelength by the simulation corresponded to the experimental results, which affected the electron density distribution along the Z-direction. The electric field attenuation in the axial direction had a considerable influence on the axial distribution of the inhomogeneous plasma. Figure 11 shows the simulation of the attenuation of the normalized E-field amplitude along the wave propagation direction. In general, the rate of attenuation of the wave propagating to the lossy media (X-direction) is expressed as a value proportional to e(α : attenuation coefficient) [1].

Figure 11. Attenuation of electric field norm |𝐸| along Z-direction.

The attenuation rate of the electric field intensity (standing wave amplitude) along the wave propagation (Z-direction) could also be represented by the attenuation coefficient α. In the presence of the lossy media, the power absorption was concentrated at the beginning of the applied power [25]. The attenuation coefficient α was affected by the wavelength of the standing wave. In this simulation, the value of the coefficient was Appl. Sci. 2021, 11, x FOR PEER REVIEW 12 of 20

Appl. Sci. 2021, 11, 5358 12 of 20

Figure 10. Electron temperature at 500 [mTorr] MWP. (a) TEM mode of quasi-coaxial linear MWP (b) circular TE11 mode waveguiding structure MWP.surface in the XY plane. In the radial direction, the electric field strength was maximum at the copper antenna surface (inner conductor) and decreased as it was emitted in all directionsOn the of other plasma–dielectric hand, in the TE contact11 mode, window the electric surfaces field [10 radiated]. locally in the radial direction from the continuous line slot antenna, and the radially radiated electric field was On the other hand, in the TE11 mode, the electric field radiated locally in the radial paralleldirection to fromthe tangential the continuous plane lineof the slot quartz antenna, window and the surface. radially In radiated the radial electric direction, field wasthe electricparallel field to the strength tangential was maximal plane of at the the quartz dielec windowtric surface surface. (alumina), In the which radial contacted direction, a slot the surfaceelectric of field the cylindrical strength was waveguiding maximal at struct the dielectricure and it surface decreased (alumina), with radial which emission. contacted a slotIn surface the standing of the cylindrical waveform, waveguiding the half-wavelength structure of and the it propagating decreased with quasi-coaxial radial emission. line TEM modeIn the through standing the waveform, coaxial line the was half-wavelength approximately of 48 the mm. propagating In the TE quasi-coaxial11 mode, the half line wavelengthTEM mode throughof the wave the coaxial propagating line was thro approximatelyugh the dielectric 48 mm. was In the 22 TE mm,11 mode, which the was half approximatelywavelength of the2.1 wave times propagating smaller. throughThe ca thelculated dielectric wavelength was 22 mm, by which the wassimulation approxi- correspondedmately 2.1 times to the smaller. experimental The calculated results, wavelength which affected by the the simulation electron density corresponded distribution to the alongexperimental the Z-direction. results, which affected the electron density distribution along the Z-direction. TheThe electric electric field field attenuation inin thethe axial axial direction direction had had a considerablea considerable influence influence on on the theaxial axial distribution distribution of theof the inhomogeneous inhomogeneous plasma. plasma. Figure Figure 11 shows11 shows the the simulation simulation of theof theattenuation attenuation of theof the normalized normalized E-field E-field amplitude amplitude along along the the wave wave propagation propagation direction. direction. In Ingeneral, general, the the rate rate of of attenuation attenuation of of the the wave wave propagating propagating to to the the lossy lossy media media (X-direction) (X-direction) is isexpressed expressed as as a a value value proportional proportional to to e −eαx(α(α: attenuation: attenuation coefficient) coefficient) [1 [1].].

FigureFigure 11. 11. AttenuationAttenuation of of elec electrictric field ﬁeld norm norm ||𝐸E|| alongalong Z-direction.Z-direction.

TheThe attenuation attenuation rate rate of of the the electric electric field field intensity intensity (standing (standing wave wave amplitude) amplitude) along along thethe wave propagationpropagation (Z-direction) (Z-direction) could could also bealso represented be represented by the attenuationby the attenuation coefficient coefficientα. In the presenceα. In the presence of the lossy of the media, lossy themedia, power the power absorption absorption was concentrated was concentrated at the atbeginning the beginning of the of applied the applied power powe [25r]. [25]. The The attenuation attenuation coefficient coefficientα was α was affected affected by theby thewavelength wavelength of of the the standing standing wave. wave. In In this thissimulation, simulation, thethe valuevalue of the coefficient coefficient was was represented by 5 in the quasi-coaxial line TEM and 10 in the circular TE11. The value was inversely proportional to the wavelength. In the circular TE11 wave mode with a short wavelength (which propagated in dielectric space), the power absorption was higher than the quasi-coaxial line TEM at the beginning of wave propagation. In the linear microwave source, from a macroscopic point of view, two factors affected the spatial distribution of the electron density significantly, namely, the attenuation of the field strength along the wave propagation direction (axial direction) and the coupled field profile at the window surface (radial direction). First, the electron density distribution along the wave propagation direction was proportional to the attenuation of the electric field strength. As mentioned in the previous section, power absorption mechanism in the plasma was related to the heat source from the electromagnetic wave power. The absorbed power was represented as a function of the variable E. Thus, the Re(J·E) of the power dissipation in the plasma chamber followed the E field profile. In both the cases of LMPS, power dissipation in the axial direction was concentrated at the surface of dielectric near field region. Appl. Sci. 2021, 11, x FOR PEER REVIEW 13 of 20

represented by 5 in the quasi-coaxial line TEM and 10 in the circular TE11. The value was inversely proportional to the wavelength. In the circular TE11 wave mode with a short wavelength (which propagated in dielectric space), the power absorption was higher than the quasi-coaxial line TEM at the beginning of wave propagation. In the linear microwave source, from a macroscopic point of view, two factors affected the spatial distribution of the electron density significantly, namely, the attenuation of the field strength along the wave propagation direction (axial direction) and the coupled field profile at the window surface (radial direction). First, the electron density distribution along the wave propagation direction was proportional to the attenuation of the electric field strength. As mentioned in the previous section, power absorption mechanism in the plasma was related to the heat source from the electromagnetic wave power. The absorbed power was represented as a function of the variable 𝑬. Thus, the Re(J·E) of the power dissipation in the plasma chamber followed the 𝑬 field profile. In both the cases of LMPS, power dissipation in the axial direction was concentrated at the surface of dielectric near field region. However, the power dissipation in the XY plane appeared differently depending on the shape of the emitted field direction. In Figures 12 and 13, at a distance of 5 mm, 15 mm, and 25 mm from the quartz window surface (XZ plane at Y = 0), the electron density along the Z-axis is attenuated in proportion to the decrease in the electric field strength, as shown in Figure 11. In the circular TE11 mode, the attenuation coefficient of the normalized electron density was five times higher than that of the quasi-coaxial line TEM Appl. Sci. 2021, 11, 5358 mode, and the electron generation was concentrated at the initial 100 mm of the power13 of 20 application. Near the window surface, the same fluctuations in the electron density appeared as a change in the intensity of the amplitude with a standing wave effect. At a distance of 5 mm, 15 mm, and 25 mm from the quartz window surface along the X-axis, in theHowever, case of quasi-coaxial the powerdissipation line TEM mode, in the whose XY plane wavelength appeared was differently longer than depending that of the on the shape of the emitted field direction. In Figures 12 and 13, at a distance of 5 mm, 15 mm, circular TE11, the tendency of oscillation was higher than that of the circular TE11.The short and 25 mm from the quartz window surface (XZ plane at Y = 0), the electron density wavelength of circular TE11 mode was less affected and showed a relatively uniform along the Z-axis is attenuated in proportion to the decrease in the electric field strength, as electron density spatial distribution at 25 mm away from the window surface (with shown in Figure 11. In the circular TE mode, the attenuation coefficient of the normalized smoothing effect) [46]. 11 electron density was five times higher than that of the quasi-coaxial line TEM mode, and Although the generation of electrons in the circular TE11 mode was concentrated at the electron generation was concentrated at the initial 100 mm of the power application. the initial 100 mm of wave propagation, the electron density (X = 5, 15, and 25 mm) at Z > Near the window surface, the same fluctuations in the electron density appeared as a 100 mm was 1.5 to 2 times higher than the quasi-coaxial TEM. In the TE11 mode, the change in the intensity of the amplitude with a standing wave effect. At a distance of electron density spatial distribution was formed close to the planar type. The 5 mm, 15 mm, and 25 mm from the quartz window surface along the X-axis, in the case of waveguiding structure and the emitted field direction affected the attenuation of the quasi-coaxial line TEM mode, whose wavelength was longer than that of the circular TE11, electron density along the radial distance, the ratio of the electron density of 5–25 mm in the tendency of oscillation was higher than that of the circular TE11.The short wavelength the X-axis (at Z = 0) was 20% in the quasi-coaxial TEM mode and 33% in the circular TE11 of circular TE11 mode was less affected and showed a relatively uniform electron density mode.spatial distribution at 25 mm away from the window surface (with smoothing effect) [46].

Appl. Sci. 2021, 11, x FOR PEER REVIEW 14 of 20

Figure 12. Attenuation of electron density along the axial direction (Z-axis) in the XZ plane (quasi- Figure 12. Attenuation of electron density along the axial direction (Z-axis) in the XZ plane (quasi- coaxial TEM mode), distance (5 mm, 15 mm, and 25 mm for black, red, and blue lines, respectively) respectively)from the window from the surface window along surfac thee X-axis, along normalizedthe X-axis, normalized norm |E| on norm the | inner𝐸| on conductor the inner (green conductorline), and the(green window line), surfaceand the (purplewindow line) surface are to(purple compare line) the are electron to compare density the electron distribution density along distributionthe E-ﬁeld. along the E-field.

Figure 13. Attenuation of electron density along the axialaxial directiondirection (Z-axis)(Z-axis) inin thethe XZXZ planeplane (circular (circular TE11 waveguiding structure), distance (5 mm, 15 mm, 25 mm for black, red, and blue lines, TE11 waveguiding structure), distance (5 mm, 15 mm, 25 mm for black, red, and blue lines, respec- respectively) from the window surface along the X-axis, normalized norm |𝐸| on the cut-surface of tively) from the window surface along the X-axis, normalized norm |E| on the cut-surface of the the cylindrical waveguiding structure (surface of the inner dielectric rod shown by the green line), cylindrical waveguiding structure (surface of the inner dielectric rod shown by the green line), and and the window surface (purple line) are to compare the electron density distribution along the E- fied.the window surface (purple line) are to compare the electron density distribution along the E-ﬁed.

When the same power per unit volume was applied to the plasma generation in the simulation, the number of electrons generated in the total volume was 2.8 × 1015 m−3 in the quasi-coaxial line TEM mode and 2.3 × 1015 m−3 in the circular TE11 mode. Although the number of electrons produced in the entire volume was 20% higher in the quasi-coaxial line TEM mode than that in the circular TE11, the number of electrons generated in the actual deposition region was 50% higher in the circular TE11 mode than that in the quasi- coaxial TEM mode. In Figure 10, the spatial profiles of the electron temperature for each source are represented in the axial and radial directions. For the axial direction (XZ plane, Y = 0), the electron temperature was nearly constant along the axial distance. For radial distances in the XZ plane (Y = 0), near the window surface, the electron temperature was relatively high with a value of 3.5 eV while in the case of radial distances > 10 mm from the quartz window surface, the electron temperature with the value of 0.8~1.3 eV weakly depended on the radial distance. In Figure 10, the electron temperature distribution of the XY plane in each source varied depending on the shape of the emitted field profile such as the electron density distribution. The electron density and the electron temperature near the substrate surface (z = 20 and 25 mm) measured by a single LP are compared with the simulation results in Figures 14 and 15. The results of the experimental diagnosis show that the tendency is consistent with the simulation results. The experimental results in Figure 14a shows that the tendency of the electron density distribution along the Z-axis is consistent with the simulation result in Figure 14b. The electron density decreased along the wave propagation direction, and the attenuation ratio was higher in the circular TE11 mode. The electron density fluctuations due to the standing wave effect were prominent in the quasi-coaxial TEM mode, and the effect decreased along the X-axis. When comparing the electron density according to the wave mode, in both cases, the electron density near the substrate was measured to be approximately 1.5~2 times higher in the circular TE11 mode than that in the quasi-coaxial line TEM mode. In the experiment, the rate of increase in density was 2, which was more than the simulation value of 1.5. This is Appl. Sci. 2021, 11, 5358 14 of 20

Although the generation of electrons in the circular TE11 mode was concentrated at the initial 100 mm of wave propagation, the electron density (X = 5, 15, and 25 mm) at Z > 100 mm was 1.5 to 2 times higher than the quasi-coaxial TEM. In the TE11 mode, the electron density spatial distribution was formed close to the planar type. The waveguiding structure and the emitted field direction affected the attenuation of the electron density along the radial distance, the ratio of the electron density of 5–25 mm in the X-axis (at Z = 0) was 20% in the quasi-coaxial TEM mode and 33% in the circular TE11 mode. When the same power per unit volume was applied to the plasma generation in the simulation, the number of electrons generated in the total volume was 2.8 × 1015 m−3 in the 15 −3 quasi-coaxial line TEM mode and 2.3 × 10 m in the circular TE11 mode. Although the number of electrons produced in the entire volume was 20% higher in the quasi-coaxial line TEM mode than that in the circular TE11, the number of electrons generated in the actual deposition region was 50% higher in the circular TE11 mode than that in the quasi-coaxial TEM mode. In Figure 10, the spatial profiles of the electron temperature for each source are represented in the axial and radial directions. For the axial direction (XZ plane, Y = 0), the Appl. Sci. 2021, 11, x FOR PEER REVIEW 15 of 20 electron temperature was nearly constant along the axial distance. For radial distances in the XZ plane (Y = 0), near the window surface, the electron temperature was relatively high with a value of 3.5 eV while in the case of radial distances > 10 mm from the quartz becausewindow the surface, electron the loss electron from temperaturethe quartz wind withow the surface value along of 0.8~1.3 the direction eV weakly of the depended electric fieldon the was radial not distance.considered In in Figure detail 10 in, thethis electron simulation temperature model. distribution of the XY plane in eachIn the source experiment, varied depending the energy ondistribution the shape fu ofnction the emitted of electrons field of profile radial such distance as the ≥ 20electron mm followed density distribution. the Maxwell The distribution electron density function. and The the electronelectron temperaturetemperature near profile the shownsubstrate in Figure surface 15a (z =is 20consistent and 25 mm)with the measured simulation by a results single in LP Figure are compared 15b, which with shows the thatsimulation when the results radial in Figuresdistances 14 >and 20 mm15. The from results the quartz of the window experimental surface, diagnosis the electron show temperaturethat the tendency is weakly is consistent dependent with on thethe simulationradial distance. results. The experimental results in FigureTo 14 considera shows each that source the tendency and the of plasma the electron characteristics density distribution more deeply, along it was the necessary Z-axis is toconsistent consider with the theeffects simulation by resolving result the in Figure electr ic14 fieldb. The into electron the radial density and decreased axial direction along electricthe wave field propagation components. direction, The material and the attenuationproperties of ratio plasma was higheract like in a the lossy circular medium, TE11 whichmode. cause The electron not only density the transverse fluctuations field due components to the standing but also wave the effect axial were field prominentcomponents in tothe exist quasi-coaxial [16,17]. The TEM presence mode, of and an theaxial effect comp decreasedonent of alongthe wave the electric X-axis. Whenfield in comparing the quasi- coaxialthe electron line source density was according detailed to by the H. wave Nowakows mode,ka in et both al. [61]. cases, In the the electron presence density of the axial near componentthe substrate of wasthe wave measured field, toin bethe approximately high electron density 1.5~2 times region higher (ne > in1018 the), internal circular wave TE11 wasmode represented than that in by the a quasi-coaxialwave that propagated line TEM mode. near the In the window experiment, surfaces the along rate of the increase axial direction.in density Power was 2, dissipation which was in more the thanplasma the chamber simulation is valueconcentrated of 1.5. Thisnear isthe because dielectric the windowelectron losssurface from region, the quartz so the window presence surface of an internal along the wave direction is important of the electric as a component field was thatnot consideredaffects the electron in detail heat in thising simulation in the axial model. direction.

(a) (b)

FigureFigure 14. ( 14.a) Electron(a) Electron density density at the at su thebstrate substrate (Experiment) (Experiment) and and(b) electron (b) electron density density at the at thesubstrate substrate (Simulation). (Simulation).

(a) (b) Figure 15. (a) Electron temperature at the substrate (Experiment) and (b) electron temperature at the substrate (Simulation).

In Figure 12, a normalized norm |𝐸| of the inner conductor (green line) and the window surface (purple line) in the quasi-coaxial TEM source are set to compare with the electron density distribution along the axial direction (Z-axis) in the XZ plane. Normalized norm |𝐸| was expressed as the RSS (Root Sum Square: ∑ 𝜎 ) of the axial and radial Appl. Sci. 2021, 11, x FOR PEER REVIEW 15 of 20

because the electron loss from the quartz window surface along the direction of the electric field was not considered in detail in this simulation model. In the experiment, the energy distribution function of electrons of radial distance ≥ 20 mm followed the Maxwell distribution function. The electron temperature profile shown in Figure 15a is consistent with the simulation results in Figure 15b, which shows that when the radial distances > 20 mm from the quartz window surface, the electron temperature is weakly dependent on the radial distance. To consider each source and the plasma characteristics more deeply, it was necessary to consider the effects by resolving the electric field into the radial and axial direction electric field components. The material properties of plasma act like a lossy medium, which cause not only the transverse field components but also the axial field components to exist [16,17]. The presence of an axial component of the wave electric field in the quasi- coaxial line source was detailed by H. Nowakowska et al. [61]. In the presence of the axial component of the wave field, in the high electron density region (ne > 1018), internal wave was represented by a wave that propagated near the window surfaces along the axial direction. Power dissipation in the plasma chamber is concentrated near the dielectric window surface region, so the presence of an internal wave is important as a component that affects the electron heating in the axial direction.

Appl. Sci. 2021 11 , , 5358 (a) (b) 15 of 20 Figure 14. (a) Electron density at the substrate (Experiment) and (b) electron density at the substrate (Simulation).

(a) (b)

Figure 15.15.( a()a Electron) Electron temperature temperature at the at substrate the substrate (Experiment) (Experiment) and (b) electronand (b) temperatureelectron temperature at the substrate at the (Simulation). substrate (Simulation). In the experiment, the energy distribution function of electrons of radial distance ≥20In mm Figure followed 12, a the normalized Maxwell distributionnorm |𝐸| of function. the inner The conductor electron (green temperature line) and profile the shownwindow in surface Figure (purple15a is consistent line) in the with quasi-coaxi the simulational TEM results source in are Figure set to 15 compareb, which with shows the thatelectron when density the radial distribution distances along >20 the mm axial from direction the quartz (Z-axis) window in the XZ surface, plane. theNormalized electron temperaturenorm |𝐸| was is weaklyexpressed dependent as the RSS on (Root the radial Sum distance. Square: ∑ 𝜎 ) of the axial and radial To consider each source and the plasma characteristics more deeply, it was necessary to consider the effects by resolving the electric field into the radial and axial direction electric field components. The material properties of plasma act like a lossy medium, which cause not only the transverse field components but also the axial field components to exist [16,17]. The presence of an axial component of the wave electric field in the quasi-coaxial line source was detailed by H. Nowakowska et al. [61]. In the presence of the axial component of the wave field, in the high electron density region (ne > 1018), internal wave was represented by a wave that propagated near the window surfaces along the axial direction. Power dissipation in the plasma chamber is concentrated near the dielectric window surface region, so the presence of an internal wave is important as a component that affects the electron heating in the axial direction. In Figure 12, a normalized norm |E| of the inner conductor (green line) and the window surface (purple line) in the quasi-coaxial TEM source are set to compare with the electron density distribution along the axial direction (Z-axis) in the XZ plane. Normalized s n 2 norm |E| was expressed as the RSS (Root Sum Square: ∑ σi ) of the axial and radial i=1 components of the electric field. Figure 12 shows that the electron density distribution along the axial direction in the XZ plane follows the norm |E| profile in the window surface rather than the profile of the norm |E| in the inner conductor surface. This result is due to the axial field formed near the window surface region, and it can be observed in more detail in Figure 16. Figure 16 shows the distribution of the power dissipation, and the electron density distributions according to the electric field components in the axial and radial directions. Appl. Sci. 2021, 11, x FOR PEER REVIEW 16 of 20

components of the electric field. Figure 12 shows that the electron density distribution along the axial direction in the XZ plane follows the norm |𝐸| profile in the window surface rather than the profile of the norm |𝐸| in the inner conductor surface. This result is due to the axial field formed near the window surface region, and it can be observed in more detail in Figure 16. Figure 16 shows the distribution of the power dissipation, and the electron density distributions according to the electric field components in the axial and radial directions. In the TEM wave mode, because the radially radiated electric field was directed in all directions with the same value, Ex (= Ey) represented the component of the radial field, and Ez represented the component of the axial field. In the case of the axial electric field Ez, the field strength is the highest at 4 × 103 V/m for the window surface, and for the radial electric field Ex, the field strength is the highest at 3 × 104 V/m for the inner conductor surface. In Figure 16a,c, it is possible to compare the spatial distribution of the electron density according to each electric field component. Similar to Figure 12, it can be seen that the electron density distribution on the XZ plane follows the axial field component and not the radial field component. In Figure 16b,d, the spatial distribution characteristics of the power dissipation deposited in the plasma can be seen along each component of the electric field. In the figures, the maximum strength of the radial field is 3 × 104 V/m and has a value greater than 4 × 103 V/m of the axial field, while the maximum value of the power dissipation along the radial field near the surface region is 1 × 105 W/m3, which is lower than 4 × 105 W/m3 of the axial field. When the power dissipation value deposited in the plasma discharge in the plasma chamber was volume-integrated according to the radial and axial fields, in the quasi-coaxial TEM MWP, the power dissipation value by the axial field ≈ 400 W, and the power consumption by the radial field ≈ 200 W. In this simulation model, the power application method that inputted 600 W was fully deposited to the conductive material, and the plasma was applied. The power consumed by the conductive material, including the inner copper antenna, was less than 0.1 W. Therefore, when the total power of 600 W was applied to generate the plasma, power dissipation by the axial field was doubled compared to the radial field. Thus, in the quasi-coaxial TEM MWP sources, it was observed that axial field components in a horizontal form on the window surface compared to radial field components in a perpendicular form on the Appl. Sci. 2021, 11, 5358 window surface (electron losses occur at the wall boundary) dominantly affected16 ofthe 20 electron heating in the plasma discharge.

1 ∗ Figure 16. Electron density and power dissipation Qh,z (=Re ( 2 σ·Ez·Ez )) distributions according to the |Ez| profile, electron 1 ∗ density and power dissipation Qh,x (=Re ( 2 σ·Ex·Ex )) distributions according to the |Ex| profile in the XZ plane of quasi co-axial line TEM waveguiding structure. (a) Electron density distribution according to the profile of |Ez|,(b) the distribution of power dissipation value Qh,z according to the profile of |Ez|,(c) electron density distribution according to the profile of |Ex|, and (d) the distribution of power dissipation value Qh,x according to the |Ex| profile.

In the TEM wave mode, because the radially radiated electric field was directed in all directions with the same value, Ex (= Ey) represented the component of the radial field, and Ez represented the component of the axial field. In the case of the axial electric field Ez, the field strength is the highest at 4 × 103 V/m for the window surface, and for the radial 4 electric field Ex, the field strength is the highest at 3 × 10 V/m for the inner conductor surface. In Figure 16a,c, it is possible to compare the spatial distribution of the electron density according to each electric field component. Similar to Figure 12, it can be seen that the electron density distribution on the XZ plane follows the axial field component and not the radial field component. In Figure 16b,d, the spatial distribution characteristics of the power dissipation deposited in the plasma can be seen along each component of the electric field. In the figures, the maximum strength of the radial field is 3 × 104 V/m and has a value greater than 4 × 103 V/m of the axial field, while the maximum value of the power dissipation along the radial field near the surface region is 1 × 105 W/m3, which is lower than 4 × 105 W/m3 of the axial field. When the power dissipation value deposited in the plasma discharge in the plasma chamber was volume-integrated according to the radial and axial fields, in the quasi-coaxial TEM MWP, the power dissipation value by the axial field ≈ 400 W, and the power consumption by the radial field ≈ 200 W. In this simulation model, the power application method that inputted 600 W was fully deposited to the conductive material, and the plasma was applied. The power consumed by the conductive material, including the inner copper antenna, was less than 0.1 W. Therefore, when the total power of 600 W was applied to generate the plasma, power dissipation by the axial field was doubled compared to the radial field. Thus, in the quasi-coaxial TEM MWP sources, it was observed that axial field components in a horizontal form on the window surface compared to radial field components in a perpendicular form on the window surface (electron losses occur at the wall boundary) dominantly affected the electron heating in the plasma discharge. In Figure 13, normalized norm |E| on the cut surface of the cylindrical waveguiding structure (green line) and window surface (purple line) in the circular TE11 wave MWP source are set to compare with the electron density distribution along the axial direction (Z-axis) in the XZ plane. Unlike the result of Figure 12, Figure 13 shows that electron Appl. Sci. 2021, 11, 5358 17 of 20

density distribution along the axial direction in the XZ plane simultaneously follows the norm |E| profile in the cut surface of the cylindrical waveguiding structure and also in the window surface. This was because the axial field had a small effect on the electron generation in the spatial distribution. It represented that electron generation was mainly affected by the distribution of the radial direction the electric field component. When the volume-integrated power dissipation value deposited on the plasma discharge in the plasma chamber was expressed as components of the radial and axial fields, in the circular TE11 wave MWP, the power dissipation value by the axial field ≈ 40 W, and the power dissipation by the radial field ≈ 560 W. In this numerical model, the power application method in the circular TE11 source was applied in the same way as in the quasi-coaxial TEM source, and the power consumed by the conductive material was also less than 0.1 W. Therefore, it can be seen that when a total of 600 W was applied to generate the plasma, the dissipation of power by the radial field was more dominant than that of the axial field component. In Figure 17, the spatial distribution of the power dissipation and electron density distributions are represented according to the electric field components, which are indicated by resolving the radial fields into the Ex and Ey components. In the case of Ex, the field strength was the highest for 6 × 103 V/m near the window surface, and the field direction was perpendicular to the window surface. Similarly, for the case of Ey, the field strength was the highest for 1.5 × 104 V/m, and the field direction was parallel to the window surface. In both these cases, as shown in Figure 17, the spatial distributions of the electron generation and power dissipation coincided with the electric field concentrated region. When the volume-integrated power dissipation value deposited for plasma generation was calculated by resolving into the Ex and Ey field components, the power dissipation value E ≈ 300 W and E ≈ 260 W. Among the radial field components involved in the plasma Appl. Sci. 2021, 11, x FOR PEER REVIEWx y 18 of 20 discharge, a dominant component was Ex, which was due to the field emitted geometry characteristics of the waveguiding structure.

1 ∗ ∗ FigureFigure 17. 17. ElectronElectron densitydensity andand power power dissipation dissipationQ h𝑄,x (=Re(= Re ( 2 σ(·E𝜎x··𝐸Ex ))·𝐸distributions)) distributions according according to the to|E xthe| profile, |𝐸 | profile, electron , Q 1 σ·E ·E∗)) E electrondensity density and power and dissipationpower dissipationh,y(=Re 𝑄 ( 2 (= Rey (y 𝜎·𝐸distributions·𝐸∗)) distributions according according to the y to profile the 𝐸 in the profile XZ planein the ofXZ circular plane , TE11 waveguiding structure. (a) Electron density distribution according to the profile of |Ex|,(b) the distribution of power of circular TE11 waveguiding structure. (a) Electron density distribution according to the profile of |𝐸|, (b) the distribution dissipation value Qh,x according𝑄 to the profile of |Ex|,(c) electron|𝐸 | density distribution according to the profile of Ey , and of power dissipation value , according to the profile of , (c) electron density distribution according to the profile d Q E of( )𝐸 the, distributionand (d) the distribution of power dissipation of power valuedissipationh,y according value 𝑄, to according the y profile. to the 𝐸 profile.

6. Conclusions A conventional quasi co-axial TEM waveguiding structure and a newly developed circular TE11 waveguiding structure sources are presented to compare the plasma characteristics along the waveguiding structure. To compare the source characteristics, experiments were conducted under 500mTorr Ar plasma condition, where 0.6 kW microwave power was applied. The characteristics of the plasma was diagnosed by a single LP and analyzed by the numerical 3-D model using plasma fluid simulation. Attenuation of the electric field strength along the wave propagation direction and the coupled field profile at the window surface affected the spatial distribution of the electron density significantly. In the TE11 mode, the attenuation coefficient of the normalized electron density was 4.8 times higher than that of the TEM mode. The field direction affected the attenuation of the electron density along the radial distance, and the electrondensity reduction rate along the radial direction was higher in the TEM mode than that in the TE11 mode. The plasma characteristics of each plasma source were considered by resolving the wave electric field into the radial and axial field components. The influence of the axial electric field component was more dominant in the quasi-coaxial TEM MWP source. The number of electrons produced in the entire volume was 20% higher in the TEM mode than that in the TE11 mode, but the number of electrons generated in the actual deposition region was 50% higher in the TE11 mode than that in the TEM mode.

6. Conclusions A conventional quasi co-axial TEM waveguiding structure and a newly developed circular TE11 waveguiding structure sources are presented to compare the plasma characteristics along the waveguiding structure. To compare the source characteristics, experiments were conducted under 500mTorr Ar plasma condition, where 0.6 kW microwave power was applied. The characteristics of the plasma was diagnosed by a single LP and analyzed by the numerical 3-D model using plasma fluid simulation. Attenuation of the electric field strength along the wave propagation direction and the coupled field profile at the window surface affected the spatial distribution of the electron density significantly. In the TE11 mode, the attenuation coefficient of the normalized electron density was 4.8 times higher than that of the TEM mode. The field direction affected the attenuation of the electron density along the radial distance, and the electron-density reduction rate along the radial direction was higher in the TEM mode than that in the TE11 mode. The plasma characteristics of each plasma source were considered by resolving the wave electric field into the radial and axial field components. The influence of the axial electric field component was more dominant in the quasi-coaxial TEM MWP source. The number of electrons produced in the entire volume was 20% higher in the TEM mode than that in the TE11 mode, but the number of electrons generated in the actual deposition region was 50% higher in the TE11 mode than that in the TEM mode.

Author Contributions: Conceptualization, J.-H.C. and H.-J.L.; methodology, J.-H.C. and H.-J.L.; software, J.-H.C.; validation, J.-H.C., S.-W.K. and H.-J.L.; formal analysis, J.-H.C. and S.-W.K.; investigation, J.-H.C. and S.-W.K.; resources, J.-H.C.; data curation, J.-H.C.; writing—original draft preparation, J.-H.C.; writing—review and editing, J.-H.C.; visualization, J.-H.C.; supervision, H.-J.L.; project administration, H.-J.L.; funding acquisition, H.-J.L. All authors have read and agreed to the published version of the manuscript. Funding: This research was supported by Korea Institute for Advancement of Technology(KIAT) grant funded by the Korea Government(MOTIE) (P0012451, The Competency Development Program for Industry Specialist). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Data sharing is not applicable to this article. Acknowledgments: The authors would like to acknowledge the support of Korea Institute for Advancement of Technology(KIAT) grant funded by the Korea Government(MOTIE) (P0012451, The Competency Development Program for Industry Specialist). Conﬂicts of Interest: The authors declare no conﬂict of interest.

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