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Computational Study of Capacitively Coupled High-Pressure Glow Discharges in Helium

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Computational Study of Capacitively Coupled High-Pressure Glow Discharges in Helium
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  IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 31, NO. 4, AUGUST 2003 495 Computational Study of Capacitively CoupledHigh-Pressure Glow Discharges in Helium Xiaohui Yuan and Laxminarayan L. Raja  Abstract— Thestructure ofa capacitivelycoupledhigh-pressureglow (HPG) discharge in high-purity helium is investigated using adetailed one-dimensional modeling approach. Impurity effects aremodeled using trace amounts of nitrogen gas in helium. AverageelectrontemperaturesanddensitiesfortheHPGdischargearesim-ilar to their low-pressure counterpart. Helium-dimer ions domi-nate the discharge structure for sufficiently high-current densities,but model impurity nitrogen ions are found to be dominant forlow-discharge currents. Helium dimer metastable atoms are foundto be the dominant metastable species in the discharge. The highcollisionalityoftheHPGplasmaresultsinsignificantdischargepo-tential drop across the bulk plasma region, electron Joule heatingin the bulk plasma, and electron elastic collisional losses. High col-lisionality alsoresultsinverylowion-impactenergiesoforder1eVat the electrode surfaces.  Index Terms— High-pressure glow (HPG) discharge, compu-tational modeling, capacitively coupled helium plasma, plasmaimpurity effects. I. I NTRODUCTION L ARGE-VOLUME, high-pressure glow (HPG) dischargesare a class of electrical discharges characterized by stableand highly nonequilibrium glow plasmas that generated andsustained at pressures as high as one atmosphere [1]–[7]. HPG discharge plasmas operate in a distinctive regime of plasmaparameterspace,wheretheplasmapropertiesresemblealow-pressure glow plasmas, but at significantly higher pressureconditions. HPG discharges have traditionally been used forgas laser [8], [9] and combustion [10] applications, but there is significant resurgence in HPG discharge research kindled bynew approaches to generating HPG plasmas and applicationsfor the same. The ability to dispense with vacuum systems havefacilitated the use of HPG discharges in etching and depositionof thin films [1], [11]–[13], surface modification [14], ozone generation [15], biosterilization [16], and as reflectors and absorbers of electromagnetic radiation [17], [18]. The novelty of HPG plasma phenomena is in the stable,large-volume, nonequilibrium characteristics at high pressures.Stability of a large-volume, self-sustained discharge dependsprincipally on the current density through the discharge.Above a certain threshold current density (typically of order50 mA/cm ), instabilities develop which leads to constriction Manuscript received November 1, 2002; revised February 22, 2003. Thiswork was supported by the National Science Foundation (NSF) under an NSF-CAREER Award (CTS-0221557).The authors are with the Department of Aerospace Engineering and Engi-neering Mechanics, The University of Texas at Austin, Austin, TX 78712 USA(e-mail: lraja@mail.utexas.edu).Digital Object Identifier 10.1109/TPS.2003.815479 of the discharge volume and significant thermal heating of gas to form filamentary or arc plasmas. This phenomena iscalled the glow-to-arc transition. Pressure scaling relationshipsfor low-pressure glow discharges dictate that for a fixed totalcurrent the discharge current densities increase with increasingpressures [19]. Above a certain pressure (typically 10 torr),the current densities can exceed the threshold current densitiesfor instabilities to develop, resulting in a glow-to-arc transition.Traditional HPG discharge concepts rely on techniques thatlimit discharge current densities from exceeding the thresholdvalues for discharge stability [4]. For example, in dc HPG dis-charges, the cathode can be segmented into small sections andeach section individually ballasted with a large resistance tolimit the local current density to values below the threshold[8]. The same concept can be extended to nonsegmented cath-odesmadeofhigh-resistivitymaterials[20].Highgas-flowratesthrough the discharge have also been used successfully to limitthe effect of instabilities [21]. Another approach has been tooperate HPG discharges in the pulsed mode with peak currentdensities that exceed the threshold but with pulse durations thatare short compared to time scales for growth of instabilities[22]. Other approaches that avoid electrodes altogether, suchas microwave-driven large-volume HPG discharges in the sur-face-wave mode, have also been proposed [23].In a relatively recent development, Kanazawa  et al.  [1]have reported a dielectric-barrier concept for HPG plasmageneration. A dielectric barrier covers one or both electrodesof a parallel-plate discharge, which are driven by a low-fre-quency ( 1–50 kHz), high-voltage ( 1 kV) power source.Highly stable, large-volume, nonequilibrium HPG plasmas aregenerated in this configuration. The dielectric barrier servesto trap charge on the surface during each half cycle, which,in turn, creates a surface-charge-induced field that opposesthe applied field. The plasma is thereby extinguished beforecurrent densities reach very high values. The overall effect of the dielectric barrier is to create a plasma pulse during eachhalf cycle [6], [7]. Another concept reported recently uses a parallel-plate electrode configuration without dielectric barrier,but driven at much higher radio-frequencies of order 10 MHz[5], [24], [25]. The discharge can be classified as a capacitively coupled HPG discharge and is generated in a closed spaceconfiguration with interelectrode spacing of a few millimetersat most.Despite significant interest, our current understanding of HPG phenomena remains incomplete. Recent computationalmodeling studies have begun to reveal some preliminaryinsights into HPG phenomena in both dielectric barrier [6] aswell as capacitively coupled configurations [26]. However, 0093-3813/03$17.00 © 2003 IEEE  496 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 31, NO. 4, AUGUST 2003 a detailed understanding of the plasma dynamics, dominantphysical and chemical mechanisms, and structure of HPGdischarges is missing. We have previously reported a com-putational study of capacitively coupled HPG discharges anddescribed the role of trace impurities in such large-volume HPGplasmas [27]. In this study, we present a detailed computationalinvestigation of the structure and dynamics of capacitivelycoupled HPG discharges in pure helium. The presentation inthis paper is as follows. Section II presents a brief descriptionof the model, followed by results and discussions in Section III,and a summary with conclusions in Section IV.II. M ODEL  D ESCRIPTION  A. Governing Equations The computational model uses a one-dimensional (1-D) con-tinuummultifluiddescriptionoftheplasmawithindividualcon-tinuity equations describing the concentration of each chemicalspecies in the plasma, a current continuity equation for the elec-tric potential, and an electron energy equation to describe theelectron temperature in the discharge. The modeling approachis similar to several other models reported in the literature (see[28] for an overview) and is described briefly in the following.The species continuity is given by(1)where is the number of a species, is the species fluxdensity, is the homogeneous production/destruction rateof species through gas phase reactions, and is the totalnumber of charged and neutral gas species in the system. andare the time and interelectrode axial distance, respectively.The electric potential in discharge is described by specifyingtotal current density through the discharge as(2)where is the electric potential, is the unit charge, andis the species charge number. The electron energy equation isgiven as(3)where and are the electron temperature and gas tempera-tures, respectively, is the electron thermal flux, is theenergy lost per electron in an inelastic collision event describedby gas-reaction , istherateof progress of reaction ,and iselectron momentum transfer collision frequency with the back-ground gas. and are the molecular masses of the elec-tron and dominant background species, respectively and isthe Boltzmann constant. The collision frequency of a speciesis evaluated as(4)where is the number density of the background species,is an effective molecular speed of the species, and is themomentum transfer collision cross section of the species withthe dominant background.Closure of theprevious system of equations isachievedusingthe drift-diffusion approximation for the species number flux(5)and a Fourier’s law approximation for the electron thermal flux(6)The species diffusion coefficients are evaluated as, species mobilities as ,and the electron thermal conductivity as .  B. Boundary Conditions The boundary conditions imposed are as follows. Fluxboundary conditions are imposed for all species densities at theelectrodes. The electron and product neutral species fluxes aredetermined using a kinetically limited Maxwellian flux condi-tion as , where the signcorrespond to the lower and upper electrodes, respectively. Theions are assumed to be mobility limited at the boundaries andtheir boundary fluxes are specified as . Allmetastablespecies andionsareassumed toquench orneutralizeat the electrode surfaces and return back to the interelectrodespace as stable neutral species. The electron temperatures arefixed at the surface at 0.5 eV and secondary electron emissioneffects are ignored. We have performed sensitivity studies toconfirm that the assumptions of a fixed electron temperature atthe electrodes and zero secondary electron emission have nosignificant effect on the solutions. C. Plasma Chemistry The HPG plasma reaction mechanism for the high-purity he-lium includes pure helium and impurity species and their reac-tions.Ourpreviousworkhasshowntheimportanceofincludingtheeffectsofeventraceamountsofimpurityspeciesinthemod-elingofnoblegasHPGplasmaphenomena[27].Sincetheexactcomposition of impurity species in the discharge is unknown,we have used nitrogen as a model impurity in the simulations.The reaction mechanism is shown in Table I and is compliedfrom several literature sources [29]–[32].  D. Transport Properties Table II presents the transport properties of the plasmaspecies. The properties are given in terms of reduced diffusioncoefficients and mobilities and are defined in terms of , and , respectively, withbeing the discharge pressure in torr. These properties have beencomplied from literature data [19], [35], [36], and are evaluated assuming species transport in a helium background gas at atemperature of 393 K.  YUAN AND RAJA: COMPUTATIONAL STUDY OF CAPACITIVELY COUPLED HPG DISCHARGES IN HELIUM 497 TABLE IR EACTION  M ECHANISM FOR  H IGH –P RESSURE  H ELIUM  G LOW  P LASMA  W ITH  N ITROGEN  I MPURITY TABLE IIR EDUCED  D IFFUSION  C OEFFICIENTS AND  M OBILITIES OF  S PECIES IN A B ACKGROUND  H ELIUM  G AS III. R ESULTS AND  D ISCUSSIONS Computational resultspresented herearevalidatedusingdatafrom recent capacitively coupled HPG discharge experimentalstudies by Park   et al.  [25]. The experiments were conductedin a parallel-plate discharge configuration with stagnant (non-flowing), high-purity helium as the working gas. The stagnantgas environment allows accurate modeling using the 1-Dapproach. Discharge characteristics for varying interelectrodespacing and pressures, at a fixed frequency of 13.56 MHz aresimulated in this study.As mentioned in our previous paper [27], trace impuritiesplay an important role in determing the structure and dy-namics of noble gas HPG discharges and their effect must beincluded to predict even global discharge parameters such asthe voltage–current ( V–I  ) characteristics. The main effect of the trace impurities is to significantly decrease the differentialimpedance of the discharge compared to pure helium. Theexact concentration of model impurity is, therefore, a modelparameter that isdetermined to best match experimentalresults.We have found that model nitrogen impurity with an initialimpurity mole fraction of 5 10 (99.99995% or 0.5 ppm)in pure helium provides best comparison to experimental data[27]. This concentration is fixed for all simulation in our studyand is within the rate impurity concentration of 99.9995% forthe helium gas used in the experiments. Order-of-magnitudeestimates indicate that gas heating under discharge conditionsare not significant enough to cause a large temperature rise. Inour study, the gas temperature is assumed fixed at 393 K and isthe same as the experimentallymeasured gas temperatures [25].We first provide validation of the modeling approach by di-rect comparison between experimental data and our simulationresults for  V–I   characteristics of the discharge. Fig. 1 showsroot-mean-square (rms)  V–I   characteristics for varying inter-electrode distances of 1.6, 2.4, and 3.2 mm at a fixed dischargepressure of 600 torr. The same characteristics for varying pres-sures of 300, 450, and 600 torr at a fixed interelectrode distanceof 2.4 mm is presented in Fig. 2. All experimental  V–I   curvesshow an initial prebreakdown (no discharge) stage with linearrise in the voltage followed by a HPG stage where the voltageincreases slowly for an increase in the current. For higher cur-rentdensities,thevoltagebecomesrelativelyindependentofthecurrent through thedischarge.The differential impedanceof the  498 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 31, NO. 4, AUGUST 2003 Fig. 1. Comparison of experimental and simulated rms  V–I   characteristics forvarying interelectrode distances of 1.6, 2.4, and, 3.2 mm and a fixed pressureof 600 torr. The RF frequency is 13.56 MHz for all cases. Circle symbolscorrespond to 1.6, triangles are 2.4, and rectangles are at 3.2 mm. Simulationresults are connected by a line.Fig. 2. Comparison of experimental and simulated rms  V–I   characteristics forvarying discharge pressures of 300, 450, 600 torr, and a fixed interelectrodedistance of 2.4 mm. The RF frequency is 13.56 MHz for all cases. Circlesymbols correspond 300, triangles are 450, and rectangles are at 600 torr.Simulation results are connected by a line. HPG discharge is, therefore, small for low-current densities andnearly zero for high-current densities. HPG discharge voltagesincrease with increasing interelectrode distance for afixed pres-sure and increase with increasing pressures for a fixed inter-electrode distance. The maximum current densities for whichthe experimental data are shown correspond to threshold cur-rent densities for glow-to-arc transition. The model predicts allimportant features of the experimental data with good predic-tions of the experimental voltages at the high-current densities.The voltage is underpredicted at low-current densities but thetrends are captured adequately. Importantly, the low differentialimpedance at low-current densities followed by the near-zerodifferentialimpedanceatthehigh-currentdensitiesareobservedin the model results. We must, however, emphasize that themodeldoesnotrepresentthephysicsofthedischargeadequatelyto capture the breakdown and glow-to-arc transition limits.Fig. 3 shows the voltage- and current-density waveforms fora 600 torr discharge, with a 2.4-mm interelectrode spacing anda 21.2 mA/cm rms current density. The waveforms show asmooth and near-sinusoidal voltage characteristic for the im-posed sinusoidal current. The current is also found to lead thevoltage waveform by 35.7 . These model results are consistent Fig. 3. Simulated voltage and current density waveforms for a 600-torrdischarge with 2.4-mm interelectrode spacing, 13.56-MHz RF frequency, and21.2-mA/cm rms current density.Fig. 4. Simulated potential profiles at four times instances during an RFcycle for a 600-torr discharge with 2.4-mm interelectrode spacing, 13.56-MHzRF frequency, and 21.2-mA/cm rms current density. The fractional time0 corresponds to a positive maximum phase of the discharge current, 0.25corresponds to zero current, 0.5 corresponds to the negative maximum phaseof the discharge current, and 0.75 to the subsequent zero current. withexperimentaldata,wheresmoothandnearlysinusoidal V–I  waveforms are observed under HPG conditions, especially atlow- and intermediate-current densities [25].Fig. 4 shows the interelectrode electric potential profiles forthe same discharge parameters as in Fig. 3. Distinct regionscorresponding to the electrode sheaths and a bulk plasma inbetween them, can be identified. Large potential drops areobserved at the sheaths at cycle fractional times of 0.25 and0.75 while large drops are observed through the bulk plasmaat fractional times of 0 and 0.5. The cycle fractional timesof 0.25 and 0.75 correspond to the zero current phases of the cycle, while fractional times of 0 and 0.5 correspond tothe maximum current phases of the cycle. These dischargepotential profiles show significant differences compared toclassical low-pressure capacitively coupled glow discharges,wherethedischargepotentialdropsoccuralmost entirelyacrossthe sheaths at all times during an RF cycle. The large bulk plasma potential drop for the HPG discharge at the maximumcurrent phases is a result of the high pressures which resultsin significant resistivity of the bulk plasma. The maximumelectric field strength predicted in the sheath region of the HPGdischarge is of order 4 kV/cm which is somewhat higher thantypical field strengths ( 0.5 kV/cm) observed in the sheathsof low-pressure capacitively coupled discharges [31], [33].
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