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

IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 31, NO. 4, AUGUST 2003 495 Computational Study of Capacitively Coupled High-Pressure Glow Discharges in Helium Xiaohui Yuan and Laxminarayan L. Raja Abstract The structure of a capacitively coupled high-pressure glow (HPG) discharge in high-purity helium is investigated using a detailed one-dimensional modeling approach. Impurity effects are modeled using trace amounts of nitrogen gas in helium. Average electron temperatures and densities for the HPG discharge are similar to their low-pressure counterpart. Helium-dimer ions dominate the discharge structure for sufficiently high-current densities, but model impurity nitrogen ions are found to be dominant for low-discharge currents. Helium dimer metastable atoms are found to be the dominant metastable species in the discharge. The high collisionality of the HPG plasma results in significant discharge potential drop across the bulk plasma region, electron Joule heating in the bulk plasma, and electron elastic collisional losses. High collisionality also results in very low ion-impact energies of order 1 ev at the electrode surfaces. Index Terms High-pressure glow (HPG) discharge, computational modeling, capacitively coupled helium plasma, plasma impurity effects. I. INTRODUCTION LARGE-VOLUME, high-pressure glow (HPG) discharges are a class of electrical discharges characterized by stable and highly nonequilibrium glow plasmas that generated and sustained at pressures as high as one atmosphere [1] [7]. HPG discharge plasmas operate in a distinctive regime of plasma parameter space, where the plasma properties resemble a low-pressure glow plasmas, but at significantly higher pressure conditions. HPG discharges have traditionally been used for gas laser [8], [9] and combustion [10] applications, but there is significant resurgence in HPG discharge research kindled by new approaches to generating HPG plasmas and applications for the same. The ability to dispense with vacuum systems have facilitated the use of HPG discharges in etching and deposition of 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 depends principally on the current density through the discharge. Above a certain threshold current density (typically of order 50 ma/cm ), instabilities develop which leads to constriction Manuscript received November 1, 2002; revised February 22, 2003. This work was supported by the National Science Foundation (NSF) under an NSF- CAREER Award (CTS-0 221 557). The authors are with the Department of Aerospace Engineering and Engineering 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 is called the glow-to-arc transition. Pressure scaling relationships for low-pressure glow discharges dictate that for a fixed total current the discharge current densities increase with increasing pressures [19]. Above a certain pressure (typically 10 torr), the current densities can exceed the threshold current densities for instabilities to develop, resulting in a glow-to-arc transition. Traditional HPG discharge concepts rely on techniques that limit discharge current densities from exceeding the threshold values for discharge stability [4]. For example, in dc HPG discharges, the cathode can be segmented into small sections and each section individually ballasted with a large resistance to limit the local current density to values below the threshold [8]. The same concept can be extended to nonsegmented cathodes made of high-resistivity materials [20]. High gas-flow rates through the discharge have also been used successfully to limit the effect of instabilities [21]. Another approach has been to operate HPG discharges in the pulsed mode with peak current densities that exceed the threshold but with pulse durations that are short compared to time scales for growth of instabilities [22]. Other approaches that avoid electrodes altogether, such as microwave-driven large-volume HPG discharges in the surface-wave mode, have also been proposed [23]. In a relatively recent development, Kanazawa et al. [1] have reported a dielectric-barrier concept for HPG plasma generation. A dielectric barrier covers one or both electrodes of a parallel-plate discharge, which are driven by a low-frequency ( 1 50 khz), high-voltage ( 1 kv) power source. Highly stable, large-volume, nonequilibrium HPG plasmas are generated in this configuration. The dielectric barrier serves to trap charge on the surface during each half cycle, which, in turn, creates a surface-charge-induced field that opposes the applied field. The plasma is thereby extinguished before current densities reach very high values. The overall effect of the dielectric barrier is to create a plasma pulse during each half 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 space configuration with interelectrode spacing of a few millimeters at most. Despite significant interest, our current understanding of HPG phenomena remains incomplete. Recent computational modeling studies have begun to reveal some preliminary insights into HPG phenomena in both dielectric barrier [6] as well 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, dominant physical and chemical mechanisms, and structure of HPG discharges is missing. We have previously reported a computational study of capacitively coupled HPG discharges and described the role of trace impurities in such large-volume HPG plasmas [27]. In this study, we present a detailed computational investigation of the structure and dynamics of capacitively coupled HPG discharges in pure helium. The presentation in this paper is as follows. Section II presents a brief description of the model, followed by results and discussions in Section III, and a summary with conclusions in Section IV. where is the number density of the background species, is an effective molecular speed of the species, and is the momentum transfer collision cross section of the species with the dominant background. Closure of the previous system of equations is achieved using the drift-diffusion approximation for the species number flux and a Fourier s law approximation for the electron thermal flux (5) II. MODEL DESCRIPTION A. Governing Equations The computational model uses a one-dimensional (1-D) continuum multifluid description of the plasma with individual continuity equations describing the concentration of each chemical species in the plasma, a current continuity equation for the electric potential, and an electron energy equation to describe the electron temperature in the discharge. The modeling approach is 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 where is the number of a species, is the species flux density, is the homogeneous production/destruction rate of species through gas phase reactions, and is the total number of charged and neutral gas species in the system. and are the time and interelectrode axial distance, respectively. The electric potential in discharge is described by specifying total current density through the discharge as where is the electric potential, is the unit charge, and is the species charge number. The electron energy equation is given as where and are the electron temperature and gas temperatures, respectively, is the electron thermal flux, is the energy lost per electron in an inelastic collision event described by gas-reaction, is the rate of progress of reaction, and is electron momentum transfer collision frequency with the background gas. and are the molecular masses of the electron and dominant background species, respectively and is the Boltzmann constant. The collision frequency of a species is evaluated as (1) (2) (3) (4) 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. Flux boundary conditions are imposed for all species densities at the electrodes. The electron and product neutral species fluxes are determined using a kinetically limited Maxwellian flux condition as, where the sign correspond to the lower and upper electrodes, respectively. The ions are assumed to be mobility limited at the boundaries and their boundary fluxes are specified as. All metastable species and ions are assumed to quench or neutralize at the electrode surfaces and return back to the interelectrode space as stable neutral species. The electron temperatures are fixed at the surface at 0.5 ev and secondary electron emission effects are ignored. We have performed sensitivity studies to confirm that the assumptions of a fixed electron temperature at the electrodes and zero secondary electron emission have no significant effect on the solutions. C. Plasma Chemistry The HPG plasma reaction mechanism for the high-purity helium includes pure helium and impurity species and their reactions. Our previous work has shown the importance of including the effects of even trace amounts of impurity species in the modeling of noble gas HPG plasma phenomena [27]. Since the exact composition 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 complied from several literature sources [29] [32]. D. Transport Properties Table II presents the transport properties of the plasma species. The properties are given in terms of reduced diffusion coefficients and mobilities and are defined in terms of, and, respectively, with being the discharge pressure in torr. These properties have been complied from literature data [19], [35], [36], and are evaluated assuming species transport in a helium background gas at a temperature of 393 K. (6)

YUAN AND RAJA: COMPUTATIONAL STUDY OF CAPACITIVELY COUPLED HPG DISCHARGES IN HELIUM 497 TABLE I REACTION MECHANISM FOR HIGH PRESSURE HELIUM GLOW PLASMA WITH NITROGEN IMPURITY TABLE II REDUCED DIFFUSION COEFFICIENTS AND MOBILITIES OF SPECIES IN A BACKGROUND HELIUM GAS III. RESULTS AND DISCUSSIONS Computational results presented here are validated using data from recent capacitively coupled HPG discharge experimental studies by Park et al. [25]. The experiments were conducted in a parallel-plate discharge configuration with stagnant (nonflowing), high-purity helium as the working gas. The stagnant gas environment allows accurate modeling using the 1-D approach. Discharge characteristics for varying interelectrode spacing and pressures, at a fixed frequency of 13.56 MHz are simulated in this study. As mentioned in our previous paper [27], trace impurities play an important role in determing the structure and dynamics of noble gas HPG discharges and their effect must be included to predict even global discharge parameters such as the voltage current (V I) characteristics. The main effect of the trace impurities is to significantly decrease the differential impedance of the discharge compared to pure helium. The exact concentration of model impurity is, therefore, a model parameter that is determined to best match experimental results. We have found that model nitrogen impurity with an initial impurity 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 study and is within the rate impurity concentration of 99.9995% for the helium gas used in the experiments. Order-of-magnitude estimates indicate that gas heating under discharge conditions are not significant enough to cause a large temperature rise. In our study, the gas temperature is assumed fixed at 393 K and is the same as the experimentally measured gas temperatures [25]. We first provide validation of the modeling approach by direct comparison between experimental data and our simulation results for V I characteristics of the discharge. Fig. 1 shows root-mean-square (rms) V I characteristics for varying interelectrode distances of 1.6, 2.4, and 3.2 mm at a fixed discharge pressure of 600 torr. The same characteristics for varying pressures of 300, 450, and 600 torr at a fixed interelectrode distance of 2.4 mm is presented in Fig. 2. All experimental V I curves show an initial prebreakdown (no discharge) stage with linear rise in the voltage followed by a HPG stage where the voltage increases slowly for an increase in the current. For higher current densities, the voltage becomes relatively independent of the current through the discharge. The differential impedance of the

498 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 31, NO. 4, AUGUST 2003 Fig. 1. Comparison of experimental and simulated rms V I characteristics for varying interelectrode distances of 1.6, 2.4, and, 3.2 mm and a fixed pressure of 600 torr. The RF frequency is 13.56 MHz for all cases. Circle symbols correspond to 1.6, triangles are 2.4, and rectangles are at 3.2 mm. Simulation results are connected by a line. Fig. 3. Simulated voltage and current density waveforms for a 600-torr discharge with 2.4-mm interelectrode spacing, 13.56-MHz RF frequency, and 21.2-mA/cm rms current density. Fig. 2. Comparison of experimental and simulated rms V I characteristics for varying discharge pressures of 300, 450, 600 torr, and a fixed interelectrode distance of 2.4 mm. The RF frequency is 13.56 MHz for all cases. Circle symbols 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 and nearly zero for high-current densities. HPG discharge voltages increase with increasing interelectrode distance for a fixed pressure and increase with increasing pressures for a fixed interelectrode distance. The maximum current densities for which the experimental data are shown correspond to threshold current densities for glow-to-arc transition. The model predicts all important features of the experimental data with good predictions of the experimental voltages at the high-current densities. The voltage is underpredicted at low-current densities but the trends are captured adequately. Importantly, the low differential impedance at low-current densities followed by the near-zero differential impedance at the high-current densities are observed in the model results. We must, however, emphasize that the model does not represent the physics of the discharge adequately to capture the breakdown and glow-to-arc transition limits. Fig. 3 shows the voltage- and current-density waveforms for a 600 torr discharge, with a 2.4-mm interelectrode spacing and a 21.2 ma/cm rms current density. The waveforms show a smooth and near-sinusoidal voltage characteristic for the imposed sinusoidal current. The current is also found to lead the voltage waveform by 35.7. These model results are consistent Fig. 4. Simulated potential profiles at four times instances during an RF cycle for a 600-torr discharge with 2.4-mm interelectrode spacing, 13.56-MHz RF frequency, and 21.2-mA/cm rms current density. The fractional time 0 corresponds to a positive maximum phase of the discharge current, 0.25 corresponds to zero current, 0.5 corresponds to the negative maximum phase of the discharge current, and 0.75 to the subsequent zero current. with experimental data, where smooth and nearly sinusoidal V I waveforms are observed under HPG conditions, especially at low- and intermediate-current densities [25]. Fig. 4 shows the interelectrode electric potential profiles for the same discharge parameters as in Fig. 3. Distinct regions corresponding to the electrode sheaths and a bulk plasma in between them, can be identified. Large potential drops are observed at the sheaths at cycle fractional times of 0.25 and 0.75 while large drops are observed through the bulk plasma at fractional times of 0 and 0.5. The cycle fractional times of 0.25 and 0.75 correspond to the zero current phases of the cycle, while fractional times of 0 and 0.5 correspond to the maximum current phases of the cycle. These discharge potential profiles show significant differences compared to classical low-pressure capacitively coupled glow discharges, where the discharge potential drops occur almost entirely across the sheaths at all times during an RF cycle. The large bulk plasma potential drop for the HPG discharge at the maximum current phases is a result of the high pressures which results in significant resistivity of the bulk plasma. The maximum electric field strength predicted in the sheath region of the HPG discharge is of order 4 kv/cm which is somewhat higher than typical field strengths ( 0.5 kv/cm) observed in the sheaths of low-pressure capacitively coupled discharges [31], [33].

YUAN AND RAJA: COMPUTATIONAL STUDY OF CAPACITIVELY COUPLED HPG DISCHARGES IN HELIUM 499 Fig. 5. Spatial profiles of important discharge parameters. The discharge operating conditions are the same as in Fig. 4. The top panel shows the time-averaged electron temperature and number densities. The center panel shows the dominant ion densities and the bottom panel shows the neutral species densities. Spatial profiles of time-averaged electron temperature and species number densities are shown in Fig. 5. The discharge operating conditions are the same as in Fig. 4. The top panel shows time-averaged profiles of the electron temperature and electron number densities. The average temperature is nearly uniform in the bulk plasma (about 1 ev) but rises to peak values of about 2.5 ev within the sheaths. The average electron density is a maximum at the center of the discharge and drops toward the electrodes. The peak calculated electron density is about 1.8 10 m at the center of the discharge and is close to the experimental estimate of 3 10 m [25]. A small hump in the electron density profile is observed inside the sheaths and is a consequence of significant volumetric production of electrons through plasma reactions in the sheaths. This phenomena must be contrasted with low-pressure glow discharge sheaths where effect of plasma chemistry is negligible and charge generation is mostly confined to the sheath-bulk plasma interface and bulk plasma region [31], [33], [34]. The center panel shows time-averaged ion density profiles in the discharge. The ion densities experience negligible modulation during an RF cycle owing to their heavier mass, although relatively small modulations are noticed for the helium ions within the sheaths. The dominant ion in the bulk plasma is He, while the impurity ion N dominates in the sheath region. N ion density profile resembles the He ions with a maximum at the center of the discharge and much lower values in the sheaths. He ion densities are negligible throughout the discharge. The ion density profiles indicate that He and N ions are generated by reactions in the bulk plasma or the sheath-bulk plasma interface regions while the N ions are generated predominantly within the sheath regions. The Fig. 6. Time-averaged contributions of gas-phase reaction pathways to the generation/destruction of electrons in the HPG discharge. The discharge operating conditions are the same as in Fig. 4. neutral species profiles are shown in the bottom panel. Both the helium metastable species He and He have peaks within the sheaths, indicating significant volumetric production of these species inside the sheath regions. The helium metastable profiles have a minimum at the center of the discharge owing to net volumetric destruction in the bulk plasma. The metastable densities drop close to the electrodes owing to surface quenching effects. The nitrogen atom N shows a peak at the center of the discharge and drop toward the electrodes. The nitrogen (impurity) molecules N are depleted at the center of the discharge and are regenerated at the two electrodes by surface neutralization of nitrogen ions and recombination of N radicals. The He background species density is nearly uniform throughout the discharge and has a value of 1.47 10 m. The previous spatial profiles of important species in the plasma are established by the combined effect of gas-phase plasma reactions, transport, and surface reactions at the electrodes. The time-averaged contributions of the gas-reaction pathways to the productions/destruction of electrons in the discharge are presented in Fig. 6. The discharge operating conditions are the same as in Fig. 4. The figure shows rates of 11 reactions (see Table I) that contribute to the electron density balance. The reactions with highest contribution to the volumetric production rate of electrons are shown in the top panel. Reaction, which is the Penning ionization of N by metastable He, is the dominant reaction for electron production and plays an important role only within the sheaths where N densities are high. The second most important contribution comes from reaction, which is the electron impact ionization of the He background atoms. Again the contribution of this reaction is dominant in the sheaths where the electron

500 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 31, NO. 4, AUGUST 2003 Fig. 7. Time-averaged contributions of Joule heating, and elastic and inelastic collisions to the electron energy balance in the discharge. The discharge operating conditions are the same as in Fig. 4. temperatures are high. The center and bottom panels show that reactions (Penning ionization of N by metastable He ), (stepwise ionization of He ), (electron impact ionization of N), (stepwise ionization of He ), and (electron impact ionization of N ) also play a relatively minor role in the electron production inside the sheaths. In the bulk plasma, the dominant contributors to electron production are, followed by. The bottom panel shows that the electrons are also consumed within the discharge by reactions (dissociative recombination of N ) and (dissociative recombination of He ). The remaining electrons are consumed at the electrodes. Fig. 6 provides a vivid picture of how the impurity species (N ) alters the charge balance in a noble gas HPG discharge by participating in Penning ionizations reactions within the sheaths. The figure also points to another important distiction between low-pressure glow and HPG discharges. Unlike low-pressure capacitively coupled discharges where charge production is confined mostly to the sheath-bulk plasma interface region [31], [33], [34], the charge production in HPG discharges is distributed throughout the discharge and in particular is very high within the sheath regions. The time-averaged contributions of volumetric source/sink terms that contribute to the electron energy balance in the discharge are shown in Fig. 7. These include Joule heating, inelastic collisional loss/gain, and elastic collisional loss terms. These are the third, fourth, and fifth terms in (3), respectively. Joule heating is the principal source of electron heating in the discharge and is dominant in the bulk plasma as well as the sheath-bulk plasma interface region. The main volumetric loss of electron energy comes from elastic collisions of the high-temperature electrons with the low-temperature background heavy species. Inelastic collisions contribute to a net loss of electron energy although the magnitude of the inelastic loss is small compared to the elastic collisional loss of electron energy. Fig. 7 also points to important differences in the mechanisms of electron energy balance in HPG discharges and low-pressure glow discharges. In capacitively coupled low-pressure glow discharges, Joule heating is largely confined to the sheath-bulk plasma interface regions where electric field strengths are high and electron particle fluxes are significant [33], [34]. In the capacitively coupled HPG discharge, however, electric field strengths are high in the bulk plasma as well as the sheaths and, hence, Joule heating Fig. 8. Dependence of time-averaged electron density profiles for varying discharge parameters. The top panel shows variation with rms current density for fixed pressure of 600 torr and 2.4-mm interelectode gap. The middle panel shows variations with pressure for a fixed rms current density of 21.2 ma/cm and 2.4-mm interelectode gap. The bottom panel shows variations with interelectrode gap for a fixed pressure of 600 torr and rms current density of 21.2 ma/cm. The RF frequency is 13.56 MHz for all cases. The units for each parameter varied are indicated in brackets. is distributed throughout the discharge, except near the electrode where electron densities are low. Another major difference between low-pressure and HPG discharges is the contribution of elastic collisional loss terms. Elastic collisional loss to the background gas is negligible in most low-pressure glow discharges and is often neglected in the modeling of such discharges [28]. However, elastic collisions are the dominant volumetric electron energy loss mechanism in HPG discharges. The effect of changes in discharge operating parameters is discussed next. Fig. 8 shows the time-averaged electron density profiles for changes in the rms current density, pressure, and interelectrode gap. The magnitude of the current densities through the discharge has a large impact on the discharge structure. The electron densities increase for increasing current densities. In addition, electron production due to Penning ionization reactions within the sheaths depends significantly on the current densities through the discharge. For the lowest current density case shown (8.5 ma/cm ), the electron production in the sheaths is negligible compared to the higher current density cases. This, in turn, manifests itself as an increasingly prominent hump in the density profiles within the sheath regions for increasing current densities. As shown in the center panel, the electron densities are nearly unchanged for changes in discharge pressure, indicating that under high-pressure conditions, the magnitude of the discharge pressure itself is relatively unimportant in determining the global characteristics of an HPG plasma. From the bottom panel it is seen that changes in the gap distance results in a relatively small increase in the maximum electron number densities at the center of the discharge. Since the sheath thick-

YUAN AND RAJA: COMPUTATIONAL STUDY OF CAPACITIVELY COUPLED HPG DISCHARGES IN HELIUM 501 Fig. 9. Dependence of the time-averaged electron temperatures for varying discharge parameters. The parameters varied in each panel are the same as in Fig. 8. ness remains relatively constant for all gap lengths, the main effect of increasing the gap length is the increase in the length of the bulk plasma region. The effect of varying discharge operating parameters on the time-averaged electron temperature profiles is shown in Fig. 9. The top panel shows that with the exception of the lowest current density case (8.5 ma/cm ), the electron temperatures are relatively independent of the magnitude of the current flow through the discharge. For the low-current density case, the average electron temperature in the bulk plasma is about 0.2 ev, which is significantly lower than the 1-eV average temperature for the other cases. As in the case of electron densities, the electron temperatures are relatively independent of the discharge pressures. Also, variations in the gap length results in a longer bulk plasma region with negligible change in magnitudes of the bulk plasma temperature and peak sheath temperature. Results from both Figs. 8 and 9 indicate that the rms current density through the discharge has the most significant effect on the HPG discharge properties. In particular, two distinct regimes in the current density can be identified; one being the low-current density regime and the other the intermediate to high-current density regime. These two regimes were identified in our earlier discussion on the discharge V I characteristics, as regimes with low-differential impedance (low-current densities) and near-zero differential impedance (intermediate-to-high current densities). Further insights into the discharge structure in these current regimes can be obtained from Fig. 10, where the time-averaged profiles of all ions in the discharge are plotted at the three rms currents densities for a fixed pressure of 600 torr and a gap of 2.4 mm. The intermediate (21.2 ma/cm ) and high-current density (31.8 ma/cm ) cases are characterized by He as the dominant ion in the bulk plasma region and N Fig. 10. Dependence of the time-averaged ion density profiles on the current densities through the discharge. The pressure is fixed at 600 torr, the RF frequency is 13.56 MHz, and the gap distance is 2.4 mm. The numbers against each curve indicates the the rms current density in ma/cm. as the dominant ion in the sheath regions. Somewhat lower N ions are also observed in the bulk-plasma region. However, in the low-current density case (8.5 ma/cm ), the discharge structure swithes to a different regime where the impurity ion N is the only dominant ion in the discharge with all other ion densities being negligible. He ions are negligible for all cases. An detailed analysis of the gas reaction pathways for the low-current density case compared to the intermediate and high-current density cases reveals reasons for the switch in the dominant bulk plasma ion species at low-current densities compared to intermediate and high-current densities. The relatively low bulk plasma electron temperatures of 0.2 ev in the low-current density case causes Penning ionization of the impurity molecule N (reactions and ) to dominate the overall ionization rate when compared to direct or stepwise ionization of helium (reactions or ). This is owing to the fact that direct and stepwise ionization of helium are activated processes and require higher electron temperatures for the corresponding rates to be high. As a consequence, N ions are the dominant ion species at the low current densities. At higher current densities, the plasma electron temperatures are higher, causing the direct and stepwise ionization of helium to dominate the plasma ionization mechanism. He ions produced thereby, are rapidly converted to He ions through three-body reaction, resulting in dominant He in the bulk plasma for the intermediate- to high-current density cases. Finally, the ion impact energy distribution functions (IEDF) at one of the electrodes for discharge pressures of 600 and 300 torr are presented in Fig. 11. The IEDF is defined as the fractional flux of each type of ions impacting the surface at a

502 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 31, NO. 4, AUGUST 2003 ions. For example, at 300 torr, the maximum ion impact energy of N increases to about 3.7 ev compared to 1 ev at 600 torr. Fig. 11. Ion impact energy distribution functions for each ion species impacting an electrode. The discharge parameters correspond to 2.4-mm interelectrode gap, 13.56-MHz RF frequency, and 21.2-mA/cm rms current density. The top panel shows results for 600 torr and the bottom panel for 300-torr discharge pressures. given impact energy, per unit impact energy. The IEDFs for all ions are bimodal with a peak at the minimum energy of ion impact and another peak at the maximum energy of ion impact. The bimodal IEDF is also observed for RF biased surfaces in low-pressure glow discharges. For the HPG discharge, the minimum energy peaks correspond to near-zero ion impact energies for all ions, while the maximum energy peak varies significantly depending on the type of ion and the pressure. The ion impact energy distribution is found to be widest for the N ions, followed by N, He, and He in order of decreasing distribution widths. The maximum ion impact energy at 600 torr is about 1 ev for the N ions and about 0.05 ev for the He ions. The corresponding maximum ion impact energies at 300 torr are about 3.6 ev for N ions and 0.2 ev for He ions. The previous ion impact energy distribution trends are contrary to trends observed for RF biased surfaces in low-pressure glow discharges. In low-pressure glow discharges the distribution widths increase with decreasing ion mass [37] [39] while in the HPG discharge the widths decrease with decreasing ion mass. For low-pressure glow discharges, the sheaths are weakly collisional or collisionless which causes ion transport in the sheath to be dominated by inertial effects resulting in the IEDF widths being inversely related to the ion mass. In HPG discharges, the sheaths are highly collisional and the ion transport depends largely on the electric-field-induced species mobility. Ions with higher mobility are able to follow the sheath electric field oscillation more closely and hence experience wider IEDFs at the electrode surface. Lower mobility ions are much more sluggish in their response to sheath electric field oscillations, which results in a narrower IEDFs. In a helium background gas, the ions N,N,He, and He ions have decreasing mobility in that order (see Table II) and, hence, their ion impact energy distributions have correspondingly narrower distributions. A decrease in the discharge pressure results in an overall increase in the mobility of all ions, which results in wider distribution for all IV. CONCLUSION We have presented a detailed computational study of capacitively coupled, HPG discharges in high purity helium. A 1-D, self-consistent, continuum plasma model is developed and used. Small concentrations of a model nitrogen impurity in pure helium (5 10 in mole fraction or 0.5 ppm) is required to model discharge properties accurately. The model predicts the experimental V I characteristics for a range of pressures and gap distances. The discharge structure consists of a bulk plasma region and sheath regions adjacent to the electrodes. The predicted average electron temperatures of order 1 ev and electron number densities of order 10 cm are comparable to those found in most low-pressure glow discharges. The electron temperatures are relatively independent of the current density through the discharge as well as discharge pressures, except for low-current densities where the temperature drops significantly. The electron temperatures depend largely on Joule heating in the bulk plasma and the sheath-plasma interface regions as well as electron energy loss by elastic collisions with colder heavy species. This contrasts with low-pressure capacitively coupled glow discharges where elastic collision losses are negligible and Joule heating is dominant only in the plasma-sheath interface region. The plasma electron density depends strongly on the current density through the discharge but is relatively independent of the discharge pressure. The ion concentration in the discharge is dominated by dimer helium ions He in the bulk plasma and impurity N ions in the sheaths. However, at low-current densities the impurity ions dominate almost the entire discharge structure. The dimer helium metastables He are observed to be the dominant metastable species in the discharge with densities of order 10 cm. Owing to highly collisional sheaths, the ion-impact energies at the electrodes are found to range from near-zero values to a maximum of a few electronvolts. These energies are very low compared to low-pressure glow discharges where ion impact energies can range from order 10 to a few 100 ev. 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Data Tables, vol. 17, pp. 177 210, 1976. [37] M. S. Barnes, J. C. Forster, and J. H. Keller, Ion kinetics in low-pressure, electropositive, RF glow discharge sheaths, IEEE Trans. Plasma Sci., vol. 19, pp. 240 244, Apr. 1991. [38] P. A. Miller and M. E. Riley, Dynamics of collisionless RF plasma sheaths, J. Appl. Phys., vol. 82, pp. 3689 3709, 1997. [39] L. L. Raja and M. Linne, Analytical model for ion angular distribution functions at RF biased surfaces with collisionless plasma sheaths, J. Appl. Phys., vol. 93, pp. 7032 7040, 2003. Xiaohui Yuan received the B.S. degree in chemical engineering from Tsinghua University, Beijing, China, in 1999, and is currently working toward the Ph.D. degree. Laxminarayan L. Raja received the B.Tech. degree in aerospace engineering from the Indian Institute of Technology, Chennai, India, in 1990, the M.S. degree in nuclear engineering from Texas A&M University, College Station, in 1992, and the Ph.D. degree in mechanical engineering from The University of Texas at Austin, in 1996. He is currently an Assistant Professor of aerospace engineering at The University of Texas at Austin. His research interests include glow-discharge plasmas, computational modeling and experimental studies of high-pressure glow discharges, materials processing discharges, and plasma propulsion for spacecrafts.