A comparative study on continuous and pulsed RF argon capacitive glow discharges at low pressure by fluid modeling

A comparative study on continuous and pulsed RF argon capacitive glow discharges at low pressure by fluid modeling A comparative study on continuous and pulsed RF argon capacitive glow discharges at l[.]

A comparative study on continuous and pulsed RF argon capacitive glow discharges at low pressure by fluid modeling , , , and Citation: Phys Plasmas 24, 013517 (2017); doi: 10.1063/1.4974762 View online: http://dx.doi.org/10.1063/1.4974762 View Table of Contents: http://aip.scitation.org/toc/php/24/1 Published by the American Institute of Physics Articles you may be interested in A time-dependent model of pulse-driven radio frequency capacitively coupled collisional plasma sheath Phys Plasmas 24, 013516013516 (2017); 10.1063/1.4974765 An analytical model of multi-component radio frequency capacitively coupled plasma and experimental validation Phys Plasmas 24, 013503013503 (2017); 10.1063/1.4973233 The effect of intermediate frequency on sheath dynamics in collisionless current driven triple frequency capacitive plasmas Phys Plasmas 24, 013509013509 (2017); 10.1063/1.4973889 PHYSICS OF PLASMAS 24, 013517 (2017) A comparative study on continuous and pulsed RF argon capacitive glow discharges at low pressure by fluid modeling Ruiqiang Liu (刘睿强),1,2 Yue Liu (刘悦),1,a) Wenzhu Jia (贾文柱),1 and Yanwen Zhou (周艳文)3 Key Laboratory of Materials Modification by Laser, Ion and Electron Beams (Ministry of Education), School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024, China College of Applied Electronics, Chongqing College of Electronic Engineering, Chongqing 401331, China School of Materials and Metallurgy, University of Science and Technology Liaoning, Anshan 114051, China (Received 20 October 2016; accepted January 2017; published online 26 January 2017) Based on the plasma fluid theory and using the drift-diffusion approximation, a mathematical model for continuous and pulsed radial frequency (RF) argon capacitive glow discharges at low pressure is established The model is solved by a finite difference method and the numerical results are reported Based on the systematic analysis of the results, plasma characteristics of the continuous and pulsed RF discharges are comparatively investigated It is shown that, under the same condition for the peak value of the driving potential, the cycle-averaged electron density, the current density, and other essential physical quantities in the continuous RF discharge are higher than those from the pulsed RF discharge On the other hand, similar plasma characteristics are obtained with two types of discharges, by assuming the same deposited power Consequently, higher driving potential is needed in pulsed discharges in order to maintain the same effective plasma current Furthermore, it is shown that, in the bulk plasma region, the peak value of the bipolar electric field from the continuous RF discharge is greater than that from the pulsed RF discharge In the sheath region, the ionization rate has the shape of double-peaking and the explanation is given Because the plasma input power depends on the driving potential and the plasma current phase, the phase differences between the driving potential and the plasma current are compared between the continuous and the pulsed RF discharges It is found that this phase difference is smaller in the pulsed RF discharge compared to that of the continuous RF discharge This means that the input energy coupling in the pulsed RF discharge is less efficient than the continuous counterpart This comparative study, carried out also under other conditions, thus can provide instructive ideas in applications C 2017 Author(s) All article using the continuous and pulsed RF capacitive glow discharges V content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/) [http://dx.doi.org/10.1063/1.4974762] I INTRODUCTION Because the radial frequency (RF) discharges at low pressure can generate a large area of uniform plasmas and the associated devices are simple and easy to control, they have a wide range of applications in manufacturing the modern integrated circuit chips and new types of plate display units.1–3 In particular, in plasma etching and thin film deposition, this technique cannot be replaced by other means.4 Also, the RF discharges at low pressure play very important roles in modifying the material surfaces and in many other areas In order to improve the efficiency of plasma applications, the characteristics of the RF wave induced plasmas need to be thoroughly investigated Extensive studies have been carried out for continuous RF discharges in the past1 but less so for pulsed discharges Compared to the continuous RF discharge, the pulsed discharge may increase the selective ratio of species in the reactions,5–7 improve the etching uniformity and decrease the etching and depositing velocities, especially for electronegative gases.8,9 Using pulsed RF discharge may a) Author to whom correspondence should be addressed Electronic mail: liuyue@dlut.edu.cn 1070-664X/2017/24(1)/013517/12 generate ion-ion plasmas Importantly, this allows negative ions, confined in the central plasma region, to move outwards, neutralizing positive charges on the material surface, thus avoiding the accumulation of charged particles during etching Pulsed discharges also result in many other advantages by, for instance, affecting the orbit of etching ions, reducing the damage of substrates, reducing the heating quantity of substrates, and saving the source energy These advantages have attracted the interest of many researchers and applicators working on theoretical, numerical and experimental characterization of the pulsed RF discharges More specifically, using the pulsed RF discharges for depositing silicon nitride films, Kim and Kim increased the ion energy and the plasma density to increase the depositing power, through decreasing the pulsed duty ratio.10 Ashida et al found that varying pulsed modulating frequency had an important effect on the depositing process in the pulsed RF discharge.11 In experiments performed by Mukherjee et al., a Hz pulse was used to modulate the 100 MHz high frequency power They found that the optical characteristics of the non-crystalline silicon films have been significantly improved while keeping very large depositing power The reason is that the pulsed modulation allows selective control 24, 013517-1 C Author(s) 2017 V 013517-2 Liu et al Phys Plasmas 24, 013517 (2017) of the particle energy.12 Lieberman et al used a global model to study pulsed high density, low pressure plasmas They found that, with the same input power, the averaged electron density from the pulsed RF discharges is higher than that in continuous discharges.13,14 Due to the rather complicated physics mechanisms occurring in the pulsed RF discharges, many problems remain to be solved Since the time scale of the pulsed discharge is normally very small, it is difficult to carry out the experimental study Numerical investigation is also challenging Low pressure, pulsed and continuous RF discharges are therefore still active research areas in gas discharges In this work, a systematic numerical analysis is carried out, resulting in a comparative investigation of the continuous versus pulsed RF discharges at low pressure This approach allows us to find out the similarity and the difference between these two types of RF discharges, leading to a more complete and deeper understanding of the plasma characteristics More specifically, based on the plasma fluid theory, a model of capacitive RF glow discharge at low pressure is established, using argon as the working gas.15–20 The particle species included into the model are the argon atom, argon molecule, metastable argon atom, resonant argon atom and electron The model adopts the drift-diffusion approximation and includes the continuity equations for the particle density, the electron energy equation and the Poisson equation.21–23 Utilizing a finite difference method, the model equations are numerically solved Analyzing the computational results, we find the systematic differences and similarities between the continuous and pulsed RF argon discharges at low pressure This provides a theoretical foundation for further study of pulsed RF discharges The mathematical model of RF discharges is described in Section II Section III reports the main computational findings Section IV summarizes the results and draws the conclusion II THE COMPUTATIONAL MODEL Consider a discharge between two parallel-plate electrodes Adding a finite value RF voltage on the left electrode and grounding the right one, the gas between the two electrodes can be ionized to generate the so called capacitively coupled plasma (CCP) When the size of the electrodes is much larger than the gap between them, onedimensional model can be used For the plasma in this model, the particles considered are electrons, argon atoms, argon molecules, metastable argon atoms, resonant argon atoms and argon ions, as listed in Table I In Table I, the units of all rate coefficients are cm3/s except for k3q, which is in cm6/s The electron temperature Te is in eV In this work, the basic assumptions of the model are the same as in Refs 21 and 24 Under these assumptions, the argon discharge can be described following the fluid approximations The continuity equation for electrons is @ne ỵ r  Je ẳ ki nn ne ỵ ksi nm ne ỵ kmp n2m : @t (1) The continuity equation for positive ions is @ni þ r  Ji ¼ ki nn ne þ ksi nm ne ỵ kmp n2m : @t (2) The continuity equation for metastable atoms becomes @nm ỵ r  Jm ¼ kex nn ne  ksi nm ne  ksc nm ne  kr nm ne @t  2kmp n2m  k2q nn nm  k3q n2n nm ; (3) where the corresponding particle fluxes are Je ¼ De rne  le ne E; (4) Ji ẳ Di rni ỵ li ni E; (5) Jm ¼ Dm rnm : (6) The electron energy equation is as follows:
 @ ne kTe ỵ r  qe ỵ eJe  E ỵ Hi ki nn ne @t ỵ Hex kex nn ne ỵ Hsi ksi nm ne ỵ Hsc ksc nm ne ¼ 0; (7) where the electron energy flux is qe ẳ Ke rTe ỵ kTe Je ; (8) with the thermal conductivity of electrons being Ke ¼ kDe ne : (9) The electric field satisfies rEẳ e ni  ne ị; e0 (10) TABLE I Main collision processes in the argon CCP discharge No Reaction Hj (eV) Rate coefficient References e ỵ Ar ! Arỵ þ 2e e þ Ar ! Ar þ e e þ Ar ! Arþ þ 2e e þ Ar ! Ar ỵ e e ỵ Ar ! Arr ỵ e Ar ỵ Ar ! Arỵ ỵ Ar ỵ e Ar þ Ar ! 2Ar  Ar þ 2Ar ! Ar þ Ar2 15:7 11:56 4:14 11:56 ki ¼ 1:235  107 exp18:687=Te ị kex ẳ 3:712  108 exp15:06=Te ị ksi ẳ 2:05  107 exp4:95=Te ị ksc ẳ 1:818  109 exp2:14=Te ị kr ẳ  107 kmp ¼ 6:2  1010 k2q ¼ 3:0  1015 k3q ¼ 1:1  1031 2 2 013517-3 Liu et al Phys Plasmas 24, 013517 (2017) E ¼ rV: (11) In the above equations, ne , Je , Te , De and le are the electron density, electron flux, electron temperature, electron diffusivity and electron mobility, respectively; ni , Ji , Di and li are the density, flux, diffusivity and mobility, respectively, for ions; nm , Jm and Dm are the density, flux and diffusivity, respectively, for metastable atoms; V is the electric potential and E is the electric field The initial conditions are specified as follows: h i ne ẳ ni ẳ nm ẳ ne e ỵ 161  x=Lị2 x=Lị2 ; Te ẳ Tei ; V ẳ 0; e ¼ 103 ; where L is distance between two electrodes The boundary conditions are @ne @ni @nm at x ¼ 0; ¼ 0; ¼ 0; ¼ 0; @x @x @x Te ¼ Teb ; V ¼ Vf sinð 2pftị @ne @ni @nm ẳ 0; ẳ 0; ẳ 0; at x ¼ L; @x @x @x Te ¼ Teb ; V ¼ 0; where f is the frequency of the applied voltage source Some of the basic parameter values are specified in Table II III RESULTS AND ANALYSIS OF THE RESULTS The applied voltage is Vrf ẳ Vf sin2pftị for the contin Vf sinð2pftÞ;  t  ab uous RF discharge and Vprf ¼ 0; ab  t  b for pulsed RF, where b is the period of the pulsed modulation, and a (the duty ratio of the pulsed modulation) the fraction factor within each period, when the voltage source is switched on In this work, we chose b ¼ 40 T, with T ¼ 1=f being the period of the wave Thus, for the RF discharge with f ¼ 13.56 MHz, the frequency of the pulsed modulation, with a rectangular window, is fm ¼ 339 kHz In this work, the duty ratio is assumed to be a ¼ 20% Note that we use the subscript “rf ” (radio frequency) to denote the continuous RF drive and “prf ” stands for pulsed RF drive We also note that, with the same peak value of the applied voltages, Vrf ¼ Vprf , for the two types of discharges, the averaged input powers are different This is an important aspect when we compare the performance of both TABLE II Chosen values for basic parameters in the argon CCP discharge Name Peak value of applied voltage RF frequency Gap between electrodes Gas pressure Neutral gas density Electron diffusivity Electron mobility Ion diffusivity Ion mobility Symbol Value 100 (V) Vf f 13.56 (MHz) L 2.54 (cm) P (Torr) nn 3:22  1016 P (cm3) nn De 3:86  1022 P (cm1 s1) nn le 9:66  1021 (V1 cm1 s1) nn Di 2:07  1018 P (cm1 s1) nn li 4:65  1019 (V1 cm1 s1) References 2 2 discharges The other obvious way of comparison is to allow the deposited power to be the same for both discharges This would imply different input voltage Therefore, in most of the results presented in the following subsections, we fix the input voltage of the continuous RF discharge to be 100 V, while investigating the sensitivity of the pulsed discharge performance against the variation of the source voltage, by considering several peak values of the applied voltage including the 100 V case Whilst the discussions in the following Subsections III A–III F will be largely focused on the comparison of two types of discharges with the same applied voltage of 100 V, Subsection III G will specifically address the performance comparison, when the deposited power matches between these two types of discharges A Comparison of the plasma particle and current densities After 2000 cycles (about 150 ls), both the continuous and the pulsed RF discharges reach steady state During this stage, the averaged electron densities in the bulk plasma region essentially not change [In this paper, for the pulsed discharge, the average is taken over one period of the pulse modulation.] At the center of the bulk plasma region, the averaged electron density in the continuous RF discharge reaches 3:62  1010 cm3 On the other hand, the averaged electron density in the pulsed RF discharge is only 1:09  1010 cm3, as shown in Fig 1(a) This is because, during one pulse period, the time of the pulsed RF discharge is shorter—only 1/5 of the time of the continuous discharge The plasma in the pulsed discharge thus obtains far less energy from the electric field, so is the ionization (the averaged electron density) In both the kinds of discharges, in the bulk plasma region, the averaged ion density matches the corresponding electron density In the sheath regions, however, the averaged ion density is about 0:1  1010 cm3, higher than the averaged electron density that is nearly zero.25 With the same peak value (100 V) of the applied voltage and at the steady state stage for both types of discharges, the averaged metastable argon atom density at the center of the bulk plasma reaches 11:51  1010 cm3 for the continuous discharge and 3:58  1010 cm3 for the pulsed discharge In the sheath regions, the peak value of the averaged metastable argon atom density is 20:34  1010 cm3 and 6:13 1010 cm3, respectively, as shown in Fig 1(b) It is evident that, in both continuous and pulsed discharges, the maxima of the averaged metastable argon atom density are much larger in the sheath regions, compared to that of the center of the bulk plasma This is because in the sheath regions the averaged electric fields are large, the averaged electron temperatures are high, the collision between the argon atoms is strong, and the degree of ionization is therefore high On the other hand, the central bulk plasma region is characterized by weak averaged electric fields and high averaged electron densities Meanwhile, due to the effect of step-wise ionization and quenching to resonance for metastable argon atoms, a large amount of metastable argon atoms are used up Consequently, the averaged densities of these atoms become low in the center of the bulk plasma.26,27 013517-4 Liu et al Phys Plasmas 24, 013517 (2017) peak value of the central plasma current density is 2.5 mA/ cm2 for the same discharge (Fig 2(c)) The electron and ion densities of the pulsed RF discharge, on the other hand, experience periodic variations between 1:07  1010 cm3 and 1:09  1010 cm3, as shown in Fig 2(b) In the pulsed discharge, during the time window when the applied voltage vanishes, the plasma density gradually decreases This is due to the gradual reduction of ionization (to be shown in later figures) as a result of the lack of the input power Figure 2(d) shows that the peak value of the plasma current density reaches 2.2 mA/cm2 during the duty cycle of the pulsed modulation Outside the duty cycle window, the current vanishes Now, instead of the peak value, we shall consider the root mean square (RMS) of certain quantities, defined as qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P Xrms ¼ 1n ni¼1 x2i , showing the effective value of quantity x.28 We compare the applied voltage, the induced plasma voltage and the plasma current, for the time period when the discharges reach steady state The results are summarized in Fig 3, where we scan the amplitude of the applied voltage Figure 3(a) compares the RMS of the applied voltage with that of the plasma voltage, as functions of the RMS of the plasma current, for the continuous RF discharge Similar plot is shown in Fig 3(b) for the pulsed discharge A general observation, valid for both types of discharge, is that, at low plasma current density, the RMS of the plasma voltage is larger than that of the applied voltage The situation reverses at high plasma current Figure 3(c) compares the RMS of the plasma voltage between the continuous and the pulsed discharges It is clear that, when the plasma currents have the same RMS value, the pulsed discharge has higher plasma voltage than the continuous discharge This is due to the fact that, to keep the same plasma current, the pulsed RF discharge requires higher voltage In other words, with the same level of the applied voltage, the pulsed discharge induces less plasma current compared to the continuous discharge This is also evident from Figs 2(c) and 2(d) B Comparison of the electron temperatures in the plasma FIG Comparison of the steady state spatial distributions of (a) the averaged electron density and (b) the averaged metastable atom density, and (c) the averaged ion density between the continuous (labeled as “rf”) and pulsed (labeled “prf”) RF CCP discharges, with various choices of the input voltage peak values of 100 V, 191 V, 257 V, and 400 V The steady state simulation results in time domain are presented in Fig The electron and ion densities in the center of the bulk plasma reach a constant value of about 4:2  1010 cm3 in the continuous RF discharge (Fig 2(a)) The Comparison of the spatial and temporal steady state distributions of the electron temperature is shown in Figs 4(a) and 4(b), respectively, for the continuous versus pulsed RF discharges The spatial distribution (Fig 4(a)) shows that, with the same applied voltage of 100 V, the electron temperature of the continuous discharge is slightly higher (1.43 eV) in the middle of the bulk plasma region, compared to that of the pulsed discharge (1.23 eV) This can be understood from the temporal behavior shown in Fig 4(b) During the pulsed discharge, at the initial phase of the pulse modulation, the averaged electron density is very low in the plasma region This allows deep penetration of the electric field into the plasma core The spontaneous response of electrons to the field change creates violent thermal motions that sharply increase the average electron temperature At the duty cycle off phase, the applied voltage vanishes The reaction particles, with the loss of energy source, experience less 013517-5 Liu et al Phys Plasmas 24, 013517 (2017) FIG Comparison of the temporal behavior of steady state phase for (a), (b) the particle densities, and (c), (d) the plasma current density, between the (a), (c) continuous and (b), (d) pulsed RF discharges Shown are the values at the center of the bulk plasma The applied voltage peak value is assumed to be 100 V in both discharges frequent collision and hence produce less electrons The electrons themselves also lose the source energy during this period of time The electron temperature thus drops On the other hand, during the continuous RF discharge, the constant presence of the applied voltage helps to drive the plasma to a steady state This leads to a continuous absorption of energy by electrons and, consequently, a steady state condition for the averaged electron temperature, which is higher than that of the pulsed discharge In the sheath regions, under the steady state condition, the peak value of the averaged electron temperature is 6.49 eV during the continuous RF discharge and 2.12 eV during the pulsed discharge On the other hand, the sheath is thicker in the pulsed discharge This is because the continuous discharge produces larger current density (Figs 2(c) and 2(d), 3(c)), which, according to the Child law, is related  1=2 V03=2 29,30 where J0 to the sheath thickness via J0 ¼ 49 e0 2e M s2 , is the ion current density and s is the sheath thickness Thus, the larger current (in continuous discharge) leads to thinner sheath C Comparison of temporal behavior of plasma voltage and electric field Figures 5(a) and 5(b) compare the steady state temporal behavior of the plasma voltage and the electric field, respectively, between the continuous and pulsed RF discharges The steady state, averaged spatial distributions of the plasma potential are compared in Fig 5(c) The continuous discharge produces an RF plasma voltage with the peak value of 50 V Similar peak value is also obtained for the pulsed discharge, but with modulations Specifically, after switching off the source, the plasma voltage drops to 32.35 V within RF time periods This voltage level is then kept constant until the next modulation period, when the plasma voltage sharply arises again (Fig 5(a)) The continuous discharge produces RF electric field with the peak value of 1.27 V/cm The corresponding peak value is 3.57 V/cm for pulsed discharges, as shown in Fig 5(b) This is because during the continuous discharge, the plasma is in nearly steady state, and thus with a weak electric field But during the pulsed discharge, in particular, when the applied 013517-6 Liu et al Phys Plasmas 24, 013517 (2017) FIG The RMS values of the applied and the produced plasma voltage versus the plasma current density during (a) the continuous RF discharge and (b) the steady state phase of the pulsed RF discharge The RMS values of the plasma voltage and current density are also compared in (c) between two discharges The amplitude of the applied voltage is scanned voltage is switched on/off, the ion response to the electric field is slightly slower, resulting in slightly higher argon ion (Ar þ ) density in the bulk plasma, as compared to the electron density This leads to a slightly higher electric field in the bulk plasma of the pulsed discharge The other way of explaining this bi-polar field phenomenon31 is based on the Debye length pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi kD ¼ e0 Te =ene 32,33 In the pulsed discharge, relatively low electron density and high temperature increase the Debye FIG Comparison of (a) the spatial and (b) the temporal, steady state distributions of the electron temperature between the continuous and pulsed RF discharges The electron temperature is time averaged in (a) and is taken at the center of the bulk plasma in (b) The applied peak voltage is assumed to be 100 V in the continuous discharge in both (a) and (b) The applied peak voltage in the pulsed discharge is 100 V in (b), and 100 V, 191 V, 257 V, 400 V, respectively, in (a) 013517-7 Liu et al Phys Plasmas 24, 013517 (2017) FIG Comparison of the steady state temporal behaviour between the continuous and pulsed RF discharges, for (a) the plasma potential and (b) the electric field, at the center of the bulk plasma The steady state spatial distributions of the averaged plasma potential are compared in (c) The applied peak voltage is assumed to be 100 V in both discharges FIG Comparison of the steady state spatial distributions of (a) the averaged electron energy density, (b) the averaged power dissipation density, and (c) the overall power density absorption between the continuous RF discharge with 100 V applied peak voltage and the pulsed discharges with varying applied peak voltage length The corresponding electric field also increases Figure 5(b) does show the lower (higher) electron density (temperature) at the moment when the applied voltage is switched on/ off, resulting in higher electric field Figure 5(b) also shows that, after switching off the RF voltage, the output electric field vanishes But at the arrival of the next first RF pulse, a large electric field peaking occurs This is because during the switching on phase of the 013517-8 Liu et al Phys Plasmas 24, 013517 (2017) FIG Comparison of the steady state spatial distributions of various power density components between (a) the continuous and (b) the pulsed RF discharges with the applied peak voltage of 100 V RF wave, the applied external electric field penetrates deep into the plasma core Meanwhile, the internal electric field, due to the charge separation, is still relatively weak As a result, the field peaking occurs D Comparison of the plasma energy density and power density distribution The spatial distribution of the averaged electron energy density, the averaged power deposition density, and the overall power density absorption are plotted and compared in Figs 6(a), 6(b) and 6(c), respectively During one pulse period, the continuous RF discharge produces plasma with the average electron energy density of 5:19  1010 cm3 eV at the center of the bulk plasma Much smaller central energy density, of 1:34  1010 cm3 eV, is obtained in the pulsed discharge with the same applied voltage (100 V), as shown in Fig 6(a) This is because the energy gained by the plasma is much lower in the pulsed discharge, compared to that of the continuous discharge (with the same applied voltage).33 Inside the sheath layers, the averaged electron energy density is close to in both types of discharges, due to the presence of nearly vanishing electron density According to Fig 6(b), the averaged power density Pd  0:5ðJi  Je Þ  E, deposited in the center of the bulk plasma, is 0.75 mW/cm3 in the continuous RF discharge The corresponding power deposition is 0.36 mW/cm3 for the pulsed discharge.34 On the other hand, the peak power density deposited into the sheath layers reaches 23.62 mW/cm3 in the continuous discharges, and only 3.15 mW/cm3 in the pulsed discharge The much higher power deposition in the sheath layers, compared to the bulk plasma region, is explained by the fact that the source power is coupled to sheath mainly via Ohmic heating.30,35 In the bulk plasma, however, the averaged electric field is relatively weak and the averaged electron temperature is relatively low, thus leading to lower power deposition This holds for both continuous and pulsed RF discharges.36 Now we consider various components in the power balance In this model, we define four components as follows:24,37 Electron heating power: Pcurrent ¼ eJe  E ẳ eDe rne  E ỵele ne E2 , Power due to electron energy loss: Ploss ¼ Hi ki nn ne ỵHex kex nn ne ỵ Hsi ksi nm ne ỵ Hsc ksc nm ne , Absorbed power associated with total electron energy flux: Pf lux ¼ r  qe , Electron net power absorption: Pnet ¼ Pf lux þ Pcurrent Ploss The spatial distributions of the aforementioned power density components are compared in Figs 7(a) and 7(b) for the continuous and pulsed RF discharges, respectively The corresponding values at the center of the bulk plasma, as well as in the sheath regions, are listed in Table III for both types of discharges In general, the trend of change of the above four cases is similar In particular, the net power Pnet vanishes in all four cases The major difference is that, in the plasma center, and for the continuous RF discharge, the power Pcurrent associated with the electron heating is lower than that due o the electron loss, Ploss The opposite, however, holds for the pulsed RF discharge The large electron loss power in the continuous discharge, as compared to that of the pulsed discharge, is due to the much larger averaged electron density in the bulk plasma—a factor of as shown in Fig 2—in the continuous discharge Meanwhile, the averaged electron temperature in the bulk plasma is only slightly higher in the continuous discharge—by 0.2 eV as shown in Fig 4(a) This leads to more frequent particle TABLE III Comparison of various power components between the continuous and pulsed RF discharges and between the sheath regions and the bulk plasma regions The applied peak voltage is 100 V in both discharges Continuous RF discharge Pcurrent (mW/cm3) Ploss (mW/cm3) Pf lux (mW/cm3) Pnet (mW/cm3) Pulsed RF discharge Bulk plasma Sheath Bulk plasma Sheath 1.51 3.44 3.19 15.62 8.29 9.98 0.98 0.83 0.11 2.64 2.19 2.96 013517-9 Liu et al collisions (in the continuous discharge) and subsequently more power loss E Comparison of plasma ionization rate Detailed ionization characteristics are reported and compared in Fig 8, for both continuous and pulsed RF Phys Plasmas 24, 013517 (2017) discharges In both cases, the time-averaged ionization rate ki nn ne exhibits a double-peaking spatial structure between the boundary and the center of the plasma The spatial distribution of the ionization rate generally increases starting from the boundary, then decreases followed by another increasing phase, and decreases again followed by a gradual saturation towards the center of the bulk plasma This double-peaking FIG Comparison of the steady sate spatial (a, b) and temporal (d) distributions of the averaged ionization rate between the continuous and pulsed RF discharges, as well as (c) the averaged electron temperature during the RF switch-on phase in both discharges, and (e) the spatial distribution of the averaged ionization rate during the power-off time window of the pulsed RF discharge The applied peak voltage is assumed to be 100 V in both discharges 013517-10 Liu et al structure is ultimately associated with the offset of the peaking positions between the average electron density ne and the average electron temperature Te On the other hand, the averaged ionization rate coefficient ki monotonically increases with increasing Te , resulting in the same peaking location between ki and Te 24 The detailed spatial structures are compared in Fig 8(b) between the continuous and pulsed discharges In the region of x/L ¼  0:05, the averaged electron temperature (Fig 8(c)) and the averaged electron density (Fig 1(a)) are both increasing, which leads to increasing ionization rate as a function of x/L Because the averaged electron temperature is higher in the continuous discharge, compared to that of the pulsed discharge (the averaged electron density is similar in both discharges), the continuous discharge has higher ionization rate than the pulsed one in this region of plasma In the region of x/L ¼ 0:05  0:08, the averaged electron temperature sharply decreases, with only moderate increase in the electron density Thus, the ionization rate decreases Furthermore, in the region of x/L ¼ 0:08  0:12, the averaged electron temperature is nearly constant, but the temperature sharply increases, resulting in increasing ionization rate Finally, in the region of x/L ¼ 0:12  0:5, the averaged electron temperature continues slow decreasing, accompanied by the slight increase in the density The overall effect is the slight decrease in the ionization rate that gradually saturates We observe that, in the spatial region of x/L ¼ 0:05  0:35, the pulsed discharge has higher ionization rate than the continuous counterpart, largely due to the fact that the averaged electron temperature is higher in the pulsed discharge On the other hand, in the region of x/L ¼ 0:35  0:5, the pulsed discharge has slightly lower electron temperature but much lower (factor of 4) electron density, yielding much lower ionization rate than the continuous discharge Figure 8(d) compares the temporal behavior (at a fixed spatial point of X/L ¼ 0.5) of the ionization rate between the two types of discharges during the steady state operation In the pulsed discharge, the ionization rate quickly increases from nearly to the peak value of 7:1  1014 cm3 s1 after switching on the source voltage during the pulse modulation During the following RF periods, when the source power is switched off, the ionization rate ki ẳ 1:235  107 exp18:687=Te ị quickly decreases, following the reduction of the electron temperature, as shown in Fig 4(b), down to the initial level of 104 The spatial distributions of the ionization rate during this time period are shown in Fig 8(e) at various time slices On the other hand, for the continuous RF discharge, it is evident from Fig 8(d) that the ionization rate stays at an almost constant level of 3:63  1014 cm3 s1 F Comparison of the plasma phasing We find that the plasma phasing is somewhat different between the continuous and pulsed RF discharges In the continuous discharge, the plasma current density has a phase lead of wrf ¼ 85:7 with respect to the applied voltage This phase lead is wprf ¼ 68:6 for the pulsed discharge, as shown in Fig 9(a) This means that, with the same applied stimulating voltage, the continuous RF discharge injects more power Phys Plasmas 24, 013517 (2017) than the pulsed one The plasma density is also higher, thus exhibiting better compatibility.38,39 An interesting observation is that, for both types of discharges, the aforementioned phase lead is almost invariant with respect to the change of the applied voltage (and the subsequent change of the plasma current) This is clearly shown in Fig 9(b) for the pulsed discharge Associated with the plasma phasing is the phase space comparison of various reaction rates Of particular interest is the excitation rate coefficient kex of metastable argon atoms Figures 9(c) and 9(d) show the phase space comparison of kex between the continuous and pulsed discharges Since kex ¼ 3:712  108 expð15:06=Te Þ increases with the averaged electron temperature Te and Te is higher in the pulsed discharge during the duty cycle phase, the corresponding metastable excitation rate is higher than that during the continuous discharge, as shown in Figs 9(c) and 9(d) G Comparison of plasma parameters with comparable power deposition As has been pointed out in the beginning of Section III, with the same applied voltage, the deposited power in the plasma is different between the continuous and pulsed discharges In this subsection, we shall vary the applied voltage (thus varying the power deposition) for the pulsed discharge, whilst keeping the same voltage, of 100 V, for the continuous discharge With increasing source voltage in the pulsed discharge, the injected energy also increases.40,41 Followed with this is the increase in the averaged electron density, the ion density, the metastable atoms density, the plasma voltage and electric field, and the deposited power and energy, as shown in Table IV and in some of the earlier figures (e.g., Figs and 6) In particular, with the applied voltage of 257 V, the pulsed discharge achieves the same averaged electron density and the averaged power density (as well as the total power) deposition, as that of the continuous discharge with 100 V applied voltage Interestingly, for all the levels of source voltages listed in Table IV, the pulsed discharge always yields lower averaged electron temperature, compared to the continuous discharge This lower temperature is beneficial for the plasma deposition technology as well as for various material surface processing applications.42 Table IV also demonstrates the flexibility of the pulsed discharge in terms of the plasma parameter tuning IV SUMMARY AND CONCLUSION Based on the fluid model for the plasma, we have numerically modelled both continuous and pulsed RF discharges, assuming argon as the working gas and assuming 1D CCP discharges We focus on the systematic comparison of various plasma parameters between these two types of discharges, including the averaged electron density, the ion density, the metastable atoms density, the plasma voltage and electric field, the electron energy density, the electron temperature, and various power sink and source terms, which in turn depend on the phase offset between the applied voltage and the plasma current 013517-11 Liu et al Phys Plasmas 24, 013517 (2017) FIG Comparison of phase-related quantities between the continuous and pulsed RF discharges in terms of (a) the temporal distribution of the plasma current density at the center of the bulk plasma versus the applied voltage with the peak value of 100 V, (b) the temporal distribution of the plasma current density at the center of the bulk plasma in the pulsed RF discharges with varying applied peak voltage, (c) the phase-space portrait of the excitation rate for the continuous discharge with 100 V applied peak voltage, and (d) the phase-space portrait of the excitation rate for the pulsed discharge with 100 V applied peak voltage Our results show that, at the same applied voltage, the continuous RF discharge produces plasmas with generally higher values for all the basic parameters, as compared to the pulsed discharge This is mainly because the continuous discharge gains much more energy from the applied source voltage Moreover, whilst the averaged plasma particle density, current density, electron temperature, electric field, and ionization rate remain at nearly constant level at steady state during the continuous discharge, these parameters experience periodic variations in the pulsed discharge, with the periodicity being directly related to the pulse modulation period In terms of RMS values, in order to produce the same plasma current density, the pulsed discharge requires larger input voltage and thus operates at higher plasma voltage as TABLE IV Comparison of the simulated main plasma parameters between the continuous and pulsed RF discharges Four peak values (100 V, 191 V, 257 V, 400 V) of the applied voltage are chosen for the pulsed discharge Vprf Vrf Applied peak potential (V) Electron density (cm3) Positive ion density (cm3) Metastable density (cm3) Potential (V) Electron field (V/cm) Bulk electron temperature (eV) Electron energy density (cm3 eV) Power dissipation (mW/cm3) 100 3.62  1010 3.62  1010 11.51  1010 66.68 4.59  102 1.43 5.19  1010 0.75 100 1.09  1010 1.09  1010 3.58  1010 40.61 2.54  102 1.226 1.34  1010 0.42 191 2.51  1010 2.51  1010 6.48  1010 48.34 3.58  102 1.229 3.05  1010 0.95 257 3.62  1010 3.62  1010 7.89  1010 54.61 4.56  102 1.234 3.49  1010 1.28 400 5.93  1010 5.93  1010 9.62  1010 67.47 5.54  102 1.245 7.3  1010 1.96 013517-12 Liu et al well Across the sheath layers and the bulk plasma, the pulsed discharge produces lower electron temperature than the continuous discharge This characteristic is usually beneficial for the material processing The sheath layers are generally thicker in the pulsed discharge In the temporal domain, we found and explained the phenomenon that the pulsed RF discharge produces higher electric field in the bulk plasma region, via the bipolar effect We also find that, in the continuous discharge, the electron heating power Pcurrent is lower than the power Ploss due to the electron energy loss This is opposite to what occurs in the pulsed discharge We have also performed comparative investigations of averaged ionization rate between the two types of discharges In particular, the double-peak spatial distribution of the ionization rate has been observed and explained We also find that the relative phase lead of the plasma current (with respect to the applied voltage) in the pulsed discharge is smaller than that in the continuous discharge But interestingly, this phase lead is basically independent of the applied voltage amplitude in the pulsed discharge Finally, we point out that, in this work, we fixed the duty cycle ratio in the pulsed discharge The effect of varying duty cycle ratio on the plasma performance will be reported in a future work Also, our 1D model does not allow studying the plasma uniformity issues in CCP discharges The model will be upgraded in the future ACKNOWLEDGMENTS The authors would like to thank Dr Tagra Samir for her useful discussions This work was supported by the NSFC Grant (No 51172101) and by the Fundamental Research Funds for the Chinese Central Universities (Nos DUT14LK27 and DUT13ZD(G)05) This work was also supported by the Chongqing Municipal Education Commission Science and Technology Research Projects (Grant No KJ1602907) Y S Lee, J W Lee, G J Park, and H Y Chang, “Advanced Etch Technology for Nanopatterning III,” Proc SPIE 9054, 90540K (2014) A Anders, Surf Coat 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PLASMAS 24, 013517 (2017) A comparative study on continuous and pulsed RF argon capacitive glow discharges at low pressure by fluid modeling Ruiqiang Liu (刘睿强),1,2 Yue Liu (刘悦),1 ,a) Wenzhu Jia