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[.]

at low pressure by fluid modeling

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Citation: Phys Plasmas 24, 013517 (2017); doi: 10.1063/1.4974762

View online: http://dx.doi.org/10.1063/1.4974762

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Published by the American Institute of Physics

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

RuiqiangLiu (刘睿强),1,2

YueLiu (刘悦),1, a)

WenzhuJia (贾文柱),1

and YanwenZhou (周艳文)3

1

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

2

College of Applied Electronics, Chongqing College of Electronic Engineering, Chongqing 401331, China

3

School of Materials and Metallurgy, University of Science and Technology Liaoning, Anshan 114051, China

(Received 20 October 2016; accepted 9 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

continu-ous and pulsed RF discharges are comparatively investigated It is shown that, under the same

con-dition 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

contin-uous 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

cou-pling 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

using the continuous and pulsed RF capacitive glow discharges V C 2017 Author(s) All article

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

pres-sure 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

inte-grated circuit chips and new types of plate display units.13In

particular, in plasma etching and thin film deposition, this

technique cannot be replaced by other means.4Also, the RF

discharges at low pressure play very important roles in

modi-fying 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 past1but less so for

pulsed discharges Compared to the continuous RF discharge,

the pulsed discharge may increase the selective ratio of

spe-cies in the reactions,57 improve the etching uniformity and

decrease the etching and depositing velocities, especially for

electronegative gases.8,9 Using pulsed RF discharge may

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 dam-age 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.11In experiments performed by Mukherjeeet al., a

2 Hz pulse was used to modulate the 100 MHz high fre-quency 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

a) Author to whom correspondence should be addressed Electronic mail:

liuyue@dlut.edu.cn

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

dis-charge is normally very small, it is difficult to carry out the

experimental study Numerical investigation is also

challeng-ing 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.15–20The 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 SectionII SectionIIIreports the main computational

find-ings Section IV summarizes the results and draws the

conclusion

II THE COMPUTATIONAL MODEL

Consider a discharge between two parallel-plate

trodes Adding a finite value RF voltage on the left

elec-trode 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,

one-dimensional 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 TableI

In Table I, the units of all rate coefficients are cm3/s except for k3q, which is in cm6/s The electron temperature

Teis in eV In this work, the basic assumptions of the model are the same as in Refs.21and24 Under these assumptions, the argon discharge can be described following the fluid approximations The continuity equation for electrons is

@ne

@t þ r  Je¼ kinnneþ ksinmneþ kmpn2m: (1) The continuity equation for positive ions is

@ni

@t þ r  Ji¼ kinnneþ ksinmneþ kmpn2m: (2) The continuity equation for metastable atoms becomes

@nm

@t þ r  Jm¼ kexnnne ksinmne kscnmne krnmne

 2kmpn2m k2 nnnm k3 n2nnm; (3) where the corresponding particle fluxes are

Je¼ Derne leneE; (4)

Ji¼ Dirniþ liniE; (5)

The electron energy equation is as follows:

@

@t

3

2nekTe

þ r  qeþ eJe E þ Hikinnne

þ Hexkexnnneþ Hsiksinmneþ Hsckscnmne¼ 0; (7) where the electron energy flux is

qe¼ KerTeþ5

with the thermal conductivity of electrons being

The electric field satisfies

r  E ¼ee

0

ni ne

TABLE I Main collision processes in the argon CCP discharge.

E ¼ rV: (11)

In the above equations,ne,Je,Te,Deandleare 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,

respec-tively, for metastable atoms;V is the electric potential andE is

the electric field The initial conditions are specified as follows:

ne¼ ni¼ nm¼ ne e þ 16ð1  x=LÞ2

ðx=LÞ2

;

Te¼ Tei; V ¼ 0; e ¼ 103;

where L is distance between two electrodes The boundary

conditions are

atx¼ 0; @ne

@x ¼ 0;

@ni

@x ¼ 0;

@nm

@x ¼ 0;

Te¼ Teb; V ¼ Vfsin 2ð pftÞ

atx¼ L; @ne

@x ¼ 0;

@ni

@x ¼ 0;

@nm

@x ¼ 0;

Te¼ Teb; V ¼ 0;

wheref is the frequency of the applied voltage source Some

of the basic parameter values are specified in TableII

III RESULTS AND ANALYSIS OF THE RESULTS

The applied voltage isVrf ¼ Vfsinð2pftÞ for the

contin-uous RF discharge and Vprf ¼ Vfsinð2pftÞ; 0  t  ab

0; ab  t  b



for pulsed RF, where b is the period of the pulsed

modula-tion, anda (the duty ratio of the pulsed modulation) the

frac-tion factor within each period, when the voltage source is

switched on In this work, we choseb ¼ 40 T, with T ¼ 1=f

being the period of the wave Thus, for the RF discharge

withf¼ 13.56 MHz, the frequency of the pulsed modulation,

with a rectangular window, isfm¼ 339 kHz In this work, the

duty ratio is assumed to bea 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,Vrf¼ 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

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 fol-lowing SubsectionsIII A–III Fwill 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 150ls), both the continuous and the pulsed RF discharges reach steady state During this stage, the averaged electron densities in the bulk plasma region essentially do 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 aver-aged electron density in the continuous RF discharge reaches

3:62  1010cm3 On the other hand, the averaged electron density in the pulsed RF discharge is only 1:09  1010cm3,

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 den-sity In the sheath regions, however, the averaged ion density

is about 0:1  1010cm3, 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  1010cm3 for the continuous discharge and 3:58  1010cm3 for the pulsed discharge

In the sheath regions, the peak value of the averaged meta-stable argon atom density is 20:34  1010cm3 and 6:13

1010cm3, 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 tem-peratures 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 ioniza-tion 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

TABLE II Chosen values for basic parameters in the argon CCP discharge.

Peak value of applied voltage V f 100 (V)

Gap between electrodes L 2.54 (cm)

Neutral gas density n n 3 :22  10 16 P (cm3)

Electron diffusivity n n D e 3:86  10 22 P (cm1s1) 2

Electron mobility n n l e 9 :66  10 21 (V1cm1s1) 2

Ion diffusivity n n D i 2:07  10 18 P (cm1s1) 2

Ion mobility n n l i 4 :65  10 19 (V1cm1s1) 2

The steady state simulation results in time domain are

presented in Fig.2 The electron and ion densities in the

cen-ter of the bulk plasma reach a constant value of about 4:2 

1010 cm3 in the continuous RF discharge (Fig 2(a)) The

peak value of the central plasma current density is 2.5 mA/

cm2for 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  1010cm3 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 Figure2(d) shows that the peak value of the plasma current density reaches 2.2 mA/cm2during the duty cycle of the pulsed mod-ulation 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

Xrms¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

n

Pn

i ¼1x2i

q

, 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 summa-rized in Fig.3, where we scan the amplitude of the applied voltage Figure3(a)compares the RMS of the applied volt-age with that of the plasma voltvolt-age, 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)and2(d)

B Comparison of the electron temperatures in the plasma

Comparison of the spatial and temporal steady state dis-tributions of the electron temperature is shown in Figs.4(a) and4(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 temper-ature 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 par-ticles, with the loss of energy source, experience less

FIG 1 Comparison of the steady state spatial distributions of (a) the

aver-aged electron density and (b) the averaver-aged 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.

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

contin-uous discharge produces larger current density (Figs 2(c)

and2(d),3(c)), which, according to the Child law, is related

to the sheath thickness viaJ0¼4

9e0 2M

 1 =2 V 3=2 0

s 2 ,29,30whereJ0

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

Figures5(a)and5(b)compare the steady state temporal behavior of the plasma voltage and the electric field, respec-tively, 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 dis-charge 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 5

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

FIG 2 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.

voltage is switched on/off, the ion response to the electric field

is slightly slower, resulting in slightly higher argon ion (Arþ)

density in the bulk plasma, as compared to the electron

den-sity 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 phenomenon31is based on the Debye length

kD¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffie0Te=ene

p

.32,33In the pulsed discharge, relatively low electron density and high temperature increase the Debye

FIG 3 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.

FIG 4 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 contin-uous 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).

length The corresponding electric field also increases Figure

5(b)does show the lower (higher) electron density

(tempera-ture) 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

FIG 5 Comparison of the steady state temporal behaviour between the

con-tinuous 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

distri-butions of the averaged plasma potential are compared in (c) The applied

peak voltage is assumed to be 100 V in both discharges.

FIG 6 Comparison of the steady state spatial distributions of (a) the aver-aged electron energy density, (b) the averaver-aged power dissipation density, and (c) the overall power density absorption between the continuous RF dis-charge with 100 V applied peak voltage and the pulsed disdis-charges with vary-ing applied peak voltage.

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

over-all 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 cm3eV

at the center of the bulk plasma Much smaller central energy

density, of 1:34  1010 cm3eV, 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 0 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 JeÞ  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/cm3for the

pulsed discharge.34On the other hand, the peak power

den-sity deposited into the sheath layers reaches 23.62 mW/cm3

in the continuous discharges, and only 3.15 mW/cm3in 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

con-tinuous 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: Pcurrent¼ eJe E ¼ eDerne E þeleneE2,

Power due to electron energy loss: Ploss¼ Hikinnne

þHexkexnnneþ Hsiksinmneþ Hsckscnmne, Absorbed power associated with total electron energy flux:

Pf lux¼ r  qe, Electron net power absorption: Pnet¼ Pf luxþ Pcurrent

Ploss The spatial distributions of the aforementioned power density components are compared in Figs 7(a)and7(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 TableIIIfor 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 cen-ter, 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 elec-tron density in the bulk plasma—a factor of 4 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

FIG 7 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.

TABLE III Comparison of various power components between the continu-ous 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 Pulsed RF discharge Bulk plasma Sheath Bulk plasma Sheath

collisions (in the continuous discharge) and subsequently

more power loss

E Comparison of plasma ionization rate

Detailed ionization characteristics are reported and

com-pared in Fig 8, for both continuous and pulsed RF

discharges In both cases, the time-averaged ionization rate

kinnne exhibits a double-peaking spatial structure between the boundary and the center of the plasma The spatial distri-bution 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 8 Comparison of the steady sate spatial (a, b) and temporal (d) distributions of the averaged ionization rate between the continuous and pulsed RF dis-charges, as well as (c) the averaged electron temperature during the RF switch-on phase in both disdis-charges, and (e) the spatial distribution of the averaged ioni-zation 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.