9
1616 S. Rebiaï et al.: 2-D Simulation of Dual Frequency Capacitively Coupled Helium Plasma, using COMSOL Multiphysics 1070-9878/13/$25.00 © 2013 IEEE 2-D Simulation of Dual Frequency Capacitively Coupled Helium Plasma, using COMSOL Multiphysics S. Rebiaï, H. Bahouh and S. Sahli Laboratoire de Microsystèmes et Instrumentation (LMI) Département d'électronique Faculté des sciences de la technologie Université Constantine 1, Algérie ABSTRACT A two–dimensional (2D) self-consistent fluid simulation of dual frequency capacitively coupled radio discharges of helium plasma is presented. The model solves the continuity equations for charged species and the electron energy balance equation, coupled with Poisson’s equation by finite element method, using COMSOL Multiphysics software. In this study, the low frequency (LF) is set to 13.56 MHz with low frequency voltage of 250 V and the high frequency (HF) is set to 54.24 MHz with high frequency voltage of 100 V. The simulations yield the two-dimensional profiles of plasma components as well as the charge densities, electric field, electron temperature and ionization rate between symmetric parallel plate electrodes. The effects of low and high frequency sources parameters such as frequency values and applied voltage amplitude on the discharge characteristics are investigated. It is shown that the increase of the HF frequency causes a moderate increase of electron temperature and plasma density, whereas, the increase of the LF potential produced an increase in the plasma potential, the voltage of the sheath and the ion energy. Index Terms RF capacitive discharge, plasma reactor simulation, helium, dual frequency, COMSOL Multiphysics software. 1 INTRODUCTION RADIO frequency glow discharges are widely used in number of applications in modern science and technology [1- 4]. One of the important fields of their application is the microelectronics industry, where glow discharges are used extensively for materials processing, surface modification and integrated circuits manufacturing steps [5, 6]. The fabrication of electronic devices needs more precision to produce structural form on the substrate with minimum defect. This optimization can be obtained by the precise control of both ion bombardment energy and ion flux during material elaboration. Conventional capacitively coupled reactors powered by single frequency (SF-CCP) [7, 8] face difficulties providing from independent control of sheath voltage (ion energy) and plasma density (ion flux) inducing non desirable effects to fragile surfaces which may be damaged by highly energetic ions. For that reason, multi-frequency sources technique has been introduced to control plasma characteristics. Classical dual frequency capacitively coupled plasma (DF-CCP) [9- 13] discharges play an important role in film depositions, sputtering, cleaning, selective and anisotropic etchings and other surface treatments [14, 15]. In typical dual-frequency discharges, the lower frequency is typically a few MHz and the higher frequency is in the order of tens of MHz. The high frequency power source is assumed to sustain the plasma and to control the ion flux reaching the wafer surface [16, 17]. However, the lower frequency source controls the sheath width, plasma potential and ion bombardment energy [17, 18]. Using both high and low frequency sources, independent control of the ion flux and energy can be achieved. In this work, a two-dimensional (2D) fluid model is presented to investigate some general features of dual frequency capacitively coupled plasmas. For simplicity, helium is chosen as a model gas, because it is one of the most important elements used experimentally in gas mixture [19- 21]. The simulation is carried out for a helium discharge operating at a pressure of 133.3 Pa (1 Torr) and created by a combination of multiple-frequencies (13.56 - 54.24 MHz). The outputs results such as the steady-state solution for charged particle density, electron temperature and electric field have been calculated with the use of the commercial finite element software COMSOL Multiphysics. The main purpose of this study is to analyze the influence of frequency variations on the characteristics of the helium plasma discharges produced in a dual frequency CCP reactor Manuscript received on 29 October 2012, in final form 5 July 2013.

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Page 1: 2-D simulation of dual frequency capacitively coupled helium plasma, using COMSOL multiphysics

1616 S. Rebiaï et al.: 2-D Simulation of Dual Frequency Capacitively Coupled Helium Plasma, using COMSOL Multiphysics

1070-9878/13/$25.00 © 2013 IEEE

2-D Simulation of Dual Frequency Capacitively Coupled Helium Plasma, using COMSOL Multiphysics

S. Rebiaï, H. Bahouh and S. Sahli

Laboratoire de Microsystèmes et Instrumentation (LMI) Département d'électronique

Faculté des sciences de la technologie Université Constantine 1, Algérie

ABSTRACT

A two–dimensional (2D) self-consistent fluid simulation of dual frequency capacitively coupled radio discharges of helium plasma is presented. The model solves the continuity equations for charged species and the electron energy balance equation, coupled with Poisson’s equation by finite element method, using COMSOL Multiphysics software. In this study, the low frequency (LF) is set to 13.56 MHz with low frequency voltage of 250 V and the high frequency (HF) is set to 54.24 MHz with high frequency voltage of 100 V. The simulations yield the two-dimensional profiles of plasma components as well as the charge densities, electric field, electron temperature and ionization rate between symmetric parallel plate electrodes. The effects of low and high frequency sources parameters such as frequency values and applied voltage amplitude on the discharge characteristics are investigated. It is shown that the increase of the HF frequency causes a moderate increase of electron temperature and plasma density, whereas, the increase of the LF potential produced an increase in the plasma potential, the voltage of the sheath and the ion energy.

Index Terms — RF capacitive discharge, plasma reactor simulation, helium, dual frequency, COMSOL Multiphysics software.

1 INTRODUCTION

RADIO frequency glow discharges are widely used in number of applications in modern science and technology [1- 4]. One of the important fields of their application is the microelectronics industry, where glow discharges are used extensively for materials processing, surface modification and integrated circuits manufacturing steps [5, 6]. The fabrication of electronic devices needs more precision to produce structural form on the substrate with minimum defect. This optimization can be obtained by the precise control of both ion bombardment energy and ion flux during material elaboration.

Conventional capacitively coupled reactors powered by single frequency (SF-CCP) [7, 8] face difficulties providing from independent control of sheath voltage (ion energy) and plasma density (ion flux) inducing non desirable effects to fragile surfaces which may be damaged by highly energetic ions. For that reason, multi-frequency sources technique has been introduced to control plasma characteristics. Classical dual frequency capacitively coupled plasma (DF-CCP) [9- 13] discharges play an important role in film depositions, sputtering, cleaning, selective and anisotropic etchings and

other surface treatments [14, 15]. In typical dual-frequency discharges, the lower frequency is typically a few MHz and the higher frequency is in the order of tens of MHz. The high frequency power source is assumed to sustain the plasma and to control the ion flux reaching the wafer surface [16, 17]. However, the lower frequency source controls the sheath width, plasma potential and ion bombardment energy [17, 18]. Using both high and low frequency sources, independent control of the ion flux and energy can be achieved.

In this work, a two-dimensional (2D) fluid model is presented to investigate some general features of dual frequency capacitively coupled plasmas. For simplicity, helium is chosen as a model gas, because it is one of the most important elements used experimentally in gas mixture [19-21]. The simulation is carried out for a helium discharge operating at a pressure of 133.3 Pa (1 Torr) and created by a combination of multiple-frequencies (13.56 - 54.24 MHz). The outputs results such as the steady-state solution for charged particle density, electron temperature and electric field have been calculated with the use of the commercial finite element software COMSOL Multiphysics.

The main purpose of this study is to analyze the influence of frequency variations on the characteristics of the helium plasma discharges produced in a dual frequency CCP reactor Manuscript received on 29 October 2012, in final form 5 July 2013.

Page 2: 2-D simulation of dual frequency capacitively coupled helium plasma, using COMSOL multiphysics

IEEE Transactions on Dielectrics and Electrical Insulation Vol. 20, No. 5; October 2013 1617

with constant electric power. Since the lower frequency source principally determines the sheath parameters and the higher frequency source principally controls bulk plasma parameters, we analyze the model for two cases:

1) The lower frequency is set to 13.56 MHz with voltage (VLF) of 250 V while adjusting the parameters of higher frequency source at 40.68, 54.24, 81 and135.6 MHz, with voltage (VHF) of 100 V.

2) The higher frequency is set to 13.56 MHz with voltage (VHF) of 250 V while adjusting the parameters of lower frequency source at 1.356, 1.93, 2.71, 3.39 and 6.78 MHz, with voltage (VLF) of 400 V.

The paper is organized in the following manner. The computational model, including the basic equations, boundary conditions and some assumptions are presented in Section 2. Modeling results are given and discussed In Section 3. The theoretical results are compared with some experimental results reported in the literature. Section 4 concludes the presented paper. Unfortunately, the comparisons with experimental results which used the same experimental conditions have not been performed due to the lack of experimental data.

2 DESCRIPTIONS OF THE COMPUTATIONAL MODEL

There exist different kinds of modelling approaches used to simulate plasma discharges. We can distinguish between three classes of models [3]: statistical (or particle) models [22, 23], fluid (or continuum) models [24, 25] and hybrid models [25, 26]. All these different models have their specific advantages and drawbacks and are principally useful in certain conditions. In this paper, we use a fluid approach to describe the particle transport in radio frequency discharges. The model solves Poisson’s equation and the first two moments of the Boltzmann equation to obtain the density, momentum and energy of each species. We used a simple atomic model based on the fluid modeling aspects of the dual frequency dynamics in the capacitively coupled discharge to describe a simplified behavior of the plasma chemistry which can be extended in future research for other atomic model.

The helium plasma considered in this model which contains only electrons (e), positively charged helium ions (He+), metastable (He*) and neutral (He) atoms can be described by the continuity equation:

)3(

)2(

)1(

** NnKt

n

NnKt

n

NnKt

n

eex

eipp

eiee

In the above equations, gn and g

(g =e, p, *) are the

particle density and the flux of particle g, respectively. Subscripts e, p, and * indicate electrons (e), positive ions

(He+), and metastable atoms (He*), respectively. N , iK

and

exK are the density of neutral gas, the ionization rate

coefficient and excitation rate coefficient, respectively.

The rate coefficients for process j (the index j can indicate ionization (i) and excitation (ex)) are defined by the following relation [27, 28]:

)4()()()(0

dvfK jj

Here is the electron energy, i the collision cross-

section, v the electron velocity and )(f is the electron

energy distribution function (EEDF). When the pressure is greater than 6.66 Pa, EEDF may be approximated to a Maxwellian distribution function according to the work reported in [29-31].

The momentum balance for all species is expressed by the drift diffusion approximation which is the superposition of diffusion in a concentration gradient and drift under the effect of an electric field. Drift expression is not used for metastable atoms which are not charged [32-35]:

)7(

)6(

)5(

*** nD

nDEn

nDEn

ppppp

eeeee

In these equations, g , gD and E

are the particle species

mobility, the diffusion coefficient and the RF electric field, respectively.

The energy balance is solved only for electrons:

)11(2

3

)10(

)9()(

)8()(

e

e

e

e

T

nn

nDEn

SEt

n

were n is the electron energy density, the electron mean

energy, eT the electron temperature, the mean energy flux,

S the source term for electron energy. and D are the

electron mobility and diffusion coefficient for the energy flux, respectively.

For a self consistent calculation of the electric field, Poisson’s equation is solved simultaneously with the fluid equations:

)12()(0

VEandnnq

V ep

where V is the electrostatic potential, q is the elementary

charge and 0 the vacuum permittivity.

Page 3: 2-D simulation of dual frequency capacitively coupled helium plasma, using COMSOL multiphysics

1618 S. Rebiaï et al.: 2-D Simulation of Dual Frequency Capacitively Coupled Helium Plasma, using COMSOL Multiphysics

The assumptions made in our model are summarized into several points:

1) We assume that helium neutral atoms are the dominant species in the discharge. They are uniformly distributed in the reactor and their density is determined by the system pressure and gas temperature.

2) Due to the big difference between ions and electrons mass, ions can gain only small energy from the applied field and loss a significant energy by collisions with electrons. Therefore, the ions mean energy is usually much lesser than the electron mean energy. For that reason the ions temperature (Ti) is assumed to be the same as the neutral gas temperature (Tg) and the ions energy equation is not needed. 3) In our simulation, electrons are reflected with a probability of

20% ( 2.0er ) and the electron emission coefficient p set

to 0.45 which is reasonable for Si electrodes. These two important parameters are close to those used in the experimental and simulation studies of J. Schulze et al for helium gas in dual capacitively plasma discharges [36].

4) We performed calculations for helium gas at a pressure p of 133.32 Pa. The various chemical reactions considered in gas phase are listed in Table 1 [37].

The model accounts for elastic, excitation and ionization

electron-neutral collisions. Collision between electrons, excited

and ionized species are not considered in this simple approach.

5) The cross section data used in the simulation for electronhelium collisions are obtained with the Boltzmann code BOLSIG [38], as shown in Figure 1.

The plasma is sustained between two symmetric parallel plate electrodes of 0.03 m in length, separated by 0.156 m. One electrode is electrically grounded while the other is driven by two RF sources oscillating at two different frequencies. The resulting voltage waveform on the powered electrode is in the following form:

)13()2sin()2sin( tfVtfVV LFLFHFHFrf

where, VHF and VLF are the high and low frequency voltage

amplitudes, respectively. LFf and HFf are the low and high

frequency respectively (the high and low frequencies are always chosen to be integer multiples of each other). No DC self-bias voltage is considered because both electrodes have the same size. The processed wafer or substrate may be placed on the powered electrode.

The two-dimensional geometry with meshes of DF-CCP reactor is shown in Figure 2. The model is carried out with triangular mesh consisting of 1832 non uniform elements. An extra fine mesh is chosen in the simulation domains in order to obtain accuracy resolutions. The choice of extremely fine mesh leads to an increase of computation time with no important improvements in the simulation results.

Because differential equations (1)-(13) are strongly coupled, this simulation has been solved by the finite element method by means of the commercial multiphysics software COMSOL, using the following boundary and initial conditions [39]:

2.1 BOUNDARY CONDITIONS 1) The electron flux normal to the electrodes and the reactor walls is:

)14(.

8

).()2

1(

1

1

e

eBth

pppeth

e

ee

m

TkV

nnVr

rn

Energy (eV)

c

a

Cross section (m2)

b

Figure 1. Cross sections of the electron impact reactions with helium as a

function of the electron energy (a: Momentum, b: Ionization, c: Excitation).

Table 1. Important collision processes in helium discharges [37].

Reaction

Formula

Type Δ (EV)

1 2 3

e+Hee+He

e+Hee+He* e+He2e+He+

Elastic Excitation Ionization

0 19.80 24.6

Figure 2. Drawing and meshing of the simulated area of the dual frequency capacitively coupled plasma reactor.

Chamber wall

Powered electrode

Grounded electrode

Page 4: 2-D simulation of dual frequency capacitively coupled helium plasma, using COMSOL multiphysics

IEEE Transactions on Dielectrics and Electrical Insulation Vol. 20, No. 5; October 2013 1619

where n is the unit vector normal to the wall, thV the electron

thermal velocity, Bk the Boltzmann constant and em the

electron mass. The second term of equation (14) is the gain of electrons due to secondary emission effects. 2) The electron energy flux towards the electrodes and walls is given by:

)15().()6

5(

1

1

p

pppthe

e nnVr

rn

The second term in equation (15) is the secondary emission

energy flux, p being the mean energy of the secondary

electrons.

3) finally, the electric potential must satisfy: 0V at the grounded electrode.

rfVV at the driven electrode.

2.2 Initial values

1) Initial electron density ne,0 represents some initial seed electrons in the plasma:

)/1(1410 30,

mEne

2) Initial mean electron energy )(40 V

According to initial mean electron energy value, the initial electron temperature Te was set to 2.66 eV throughout our domain including the electrodes and walls.

3) Electric potential )(0 VV

The data necessary to carry out the calculations of discharge

for helium plasma (Tg, p, e ) are taken from reference [33].

3 RESULTS AND DISCUSSIONS

Typical results of the fluid model for helium glow discharge

plasma are the densities of the various species ( nnn pe ,, ),

the electric field (E), the electron temperature (Te), the ionisation and the excitation rate profiles as a function of distance between the electrodes and as a function of time in the RF cycle. The convergence criterion is attained after a few hours (4-6 h) on Intel, Core (TM) 2 Duo CPU, 2.93GHz, 2.94 GHz. The simulations are carried out for a pressure of 133.32 Pa. The gas temperature is set to 300 K. A secondary electron

emission coefficient of 45.0p and an electron reflection

coefficient of 2.0er are used as input parameters in the

simulation process. One electrode is grounded where the other is driven by dual frequency (13.56-54.24) MHz power sources. The amplitude of the high frequency voltage is 100V and the low frequency voltage is 250 V. The two-dimensional spatiotemporal variation of various plasma parameters during the low frequency period are presented in Figure 3, Figure 4, Figure 5 and Figure 6. The

cathode and anode walls are represented by the thick white lines, respectively, at the left and the right sides of the figures, whereas the other borders of the figures represent the reactor walls. As shown in Figure 3a, the electron density reaches a maximum value of 2.57×1014 m−3 at about 0.06 m from the cathode. Due to electrons flux from the plasma bulk to the walls, the electron density decreases drastically in the radial and axial directions. In the plasma bulk (the most intense region) where quasi-neutrality is maintained, the ion density profile is very similar to the electron density profile (Figure 3a). Whereas, near the electrodes, the ion density is significantly higher than the electron density, which produces a strong positive space charge adjacent to the walls (Figure 3b). The steady state solution for the electron temperature is presented in Figure 4. The electron temperature remains relatively uniform in the plasma bulk (about 3.58 eV) but increases sharply within the sheath regions. It is evident that the electric field in the bulk plasma is much weaker than that in the sheath; hence the bulk electron temperature is lower than that near the sheaths. From this Figure we can see also that the electron temperature is higher in the rf powered sheath (a maximum of 68.7 eV) than in the grounded one (53.30 eV).

a

Figure 3. 2D, time-average (a) electron number density and (b) ion

number density for: MHzf HF 24.54 , MHzfLF 56.13 ,

VVHF 100 , VVLF 250 and Pap 32.133 .

Page 5: 2-D simulation of dual frequency capacitively coupled helium plasma, using COMSOL multiphysics

1620 S. Rebiaï et al.: 2-D Simulation of Dual Frequency Capacitively Coupled Helium Plasma, using COMSOL Multiphysics

0,00 0,04 0,08 0,12 0,16

0,0

2,0x1014

4,0x1014

6,0x1014

8,0x1014

1,0x1015

1,2x1015

1,4x1015

He+

e

He*

Te

Position (m)

Pla

sma

sp

eci

es

(m-3)

0

10

20

30

40

50

60

70

Electro

n Tem

pera

ture (eV

)

Figure 7. Axial profile of particle densities (e, He+ and He*) and the electron temperature (Te) between the electrodes.

The electric field E calculated from the potential relation

( VE ) is plotted in Figure 5. Strong electric field is found in the sheath regions, which reflects electrons moving toward the walls back into the plasma and accelerates the ions to the surface, keeping the plasma quasineutral.

It is interesting to note that because of this effect, electrons traveling to the discharge bulk with high energy involved in ionization of gas to produce the positive ions which bombard the substrate. The most of the ionization processes occur at the plasma-sheath interface and inside the bulk (Some ionization of helium atoms) as shown in Figure 6. An examination of this Figure demonstrates that the ionization rate presents two peaks, situated at positions of x= 0.0547 m and x = 0.1012 m. These maxima coincide with the maximum of the variation of electron density. Figure 7 shows the evolution of electrons temperature and different type of species density at the reactor center line between the electrodes. The axial metastable density

distribution showed a valley in the center of the discharge and distinct peaks in the plasma/sheath interfaces. The peaks in metastable density are due to enhanced creation of metastables near the electrodes regions where the electrons temperature is high. Since metastable particles are not influenced by the electric field, they are able to diffuse beyond the plasma region. For this reason a considerable metastable density in the sheath region is noticed.

3.1 THE EFFECT OF VARYING HIGH FREQUENCY

HFf AND HIGH VOLTAGE VHF

In order to better understand the dynamics of DF-CCP discharge under the influence of the high frequency, it is reasonable to fix the frequency and the voltage of the lower frequency source at 13.56 MHz and 250V, respectively, while varying the parameters of higher frequency source. Some simulations are performed under different values of the high frequencies (40.68, 54.24, 81.36 and 135.6 MHz) and the

Figure 4. 2D, time-average profile of electron temperature.

Electron temperature (V)

Figure 5. 2D, time-average variation of electric field.

Electric field (V/m)

Ionization rate (mol/ (m3.S))

Figure 6. 2D ionization rate profiles calculated under the same conditions as in Figure 3.

Page 6: 2-D simulation of dual frequency capacitively coupled helium plasma, using COMSOL multiphysics

IEEE Transactions on Dielectrics and Electrical Insulation Vol. 20, No. 5; October 2013 1621

amplitude voltage VHF (100 V). The variation of plasma potential VP, the plasma density, the ionisation rate the profile of electron temperature and electric field are presented in Figure 8 and Figure 9.

Figure 8a depicts the influence of HFf variation in the

range of 40.68 −135.6 MHz, on the plasma potential and the plasma density in the center of the discharge, respectively. It has been found that the plasma potential VP increases considerably as the frequency increases.

The evolution of plasma density and plasma potential as a function of high frequency are in good agreement with the results reported in [40, 41].

The evolution of plasma density and plasma potential as a function of high frequency are in good agreement with the results reported in [40, 41].

As the high frequency increases, the neutral density in the reactor increases leading to higher electron and ion densities due to more ionization which is responsible for the plasma density being at maximum in the center. This can be observed through

the evolution of ionization rate with frequency in Figure 8b. The strong dependence of electron temperature Te and electric field E on the high frequency is observed in Figures 9a and 9b, respectively. We can see in these Figures that the width of the plasma region decreases with increasing the high frequency value. With increasing HFf , the electron temperature in the

bulk region increases slightly but in the plasma-sheath regions we can observe a significant rising of electron temperature from 35.98 to 85.13 eV, in the cathodic sheath region and from 25.91 to 66.96 eV in the anodic one. The reason of this behaviour is explained by the enhancement of the electric field with the growing of the high frequency in the sheath regions (Figure 9b). As expected, the number of collisions between electrons and helium neutral atoms increases with increasing the RF field as a consequence of the enhancement of electron production. The high energetic electrons are produced in the sheath regions and induce ionization and excitation when they enter the plasma volume, which explain the strong electron temperature in the same regions.

The effect of the high frequency voltage amplitude VHF on the ion flux and the charge densities has been studied for five different voltages (50, 100, 150, 250 and 300 V) with a fixed high frequency at 54.24 MHz. The axial profiles of the ions flux and charged particles are plotted in Figures 10 and 11, respectively, for different values of applied voltage.

40 60 80 100 120 140

1,5x1014

2,0x1014

2,5x1014

3,0x1014

3,5x1014

fH (MHz)

Pla

sma

De

nsity

(m

-3)

Pla

sma

Po

tentia

l (V)

a

200

250

300

350

400

450

0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,160,0

2,0x10-5

4,0x10-5

6,0x10-5

8,0x10-5

1,0x10-4

b

40.68MHz

81.36MHz

54.24MHz

135.6MHz

Re

act

ion

ra

te (

mo

l/m3.S

)

Position (m)

Figure 8. Effects of HF frequency on (a): the plasma potential and density and (b): the ionization rate for fLF= 13.56 MHz, VLF= 250 V and VHF =100 V.

0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16

0

10

20

30

40

50

60

70

80

90

Ele

ctro

n t

em

per

atur

e (V

)135.6 MHz

81.36 MHz

54.24 MHz

40.68 MHz

a

-0,02 0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16-2,0x104

-1,5x104

-1,0x104

-5,0x103

0,0

5,0x103

1,0x104

1,5x104

2,0x104

b

ele

ctric

fie

ld (

V/m

)

Position (m)

13.56MHz 54.24MHz 81.36MHz 135.6MHz

Figure 9. Effects of HF frequency on (a): the profile of electron temperature and (b) the electric field (V/m) for fLF = 13.56 MHz, VLF = 250 V and VHF =100 V.

Page 7: 2-D simulation of dual frequency capacitively coupled helium plasma, using COMSOL multiphysics

1622 S. Rebiaï et al.: 2-D Simulation of Dual Frequency Capacitively Coupled Helium Plasma, using COMSOL Multiphysics

0,00 0,04 0,08 0,12 0,16

0

1x1014

2x1014

3x1014

4x1014

5x1014

6x1014

1OO V

5O V

15O V

25O V

3OO V

Tim

e A

vera

ge D

ensi

ty (

m-3

)

Position (m)

Figure 11. Influence of the high frequency voltage amplitude VHF on the charge densities for fHF = 54.24 MHz

As shown in these figures, the increase of VHF contributes

principally for enhancing the ion fluxes towards electrodes. Similar to the ion fluxes, the plasma density is mainly determined by the HF source. With increasing the VHF, the electron and ion densities also increase while the sheath length decreases. These observations confirm that the density and the flux of ions can be controlled by the high-frequency voltage. Analogous results have been obtained by Z. Donkó [42] and Z. Donkó et al [43] in DF-CCP symmetric reactor for argon plasma discharges at p = 3.333 Pa.

3.2 THE INFLUENCE OF VARYING LOW FREQUENCY LFf AND LOW VOLTAGE VLF

The aim of the simulations presented in this section is to investigate the effect of the low frequency source parameters on plasma behavior. The frequency and the voltage of the LF source are varied in order to study the influence of LF on the plasma potential, sheath voltage, sheath thickness and kinetic energy of ions. In this case the high frequency HFf is fixed to

13.56 MHz and the high voltage VHF is kept constant at 250 V. The spatiotemporal profiles of the electron and ion densities are provided in Figure 12a and Figure 12b, respectively, for different values of the driven frequency LFf (1.356, 1.93,

2.71, 3.39 and 6.78 MHz) with a fixed low voltage VLF at 400V. From these Figures, we can see a little changes of the

plasma density when the low frequency rises from 1.356 to 6.78 MHz. With increasing LFf , the plasma bulk extends its

volume with the shrinking of the sheaths length. The variation of electron temperature with low frequency is plotted in Figure 13. Contrary to the results reported in Figure 9, the effect of low frequency variation on electron temperature in plasma bulk and sheaths region is insignificant in this case. With increasing the low frequency value, we can observe a non-linear variation of electron temperature in the plasma-sheath regions

Figure 10. Effect of the high frequency voltage amplitude VHF on the ion flux for fHF = 54.24 MHz

50 100 150 200 250 300

1.0x1018

1.5x1018

2.0x1018

2.5x1018

3.0x1018

3.5x1018

4.0x1018

4.5x1018

5.0x1018

powered electrode

Ion

flux

(m-2S

-2)

VH (V)

grounded electrode

0,00 0,04 0,08 0,12 0,16

0,0

5,0x1013

1,0x1014

1,5x1014

2,0x1014

2,5x1014

3,0x1014

1.93MHz

2.71MHz

3.39MHz

6.78MHz

1.356MHz

Position (m)

aElectron Density (m-3)

0,00 0,04 0,08 0,12 0,16

0,0

5,0x1013

1,0x1014

1,5x1014

2,0x1014

2,5x1014

3,0x1014

1,93 MHz

6,78 MHz

3,39 MHz

2,71MHz

1,356MHz

Position (m)

Ion density (m-3) b

Figure 12. The effect of the low frequency on; (a): electron and, (b): ion densities, for fHF =13.56 MHz, VHF = 250 V and VLF = 400 V.

0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16

0

10

20

30

40

50

60

1.93MHz

3.39MHz

2.71MHz

6.78MHz

1.356MHz

Ele

ctro

n t

emp

erat

ure

(V)

Position (m)

Figure 13. Effects of LF frequency on the profile of electron temperature, for fhF= 13.56 MHz, VLF= 400V and VHF =250 V.

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IEEE Transactions on Dielectrics and Electrical Insulation Vol. 20, No. 5; October 2013 1623

Figure 14 is the plot of the plasma potential, the sheath voltage, the ionization reaction rate and the kinetic energy of ions over one low frequency cycle for low voltage amplitude varying from 50 to 600 V. The low frequency is set to 3.39 MHz. The results indicate that the increase of the low-frequency voltage leads to the increase of the plasma potential and the sheath voltage (Figure 14a), which is in good agreement with the results reported in reference [41] for DF-CCP parallel plate reactor used for argon discharges at p= 8.93 Pa. The same behavior is observed in Figure 14b for the ionization reaction rate. It has been found that an increase in VLF leads to a significant raises for both reaction rates.

On the other hand, the increase of the sheath voltage leads to the increase of the energy absorbed by ions in the sheath region. As can be seen from Figure 14c, the kinetic energy of ions in the bulk region is lower than in the sheath regions where the ions gain a large energy that considerably depends on the low frequency voltage. The results are similar to simulation results reported in [44] for dual-frequency (27MHz -2MHz) in the case of argon discharge at p= 6 Pa.

4 CONCLUSION A two-dimensional self-consistent fluid method for a symmetric capacitive discharge has been employed to obtain a better understanding of the dynamics of a dual frequency plasma discharge in high purity helium. The simulation model has been solved by the finite element method using COMSOL Multiphysics. The 2D distributions of particles density, the electric field and electron temperature were presented for a gas pressure of 133.3 Pa and a dual frequency source of (13.56-54.24) MHz. The dependence of the plasma density, the plasma potential, the sheath width and the ion flux on the control parameters such as lower (LF) and higher (HF) frequency sources have been investigated and compared with other simulation results.

In this work notable results have been made including:

- An increase in plasma density, plasma potential and electron temperature (Te) is observed when high frequency increases, indicating an important ionization.

- The increase in the high frequency voltage leads to significant changes in the ion flux and the particle densities.

- The sheath voltage and kinetic energy of ions are increased by the increase of the low frequency voltage.

The simulations results confirm that lower frequency source parameters, such as applied voltage amplitude and frequency value, principally determine the sheath properties and the higher frequency source principally controls the bulk plasma characteristics.

ACKNOWLEDGMENT The authors would like to thank Professor A. Bellel, from Constantine 1 University, for his useful discussions.

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-0,02 0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16

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Figure 14. Effect of the low frequency voltage amplitude VLF on; (a): the plasma and sheath voltages, (b): ionization reaction rate and, (c): the kinetic energy of ions, for fLF = 3.39 MHz.

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Saida Rebiaï received the B.S. degree in Engineering Physics from the University of Constantine; Algeria in 1982. She received her Ph.D. degree in microelectronics components from Paul Sabatier University of Toulouse; France; in 1985 and her Ph.D. degree in electronics from Mentouri University of Constantine, Algeria in 2003. Since 1986, she has been an assistant Professor in the Electronic department of the University of Constantine. Her recent research works deal with modeling and simulation of processes occurring in cold plasmas used for the deposition and surface treatments.

Hanene Bahouh, graduated in electronics, option control from Constantine University, Algeria in 2001. She received the MSc degree in microelectronic from Constantine University, Algeria in 2009. She is currently a Ph.D. degree student at Constantine University. Her research interests include DC and Radiofrequency discharge plasma modeling. Salah Sahli received the B.S. degree in engineering physics from the University of Constantine (Algeria) in 1982. He received in 1986 the Ph.D. degree in microelectronic from Paul Sabatier University, Toulouse (France). From 1987 to 1998 he worked as an Assistant Professor with the Electronic Institute of Constantine University. Since 1999, he has been a Professor at the Faculty of Engineering of Constantine University. His research interests are focused on the applications of plasmas for thin films deposition, surface modification of polymers and more recently life sciences and biomedical materials.