Effect of dilution gas on the distribution characteristics of capacitively coupled plasma by comparing SiH4/He and SiH4/Ar

In this study, we focus on the difference in the spatial distribution of the plasma parameters between SiH4/He capacitively coupled plasma (CCP) and SiH4/Ar CCP. The SiH4/He mixture is modeled using the chemical reactions that were successfully derived in our previous studies. The chemical reaction model of the SiH4/Ar mixture built in this study is based on the detailed set of chemical reactions in Ar. The spatial distribution of the plasma parameters is examined with the aid of a 2D fluid model. The electron and radical densities of SiH4/Ar CCP are higher than those of SiH4/He CCP. In addition, dilution with Ar results in more uniform reaction rates, which leads to a more uniform deposition profile. Because helium requires higher threshold energies for excitation and ionization, dilution with He had little effect on the precursor production. As a result, the concentration of Si2H6 observed in the inter-electrode region when using Ar for dilution was observed to be about ten times higher than the concentration of Si2H6 observed for He. This high concentration played a large role in influencing the formation of important radicals that determine the deposition rate as well as the difference in the deposition rate profile between Ar and He as diluents. The higher concentration of Si2H6 when using Ar means that the production rate of Si2H5 is higher in Ar. An examination of the effect of the dilution gas on the deposition rate profile indicated that the deposition rate profile with Ar is 100% more uniform and the deposition rate nearly 87% higher than for dilution with He.

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Introduction
Over the past few decades, techniques related to the desired treatment of target surfaces using plasma have been used in a variety of high-tech industrial applications [1][2][3].These related technologies typically include plasma enhanced atomic layer deposition, plasma enhanced chemical vapor deposition (PECVD), and dry etching.In the microelectronics industry, the above-mentioned plasma-related technologies are highly important [4].Our focus, as part of the development of process technology, is on lowering the cost of microchip production and improving the process quality [5,6].Representative factors that could be considered to accomplish these goals include the type of dilution gas, gas pressure, power delivery, and utilization of high frequency [7,8].The plasma physical/ chemical roles of these factors are analyzed to optimize the process conditions.
Capacitively coupled plasma (CCP) is considered to be a highly suitable plasma source for optimization of the process conditions [9][10][11][12].In particular, CCP has been usefully employed for the design of PECVD reactors owing to the wide applicability of this technique.Among the research topics that have been considered important in the field of CCP discharge, the objectives of designing reactors for use as equipment for semiconductor production are to ensure the efficient use of the input power and the rapid and uniform heating of electrons in the discharge volume with the delivered power.Useful approaches to achieving these objectives would be to vary the gas pressure or adjust the excitation frequency.Another simple but effective method would entail changing the dilution gas, whereby it would be possible to control the spatial distribution of the source gas density.In addition, the electron collision reaction rate could be improved, and the uniformity of radio frequency (RF) power deposition could be improved by affecting the average energy dissipation.Furthermore, important discharge characteristics such as the surface flux of ions and radicals measured at the electrode surface could be optimized as a result of changing the dilution gas.Since the control of the plasma density distribution is of great importance to achieve process optimization, the dilution gas in CCP discharges has been studied extensively to determine its effect on the process [13][14][15][16][17][18][19][20].
At the same time, several efforts have been made to elucidate the deposition mechanism of thin films in order to analyze and understand the limitations of the deposition rate.These limitations have been sought to be overcome, for example, by improving the gas-phase reaction.Accordingly, changing the dilution gas is expected to help to increase the deposition rate similar to the way in which the deposition rate of the thin film is improved by changing the RF or gas pressure.In addition, a different dilution gas would enable the properties of the deposited thin films to be improved.Zhang and Zhang found higher-silane related reactive species (HSRS) to be an important factor for increasing the photo-induced degradation of hydrogenated amorphous silicon (a-Si:H) films [20].They controlled the generation of HSRS with the use of dilution gases such as H 2 , He, and Ar.
The deposition of silicon-based thin films using CCP is generally carried out using a larger amount of the dilution gas (Ar, He, or H 2 ) than the amount of source gas such as SiH 4 and Si 2 H 6 .In addition, in the thin film formation process, pressure conditions of 100 Pa or more are frequently used to prevent the increase in intrinsic stress caused by ion bombardment and to increase the deposition rate by increasing the efficiency of the generation of radicals in the gas phase reaction.For example, in our previous study of the deposition of an amorphous silicon layer using the SiH 4 /He mixture, the amount of SiH 4 used was only 1%-2% of the amount of He used, and the pressure exceeded 400 Pa [8,21,22].Therefore, because of the large proportion of dilution gas in the mixture, the plasma properties of the mixture are inevitably influenced more profoundly by the type of dilution gas.
Based on the aforementioned importance of the dilution gas, in this study, we investigate the difference in the spatial distribution of plasma parameters between SiH 4 /He mixture CCP and SiH 4 /Ar mixture CCP using a 2D fluid model.In fact, studies on CCP with these two mixtures have been conducted from various perspectives.For example, in our previous research, SiH 4 /He mixture CCP was used to determine the conditions under which an amorphous silicon layer could be uniformly and rapidly deposited, and ways in which to establish these conditions were studied [8,21,22].The generation of silicon nanoparticles using SiH 4 /Ar CCP was also previously studied [23][24][25][26][27].However, despite the frequency and importance of using this method, a systematic investigation of the difference between Ar and He as dilution gases does not seem to have been reported yet.
Therefore, in this paper, we present the results of a numerical analysis of the effect of the dilution gas when using SiH 4 /He mixture CCP and SiH 4 /Ar mixture CCP.Our study revealed various differences in the spatial distribution of the plasma parameters resulting from the thinner plasma sheath thickness when Ar, instead of He, was used as the dilution gas.In addition, the uniformity of the deposition rate profile was found to be consistently good in the case of argon dilution even when the input power was doubled.

Plasma model
A 2D fluid model was used to analyze the spatial distribution of plasma parameters.A self-consistent model was adopted to accurately analyze the plasma density distribution according to changes in the dilution gas and process conditions.The model considered the following physical factors: RF plasma discharges, convection resulting from gas flow, thermal energy balance by chemical reactions, balance of thermal energy according to the difference in gas temperature caused by boundary conditions, distribution of source gas density, and gas-phase reactions and surface reactions caused by the RF plasma.As the details were elaborated in our previous articles [8,21,22], only the corresponding governing equations are briefly introduced here as follows: ) where ρ is the overall density, t is the time, v is the overall velocity, p g is the gas pressure, τ is the viscous stress tensor, f is the net force per unit volume, µ is the molecular viscosity, Y i is the mass fraction of species i, j i C is the flux of species i resulting from the concentration gradients, j i T is the thermal diffusion flux of species i, G i is the rate at which species i is generated, and L i is the rate at which species i is depleted, M i is the molar mass of species i, n e is the electron density, J e is the electron flux, S e is the electron source, D e , is the electron diffusion coefficient, µ e , is the electron mobility, ϕ is the electric potential, ε is the electron energy, v e is the electron velocity, −e is the electron charge, E is the electric field, N is the neutral density, k l is the electron energy loss, ε 0 is the permittivity of space, n p is the positive ion density, and n q is the negative ion density.In equation (3), I is the unit matrix.In the case of Ar dilution, the gas velocity is decreased.
To reduce the calculation time, the 0D Boltzmann equation was solved before simulation of the 2D CCP.This solution enabled the electron energy distribution function to be obtained, whereupon the parameters related to the electron impact reaction rate and electron transport were obtained.A lookup table was created as a result of the calculations performed in this preprocessing step.

Plasma chemistry
In this study, we considered various neutral and charged species that can be observed in SiH 4 /He and SiH 4 /Ar discharges.These species include radical species, positive and negative ions, and stable and excited molecules produced from SiH 4 , He, and Ar.In addition, a sticking model was used to numerically analyze the thin film deposition phenomenon.The probability coefficients of various reactive radicals, obtained from the experimental results of other researchers, were used in this sticking model [28][29][30].
The probability coefficient of silicon ions was assumed to be a unit probability value.Additionally, first-principle density functional theory calculations were conducted on hydrogenated (H-covered) Si(001) and Si(111) surfaces to investigate Si 2 H 6 surface reactivity [31,32].
The chemical reaction model of the SiH 4 /He mixture is the model we successfully used in our previous research [8,21,22].The chemical reaction model of the SiH 4 /Ar mixture was constructed by building a detailed set of chemical reactions for this mixture and this model was applied in this study to achieve completeness of the results.Because Ar was used as the dilution gas, the chemistry of Ar was considered in detail and was verified via a quantitative comparison with the measurement results acquired with the Langmuir probe in our previous study [33].
With regard to the chemical processes involving SiH 4 /Ar mixtures, we used a subset of the reactions discussed in previous reports [21,22,28].A total of more than 200 gasphase chemical reaction equations were considered in the SiH 4 /Ar chemical reaction model to ensure the completeness of the numerical analysis results.The electron impact reactions included ionization, dissociation, and dissociative attachment.SiH 4 /Ar discharges were considered to contain 14 charged species, namely Si + , SiH + , SiH  (v=3) , H, Ar, Ar( 3 P 2 ), Ar( 3 P 1 ), Ar( 3 P 0 ), Ar( 1 P 1 ), Ar(4p), and Ar 2 * .In table 1, we list selected gasphase reactions considered to play an important role in the formation of radicals under the condition that the gas pressure exceeds 100 Pa.For brevity of notation, table A1 in the appendix lists the remaining gas phase reactions.
Furthermore, comparison of the deposition rate profiles of the amorphous silicon layers deposited using CCP simulations with the experimental values confirmed the validity of the reaction model.This comparison is presented section 3.

Surface model
A sticking model was used to numerically analyze the thin film deposition phenomenon.The probability coefficients of various reactive radicals, obtained from the experimental results of other researchers, were used in this sticking model [22].
The deposition can be described by a sticking model, which is obtained as follows: where subscript i is the species index, D i is the diffusion coefficient, n i is the density of species i, z is the axial coordinate, n i,s is the density of species i at the surface, and R i,s is the surface reaction rate of species i, respectively.In equation ( 9), the flux of species i, which reacts at the surface, is obtained as follows:  [21,28] where subscript i, s, γ, k B , T g , and M i are the species index, the sticking coefficient, the recombination probability, the Boltzmann constant, the gas temperature, and the mass of species i, respectively.Note that the loss probability β is defined as β = s + γ.The flux to be reflected back into the discharge volume is obtained as follows: where subscript j is the species index.
Finally, the deposition rate can be calculated by using the equations below: where Φ i , α i , n s , N A , M, and ρ are the deposition rate of species i, the stoichiometry of species i, the surface density of the film, the Avogadro number, the molar mass of the film, and the mass density of the film, respectively.

Experimental setup
The shape and operation method of the CCP reactor used in our experiment are the same as those of the CCP reactor considered in the simulation.Therefore, the reaction volume of the reactor during the experiment was used as the simulation domain.Details of the simulation domain will be provided at a later stage.
To verify the simulation results, the experiment was conducted by applying the same process conditions considered in the simulation.The deposition rate profile predicted in the simulation was compared with the experimentally measured deposition rate profile.In order to predict the deposition rate profile from the simulation results, the physical properties of the a-Si:H layer were measured.These physical properties were measured using an x-ray diffractometer (SmartLab, Rigaku Corporation, Japan) and an ellipsometer (SFX-200, KLA Tencor, USA) [47].The thickness of the a-Si:H layer was measured using the ellipsometer, and the value obtained by dividing the measured thickness by the total deposition time is the deposition rate.These measurements confirmed that the spatial distribution of the refractive index value of the a-Si:H layer deposited on the Si wafer using our CCP reactor was highly uniform (spatial non-uniformity < 1%).Measurement of the film density (ρ Si = 2.3 g cm −3 ) indicated that the spatial unevenness of this density was less than 1%, and a highly uniform distribution was observed.Based on the distribution of these physical properties, it was confirmed that the film had constant properties in the radial direction.As these uniform film properties were secured, the deposition model based on the radical surface flux was able to derive results that were in good agreement with the experimental results.

Results
The showerhead CCP deposition reactor, including its geometric configuration and operating conditions, are described next.Figure 1 shows a schematic representation of the reactor we are considering.Owing to its symmetric nature, the reactor can be represented with only half of its radial and axial coordinates in the r-z plane.A cylindrical reactor is normally used to process wafers.The borders on the left and right side of the diagram show the symmetrical axis and a sidewall, respectively.Our cylindrical CCP reactor has a top electrode (showerhead electrode), which is separated from the ring-shaped dielectric component.A SiH 4 /Ar or SiH 4 /He gas mixture is supplied uniformly in the radial direction through the showerhead electrode.In 2D CCP simulations and experimental measurements, this showerhead electrode is powered by RF at 13.56 MHz.The lower electrode (heater) is heated and grounded.Ring-shaped components have an inner surface that acts as a sidewall.In table 2, we summarize the detailed process conditions for each of the cases considered in this study.
As discussed in the introduction, the goal of this study is to clarify the effect of the dilution gas.To this end, the concentration of SiH 4 was set very low at 2%.To establish a baseline, we first analyzed the spatial distribution of the plasma parameters in our reactor using only argon.As mentioned above, the Ar chemistry in the torr regime was verified by comparing the results with the experimental values measured in our previous study.The spatial distributions of the excitation (Ar + e − → Ar * + e − ) rates (kmol m −3 s −1 ), ionization (Ar + e − → Ar + + e − + e − ) rates (kmol m −3 s −1 ), Ar * densities (m −3 ), and Ar + densities (m −3 ) for Case 1 are displayed in figures 2(a)-(d), respectively.The gas pressure, applied RF power, and Ar flow rate were set at 400 Pa, 200 W, and 5000 sccm, respectively.
The electron collision reaction rates shift towards the bottom grounded electrode as the plasma sheath heats the electrons (figures 2(a) and (b)).The source functions for Ar * and Ar + have the similar shape: the enhanced electrical fields at the electrode edge result in radial extremes in the excitation and ionization rates.This increases the sheath heating, which also results in a shift towards the bottom grounded electrode.Figure 2(c) shows that the Ar * density in the bulk region varies only slightly.In the corners, converging sheaths produce a high heating rate, resulting in high Ar * density.The electrons diffuse axially from the production site, with a maximum Ar + density seen near the maximum distribution of the ionization rate, as shown in figure 2(d).

Effects of dilution gas on spatial distributions of plasma parameters
The focus of this section is our observation that a change in dilution gas affects the spatial variation of the plasma parameters such as the distributions of excited species of the dilution gas (i.e.He * is produced in the case of SiH 4 /He and Ar * is produced in the case of SiH 4 /Ar), distributions of ionic species of the dilution gas (the production of He + and Ar + in the case of SiH 4 /He and SiH 4 /Ar, respectively), and distributions of electron densities (N e ) and ion fluxes.
We display the excitation rate distributions of the dilution gases in figure 3(a) for the case of SiH 4 /He (Case 2; e − + He → He * + e − ) and in figure 3(b) for the case of SiH 4 /Ar (Case 3; e − + Ar → Ar * + e − ).The distributions of excited species of the dilution gases are shown in figure 3(c) for the case of SiH 4 /He (Case 2; He * ) and in figure 3(d) for the case of SiH 4 /Ar (Case 3; Ar * ) to observe the effects of the dilution gas thereon.The following input conditions common to both dilution gases were set: the RF power was set at 200 W, the SiH 4 gas flow was set at 100 sccm, and the gas pressure was set at 400 Pa.The flow rates of both dilution gases were also set as 5000 sccm (table 2): the He gas flow rate was set at 5000 sccm in Case 2, and the Ar gas flow rate was set at 5000 sccm in Case 3.
As shown in figures 3(a) and (b), a shift in the axial direction is observed towards the bottom grounded electrode near the electrode edge, which increases the excitation rate as electrons are heated by the plasma sheath.As depicted in figure 1,    Common to both the He and Ar cases, in figures 4(a) and (b), the ionization rate is observed to increase near the bottom electrode edge, and the characteristic feature of this ionization rate distribution is that it has a distribution skewed axially toward the bottom electrode by the electrons heated in the sheath.
Furthermore, common to both the He and Ar dilutions, the excitation rate profile and the ionization rate profile have very similar distribution characteristics.Electrostatic excitation, which is one of the main sources of metastable species, has a distribution that is essentially similar to that of ionization.The interesting difference is that the axial distribution of the He + density has a 'double humped shape,' whereas the axial distribution of the Ar + density is 'bell shaped.'Apart from this, Ar + has an off-axis maximum that is 2 orders of magnitude higher than that of He + .This difference in value is attributed to the threshold value of He ionization being about 10 eV higher than that of Ar ionization, and the pressure being considered exceeds 100 Pa in this study.
In addition, we should note that the branching and rate coefficients for the charge-exchange reactions of He + with SiH 4 were set as shown below [48]: where k r represents the reaction rate coefficient.
Additionally, the branching and rate coefficients for the charge-exchange reactions of Ar + with SiH 4 were set as shown below [28,49]: where k r represents the reaction rate coefficient.
Considering the reaction rate coefficients mentioned above, it is confirmed that the depletion rate coefficient of He + is greater than that of Ar + .Therefore, because of the larger depletion rate coefficient, He + generated near the top electrode and the bottom electrode is not sufficiently transferred to the plasma bulk and is rapidly consumed near the electrodes.As a result, a 'double humped shape' is observed in the He + density distribution.On the other hand, because Ar + has a small depletion rate coefficient, it is sufficiently delivered to the plasma bulk.As a result, unlike the He + density distribution, the Ar + density distribution has a 'bell shape'.
Figures 5(a) and (b) display the time-averaged electron density (N e , m −3 ) profiles for dilution with He (Case 2) and Ar (Case 3), respectively.The increasing excitation and ionization elevate the electron density when the dilution gas is changed from He to Ar, as shown in figures 5(a) and (b).The electron density increases as a result of electron impact ionization, which is the main process whereby electrons are produced.As long as the input parameters remain the same, the electron density in SiH 4 /Ar is higher than that in SiH 4 /He.The reason may be that Ar has lower excitation and ionization threshold energies than He.As a consequence of dilution with Ar, the plasma variables are distributed more uniformly despite the higher electron density.− density (m −3 ) profiles for dilution with He (Case 2) and Ar (Case 3), respectively.Negative ions including SiH 3 − and SiH 2 − are generated from SiH 4 through dissociative attachment.The negative ion density profile was observed to be more diffuse in both the axial and radial directions as the dilution gas was changed from He to Ar.Because the potential well limits the transport of negative ions due to the low mobility of these ions, the distribution of negative ions is more closely confined to the vicinity of the site at which the negative ions are generated in the case of dilution with He.
Meanwhile, Schulze et al found that strongly electronegative discharges exhibit considerable ionization caused by electrons accelerated by strong drift and ambipolar electric fields in the plasma bulk [50].However, our process conditions differ from those of Schulze et al in that the gas pressure is high and the proportion of SiH 4 is low: Schulze et al used a gas pressure of 40 Pa and pure CF 4 .Therefore, the electronegativity is also not relatively high compared to the results for pure SiH 4 discharge or pure CF 4 discharge.Because of these important differences, the results we observed differ from those of Schulze et al.
Another important consideration is that the electron density and electron mean energy in combination determine the ionization rate, since the electron mean energy can be used to determine the ionization rate coefficient.A higher ion flux (mA cm −2 ) near the electrode edge is correlated with a higher electron mean energy.Accordingly, higher corner rates are strongly correlated with greater ion fluxes, as can be seen in figures 5(e) and (f) for He dilution and Ar dilution, respectively.Therefore, when observing the distribution of the ion flux, the excitation and ionization rates in the case of Ar dilution are understood to have a distribution biased toward the bottom electrode.The distribution of the ion flux in Ar is also observed to be more uniform in the radial direction.

Effects of dilution gas on the spatial variation of the plasma parameters related to ionic species of SiH 4
The effect of the dilution gas on the plasma parameters related to the SiH 2 + and SiH 3 + ions are considered in this section.The time-averaged ionization rate profiles (the production of SiH Dilution with He gives rise to significantly enhanced ionization rates near both the top and bottom electrode edges; thus, the radial distribution of these rates is non-uniform in figure 6(a).Substantial local enhancement occurs, particularly between the top electrode edge and the top sidewall.As shown in figure 6(b), when Ar is used as diluent, the ionization rates near the bottom electrode edge are not uniform within the axial profile.The peak ionization rate in the inter-electrode region is lower and shifts only toward the bottom electrode for Ar dilution.Additionally, the ionization rates peak near the edge at which the bottom electrode is located, but they are relatively lower and distributed uniformly at r ⩽ 130 mm in the case of Ar dilution.
In a similar manner to figures 6(a) and (b), figures 6(c) and (d) demonstrate that the depletion rates are also enhanced and localized near the electrode edge, and are therefore not uniformly distributed radially, neither for He nor for Ar dilution, respectively.
In figures 7(a) and (b), we show the time-averaged SiH 3 + density profiles for He dilution (Case 2) and Ar dilution (Case 3).Figures 7(c) and (d) show the time-averaged SiH 2 + density profiles for dilution with He (Case 2) and Ar (Case 3).As can be seen from these contours, SiH 3 + is the dominant ion.The SiH 3 + density peaks at an order of magnitude higher than the SiH 2 + density under the examined discharge conditions.In the case of Ar dilution, a greater difference between SiH 3 + and SiH 2 + appears, particularly in the midplane of the discharge.In addition, for dilution with Ar, the axial density profiles of SiH 3 + are quite different from those of SiH 2 + , and this difference is similar to that evident from the ionization rate profiles  in figure 6(b).In the case of SiH 2 + , ion consumption in the gas phase occurs rapidly via the secondary ion conversion reaction involving SiH 2 + , whereas SiH 3 + diffusion from the bulk to the sheath is followed by drift transport through the sheath and neutralization at the electrode surfaces.Because of this, the density profile of SiH 3 + is smooth with a maximum at the center of the discharge, whereas the peak value for SiH 2 + can be observed where the production of these ions is the highest.In addition, in the case of Ar dilution, the fluxes of SiH 3 + towards the electrodes and throughout the discharge are lower.
In summary, figures 6 and 7 indicate that the density distribution characteristic of the SiH 4 ions is significantly affected by the dilution gas.Since the ion collision rate increases with Ar dilution, the mean free path is decreased for the ions.The reduction of the loss rates at the electrodes increases the ion and electron density, resulting in the sheath width becoming narrower.

Effects of the dilution gas on the spatial distributions of the neutral transport parameters
The impact of the dilution gas on the spatial distribution of the neutral transport parameters is discussed in this section.Considering that the distribution of a-Si:H is influenced by SiH 3 , it was selected for the purpose of analyzing the transport of neutral species.The time-averaged production rate profiles resulting from electron impact dissociation (e − + SiH 4 → SiH 3 + H + e − ) for He (Case 2) and Ar dilution (Case 3) are depicted in figures 8(a) and (b), respectively.In addition, the time-averaged production rate profiles by hydrogen Additionally, as observed in figures 9(c) and (d), the SiH 3 depletion rate is more distributed in the case of Ar dilution.The enhancement of the disproportionation process in the case of Ar dilution has the effect of rapidly depleting the SiH 3 in the bulk: Based on equation ( 4), the reduced diffusion coefficient of SiH 3 can also induce local accumulation in the case of Ar dilution.The density distributions of neutral species could undergo marked axial variation when local depletion is increased and the diffusion coefficient is decreased in the case of Ar dilution.As a result, the density near both the top and bottom surfaces is lowered, resulting in fast SiH 3 loss in the bulk.Therefore, Ar dilution enhances the axial variations in the density distributions, as shown in figure 9.
Figures 10(a) and (b) show the spatial variations in the Si 2 H 6 densities (m −3 ) for He (Case 2) and Ar dilution (Case 3), respectively.As Ar dilution accelerates the gas phase reaction, SiH 4 is depleted rapidly, which, in turn, leads to the fast production of Si 2 H 6 in the gas phase.As a result, the concentration of Si 2 H 6 observed in the inter-electrode region in the case of Ar dilution is observed to be approximately ten times higher than the concentration of Si 2 H 6 in the case of He dilution.This high concentration plays a determinant role in governing the formation of important radicals that determine the deposition rate and in determining the difference in the deposition rate profiles for Ar dilution and He dilution.Because the concentration of Si 2 H 6 is higher in the case of Ar dilution, the rate at which Si 2 H 5 is produced (formed by the hydrogen abstraction of Si 2 H 6 ) is higher in the case of Ar dilution, as shown in figures 10(c) and (d).
Figures 11(a) and (b) show the spatial variations in the Si 2 H 5 densities (m −3 ) for Case 2 and Case 3, respectively.As predicted on the basis of the results in figure 10, the density of Si 2 H 5 has a higher distribution in the case of Ar dilution.In addition, figures 11(c) and (d) show the spatial variations in the Si 5 H 12 densities (m −3 ) for Case 2 and Case 3, respectively.In figures 11(c) and (d), He dilution reduces the efficiency of Si 5 H 12 generation, and as a result, the Si 5 H 12 reaches the bottom electrode surface less readily.As Si 5 H 12 approaches the bulk plasma region, its density distribution is commonly observed to increase regardless of the dilution gas.He dilution results in a slight increase in the thickness of the diffusion layers near the showerhead inlet.Figure 12 compares the deposition rate profiles for dilution with He (Case 2) and Ar (Case 3).The deposition rate profiles are normalized with their corresponding averaged values, and they correspond well with the experimental data.Upon examination of the effect of the dilution gas on the deposition rate profile, we found that, in the case of Ar dilution, the deposition rate profile was nearly 100% more uniform and the deposition rate approximately 87% higher than for He dilution.It is worthy to note that Ar dilution has a higher deposition rate and the deposition rate profile has higher uniformity than that using He dilution.Regarding the process results, Ar dilution delivers superior performance, although He dilution results in a lower density of Si 5 H 12 , as observed in figure 11.This means that when using He dilution, the process result could be safer with respect to particle contamination.

Effect of the dilution gas on the plasma distributions caused by the input power
In this section, we consider the extent to which and manner in which the spatial distribution of the plasma parameters varies as the input power is increased, depending on whether He or Ar is used for dilution.Figures 13(a) and (b) show the spatial variations in the ionization rates (kmol m −3 s −1 ) as the input power increases from 200 W to 400 W, for dilution with He (Case 4) and for dilution with Ar (Case 5),  respectively.An increase in the input power is accompanied by an increase in the RF voltage (V rf ).As the peak voltage increases, the resulting peak value of the plasma potential formed near the sheath also increases.Analysis of the corresponding change in the ionization rate following adjustment of the peak voltage revealed that an increase in the peak voltage leads to an increase in the maximum value of the ionization rate.The electrons gain energy by interacting with the stronger electric field near the sheath due to the plasma potential caused by the elevated peak voltage.This higher energy is associated with a higher electron temperature.
As a result, electron heating becomes more efficient, and consequently, the electrons have more kinetic energy, i.e., the electron temperature increases.Because the ionization rate is mainly expressed as a function of electron temperature, the ionization rate increases as the electron temperature increases.Therefore, by increasing the input power from 200 W to 400 W, the peak value of the ionization rate increases from Moreover, the excitation rate also increases with the peak voltage, as shown in figure 13(c) for He dilution and in figure 13(d) for Ar dilution.Ultimately, higher input power increases the electron collisions with other species, and, in turn, this promotes electron impact reactions.Thus, the most important effect of increasing the input power (or voltage) is its influence on elevating the electron density, as depicted in figure (e) for the case of He dilution and in figure (f) for the c ase of Ar dilution.At 400 W, the peak electron density reaches 9.06 × 10 15 m −3 for He dilution and 3.72 × 10 16 m −3 for Ar dilution.
Importantly, for He dilution, an increase in power causes the density distribution of the electrons to become less uniform because local heating near the electrode edge is enhanced by the higher input power.Because the spatial distribution of the plasma parameters is relatively less uniform for He dilution, as a result, the deposition rate profile for He dilution in figure 14 is considerably less uniform than that for Ar dilution.Furthermore, in the case of Ar dilution, even when the input power is 400 W, the uniformity of the deposition rate profile does not change significantly relative to the RF power of 200 W, but the edge profile rises more severely in the case of He dilution.In the case of Ar dilution, the deposition rate profile was about 113% more uniform and the deposition rate approximately 90% higher than for He dilution.Finally, the results in figure 14 confirm that the experimental and simulated values are in good agreement even when the RF power was adjusted to 400 W.

Discussions
In this study, we numerically computed the difference in the spatial distribution of the plasma parameters between SiH 4 /He mixture CCP and SiH 4 /Ar mixture CCP using a 2D fluid model.The results presented in this paper indicate that the excited species moved towards the bottom electrode and are skewed toward the corner in the case of Ar dilution.The skewness was principally determined by the shortening of the electron mean free paths (due to the higher collision frequency in the case of Ar dilution) and the increase in Ar * quenching due to the higher electron density and the related reaction rate coefficient.In the case of He dilution, the skewness was observed to have formed in the spatial distribution of the He * density, but the skewness was less prominent compared to the case of Ar dilution under the same process conditions.This relative difference arises because, with Ar dilution, the electron mean free path is shorter and the electron density is higher than in the case of He dilution.
As a result, electrons located near the electrode and heated by the plasma sheath can dissipate their energy by excitation closer to the electrode in the case of Ar dilution.The higher electron density for Ar dilution results in a thinner sheath.A greater electric field enhancement is observed along the electrode edge when the sheath collapses.This enlarges the skewness of the Ar * density profile.The collapsing sheath form resulting from an increase in the power deposition in the case of Ar dilution has sufficient short mean free paths to affect the Ar * source function.The higher plasma density also increases Ar * quenching.This increase restricts the Ar * to nearer the source of generation, and thus confines the Ar * closer to its location.However, despite this elevated skewness, the distribution of the plasma parameters in the radial direction near the bottom electrode is more uniform in the case of Ar dilution.As a result, the deposition rate profile in the case of Ar dilution was found to be more uniform than that in the case of He dilution, regardless of the change in input power.

Conclusions
Our study was concerned with modeling the difference in the spatial distribution of the plasma parameters between SiH 4 /He CCP and SiH 4 /Ar CCP.The SiH 4 /He CCP process was modeled using the chemical reaction model of the SiH 4 /He mixture we developed and successfully applied in previous studies.The chemical reaction model of the SiH 4 /Ar mixture was built in this study and is based on the detailed chemical reaction set of Ar.The spatial distribution of the plasma parameters was studied by conducting 2D fluid modeling, whereupon the simulation results of the chemical reactions in the plasma were used to numerically analyze the deposition of a hydrogenated amorphous silicon film.
The results presented in this paper show that the excited species moved toward the bottom electrode and were skewed toward the corner in the case of Ar dilution.Skewness was also observed in the case of He dilution, but the skewness was relatively less obvious compared to Ar dilution under the same process conditions.In addition, as a change in the dilution gas was shown to enhance the growth rate and improve the uniformity of the deposition profile, the effects of the dilution gas were clarified in this study.The results showed that Ar dilution leads to more uniform ionization and excitation rates and thus more uniform density distributions of ions and radicals.Investigation of the effect of the dilution gas on the deposition rate profile for an input power of 200 W confirmed that the deposition rate profile for Ar dilution was approximately 100% more uniform than that for dilution with He.In addition, the deposition rate for Ar dilution was about 87% higher.The numerical results were in good correspondence with the results of our experiments.
Finally, we determined the extent to which and the manner in which the spatial distribution of the plasma parameters changed for dilution with He and Ar by increasing the RF power from 200 W to 400 W. For dilution with Ar, even when the RF power is doubled to 400 W, the uniformity of the deposition rate profile does not change significantly; however, in the case of He dilution, the edge profile rises more severely.

Figure 1 .
Figure 1.Schematic representation of the CCP reactor we are considering.Spatial variation in the electron density (m −3 ) for Case 1 (as specified in table 2).

Figures 5 (
Figures 5(c) and (d) display the time-averaged SiH 3 − density (m −3 ) profiles for dilution with He (Case 2) and Ar (Case 3), respectively.Negative ions including SiH 3 − and SiH 2 − are generated from SiH 4 through dissociative attachment.The negative ion density profile was observed to be more diffuse in both the axial and radial directions as the dilution gas was changed from He to Ar.Because the potential well limits the

Figure 12 .
Figure 12.Effect of the dilution gas on the deposition rates.The deposition rate profiles for Case 2 and Case 3 are plotted.The experimental data of Case 2 and Case 3 are superimposed.

Figure 14 .
Figure 14.Effect of the dilution gas on the deposition rates.The deposition rate profiles for Case 4 and Case 5 are plotted.The experimental data of Case 4 and Case 5 are superimposed.

Table 1 .
Selected gas-phase reactions considered in this study.

Table 2 .
List of cases considered in this study.Case no.Dilution gas flow rate SiH 4 flow rate RF power

Table A1 .
Remaining gas-phase reactions considered in this study.The units of Te and Tg in the rate coefficients are eV and K, respectively.