Silicon https://doi.org/10.1007/s12633-018-9916-y

ORIGINAL PAPER

Monte Carlo Simulation of Chemical Reactions in Plasma Enhanced Chemical Vapor Deposition: from Microscopic View to Macroscopic Results O. Babahani1 · S. Hadjadj1 · F. Khelfaoui1 · H. O. Kebaili1 · S. Lemkeddem1 Received: 18 November 2016 / Accepted: 23 May 2018 © Springer Science+Business Media B.V., part of Springer Nature 2018

Abstract We propose in the present work a Monte Carlo Simulation (MCS) of chemical reactions occurring in Plasma Enhanced Chemical Vapor Deposition (PECVD) reactor during the a-Si:H growth. From a microscopic view of chemical reactions, this MCS allowed to obtain macroscopic results. In gas phase, important reactions have been identified that contribute to the production of H, SiH2 and SiH3 . We found that SiH4 →SiH2 +2H is the dominant silane electron-impact dissociation. We found that the reaction SiH4 +H→SiH3 +H2 plays a central role in the production of SiH3 radicals. At the surface, the microscopic view allowed us to calculate site and surface reaction probabilities of SiH3 radicals. Results at macroscopic level were consistent with other works. Keywords a-Si:H · MCS · Reactions · Microscopic level · Sites · Probabilities

1 Introduction Plasma Enhanced Chemical Vapor Deposition (PECVD) is the most widely used technique to produce hydrogenated amorphous silicon thin films (a-Si:H) for solar cells, for film transistors and electronic devices [1, 2]. The wide use of SiH4 for PECVD of a-Si:H films has motivated a vast effort in applied and basic research which now permits a better understanding of the plasma physico-chemistry and film growth process [3]. The technical development for depositing thin films of silicon with desirable properties requires a fundamental understanding of interactions at the atomic level between (Si-H) or dangling bonds DB and reactive radicals present in the plasma such as SiHx (x = 1, 2, 3). These interactions lead to silicon film growth and hydrogen (H) incorporation into the film. From the experiments alone, it is difficult to elaborate the theory of the surface chemistry because it

 F. Khelfaoui

[email protected]; [email protected] 1

Facult´e des Math´ematiques et des Sciences de la Mati`ere, Laboratoire de Rayonnement et Plasmas et Physique des Surfaces, Universit´e Kasdi Merbah Ouargla, Ouargla 30000, Algeria

is not possible to observe directly the atomic scale events occurring on the substrate surface during the deposition [4]. Monte Carlo Simulation (MCS) is a powerful numerical tool that can solve PECVD problems. Reactions during plasma deposition are complex and are not understood completely. Only a few studies reported the reactions occurring in the plasma and on the deposition surface [5]. In the gas phase, important reactions have been identified that contribute to the production and consumption of hydrogen (H), silylene (SiH2 ), and silyl (SiH3 ). The hydrogen consumption reactions SiH4 +H → SiH3 +H2 and SiH3 +H → SiH2 +H2 are found to play a central role in deciding the distribution of hydrogen [6]. Kushner undertook a detail modeling of the silane dissociation chemistry in a glow discharge [7, 8]. Kushner found that SiH4 +H → SiH3 +H2 and SiH4 + SiH2 → Si2 H6 are important gas phase reactions because they are first order reactions of the dissociation products of SiH4 . He found also that the ratio SiH3 /SiH2 increases [9]. The plasma chemistry indicates that H atoms and SiH3 radicals play an important role in the a-Si:H deposition process [10]. Experimentally, it is generally accepted that SiH3 radicals dominate a-Si:H and μc-Si films growth from SiH4 plasmas in PECVD; it is the key precursor of a-Si:H deposition [11]. The SiH3 has the highest density of all

Silicon

reactive species in the SiH4 plasma [12, 13] and a-Si:H growth is governed almost completely by SiH3 radicals [14, 15]. In a study [16] Kushner found that SiH2 and SiH3 species play a central role in the plasma because these radicals incorporate differently into the a-Si:H film; and therefore the characteristics of the film are a function of the ratio [SiH3 ]/[SiH2 ]. In a previous work [4], we proposed the concept of site probability of sticking on DB and site probability of recombination. These probabilities at atomic level allowed us to get simple analytical formulas that relate between the value of surface reaction probability, the rate of reactive sites or DB and the rate of passive sites or (Si-H) on the surface. In this work, we present details of a microscopic view of MCS of gas phase and surface reactions occurring in SiH4 /H2 plasma during the a-Si:H growth by PECVD process. This MCS is as a theoretical tool for studying the chemistry aspect of a-Si:H or other thin film as a-C:H growth by PECVD process [4, 17, 18]. In Section 2, we describe the MCS used to simulate chemical gas phase reactions. The MCS allowed us to get the ratio SiH2 /SiH3 and means value of densities of species. It provides information on SiH4 dissociation and on production of SiH3 , H, SiH2 , and Si2 H6 . We study the role of some gas phase reactions and their effects on H, SiH2 , and SiH3 generation. These results are found in Section 4.1. In Section 3, we describe the MCS used to simulate chemical reactions at a-Si:H surface. This simulation is based on chemisorption sticking of radicals on DB and recombination of radicals by H-abstraction from (≡Si–H) bonds. At atomic level and by MCS, we calculate the site probability of recombination of SiH3 , the site probability of sticking and the rate of hydrogenated sites. We calculate the SiH3 surface reaction probability and other probabilities at macroscopic scale. These probabilities and results at microscopic and macroscopic scale are found in Section 4.2. Results were discussed and we have finished this work by a conclusion in Section 5.

2 Description of Monte Carlo Simulation of Gas Phase Reactions The MCS is based on binary collisions at microscopic level. Effective collisions are those that result in a chemical reaction. A chemical reaction needs a collision involving at least two particles (atoms, ions, electrons or molecules). According to kinetic theory, gasses consist of particles in random motion. These particles move in a straight line until they collide with another particle or the walls of their container. The plasma in PECVD reactor is weakly ionized. At low temperature, particles interact occasionally with each

other and move under the effect of thermal agitation. We applied the MCS at microscopic level on 21 neutralneutral or electron-neutral reactions (Table 1). These gas phase reactions involved eight neutral species (SiH4 , SiH3 , SiH2 , H, H2 , Si2 H6 , Si2 H5 , SiH and electrons) uniformly distributed in the simulation cell. In reality, only a small fraction of collisions are effective (result in a chemical reaction). Dimensions and volume of Monte Carlo cell must take into consideration the mean free path of species. Each particle takes randomly three components of velocity given by Maxwell Boltzmann distribution. The first particle i is randomly chosen according to a probability of a neutral species Prsp,i given by: Prsp,i =

ni 8  j =1

(1)

nj

where ni is the density of specie i. After traveling a random walk given by a Gaussian distribution, the first chosen particle collides with a second particle (molecule, atom, radical or electron). The last particle j is randomly chosen according to a (i-j) collision probability Prcol,j given by: Prcol,j =

νij 9  νik

(2)

k=1

where νij is the neutral-neutral or electron-neutral collisionnal frequency. The collision theory indicates that the collision between molecules can provide the energy needed to break the necessary bonds so that new bonds can be formed [19]. Particles must have sufficient energy to initiate the reaction (activation energy) so the two chosen particles must have kinetic energy equal to or greater than the barrier energy (Ea ) of a gas phase reaction. The difference between the kinetic energy of the two particles and the activation energy define the kind of collision (effective or not effective). The activation energy is given by:   Ea = −kB T ln Kreac /νij

(3)

where the pre-exponential factor is assumed to be the collision frequency factor and Kreac is the rate constant of the gas phase reaction. The two colliding particles (the electron and SiH4 molecule for example) can interact by several reactions (R1, R2, R3 and R4 in Table 1); we choose randomly one

Silicon Table 1 List of gas phase reactions and corresponding rate constants Reaction

Reactions

R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R12 R13 R14 R15 R16 R17 R18 R19 R20 R21

SiH4 + e SiH4 + e SiH4 + e SiH4 + e H2 + e Si2 H6 + e Si2 H6 + e SiH4 + H SiH4 + SiH2 SiH3 + SiH3 SiH4 + Si2 H5 SiH3 + H SiH3 + Si2 H6 SiH2 + H Si2 H6 + H Si2 H6 + H SiH + H2 SiH2 + SiH3 SiH2 + H2 2 SiH3 SiH4 + SiH

Rate constants Kreac cm3 /s → → → → → → → → → → → → → → → → → → → → →

SiH3 + H+ e SiH2 + 2H+ e SiH + H + H2 + e SiH2 + H2 + e 2H+ e SiH3 + SiH2 + H+ e SiH4 + SiH2 + e SiH3 + H2 Si2 H6 SiH4 + SiH2 SiH3 + Si2 H6 SiH2 + H2 SiH4 + Si2 H5 SiH + H2 Si2 H5 + H2 SiH4 + SiH3 SiH3 Si2 H5 SiH4 Si2 H6 Si2 H5

of gas phase reactions occurring according to a reaction probability Prreac (i,j); Kreac (i, j ) Prreac (i, j ) =  Kreac (i, j )

(4)

 where Kreac (i, j ) is the sum of all rate constants of possible reactions between i and j. All chemical systems go naturally toward states of minimum Gibbs free energy [20]. A chemical reaction tends to occur in the direction of lower Gibbs free energy. To determine the direction of the reaction that is taking place, we use the old and new values of Kc and the equilibrium constant with reactants and products concentrations. Each set of binary collisions can be related or converted into time. Table 1 gives gas phase reactions and corresponding rate constants used in the MCS.

3 Description of Monte Carlo Simulation of Surface Reactions The complex gas phase reactions affect the morphology of plasma-deposited thin films. The main growth species is SiH3 [21–24]. The a-Si:H film growth is governed by Habstraction from the surface by a radical in an Eley-Rideal mechanism and by its sticking on the DB created [4]. The

k1 = 3*10−11 [21] K2 = 1.5*10−10 [21] K3 = 9.34*10−12 [21] K4 = 7.19 *10−12 [21] K5 = 4.49*10−12 [21] K6 = 3.72*10−10 [21] K7 = 1.1 *1010 *(1.(1./(1.+(0.63*P)))) [22] K8 = 2.8*10−11 *exp(-1250./T) [23] K9 =1.1 *1010 *(1.-(1./(1.+(0.63*P)))) [22] K10 = 0.45*1.5*10−10 [23] K11 = 5 *10−13 [21] K12 = 2 *10−11 [23] K13 = 4*10−10 *exp (-2500 / T) [23] k14 = 2 *10−11 [23] K15 = 0.66*2.4*10−10 *exp (-1250./T) [22] K16 = 0.34*2.4*10−10 * exp (-1250./T) [23] K17 = 2*10−12 [22] K18 = 3.77*10−13 [22] K19 = 3 *10−12 *(1.+(1./1.+(0.03*P))) [22] K20 = 0.1*1.5 *10−10 [22] K21 =(1.-(1./(1.+(0.33*P))))*(6.9 *10−10 ) [22]

simulation of surface reactions is based on interactions at the atomic level between hydrogenated sites (Si-H) or DB bonds and reactive radicals such as SiHx (x = 1, 2, 3) and H present near the a-Si:H surface. We considered that reactions of a-Si:H growth are: Sticking of H on DB H(g)+ ≡ Si− →≡ Si − H Sticking of SiH2 on DB SiH2 (g)+ ≡ Si− →= Si = SiH2 Sticking of SiH3 on DB SiH3 (g)+ ≡ Si− →≡ Si − SiH3 H-abstraction by SiH3 radical from ( ≡ Si − H) SiH3 (g)+ ≡ Si − H →≡ Si − (DB) + SiH4 (g) H abstraction by H radical from ( ≡ Si − −H) H(g)+ ≡ Si − H →≡ Si − (DB) + H2 (g) H-abstraction by SiH3 radical from ( = SiH2 ) SiH3 (g)+ = SiH2 → H − Si ≡ +SiH4 (g) H-abstraction by H radical from ( = SiH2 ) H(g)+ = SiH2 →≡ Si − H + H2 (g) H-abstraction by SiH3 radical from (-SiH3 ) SiH3 (g) + −SiH3 →= SiH2 + SiH4 (g) H-abstraction by H radical from (-SiH3 ) H(g) + −SiH3 →= SiH2 + H2 (g)

(RS1) (RS2) (RS3) (RS4) (RS5) (RS6) (RS7) (RS8) (RS9)

In the event of activated chemisorption, the height of activation energy of surface reaction imposes to particles wanting to enter into chemisorption well to have an incident

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4 Results and Discussions

Table 2 Values of activation energies of reactive radicals Ea (eV)

SiH3

SiH2

SiH

H

Sticking Recombination

0.09 0.2

0.1 0

0.1 0

0.1 0.1

kinetic energy greater than the height of the activation energy, in the absence of tunnel effect [4]. We found that the site probability of recombination Pγ and the site probability of sticking Ps are given by Eqs. 5 and 6 [4]:    4 2 3 = √ α + √ α exp −α 2 + [1 − erf (α)] (5) 3 π π 

Ps,γ

α=

(Ea + Ew ) kB T

(6)

4.1 Gas Phase Reactions 4.1.1 Reactions in SiH4 Plasma and Silane Dissociation We applied the MCS on (R1, R2, R3 and R4) to study the SiH4 dissociation. The reactants are SiH4 molecules and electrons. Following conditions are used for the MCS. The pressure P = 125 mTorr, gas temperature T = 523 K, electron density ne = 3.108 cm−3 and electron temperature about 2 eV. We found that R1 and R2 are the main reactions in SiH4 electron-impact dissociation. Reactions R3 and R4 do not contribute almost in silane dissociation by electron impact. The Ratios of H, SiH2 , SiH3 particles produced to the SiH4 dissociated molecules are constant. The SiH4 dissociation by electron impact yields 19% of SiH3 and 81% of SiH2, this result is closer to the result in ref [16, 26]. The ratio NH / NSiH4,d =1.8 as shown in Fig. 1. 4.1.2 Reactions in SiH4 /H2 Plasma

where erf is the error function, Ew is the potential well of SiHx interaction with surface and Ea is the activation energy of reaction on the site [4]. In the MCS, we consider that every particle k, as example SiH3 , takes randomly a direction and a velocity according to a Maxwell-Boltzmann distribution. The choice is acceptable if E ≥0. In the opposite case, we introduce the Boltzmann correction using the Boltzmann factor: exp(−E/KB T). Where E = Ec − (Ea + Ew ) and Ec is the kenitic energy. Table 2 gives activation energy of reactive radicals [25]. The simulation was written using a numerical FORTRAN program.

2.0

1.6

H

SiH2

4

N / NSiH d

1.2

0.8 SiH3

0.4

X

0.0 0

4

8

12

16

Fig. 1 Ratios of particles produced to the SiH4 dissociated molecules where τ is a unit of time

The MCS was applied on reactions (Table 1) at pressure P = 125 mTorr, gas temperature T = 673 K, electron density ne = 6.108 cm−3 and electron temperature about 2 eV. The initial reactants in this case are SiH4 , H2 molecules and electrons. The MCS gives means value of densities [17, 18]. Only 6 reactions (R1, R2, R5, R8, R9 and R12) make significant contribution to the production of H, SiH2 , SiH3 and Si2 H6 . We found that H2 is consumed at the beginning (R5) then H2 molecules are produced (R8 and R12). The gas mixture composition has an effect on products. Figure 2 shows the contribution of reactions of Table 1. We found that reaction R2: SiH4 +e → SiH2 +2H plays the central role in SiH4 dissociation by electron impact. This result is compatible with [6]. The second important chemical reaction in the SiH4 dissociation is R1: SiH4 +e → SiH3 +H. This result is compatible with Perkins et al. [26] and Doyle et al [27]. R1 and R2 become more important when the proportion of SiH4 in the mixture increases. Reactions (R3 and R4) do not contribute almost in silane dissociation by electron impact. SiH3 is the most abundant radical, although SiH2 is the major dissociation product, due to the different gas-phase reactivity of these two species [28]. We found that the reaction SiH4 +H → SiH3 +H2 plays a central role in the production of SiH3 radicals. This result is consistent with [6]. As in reference [9], we found that SiH4 +H → SiH3 +H2 and SiH4 +SiH2 → Si2 H6 are important because they are first order reactions of the dissociation products of silane.

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R1 R2 R5 R8

100 80

50 % SiH4

60 40 20

80 60 40 20

0

0

0.0

0.4

0.8

1.2

1.6

0

1

2

t (Sec)

R1 R2 R5 R8

25 % SiH4

4

5

6

R1 R2 R5 R8 R12

80 94 % SiH4 Contribution of rections ( % )

80

3 t (Sec)

100

Contribution of rections ( % )

R1 R2 R5 R8 R9 R12

100

Contribution of rections ( % )

Contribution of rections ( % )

6 % SiH4

60 40 20 0

60

40

20

0

0

1

2

3

4

5

0.0

t (Sec)

0.5

1.0

1.5

2.0

t (Sec)

Fig. 2 Contribution of gas phase reactions of Table 1 to produce SiH3 , SiH2 and H for mixture contains 6%, 25%, 50% and 94% of SiH4

Fig. 3 Ratio SiH2 /SiH3 for a mixture contains 25%, 50% and 94% of SiH4

25% 50% 94%

The ratio SiH2 / SiH3

3

2

1

0

X 0

5

10

15

20

25

Silicon Fig. 4 Site probability of SiH3 sticking on DB (Ps ) and site probability of SiH3 recombination from S-H (Pγ ) versus gas temperature for electronic density ne = 1018 m−3 and electronic energy Ee = 2.5eV

0,9

0,9

0,8

0,8

SiH3

SiH3

0,7

0,6

0,6

0,5

0,5

P

ps

0,7

0,4

0,4

0,3

0,3

0,2

0,2

0,1 200

300

400

500

600

0,1

T(K)

This MCS allows to follow the rates of production /consumption of H, SiH2 , SiH3 and Si2 H6 species. Important reactions (R2, R8 and R9) have been identified that contribute to the production and consumption of H, SiH2 , and SiH3 . This is consistent with [6, 9]. The production of SiH2 decreases while the production of SiH3 increases so that the ratio SiH2 / SiH3 decreases for a low hydrogen dilution mixture. Figure 3 shows the variation of ratio SiH2 / SiH3 for 3 mixtures. The SiH3 production is more important for a mixture contains 94% of SiH4 . The ratio SiH2 /SiH3 decreases. This result is consistent with [9]. The SiH3 production increases in percentage terms from 20%. On the other hand, the SiH2 production decreases in percentage terms from 80%. The H atoms production decreases also. As result of the increase in the SiH3 production, the reaction R12 occurs. The Si2 H6 production starts after that and reaction R9 occurs also. The increase in Si2 H6 production causes a decrease in SiH2 density.

200

300

400

500

600

T(K)

4.2 Results in the Surface 4.2.1 At microscopic Scale At microscopic or atomic scale, the MCS allowed us to calculate the site probability of reactive radicals (SiH3 , SiH2 , SiH and H) to stick on DB (Ps ) and the site probability of recombination from S-H (Pγ). These SiH3 probabilities increase with gas temperature as shown Fig. 4. The results are compatible with mathematical relationship in reference [4]. The MCS allowed us to calculate the rate of hydrogenated sites (τH ). This rate was almost constant. τH = 72.5% of all sites at the surface as shown in Fig. 5. 4.2.2 At macroscopic Scale At macroscopic scale, we calculate surface reaction probabilities of SiH3 (s), (γ) and the SiH3 surface reaction probability β (see Fig. 6) where β = s +γ. Results show also an excellent agreement with other works found in the literature [11, 29, 30].

75

5 Conclusion 74

H

73

72

71

70 300

350

400

450

500

550

600

T( K ) Fig. 5 The rate of hydrogenated sites versus gas temperature for ne = 1018 m−3 and Ee = 2.5eV

In this work, we propose a MCS as a theoretical method to study reactions occurring in PECVD reactor during aSi:H growth. The simulation was based on a microscopic analysis of physicochemical phenomena. It allowed getting macroscopic results. In gas phase, important reactions have been identified that contribute to the production of H, SiH2 , and SiH3 . The hydrogen consumption reaction SiH4 +H → SiH3 +H2 , and silane consumption reactions SiH4 +SiH2 → +Si2 H6 , are found to play a central role in mixture dissociation products. We found that SiH4 →SiH2 +2H is the dominant silane electron-impact dissociation. At surface, the MCS allowed us to calculate the site and surface

Silicon

0,4

0,5

SiH3

SiH3 0,4

0,2

0,3

S

0,3

0,1

0,2

0,0 300

350

400

450

500

550

0,1

600

300

350

T( K )

400

450

500

550

600

T(K) SiH3

0,6

0,5

0,4

0,3 300

350

400

450

500

550

600

T( K ) Fig. 6 Surface reaction probability of SiH3 sticking (s), surface reaction probability of SiH3 recombination (γ) and the SiH3 surface reaction probability versus gas temperature for ne = 1018 m−3 and Ee = 2.5eV

probabilities of reactive radicals (SiH3 , SiH2 , SiH and H). The results were consistent with other works.

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