Particle Dynamics in a Chemical Vapor Deposition Reactor - American

May 11, 2009 - A common cause of defects in the deposited film is due to the fact that the morphology of adducts in the gas phase is different from th...
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Ind. Eng. Chem. Res. 2009, 48, 5969–5974

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Particle Dynamics in a Chemical Vapor Deposition Reactor: A Multiscale Approach Yousef Sharifi† and Luke Achenie* Department of Chemical Engineering, Virginia Tech, Blacksburg, Virginia 24061

Compared to other semiconductors, zinc sulfide has a large direct band gap which makes it useful in a broad range of optical applications which demand high quality zinc sulfide films which are produced through the chemical vapor deposition method. In order to achieve high quality films with low defects, a better understanding of the deposition process is necessary. A common cause of defects in the deposited film is due to the fact that the morphology of adducts in the gas phase is different from that of the deposited film. These adducts affect the deposition efficiency and film quality. This paper strives to understand the impact of adducts through a multiscale modeling approach which is used to explain the possible link between the cluster size and the morphological defects on the deposited film. This understanding can be used within a simulation framework to optimize reaction conditions that minimize film defects. 1. Introduction

2. Multiscale Modeling

Zinc sulfide has received a significant amount of attention during the past decade. Compared to other semiconductors, the large direct band gap of zinc sulfide makes it useful in a broad range of optical applications.1–6 These applications demand high quality zinc sulfide films which are produced through the chemical vapor deposition (CVD) method. In order to achieve high quality films with low defects, a better understanding of the deposition process is necessary. A common cause of defects in the deposited film is due to the fact that the morphology of adducts in the gas phase is different from that of the deposited film.7–9 These adducts affect the deposition efficiency and film quality by (a) consuming the gas phase precursors, (b) settling down due to gravity, (c) leaving the reactor, or (d) depositing on the substrate. Depending on the size of clusters (adducts), the latter create large distorted grains on the substrate which do not normally have the same morphology as the deposited film. The concern here is how big these clusters grow and what are their morphologiessthe larger the clusters, the more chance of having defects in the deposited film. The particle size distribution can be estimated using the general dynamics equation (GDE) provided one has the necessary kinetic information such as nucleation and surface growth rates. For the case of zinc sulfide, to our knowledge, there is no indication of growth mechanism and dynamics of zinc sulfide particles in the open literature. Here, we used a multiscale approach to determine the growth mechanism of zinc sulfide particles, estimate their size, predict their morphology, and determine whether zinc sulfide adducts can create defects in the deposited films or not. Our multiscale model incorporates a macroscale computational fluid dynamics with microscale molecular dynamics and nanoscale ab initio calculations in order to estimate the nucleation, growth, dynamics, and size distribution of the particles inside the CVD reactor. The computational fluid dynamics involved a combination of the general dynamics equation (GDE) and conservation of mass, energy, and momentum. In the next sections, we discuss the methodology and present our modeling results.

In our multiscale approach, we used various molecular modeling methods (namely, density functional theory (DFT), molecular dynamics (MD), and transition state theory (TST)) in order to closely study the particle nucleation, surface growth, and deposition during the CVD process. Figure 1 shows the outline of our multiscale approach. In our approach, we did the following: (a) used DFT and TST to estimate the reaction rate constants, activation energies, and postulate growth mechanisms for the clusters. MD along with DFT were used to optimize the cluster structures and obtain the adsorption energies, (b) employed a computational fluid dynamics (CFD) code (a finite volume, second order upwind discretization on unstructured mesh) to obtain the approximate particle diameters and simulate the particle dynamics inside the CVD reactor, and (c) simulated the particle morphology based on the particle diameters obtained from the CFD code. Next, we describe the details of our quantum chemistry and CFD calculations. Molecular Modeling. Due to the existence of a wide variety of molecular structures in our system, our quantum chemistry calculation relied on various methods in order to address the variation in size of molecular structures, and the computational effort related to large molecular structures. The geometry optimization of the precursors (zinc sulfide, hydrogen sulfide, and hydrogen) were performed using Beck’s three parameter Lee-Yang-Parr correlation energy formula using a relatively large basis set (B3LYP/6-311+g(d,p)).10,11 Here, a stable condition corresponded to minimum energy structures with no imaginary frequency.12,13 A structure with one imaginary frequency was considered a transition state

* To whom correspondence should be addressed. E-mail: [email protected]. † Department of Chemical, Materials and Biomolecular Engineering, University of Connecticut, Storrs, CT 06269.

Figure 1. Multiscale approach to simulate particle dynamics in CVD.

10.1021/ie8015522 CCC: $40.75  2009 American Chemical Society Published on Web 05/11/2009

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The GDE includes specific terms to address the particle nucleation, dynamics, coagulation, and growth. The GDE is a highly nonlinear partial integral-differential equation, which lends itself only to numerical solutions. Dhaniyala and Wexler19 compared several numerical schemes for modeling aerosol growth. In another review, Zhang et al.20 summarized the numerical method to simulate the particle growth. In an Eulerian coordinate system, the general dynamics equation for particle size distribution in terms of particle volume is given by21 ∂N(V) ∂[J(V)N(V)] + ∇·(upN(V)) ) I(V0)δ(V - V0) + ∂t ∂V ∞ 1 V β(u, V)N(V - u)N(u) du - N(V) 0 β(u, V)N(u) du 0 2 (1)

∫

∫

where up ) u -

Figure 2. Algorithm for global optimization of ZnS clusters using Molecular Dynamics.

structure which was then employed to calculate the activation energy of the gaseous reactions based on transition state theory.14 Due to the computationally intensive nature of DFT calculations (for geometry optimization), it has been recommended to use molecular dynamics (MD) for optimization of large clusters.15 In our MD calculations, we used Born model interatomic potentials developed by Hamad et al.16 To gauge the accuracy of our MD calculations relative to DFT, we optimized the structures of precursors using the two techniques and the resulting structures showed a difference of less than 0.09 Å for the bond lengths and a difference of less than 4° for the bond angles. As Figure 2 shows, our molecular dynamics calculations started by initialing an NVE ensemble at 3000 K, ran molecular dynamics calculation for 50 ps, reduced the temperature by 10 K, checked if the temperature was more than 1000 K, and then ran the MD calculation for another 50 ps. The temperature reduction was repeated until the temperature reached 1000 K. Even thought this configuration is computationally intensive, it increases the chance of obtaining a globally optimized structure for zinc sulfide clusters.17 The final energy calculations of the clusters were performed on the resulting structure using DFT with a medium basis set, namely B3LYP/6-31+(d). Computational Fluid Dynamics Model. Our two-dimensional (2D) computational fluid dynamics model involved conservation of momentum, mass, and energy equations18 to simulate the transport phenomena and the general dynamics equation (GDE) to simulate particle dynamics inside the CVD reactor. The particle formation process in the CVD involves a series of physical and chemical phenomena. The process starts with particle nucleation in the gas phase reaction. After nucleation, a particle grows due to agglomeration, surface growth, and/or coagulation. The number of particles is influenced by both the gas phase and surface reactions. Particle settlement, outflow from the reactor, and the deposition process all lead to a significant reduction of particles inside the reactor. In addition to the complicated growth process, the random behavior of particle in the fluid makes it difficult to simulate this process. The conventional method for simulating particle dynamics and growth is through the use of the general dynamics equation (GDE).

Dp∇N N

here N(V) is the particle size distribution function for particles whose volumes are between V and V + dV, u is the gas velocity, up is the particle velocity, u,V are the particle volumes, V0 is the monomer volume, β(u,V) is the collision frequency function, δ is the Dirac’s delta function, zI(V0) is the nucleation rate of monomer, J(V) is the change in particle volume due to surface growth, and Dp is the diffusion coefficient of the particle. The right-hand side of eq 1 includes the nucleation rate of monomer (first term), the surface growth due to reaction at the particle surface (second term), and the effect of particle collision (the last two terms). The diffusion coefficient for a spherical particle can be expressed by the Stokes-Einstein expression with the Cunningham correction:22 Dp )

{

kBT 1.1 1 + Kn 1.257 + 0.4 exp 6πµrp Kn

[

(

Kn -

λ rp

)] }

(2) (3)

Here, µ is the gas viscosity, kB is the Boltzmann constant, Kn is the Knudsen number, λ is the mean free path of the gas and expressed using the kinetic theory of gases: λ)

µ F

πM  2RT

(4)

where M is the gas molecular weight, R is the universal gas constant, F is the gas density, and T is temperature. Assuming monodispersed particles, one can integrate the general particle dynamics equation over all particle sizes and reduce it to a set of two convection and diffusion equations for particle number density and particle volume: 1 ∇·(-Dp∇Np) + ∇·(uNp) ) - βNp2 + I 2

(5)

∇·(uVp) + ∇·(Dp∇∇p) + V0I + JNp

(6)

where β ) 8πDprp

[

rp 2rp + √2g

c)



+

8kBT πFpVp

√2Dp crp

]

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Ind. Eng. Chem. Res., Vol. 48, No. 13, 2009

g)

1 [(2rp + l)3 - (4rp2 + l2)2/3] - 2rp 6rpl

l)

8Dp πc

µ)

( ) 6Vp πNp

1/3

Here, Vp is the volume fraction of particle and dp is the particle diameter. It is assumed that all particles that reach the reactor wall attach to the wall; thus Vp ) Np ) 0 at the walls. The monomer nucleation rate and particle surface growth are respectively given by s I ) NArZnS and J ) πdp2ν0NArZnS

(7)

where NA is the Avogadro number, rZnS is the production rate s is the ZnS of zinc sulfide through gas phase reaction, and rZnS production rate at the particle surface. Next we describe estimation of the nucleation and surface growth of the particles using quantum chemistry techniques. 3. Particle Formation Mechanism In the system considered here, the zinc vapor and hydrogen sulfide (diluted in argon) reacts to form gaseous zinc sulfide and hydrogen.23,24 In a previous study,25 we showed that zinc sulfide could form via two competing pathways with relatively close activation energy (approximately 55 kcal/mol). The first pathway directly connected the zinc atom and the hydrogen sulfide molecule via one transition state structure. On the other hand, the second pathway is initiated by attaching zinc atom to one of the hydrogen atoms and is connected to the final products via two transition state structures and two intermediate complexes as follows. Pathway I kf

Zn(g) + H2S 98 ZnS · · · H2 f ZnS + H2

(8)

Pathway II kf

Zn(g) + H2S 98 ZnHSH f HZnSH + H2 + ZnS

(9)

In the second pathway, the two intermediate complexes are stable and can initiate formation of cluster in the gas phase. Once the gaseous zinc sulfide molecules are formed (nucleation), the monomers can agglomerate and form large clusters. The rate of monomer formation is the same as gas phase production of the zinc sulfide. In addition to the agglomeration, the surface growth of particles may occur due to decomposition of hydrogen sulfide on the cluster surface, adsorption of zinc atom, or zinc sulfide molecules. When possible, the rate constants for the gaseous and surface reactions involved were calculated using the transition state theory. For the barrierless reactions (i.e., addition of zinc atom or small zinc sulfide molecule to the cluster), the collision theory was used to calculate the rate constants. The collisional kinetic constant for a recombination reaction (A + B f AB) is given by

(

k ) RABNAdAB2 where

8πkBT µ

dA + dB mAmB , RAB ) RARB , d ) mA + mB AB 2

Here mA and mB are the masses, dA and dB are the diameters, the collision coefficients RA and RB are the ratios of the reactive surface to the whole surface of the reactive fragments. During the calculation of the rate constant using the collision theory, the molecule diameter was used for molecular species and covalent radius was used for atomic species; these parameters are given in Table 1.

and dp )

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)

1/2

(10)

5. Results and Discussions In order to validate our general approach, we tested our model considering the decomposition of ferrocene in the gas phase to form iron particlessthese are the only results we found in the literature to make comparisons with. We obtained the average particle diameter of 58 nm at 973 K. This value is consistent with experimental values of 60 nm reported in the literature.26 Molecular Modeling. We used quantum chemistry ab initio calculations (Figure 2) to predict the structure of various zinc sulfide particles. We observed linear, triangular, rectangular, bubble, double bubble (onion like), and crystalline structure for the zinc sulfide particles as the particle grew these structural patterns are consistent with the ones reported in the literature. Table 2 shows the optimized structures for small zinc sulfide clusters (n ) 1-12). It shows a linear structure for a zinc sulfide monomer and a diamond shaped structure for two zinc sulfide monomers. As the number of monomers increases, the shape of the structure changes from triangle to rectangle to pentagon and ultimately to a cagelike (spherical) structure. We observed a bubblelike structure for 5-45 zinc sulfide molecules and a double bubble for 45-90 molecules. These results are consistent with other results from the literature.15,16 These cluster structures are also consistent with Euler’s law which specifies the relation among faces, vertexes, and edges in a closed simple polyhedron. Euler’s theorem determines the relation between the four- and six-numbered rings (N4 and N6) in a polyhedron. Thus for ZnmSm there are six four-numbered rings, and the number of six-numbered rings is equal to N6 ) m - 6, where m is the number of atoms. The surface growth of the particles depends on the rate of hydrogen sulfide dissociation, zinc atom adsorption, and zinc sulfide molecule deposition on the surface. Table 3 summarizes the reaction rate parameters for a choice of components involved in zinc sulfide growth. Our calculations showed that zinc atom adsorption on zinc sulfide clusters proceeds through a barrierless pathway. However the addition of zinc sulfide monomers involves a very small activation energy in the range of 0-5 kcal/mol at B3LYP/6-31+g(d). However, we observed a small variation in the calculated activation energy depending on the size of clusters. The estimated adsorption energy for zinc atom Table 1. Atomic and Molecular Parameters Used to Calculate the Rate Constant Using Collision Theory molecule

diameter (Å)

steric factor RA

ZnS Zn2S2 Zn3S3 Zn4S4 H2S

4.39 5.84 7.49 7.86 2.76

1.00 1.00 1.00 1.00 0.40

atom

covalent radius Å

Zn H S

1.31 0.37 1.02

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Table 2. Globally Optimized Structure of Small Zinc Sulfide Clusters

Figure 3. Surface growth of zinc sulfide particles.

Table 3. Pre-exponential Factor and Activation Energy for Zinc Sulfide Reactions reaction ZnS + ZnS f Zn2S2 Zn2S2 + ZnS f Zn3S3 Zn3S3 + ZnS f Zn4S4 Zn4S4 + ZnS f Zn5S5 ZnS + H2S fk SZnS + H2 f Zn(g) + ZnS 98 ZnSZn H2S + ZnS(100) f H2 + SZnS(100) Zn + ZnS(100) f ZnZnS(100) ZnS + ZnS(100) f ZnSZnS(100)

A 1 1 1 1 1 1 1 1 1

× × × × × × × × ×

1014 1014 1014 1014 1014 1014 1014 1014 1014

E (kcal/mol) 0.10 5.00 4.00 0.00 41.20 0.00 34.00 0.00 0.00

and zinc sulfide monomer adsorption was 30 and 60 kcal/mol at B3LYP/6-31+g(d), respectively. Dissociation of hydrogen sulfide on zinc sulfide clusters needed different activation energies depending on the cluster size and structure. In the reaction with the zinc sulfide molecule, the activation energy was 41kcal/mol; this decreased to 36 and 34 kcal/mol for large zinc sulfide clusters and the crystalline zinc sulfide surface, respectively. As the particle grew, we observed lower activation energy for hydrogen dissociation on the surface. This variation of 5 kcal/mol is within the precision range of the density functional theory; in the CFD model, we used the average of these values. For small particles, we used bubble or double bubble shaped structures, while for very large particles (n > 600) we used crystalline structure of zinc sulfide. For large zinc sulfide clusters (BCT or zinc blend structure), the adsorption energy for hydrogen sulfide adsorption was 17.69 kcal at B3LYP/6-31+g(d). This value is very close to the value

Figure 4. Particle size distribution at the CVD reactor exit.

reported by Rodriguez et al.27 Thus approximating the film surface with a large crystal provides the necessary accuracy for our purpose of estimating the surface deposition rates. Table 3 summarizes our reaction rate parameters for surface growth of zinc sulfide. The pre-exponential factor for most of the reactions was on the order of 1014 which is of the same order of magnitude as the gas phase formation of zinc sulfide from zinc vapor and hydrogen sulfide.25 Figure 3 shows the surface growth of a zinc sulfide cluster composed of 15 zinc sulfide monomers. Hydrogen sulfide molecule adsorbs on the cluster with adsorption energy of17 kcal/mol. Subsequently, hydrogen sulfide dissociates into hydrogen sulfur and hydrogen; next the hydrogen atom is immediately adsorbed onto the neighboring zinc atom. This dissociative adsorption of hydrogen sulfide requires activation energy of (36 kcal/mol). The surface growth continues by barrierless adsorption of zinc molecule to available sulfur sites in a bridge position. Consequently, the sulfur atom in the adsorbed hydrogen sulfur releases the adsorbed hydrogen atoms by going to a bridge position and makes a bond with the bridged zinc atom; this step requires an activation energy of 34 kcal/ mol calculated at the BLYP/6-31(g) level of theory. Computational Fluid Dynamics. The fluid dynamics model including mass, momentum, and energy along with the particle

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Figure 5. Contour plot of particle number density obtained using computational fluid dynamics. The heat-map scale is shown below the plot. Reactants enter from the left.

dynamics equation were solved using the finite volume method. These calculations were performed at the operating condition of 3000 Pa and 973 K. The zinc vapor concentration was estimated from vapor pressure of zinc at 973 K and the hydrogen sulfide had a relative molar ratio of 0.5 compared to zinc sulfide. For the time dependent equations, the steady state was achieved after 280 s using the time step of 0.5 ms. Figure 4 shows the particle diameter along the reactor axis from the reactor entrance toward the substrate in the middle of the reactor. Our results indicate that for a low pressure horizontal reactor shown in Figure 5, the particle diameter increases along the reactor axis. The majority of particles deposits on the substrate. In zinc sulfide chemical vapor deposition, the gas phase reaction of zinc vapor and hydrogen sulfide dominates and causes a fast nucleation rate in the reactor. This high nucleation leads to a rapid increase in the number density of particles at the reactor entrance (Figure 5). However, the number density decreases (left to right in the reactor) due to collision/coagulation between the particles and some deposition of particles on the substrate. The high temperature and low residence time also shortens the nucleation period and promotes the surface growth of the particles. After nucleation, the particle growth is driven by Brownian coagulation and adsorption/decomposition of gas phase species on the cluster surface. The volume fraction increases at the inlet due to high diffusion effect at the entrance and then reaches a limiting value in the axial direction as the diffusion effect weakens along the reactor. The value of the Knudsen number (Kn , 1) suggests free molecular region for particles inside the reactor and the value of inter particle diffusion coefficient varies between 1 × 10-3 and 1 × 10-5 for various size particles. The value of the diffusion coefficient depends on the particle diameter, gas mean free path, and the temperature inside the reactor. Using our CFD calculations, we obtained an average diameter of 2.35 nm for the particles depositing on the substrate. A particle with this diameter has approximately 500 zinc sulfide monomers. Our simulation of a zinc sulfide cluster with 500 monomers using molecular dynamics shows a crystalline structure for zinc sulfide particles. These particles have the same morphology of the deposited films but 3 orders of magnitude smaller than the grain islands observed in experimental growth of zinc sulfide.28 6. Summary We coupled a fluid dynamics model with a particle dynamics model in order to predict the particle size distribution inside a CVD reactor. Quantum chemistry and density functional theory were used to predict the nucleation and surface growth rate and

structures of various particles. The results for the particle structure are consistent with the reported structures in the literature; the particle structure evolves from bubblelike, to double bubble, and crystalline structure as the particle grows. The predicted particle distribution shows the formation of zinc sulfide clusters with up to 500 zinc sulfide molecules in a CVD reactor considering deposition on all walls and the substrate. The predicted results are indicative of lower defects in the deposited film because the zinc sulfide clusters are small and their deposition on the deposited film creates lower defects than that of big clusters. These results indicate that in a zinc sulfide CVD reactor, cluster formation has little importance compared to other CVD systems with clusters up to a few hundred nanometers. In accordance with experimental studies, our calculation shows that the zinc sulfide particle growth is a diffusion limited processsjust like the deposition process of zinc sulfide on the substrate. Nomenclature N ) particle size distribution function u ) gas velocity up ) particle velocity u,V ) particle volume V0 ) monomer volume β ) collision frequency function δ ) Dirac delta function I ) nucleation rate of monomer J ) change in particle volume due to surface growth Dp ) diffusion coefficient of the particle rp ) particle radius kB ) Boltzmann constant Kn ) Knudsen number λ ) mean free path of the gas M ) gas molecular weight R ) universal gas constant F ) gas density T ) temperature Np ) particle number density Vp ) particle volume Fp ) particle density Vp ) volume fraction of particle dp ) particle diameter NA ) Avogadro number rZnS ) production rate of zinc sulfide through gas phase reaction s rZnS ) production rate of zinc sulfide at the particle surface mA,mB ) mass dA,dB ) diameter

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RA,RB ) collision coefficientssthe ratios of the reactive surface to the whole surface of the reactive fragments

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ReceiVed for reView October 15, 2008 ReVised manuscript receiVed April 24, 2009 Accepted April 27, 2009 IE8015522