computational fluid dynamic modeling of tin oxide

006) 1400–1410www.elsevier.com/locate/tsf

Thin Solid Films 515 (2

Computational fluid dynamic modeling of tin oxide deposition in animpinging chemical vapor deposition reactor

Mingheng Li ⁎, John F. Sopko, James W. McCamy

Glass Technology Center, PPG Industries, P.O. Box 11472, Pittsburgh, PA 15238, USA

Received 5 December 2005; received in revised form 20 February 2006; accepted 29 March 2006Available online 11 May 2006

Abstract

A fundamental framework for atmospheric pressure chemical vapor deposition of tin oxide coatings on glass using monobutyltin trichloride asthe precursor, developed using computational fluid dynamics (CFD) in an impinging flow geometry, is presented in this paper. The CFD modelexplicitly accounts for homogenous reaction in the gas phase, heterogeneous reaction on the glass surface, thermal effect of the impinging jet onthe glass, and impinging flow characteristics in the confined coating zone. A comparison of modeling results with experimental data is described.It is shown that the experimentally observed spatial distribution in the deposition rate is successfully captured by the model and the wave shape inthe deposition profile can be explained with boundary layer separation. The effects of reactor-substrate spacing and glass line speed on thesimulated deposition profile are discussed.© 2006 PPG Industries Ohio Inc. Published by Elsevier B.V. All rights reserved.

Keywords: Chemical vapor deposition; Computer simulation; Tin oxide; Diffusion

1. Introduction

On-line atmospheric pressure chemical vapor deposition(APCVD) is a critical technique used in the glass industry todeposit coatings on float glass and glass containers and isresponsible for the industry-wide production of approximately10 million m2/year of value-added products. The primaryproduct produced in this manner utilizes a fluorine-doped SnO2

layer as a low-emissivity coating. This conductive layer reflectsin the far-IR region yielding improved energy performance inarchitectural applications.

While APCVD is a cost-effective method for on-line coatingon glass [1], improvements in process efficiency are expected toresult in reduced solid waste generation and disposal, lower rawmaterials usage, and a reduction in energy consumption.Therefore, significant drivers exist for developing the funda-mental understanding of the APCVD process that will lead to anincrease in the process efficiency [2]. Generally speaking, therate and efficiency of APCVD are dependent on reaction

⁎ Corresponding author. Tel.: +1 412 820 8520; fax: +1 412 820 8640.E-mail address: [email protected] (M. Li).

0040-6090/$ - see front matter © 2006 PPG Industries Ohio Inc. Published by Elsdoi:10.1016/j.tsf.2006.03.052

kinetics, fluid flow, heat transport and mass transport in thecoating zone. An in-depth understanding of such a reaction-transport process requires high-fidelity computational fluiddynamic (CFD) models that are able to precisely capture theflow, thermal and kinetic phenomena. Representative examplesin this area include simulation of SnO2 deposition from SnCl4 ina horizontal cold wall APCVD reactor [3], computationalmodeling of silicon deposition from SiH4 in a stagnationrotating disk APCVD reactor [4], and numerical analysis ofTiO2 deposition from titanium tetra-iso-propoxide in a cold wallimpinging APCVD reactor [5]. The numerical simulation basedon CFD is able to provide quantitative information of flowbehavior and species transport, but typically relies to a largeextent on the thermodynamic data, reaction mechanism, andtransport properties. Monobutyltin trichloride (or MBTC) usedfor SnO2 deposition in the glass industry, which is of interest inthe current work, has very limited data reported in the literature[6–11]. While it is experimentally shown that the reaction ofMBTC with oxygen is accelerated in the presence of water, thefunction of water in the decomposition and/or oxidation ofMBTC, is not fully understood. To study this deposition processusing CFD, it is very important to note that the deposition rate in

evier B.V. All rights reserved.

mailto:[email protected]

http://dx.doi.org/10.1016/j.tsf.2006.03.052

MBTC+Nitrogen

Distribution holes

SubstrateHeated plate

Nitrogen Exhaust Exhaust NitrogenNitrogenWater+Air

Fig. 1. Schematic of the pilot-scale APCVD reactor (not to scale).

200

250

c)

experimentoriginal mechanism

1401M. Li et al. / Thin Solid Films 515 (2006) 1400–1410

the on-line APCVD coating on glass should exceed 20 nm/s inorder to meet the thickness requirement of the coated materialon the high line speed glass ribbon [12]. Such a high depositionrate as well as the experimental observation of the wave shapedeposition profile (will be discussed later) imply that thedeposition process of SnO2 from MBTC might be mainlylimited by the flow behavior as well as mass transport in thecoating zone and that the effect of reaction kinetics is lessimportant. This assumption is further substantiated by theexperimental measurement of tin oxide deposition rate atdifferent temperatures [7,8]. As a result, the CFD modeling ofon-line APCVD coating on glass can be done with reasonableaccuracy without a highly developed reaction mechanism andkinetic data.

The objective of this work is to provide a computationalframework for SnO2 deposition from MBTC. The currentmodel is developed using CFD with an impinging flowgeometry, and explicitly accounts for homogenous reaction inthe gas phase, heterogeneous reaction on the glass surface,

Table 1Reference operating conditions for tin oxide deposition

N2 carrier flow rate (slm) 20N2 dilute flow rate (slm) 45N2 curtain flow rate (slm) 45Air flow rate (slm) 20Exhaust flow rate (slm) 95MBTC concentration (mol%) 0.4H2O concentration (mol%) 3Inlet gas temperature (K) 436Substrate temperature at the bottom (K) 922Inlet–exhaust distance (L /B) 25Reactor-substrate spacing (H /B) 2.5

thermal effect of the impinging jet on the glass, and impingingflow characteristics in the confined coating zone. The reactionkinetics are based on modeling of deposition rates measured in astagnation-flow reactor [7,13]; certain kinetic parameters weremodified to fit the experimental data. A comparison of CFDmodel predictions with experimental measurements shows thatthe experimentally observed spatial distribution in the deposi-tion rate profile is successfully captured by the model.Especially, the observed wave shape in the deposition profilecan be explained with boundary layer separation. Based on thismodel, parametric analysis is performed to study the effect ofreactor-substrate spacing and glass line speed on the depositionprofile.

−25 −20 −15 −10 −5 0 5 10 15 20 250

50

100

150

x/B

Dep

ositi

on r

ate

(nm

/se

Fig. 2. Deposition profile obtained using the original mechanism.

1402 M. Li et al. / Thin Solid Films 515 (2006) 1400–1410

2. Experimental details

The experiments of tin oxide deposition from MBTC areconducted in a pilot-scale APCVD reactor with impinging

Fig. 3. Contours of velocity, temperature,MBTC,H2O,MBTC–H2O complex andHCl u

geometry. Fig. 1 shows a schematic view of the reactor. TheMBTC is delivered from a vaporizer with nitrogen as the carriergas. The water, which is the accelerant for the reaction ofMBTC and oxygen, is vaporized using air as the carrier gas.

nder reference operating conditions, solved using the second-order upwind scheme.

Fig. 3 (continued).


After being mixed with the diluent nitrogen right beforeAPCVD reactor, the MBTC with nitrogen and water with air aresent to the plenum, and then the V shape zone. After passing thecoating zone, where SnO2 is produced and deposited on the

surface of the substrate, the remnant reactants and by-productsexit the exhausts to be disposed. Two nitrogen curtains are usedon each side of the reactor to avoid the reactants and productsescaping from the coating zone to the atmosphere. All the inlet

Table 2Governing equations in tin oxide deposition

Continuity ∇d ðq uYÞ ¼ 0

Momentum balance∇d ðq u

YuYÞ ¼ −∇pþ∇d l ∇ u

Yþð∇ uYÞT− 2

3ð∇d u

YÞI��

þ q gY

�

Energy balance∇d u

Y qcpT� �

¼ ∇d k∇Tð Þ−X

iJYi d

∇Hi

Mi−X

i

XjHiaijR

gj ;∇d kglass∇Tglass

� ¼ 0

Species transport ∇d ðq uYYiÞ ¼ −∇d JYi þMiRja

gijR

gj ; i ¼ 1; N ;N

Ideal gas law ρ=pMw /RTDeposition rate Ji= −Di∇(ρYi)−Di

T∇(lnT)=Ris

Coupled heat transfer on the interface − k∇T= −kglass∇Tglass


and exhaust gas flow rates and temperatures are regulated byLabview process control software. Each inlet or outlet consistsof a plenum and a V shaped zone for boundary layer develop-ment with distribution holes in between. Different from theindustrial manufacturing process, the glass substrate is stagnantin this pilot reactor. The baseline parameters used in the exper-iment are given in Table 1. Under these operating conditions, theReynolds number is about 600 in the slot (based on the hydraulicdiameter of the slot) and 140 in the coating zone (based on thehydraulic diameter of the coating zone), suggesting laminar flowconditions.

3. CFD model for tin oxide deposition

The computational domain consists of the V shape zone, thecoating zone and the substrate (see Figs. 1, 2 and 3). The plenumis not included because its inclusion will not significantlychange the profile of the deposition rate. Because the depth ofthe CVD reactor is several times longer than the inlet–exhaustdistance, a two dimensional CFD model is used. The governingequations used to describe the flow dynamics and thermalbehavior in the coating zone include continuity, momentumbalance, energy balance and species transport etc., which arelisted in Table 2. While a simplification of constant surfacetemperature is commonly used in the numerical simulation ofCVD process (e.g., [4,14–16]), a conjugate heat transferbetween the heating plate below the substrate and the fluidabove the substrate will more closely match the experimentalarrangement. In the current model, this is achieved throughcoupling of the glass top surface temperature by the convectiveheat transfer of the impinging jet and the conductive heat

Table 3Reaction mechanism of tin oxide deposition from MBTC [13]

Gasphase

C4H9SnCl3+H2O→C4H9SnCl3(H2O), [C4H9SnCl3]0.72

k0=4×108 (based on mol-m-s), Ea=4.18×10

4 J/molSurface C4H9SnCl3(H2O) + OS(s)→ C4H9SnCl3(H2O)(s) , Sticking

coefficient=1C4H9SnCl3(H2O) (s) + 0.5O2→SnO2(B) + 2C2H4+3HCl+OS(s),[O2]

0.76

k0=1.6×104 (based on mol-m-s) ⁎, Ea=5.73×10

4 J/mol

⁎ Modified pre-exponential factor.

transfer within the glass with a fixed temperature at the bottomof the glass. The heat transfer due to radiation is not accountedfor in the current model and might be considered in future work.The temperature and concentration distributions are uniform atall inlets (distribution slots). The zero gradient in concentrationnormal to the surface is specified for all the surfaces except theglass top surface. The pressure outlet boundary conditions arespecified at the two exhausts and the two side flows. Thepressure in the exhausts is varied slightly such that thecalculated flow rates in the exhaust match the experimentalconditions. The wall of the reactor is assumed to maintain aconstant temperature of 436 K.

The reaction mechanism is based on modeling of depositionrates measured in a low pressure stagnation-flow reactor [7,13],but we have slightly modified the reaction constant in thesurface reaction to fit the experimental data (see Table 3). It hasbeen found that the deposition rate predicted by the CFDmodel with the original mechanism matches well with theexperimental measurement far away from the inlet slot butabout four times higher underneath the inlet slot (see Fig. 2).Since the original mechanism is in good agreement with ex-perimental data obtained under low pressure, we postulate thatthis discrepancy might be due to the significant difference inpressure or other unknown reasons. In this reaction mecha-nism, the MBTC–H2O complex is formed rapidly as the twospecies are mixed together, and the MBTC–H2O complexreacts with oxygen to form SnO2 on the high temperature glasssurface.

The thermodynamic data of MBTC and MBTC–H2Ocomplex are taken from Sandia National Laboratories [17].

Table 4Lennard–Jones parameters of the chemical species

Chemical species σ (Å) ϵ /k (K) Reference

C2H4 3.971 280.8C4H9SnCl3 5.5 528.069 [17]C4H11SnCl3O 4.5525 549.78 [17]H2O 2.605 572.4N2 3.621 97.53O2 3.458 107.4SnO2 4.534 586.983

0 5 10 15 20 250

0.2

0.4

0.6

0.8

1

1.2

1.4

x/B

Nor

mal

ized

con

cent

ratio

n gr

adie

nt

Fig. 6. Normalized concentration gradient (∂c /∂y|y=0) of MBTC–H2O complexon the surface.

−25 −20 −15 −10 −5 0 5 10 15 20 250

10

20

30

40

50

60

x/B

Dep

ositi

on r

ate

(nm

/sec

)

experiment2nd order upwind

Fig. 4. Comparison of deposition rate profile simulated using the second-orderupwind scheme with experimental data measured at the reference operatingconditions.


The calculation of heat capacity, viscosity, and thermalconductivity of the mixture is based on the property of purenitrogen. This is because the nitrogen gas is in excess of 90% inthis particular case and the estimation of these properties ofMBTC and MBTC–H2O complex is avoided. The sameapproach was employed to model the tin oxide CVD fromdimethyltin dichloride [9]. The mass diffusivity of each speciesis estimated based on kinetic theory, and the Lennard–Jonesparameters of each species are given in Table 4.

The process model is implemented into Fluent, a commercialCFD computer program, and is solved by the finite volumemethod. The governing mass, momentum and energy balanceequations together with the species transport equations aresolved first using the first-order upwind scheme to obtain aconvergent solution and then the second-order upwind schemeto precisely capture the flow characteristics. Generally it requiresabout 300 iterative steps to reduce the residuals of all thevariables to 10−5 for the first-order upwind scheme and

0 5 10 15 20 250

10

20

30

x/B

k s/h

c

k s/h

c

0 0.5 1 1.5 20

0.5

1

1.5

2

x/B

ks = hc

ks = hc

Fig. 5. Ratio of reaction constant to mass transfer coefficient.

additional hundreds of steps for the second-order upwindscheme in each simulation run.

4. Results and discussions

4.1. Modeling results under baseline operating conditions

The simulated contours of velocity, temperature and molefractions of MBTC, H2O, MBTC–H2O complex and HCl in thewhole field using the second-order upwind scheme under thebaseline conditions are shown in Fig. 3. The flow in the exhaustis not stable due to pressure outlet boundary conditions, as onecan see from Fig. 3 that the exhaust flow is pulling on the walland it is not symmetric with respect to the centerline. Betterresults of the flow in the exhausts are expected when thecomputational domain is extended to match the experimentalconditions. However, the simplification made here will notaffect the flow in the coating zone and the deposition rate on thesurface, which is of interest in this work. It is shown by the CFD

0 5 10 15 20 250

0.2

0.4

0.6

0.8

1

x/B

Nor

mal

ized

sur

face

con

cent

ratio

n

Fig. 7. Normalized concentration of MBTC–H2O complex on the surface.

−25 −20 −15 −10 −5 0 5 10 15 20 250

10

20

30

40

50

60

x/B

Dep

ositi

on r

ate

(nm

/sec

)

experiment1st order upwind2nd order upwind

Fig. 8. Comparison of deposition rate profile simulated using different numericalschemes.

0 0.5 1 1.5 2 2.5 3 3.52.8

3

3.2

3.4

3.6

3.8

4

4.2

slope = −0.459

ln(x/B)

ln(R

/[nm

/sec

])

Fig. 9. Deposition rate profile obtained using CFD simulation with first-orderupwind scheme.

−25 −20 −15 −10 −5 0 5 10 15 20 250

10

20

30

40

50

60

70

x/B

Dep

ositi

on r

ate

(nm

/sec

)

experiment2nd order upwind

Fig. 10. Comparison of deposition rate profile simulated using the second-orderupwind scheme with experimental data measured at reduced reactor-substratespacing (H /B=1.5).


simulation that with the nitrogen curtain flow, all chemicals arewell confined in the reactor and escaping from the coating zoneto the surrounding atmosphere is avoided. As the verticalvelocity is converted to horizontal velocity, there are two recir-culation zones formed in the confined coating zone. One is atthe corner of the inlet slot and the other is 5–9 slot widths awayfrom the inlet slot. Based on the kinetics of the mechanism usedhere, the reaction of water with MBTC is so fast that almost allthe MBTC is converted to MBTC–H2O complex immediatelyas it enters the reactor. On the glass surface, the MBTC–H2Ocomplex reacts with oxygen to generate SnO2, which forms thecoating layer. The byproduct, HCl, diffuses from the substrate tothe gas phase. The simulated deposition profile of SnO2 underthe baseline operating conditions is shown in Fig. 4. The CFDsimulation successfully captures the wave shape of thedeposition profile, and the deviation of average magnitude ofthe deposition rate is less than 10% of the correspondingexperimental value, indicating that the CFD model withmodified kinetic parameters reasonably predicts the depositionrate.

It is consistently found in both experiment and simulation thatthere is a dip in the center of the deposition rate profile (directlyunderneath of the inlet slot). To explain this phenomenon, wefirst note that under steady state, the surface reaction rate equalsthe diffusion flux from the gas to the surface, or

J ¼ kscs ¼ D∂c∂y

jy¼0 ð1Þ

where J is the deposition rate, ks is the surface reaction constant(assuming first-order reaction), cs is the surface concentrationandD is the diffusion coefficient. Note that J ¼ D ∂c

∂y jy¼0 insteadof J ¼ −D ∂c

∂y jy¼0 is used in Eq. (1) because the diffusion flux isin the opposite direction of the y coordinate. The diffusion fluxcan also be expressed as the product of the mass transfercoefficient and the difference in the concentration, or

J ¼ D∂c∂y

jy¼0 ¼ hcðc0−csÞ ð2Þ

where hc is the mass transfer coefficient, and c0 is the bulkconcentration. A combination of Eqs. (1) and (2) yields

J ¼ c01=ks þ 1=hc

ð3Þ

Depending upon the relative magnitude of ks and hc, theprocess can be either reaction controlled (ks≪hc) or diffusioncontrolled (hc≪ks).

It is possible to obtain the surface concentration data fromthe output of the CFD code, then the limited depositionmechanism can be justified by the following equation:

kshc

¼ c0cs−1 ð4Þ

The profile of ks /hc in the baseline case is shown in Fig. 5. It isseen that directly underneath the inlet slot, the deposition rate islimited by both surface kinetics and diffusion. Far away from the

−25 −20 −15 −10 −5 0 5 10 15 20 250

10

20

30

40

50

60

70

x/B

Dep

ositi

on r

ate

(nm

/sec

)

H/B=2.5H/B=1.5

Fig. 11. Influence of reactor-substrate spacing on the deposition rate profile.


inlet slot, the deposition is solely diffusion controlled. Thisexplains why the CFD simulation with the original reactionmechanism yields very similar results to the onewith themodifiedreactionmechanism (see Figs. 2 and 4) in the region far away fromthe inlet slot, where the reaction kinetics is ofminimal importance.

The dip in the center of the deposition profile can be readilyexplained by Eq. (1). To explain from J ¼ D ∂c

∂y jy¼0, we note thatthe thermal interaction between the impinging jet and the glass isthe largest in the center and the temperature is the lowestunderneath the inlet slot on the glass surface. According tokinetic theory, the diffusion coefficient (D∝T1.5 /P) is thelowest in the center. As will be shown later, the temperaturevariation is about 2.5%, or there is only a slight change in the

Velocity magn

H/B=2.5

H/B=1.5

H/B=2.5

H/B=1.5

A

BVelocity magn

Fig. 12. Influence of reactor-substrate

diffusion coefficient. However, due to the stagnation of theimpinging jet directly underneath the inlet, the concentrationgradient in the center is significantly lower than its neighbor-hood. This can be verified by taking concentration data from theoutput of the CFD code and calculating the concentrationgradient near the substrate surface. The concentration gradientshown in Fig. 6 is approximated by the difference ofconcentration at two adjacent grid points close to the walldivided by the grid size, or ∂c

∂yjy¼0cDcDy. It clearly shows the

concentration gradient is lower in the center than its neighbor-hood. Therefore, J ¼ D

∂c∂yjy¼0 is smaller in the center, which

leads to the dip in the deposition profile. On the other hand, wenote that ks is the smallest in the center due to the lowest surfacetemperature. However, the surface concentration is the highest inthe center and decays in the lateral direction due to the boundarylayer development, as shown in Fig. 7. As a result, there is a dipin the center of the deposition profile (J=kscs) if ks changessharply around the stagnation point due to temperature variation.

A comparison of the CFD simulation with the first-order andsecond-order upwind schemes show that although the second-ary shapes are not captured by the former scheme, the relativedifference in the average deposition rate is less than 4% withthese two numerical schemes (see Fig. 8). This implies the first-order upwind scheme is able to provide a very good estimate ofthe average deposition rate. A plot of the local deposition rateobtained by the first-order upwind scheme as a function of thelateral position shown in Fig. 9 indicates that in the region of2≤x /B≤22 (the inlet–exhaust length is 25B), the localdeposition rate is proportional to x- 0.46, which is very closeto the theoretical relationship x- 0.5 predicted by the parallelplate mass transfer boundary theory [18]. This fact further

itude (m/s): 0 1.4 2.8 4.2 5.6 7

itude (m/s): 0 1.4 2.8 4.2 5.6 7

spacing on the velocity flow field.

−25 −20 −15 −10 −5 0 5 10 15 20 25900

905

910

915

920

925

x/B

Sur

face

tem

pera

ture

(K

)

H/B=2.5H/B=1.5

Fig. 13. Influence of reactor-substrate spacing on the substrate surfacetemperature.

−25 −20 −15 −10 −5 0 5 10 15 20 250

10

20

30

40

50

60

x/B

Dep

ositi

on r

ate

(nm

/sec

)

stagnant0.2 m/sec1.0 m/sec2.0 m/sec

Fig. 15. Influence of glass moving speed on the deposition rate profile.


substantiates the conclusion that this deposition process ismainly diffusion controlled.

4.2. Influence of reactor-substrate spacing on the depositionrate profile

The deposition profile under reduced reactor-substratespacing (slot to glass distance) is shown in Fig. 10. The CFDsimulation successfully captures the deposition rate at each ofthe measurement points, except for the one in the center. Notethat there is also a dip in the deposition profile obtained from theCFD simulation, although it is hard to tell from Fig. 10. Theaverage deviation of model prediction at each measurementpoint from the experimental measurement is only 9.8% and theerror of the cumulative deposition rate from modeling accountsfor less than 6% of the corresponding experimental value,indicating that the CFD model with modified kinetic parametersreasonably predicts the deposition rate.

0.2m/se

1.0m/se

stagnan

2m/sec

Velocity magnitu

Fig. 14. Influence of glass line spe

The deposition profile is dependent on the reactor-substratespacing, similar to what is observed in heat transfer in theimpinging flow geometry [19,20]. The difference in thedeposition profile occurs in several regions (see Fig. 11). Oneis directly underneath the inlet slot. This might be caused by asmaller recirculation region in the vicinity of the inlet slot whenthe reactor-substrate spacing is reduced. Another region islocated at 5–9 slot widths away from the inlet (see Fig. 12),which can be readily explained by boundary layer separation[21]. The boundary layer tends to separate from the surface ofthe substrate under sufficient increasing fluid pressure down-stream of the flow, or known as adverse pressure gradient.When the pressure gradient is large enough such that the shearstress reduces to zero, the separation occurs and the fluid is nolonger pulling on the wall, and opposite flow develops to pushthe boundary layer off of the solid surface. The boundary layerseparation is alleviated as the flow area decreases. Anotherregion is close to the exhaust, when the flow is well developed.Since the velocity parallel to the glass increases as a result of

c

c

t

de (m/s): 0 1.4 2.8 4.2 5.6 7

ed on the velocity flow field.


decreased flow area, the boundary layer for mass transfer(δc∝x/

ffiffiffiffiffiffiffiRex

p∝

ffiffiffiffiffiffiffiffiffiffimx=u

p) decreases and the deposition is en-

hanced [18].It is worth pointing out that the wavy flow pattern due to

buoyancy induced convection in CVD processes has also beenreported in the literature (e.g., [15,22,23]). In the current work, theRayleigh number is around 300, and the mixed convectionparameter Ra/Re2Pr in the coating zone is on the order of 10−2,implying the buoyancy induced convection is minimal. Acomparison ofCFDmodelingwith andwithout natural convectionshows that the influence of buoyancy has no differentiable effecton the flow pattern and the deposition profile as well. Moreover,similar dips and humps were also observed in the heat transfercoefficient of turbulent impinging jet by Gardon and Akfirat[19,20]. However, these secondary shapes were explained with atransition of laminar to turbulent boundary layer in the vicinity ofx /B≈7. The current work suggests that boundary layer separationmight be another mechanism for the humps and dips observed inthe heat or mass transfer profile of an impinging jet.

The surface temperature under different reactor-substrate spacingis shown in Fig. 13. In either case, the temperature is the lowest inthe center, which indicates that the thermal interaction between theimpinging jet and the glass is the largest. Far away from the inlet,conduction from the depth of the glass allows the surfacetemperature to recover to a higher temperature at the gas glassinterface. This phenomenon partially explains the dip in thedeposition profile. Note that the heat transfer due to radiation is notaccounted for in the current work, the substrate temperature mightbe overestimated. Based on the convective heat transfer coefficientfrom the output of the CFD code, it is possible to estimate therelative importance of the convective heat transfer Jcon/A=h(x)(Ts−T0) and radiative heat transfer Jrad /A=σε12(Ts4−Tr4), which is notaccounted for in the current work. It is shown that the radiative heattransfer is dominant 1.5≤x /B≤25 from the inlet slot, while theconvective heat transfer is dominant directly underneath the inletslot (x /B≤1.5). Therefore, even though the surface temperature isoverestimated far away from the inlet slot, the surface temperaturedirectly underneath the inlet slot (where the dip occurs) is reasonablydescribed by coupling of the convective heat transfer of theimpinging jet and the conductive heat transfer within the glass.

4.3. Influence of line speed on the deposition rate profile

All the previous simulations are based on the stagnationgeometry. However, in the manufacturing process, the glass ismoving with a line speed of around 0.1–0.2 m/s, which impliesthat the moving boundary conditions may need to be applied onthe glass surface. At high line speeds, when moving boundarycondition is applied, it is found that the velocity field is nolonger symmetric. Instead, the flow is more towards down-stream of the inlet slot than upstream, as shown in Fig. 14. As aresult of the asymmetric flow, the deposition rate is higherdownstream of the inlet slot than upstream, as shown in Fig. 15.The effect of the moving glass on the deposition rate profile ismore apparent as the line speed becomes very fast. Undertypical line speeds, however, this drag experienced by the flowis generally negligible.

4.4. Discussions on the current reaction mechanism

It is worth pointing out that when the oxygen is in excess,ethylene might be oxidized to carbon monoxide and carbondioxide. However, no difference is found in the deposition rateprofile after this modification is made. Therefore, from aviewpoint of deposition rate, either mechanism is acceptable.However, the tin oxide deposition is shown to shift from areaction controlled deposition mechanism to a diffusioncontrolled deposition mechanism in the presence of adequateamount of water, which implies that a further increase in thesurface reaction by increasing water concentration will notresult in an increase in the deposition rate if it is diffusioncontrolled. A tentative explanation for this phenomenon is thatthe water vapor might not only reduce the activation energy forthe surface reaction, but also break the Sn–Cl bonds in MBTCto form products with smaller molecular weight and molecularsize (similar to the water–SnCl4 system). The higher the water/MBTC ratio, the smaller the product molecule and the larger thediffusion flux to the substrate. This mechanism might partiallyexplain the function of water in the tin oxide deposition, andmight be tested in the future work.

5. Conclusions

This work provides a computational framework for theAPCVD of SnO2 coatings with MBTC as the precursor. It isshown that the deposition process is mainly diffusion controlledand the effect of reaction kinetics is less important. The waveshape in the deposition profile is due to the several stagnation/recirculation regions in the coating zone.

Acknowledgement

This work is partially supported by the U.S. Department ofEnergy, Office of Industrial Technologies Glass Industry of theFuture team. Discussions with Mark Allendorf and WilliamHouf at Sandia National Laboratories and Mehran Arbab,Robert Greiner, Guosheng Kang, Thomas Sailock, WilliamSiskos, Jill Troup and Kwang Won at PPG Glass TechnologyCenter are gratefully acknowledged. The authors would alsolike to thank the anonymous reviewers for valuable commentsand suggestions.

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computational fluid dynamic modeling of tin oxide

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