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Parametric effects on thin film growth and uniformity in an atmospheric pressure impinging jet CVD reactor
ARTICLE IN PRESS
Journal of Crystal Growth 267 (2004) 22–34
Parametric effects on thin film growth and uniformity in an atmospheric pressure impinging jet CVD reactor S.P. Vanka*, G. Luo, N.G. Glumac Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, 1206 West Green Street, Urbana, IL 61801, USA Received 13 August 2003; accepted 15 March 2004 Communicated by J. J. Derby
Abstract A systematic parametric study has been performed to study the effects of various geometrical parameters on the growth rate and growth rate uniformity in a jet impingement chemical vapor deposition reactor operated at atmospheric pressure. A previously validated two-dimensional axisymmetric computational model is used to numerically solve the equations governing variable density flow, and energy and species transport. Buoyancy-induced secondary flows, which are greatly enhanced at elevated pressure, are found to strongly compromise the deposit uniformity for conditions that typically lead to uniform films at lower pressures. However, for appropriate choices of inlet flow rate, substrate rotation rate, and reactor dimensionless lengths, these detrimental effects can be effectively suppressed, leading to highly uniform deposits at atmospheric pressure. In addition, the observed growth rate and efficiency of precursor utilization are significantly improved over low-pressure reactors. These results suggest that uniformity may not necessarily have to be sacrificed in cost-effective, atmospheric pressure reactors. r 2004 Elsevier B.V. All rights reserved. PACS: 47.20; 81.15; 82.20 Keywords: A1. Convection; A1. Fluid flows; A1. Heat transfer; A1. Mass transfer; A3. Metalorganic chemical vapor deposition
1. Introduction Chemical vapor deposition (CVD) remains the most widely used deposition technique in many fields, especially for depositing thin films of optical and electronic materials. Most CVD processes are performed in a reduced pressure environment in order to achieve uniformity of the deposit, even *Corresponding author. Tel.: +1-2172448388; fax: +12172446534. E-mail address: [email protected] (S.P. Vanka).
though growth rate is often small. At low pressures, rapid diffusion minimizes spatial concentration gradients, leading to enhanced uniformity. In addition, buoyancy-induced flows are minimized since the Grashof number is low. The Grashof number Gr ¼ gbDTL3 r2 =m2 ; scales with the density squared, and thus buoyancy effects should increase rapidly with increasing pressure. Due to the high capital and operating costs associated with vacuum system infrastructure, it is nevertheless desirable to operate a deposition system at atmospheric pressure, which may allow
0022-0248/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jcrysgro.2004.03.039
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for a significant reduction in process cost in some applications. Indeed atmospheric pressure CVD (APCVD) is a rapidly growing field. In general, however, films produced by APCVD do not meet the uniformity requirements of some of the more stringent CVD applications, where percent level or better uniformity over large wafers is required. The stagnation flow geometry has been widely applied to CVD, primarily at low pressure. The reactor design involves an axisymmetric chamber with an inlet of uniformly distributed flow impinging upon a susceptor. Under appropriate conditions (i.e. large susceptor radius as compared to inlet-to-susceptor distance, low Reynolds number, negligible buoyancy effects), the flow field resembles that predicted by the similarity solution for a stagnation flow in which radial gradients in concentration and temperature disappear. In practice, however, the inlet-to-susceptor distance and susceptor diameter are at least of the same order, and buoyancy effects are present except at very low pressures. In order to mitigate these effects, susceptor rotation has been widely applied to enhance uniformity and suppress buoyancy effects. Success at low pressure in suppressing buoyancy-induced flow has been great, as evidenced by the wide use of the stagnation flow geometry in research as well as in commercial reactors. Both upflow and downflow stagnation reactor configurations have been used and several variants of this reactor have been successfully implemented. However, rarely is the stagnation flow reactor used at elevated pressures since rotation alone cannot counteract buoyancy effects above 100 Torr or so. In a previous study [1], we explored the performance of a new impingement jet reactor geometry in which the inlet gases entered the reactor geometry through a narrow inlet and impinged on the substrate. Also, the height of the top boundary was lowered such that the natural convection is significantly weakened. The momentum of the inlet jet counteracted the natural convection flow, producing uniform and high growth rates of the deposit under the assumption of mass transfer limited deposition. The performance of the geometry was compared with the traditional stagnation flow geometry, and
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it was observed that the proposed configuration overcomes the negative effects of atmospheric pressure operation, while also producing high growth rates. This study led us to investigate if the geometry can be further optimized by changing the various dimensions. The results of such a study are reported in this paper. Currently, the investigation has been only computational. The governing Navier–Stokes equations, along with the equations for energy and species transport are numerically solved using a finite volume procedure. The effects of variable density and buoyancy forces are fully taken into account. Several parameters are varied and their effects on the growth rate and deposit uniformity are studied. In addition, the precursor utilization efficiency is computed for each case to evaluate the extent to which the precursor is incorporated into the film as opposed to being exhausted from the reactor. The results of this study are useful to future experiments which can provide corroborative evidence of an optimized atmospheric CVD reactor geometry.
2. Previous work A significant amount of previous research on the stagnation flow CVD reactor geometry has appeared in the literature, though mostly at reduced pressure. Houtman et al. [2] and Coltrin et al. [3] performed some of the first detailed computations of CVD in stagnation flows. Evans and Grief [4,5] presented a detailed two-dimensional simulation of a stagnation flow reactor and showed that buoyancy-induced flows could be mitigated by substrate rotation and/or increased inlet velocity over a limited range of conditions. They suggested 3=2 that the key parameter was the ratio Gr=Rew ; where Rew is the rotational Reynolds number. 3=2 Values of Gr=Rew > 3 lead to strong buoyancyinduced secondary flows. It was seen that increasing the reactor inlet velocity can reduce the buoyancy effect and result in more uniform heat transfer. Compared to an adiabatic wall, the cooled isothermal wall boundary conditions allow a larger value of the Grashof number to be employed without recirculation. Wang et al. [6] investigated a vertical rotating-disk metal organic
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CVD (MOCVD) reactor operating at reduced pressure (0.2 atm) using both computations and experiments. They focused on eliminating buoyancy-induced effect and found, in agreement with Evans and Grief, that susceptor rotation is a critical parameter. Further work from the same group [7] involved a parametric study of the effects of reactor parameters on thin film uniformity. It was found that the secondary flows caused by buoyancy effects, reactor shape, forced convection, and substrate rotation can be eliminated by appropriate choice of operating pressure, gas flow and substrate rotation rate, albeit still in a vacuum environment. Fotiadis et al. [8, 9] established through computational studies that the effects of the geometry of the reactor on the deposit uniformity were significant in stagnation flow reactors. They suggest inverting the reactor, shortening distance between inlet and susceptor, introducing baffles, and reshaping reactor wall to mitigate buoyancy effects. Although they looked at several pressures, they were only able to predict uniform films for pressures much less than atmospheric. The study of Gadgil [10] reached similar conclusions in an experimental study that demonstrated through flow visualization that secondary flows were strongly influenced by the gas inlet configuration though no growth measurements were made. Other experimental work was performed by Kondo et al. [11] in a study that systematically varied several key reactor parameters to assess their effect on the low-pressure CVD environment. Dilawari and Szekely [12] presented numerical results for a modified stagnation point flow reactor. The major difference between their modified reactor and classical vertical stagnation reactor is that the reactor is inverted and the distance between the inlet showerhead and wafer was reduced to low values. They found that the inverted reactor is helpful in minimizing thermal natural convection and the inlet-wafer distance is critical in obtaining good spatial uniformity of deposition rate in their design. The inlet to wafer distance of 10 mm was seen to provide good spatial uniformity for a diameter of the reactor tube of 200 mm. They argue that the small inlet- to wafer distance reduces the ability of the carrier gases to
entrain fluid from the surroundings, thus preventing the formation of the secondary flows. Cho et al. [13] studied the optimization of inlet concentration profile of the reactant gas on the uniformity of the growth rate. Their results showed that the film uniformity could be significantly improved by enforcing an optimum inlet concentration distribution. However, they noted that controlling the inlet concentration is not easy. To make the optimization procedure more practical, Cho et al. [14] also devised a procedure to find the optimum inlet velocity profile. These calculations showed that a properly arranged inlet velocity profile can suppress buoyancy-driven recirculation, thus improving the growth rate uniformity. Pawlowski et al. [15] and Theodoropoulos et al. [16] also investigated the effect of inlet velocity configuration in the stagnation flow reactor at pressures up to 0.2 atm. They found that uniformity was sensitive to the inlet geometry used, as well as to inlet velocity and inlet-to-susceptor distance. Most previous simulations of stagnation flow CVD reactors invoke the axisymmetric assumption, though this assumption is not always valid, as shown in a series of papers by van Santen et al. [17–19]. Those works suggest that asymmetric flows do arise under conditions that are commonly used in CVD reactors, though sufficiently high inlet flow and rotation of the wafer guarantees a perfectly axisymmetric flow, and a decrease in distance between wafer and inlet can also suppress asymmetry. In a recent paper [1], we had demonstrated that uniform thin films can be grown under atmospheric conditions using a certain combination of geometric parameters of a stagnation flow-type reactor. This reactor, named an impinging jet reactor, carefully balanced the inlet jet momentum with the natural convection flow, to obtain a uniform mass transfer rate. However, this study did not explore the influence of the various parameters on the growth rate and its uniformity. Early computational work on a similar impinging jet configuration, where the inlet diameter is smaller than that of the susceptor, was performed by Snyder et al. [20] in a CdTe reactor, and they
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demonstrated that fairly uniform deposits were possible at 0.1 atm, though radial growth rate nonuniformities were typically several percent or more. Thus, there is an emerging consensus on viable techniques for suppression of buoyancy-induced secondary flows. However, most studies address reduced pressure reactors where such effects are reduced in the first place. Mitigation schemes used in low-pressure flows, such as increasing Rew to 3=2 maintain low values of Gr=Rew ; are not practical at elevated pressures since the required rotation rates would exceed practical values. Thus, attaining uniform deposition at atmospheric pressure will likely require careful simultaneous selection of many reactor parameters to attain highly uniform deposition. Our approach attempts to build upon these previous works to attempt to isolate a reactor configuration and set of conditions that lead to uniform deposition at atmospheric pressure, as well as to examine the effect of reactor parameters on deposit uniformity in the vicinity of such a solution. In addition, we examine the effect of reactor parameters on precursor utilization efficiency Zp, that is the fraction of the relevant precursor atoms or molecules that are incorporated into the film, which has received significantly less attention than growth rate or uniformity as a process characteristic. However, with the high expense of some metalorganic precursors, often exceeding several hundred dollars per gram, precursor costs can constitute a significant fraction of the process cost. Thus, optimizing Zp may result in substantial cost savings.
3. Governing equations and numerical procedure 3.1. Governing equations The velocities encountered in a typical CVD reactor are small. Hence, the flow can be treated essentially as incompressible. However, the density variations in the fluid are significant to the extent that the Boussinesq approximation cannot be considered to be accurate. Hence, the local density variations must be accounted for in the convective terms, in addition to the gravitational term. We
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consider here the non-dimensional equations obtained by using the scales d (diameter of the reactor), V (inlet velocity), rref V 2 ; DTc ðTwafer Tinlet Þ; Yinlet ; and d/V for length, velocity, pressure, temperature, concentration, and time, respectively. The governing equations for mass, momentum, energy, and species concentration can be stated as [19]: @r þ = ðruÞ ¼ 0; ð1Þ @t @ru þ = ðruuÞ @t 1 ¼ =p þ =fm½=u þ ð=uÞT 23ð=uÞ I g Re " # Y 12 Gr þ 2 ex ; Re Y 12 Ga þ 1 Cp
@rY 1 þ Cp = ðruYÞ ¼ = ðk=YÞ; @t Re Pr
@rY 1 þ = ðruY Þ ¼ = ðrDAB =Y Þ; @t Re Sc
ð2Þ
ð3Þ ð4Þ
where u is the velocity vector, I is the unit tensor, ex is the unit vector with component only in the x direction (x positive direction points upwards), p is pressure, Y is the temperature, Y is the mass fraction of precursor gas, and t is the time. The superscript T on ru refers to the transpose of the tensor. All variables are non-dimensional. The material properties, density r, dynamic viscosity m, thermal conductivity k, heat capacity Cp, and the mass diffusivity DAB are made dimensionless with their value at the reference temperature Tref ¼ ðTwafer þ Tinlet Þ=2: The Dufour and Soret diffusion are assumed to be small for the particular gases considered here and hence neglected. The Reynolds (Re), Prandtl (Pr), Schmidt (Sc), Grashof (Gr), and Gay–Lusac (Ga) numbers appearing in the above equations are defined as Re ¼ rref Vd=mref ; Pr ¼ mref Cpref =kref ; Gr ¼
Sc ¼ mref =ðrref Dref Þ; 2 grref d 3 ðTwafer Tinlet Þ=ðm2ref Tref Þ;
ð5Þ
Ga ¼ ðTwafer Tinlet Þ=Tref ; where g is the acceleration due to gravity, Twafer and Tinlet represent dimensional temperatures at
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the wafer and at the inlet. Reference values denoted by the subscript ref are taken at reference temperature. Expansion effects caused by density changes with heating of the gas phase are modeled by ideal gas law. This gives the following dimensionless relation. 1 r ¼ Y 12 Ga þ 1 : ð6Þ The current study assumed axisymmetric flow because of the computational simplicity provided, and the large number of parametric computations that were planned. However, natural convection flows do become three-dimensional in some parameter ranges. There is currently no information on the parameter space in which the flow becomes three-dimensional, as the forced flow can make an originally three-dimensional flow to become axisymmetric (as in Refs. [17–19]). For the low heights considered here, the natural convection cells are swept away by the forced flow. When a steady axisymmetric solution is found, there is a high probability that the flow is indeed twodimensional. However, when a time-dependent solution was found, the flow may have also transitioned to be three-dimensional. To fully validate the axisymmetric assumptions threedimensional calculations are needed. These need to be performed in future for selected parameter combinations. The spatial terms in the governing equations are discretized using a second-order finite volume method on a non-staggered cylindrical polar grid. The time integration is performed using a predictor–corrector method similar to that used by Najm et al. [21] and Boersma [22]. 2.2. Boundary conditions At the top surface, the velocities and concentration values corresponding to the inflow gases are prescribed as Dirichlet conditions. At the wafer, the temperature is fixed at 900 K, and the nondimensional concentration is prescribed to be zero. The normal and radial velocities are also prescribed to be zero at the wafer surface with the tangential velocity prescribed by the rotation rate. At the outlet of the reactor, the normal derivatives of normal velocities and the scalar variables are
prescribed to be zero. Also, the outflow boundary is sufficiently far away from the wafer surface that its boundary conditions should not influence the deposition profiles on the wafer. The temperature at the outer wall is an important aspect for the operation of the reactor. It is necessary to select this in such a way that there is no deposit on the outer wall, but at the same time the buoyancy forces due to the cold outer walls are mitigated. In this study, we considered two different boundary conditions to understand the effect of outer wall thermal boundary condition on the flow inside the reactor. The first condition considered was an adiabatic outer wall. The second condition was an isothermal wall, implying some form of external cooling to maintain the walls at the temperature of the inlet gases. This second condition was used in most of the calculations reported in this paper. On the pedestal side wall, a linear temperature variation from the wafer surface temperature to the ambient of 300 K was prescribed. We believe that this condition will not affect the deposition patterns on the wafer; hence, other conditions appropriate to an industrial setting may also be considered. 2.3. Properties and deposition parameters The present simulations have been performed with argon and acetone as the carrier and precursor gases, respectively. The dynamic viscosity, specific heat, and conductivity of the carrier gas are obtained from database of National Institute of Standards and Technology (NIST) [23]. Binary diffusion coefficients are calculated from the Chapman-Enskog theory. For details, see Ref. [24]. For the present study, the rate of deposition is assumed to be limited by the rate of mass transfer, implying fast chemical kinetics. Thus, the growth rate is taken to be proportional to the gradient of the concentration normal to the wafer surface Growth ratepSh ¼ @Y =@xwafer : Here the growth rate is derived in a non-dimensional sense, as the inlet concentration is fixed at a nondimensional value of unity. The growth rate is given by the product of the local density, diffusion coefficient and the concentration gradient. In our
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study, the variations of density and diffusion coefficients are small because of the dilute concentrations of the precursor and uniform wafer temperature. When the deposition rate is limited by the kinetics of the reaction, it is necessary to include the specific kinetic mechanisms before actual film deposition rates are estimated. By appropriately specifying a value of the inlet concentration, a dimensional value can be then obtained. Hence the units for current growth rates are arbitrary. The non-uniformity and usage are defined as follows: Non-uniformity ¼
Z
% Sh Sh
2
% 2 Awafer dA=Sh
1=2 ;
Awafer
ð7Þ R % where Sh ¼ Awafer Sh dA=Awafer is the average growth rate and Awafer is the area of the wafer. R rDAB ð@Y =@xÞwafer dA A : ð8Þ Usage ¼ wafer R Ainlet rVYinlet dA 2.4. Computational domain and parameters The computational domain is shown in Fig. 1, and the important lengths are identified. All relevant lengths are scaled to the reactor diameter
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d (13.5 cm). For our baseline configuration, the inlet entry length is 3d/8, the gap distance (between the exit plane of the entry length and the susceptor surface is d/8, and the susceptor diameter is 0.56d. The spatial distribution of the inlet gases in the baseline configuration is uniform. We systematically varied reactor dimensions and other reactor parameters while keeping the pressure fixed at 1 atm and the flow rate of the precursor and carrier gas fixed at 10 SLM. For each configuration, we examined three rotation rates: 0, 1007, and 1511 rpm which span the range of typical rotation rates seen in stagnation flow CVD reactors. A non-uniform cylindrical grid with finite volume cells only in the computational domain was used. The total number of cells in the domain was in excess of 18 000. The computations were performed on a high-end personal computer and typically required about one day of CPU time per calculation when the flow was steady. The gridindependency of the solution was checked by quadrupling the total number of cells. It was found that the maximum difference in local growth rate between the coarse and fine grids was less than 0.5%.
4. Results
3d/8
d/4
d/8
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4.1. Baseline configuration
d/2
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Fig. 1. Schematic of a modified impinging jet CVD reactor.
There are three geometrical parameters that describe the present configuration: (a) the height of the cover plate from the susceptor plate; (b) the diameter of the inlet jet; and (c) the diameter of the inlet jet of the species (which can be different from the jet of carrier gas). These dimensions are nondimensionalized with the diameter (d) of the reactor chamber. The baseline configuration corresponds to our previous work in which a series of calculations were made for a configuration with a jet diameter of (d/4) and height of d/8. The precursor and carrier gases both were supplied through the entire inlet diameter (d/4). The base line case was studied for three rotation rates of 0, 1007 and 1511 rpm. Figs. 2a and b show velocity vectors, contours of stream function, temperature and concentration
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Fig. 3. Growth rates along the wafer for different substrate rotation rates for baseline configuration.
Fig. 2. Streamlines, concentration (left) and temperature (right) contours and velocity vectors for baseline configuration: (a) O = 0 rpm, (b) O = 1511 rpm.
for the zero rotation and 1511 rpm cases. Fig. 3 shows the corresponding growth rate distribution along the substrate. The growth rate is in arbitrary units, based on the gradient at the substrate and an inlet non-dimensional concentration of unity. The pressure in the reactor is atmospheric. It can be seen that in contrast with what is seen in conventional stagnation flow reactors, there are no vortices due to natural convection. A vortex is formed at the edge of the substrate due to the flow turning and rotation of the substrate. We have
assumed that deposition occurs over the complete substrate. It can be seen that the deposition is nonuniform at zero rotation rate with dips and peaks. However, when rotation is included, deposition becomes uniform except at the edges where a local peak is observed. This region can be neglected for practical CVD depositions because the substrate typically does not extend to the susceptor edge. The growth rate increases with rotation because of the viscous pumping caused by the rotational forces and the resulting thinning of the boundary layer. The growth rate at 1511 rpm is nearly twice that of the rate at zero rotation. In addition, precursor utilization efficiency also increases with rotation rate, beginning at around 10% for zero rotation, and nearly doubling to 19% at 1511 rpm. This baseline configuration represents our initial guess of a reactor configuration that showed enhanced uniformity at atmospheric pressure, based on the work of others and on our initial simulations. This configuration actually performs fairly well in these simulations, and the 1511 rpm case would likely meet some of the more stringent uniformity requirements for a substrate that was up to 75% the diameter of the substrate. However, other combinations of the parameters may give results superior to these results, and are next explored.
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4.2. Effect of the inlet diameter
29 Ω =0 rpm Ω = 1 007 rpm Ω = 1 511 rpm
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Our attempts to investigate how reactor parameters affect uniformity first focused on the diameter of the gas inlet. Fig. 4 shows the flow pattern for the case in which the inlet diameter is increased to 66% of the susceptor diameter, and the growth rate distribution is shown in Fig. 5. The zero rotation case converges to a periodic solution, and the time-averaged growth rate, shown in Fig. 5, has a non-uniformity of 32.08%. However, with rotation, the uniformity is improved slightly over the baseline case, with only a very slight reduction in efficiency. The dip in the center is reduced over the baseline case. Fig. 6 shows the case where the inlet diameter has been further increased all the way to the to the susceptor diameter. The growth rates and profiles are shown in Fig. 7. Under these conditions, neither the zero rotation nor the 1511 rpm case converges to a steady-state solution. Only the 1007 rpm case has a steady solution, and uniformity continues to improve over the narrower inlet lengths. Thus, while widening the inlet does appear to improve uniformity with small efficiency penalties, the range of parameter space over which stable solutions is observed is greatly reduced. Since we integrated the time-dependent governing equations, we are able to capture periodic time-dependent solutions. However, the
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Fig. 5. Growth rates along the wafer for different substrate rotation rates for inlet diameter of 0.66 of susceptor.
Fig. 6. Streamlines, concentration (left) and temperature (right) contours and velocity vectors for inlet diameter equal to susceptor diameter at 1007 rpm.
Fig. 4. Streamlines, concentration (left) and temperature (right) contours and velocity vectors for inlet diameter of 0.66 of susceptor at 1007 rpm.
flow may be even three-dimensional [17–19], which our current method is unable to capture. Since we are not interested in such time-dependent solutions, further study of such cases is not considered. For these unsteady solutions, the instantaneous flow fields are observed to be very complex, with multiple vortices located on the susceptor. These vortices are certainly not conducive to obtaining uniform deposition rates, even in the limit of large amounts of ensemble averaging of the flow fields. The present configurations may also be compared with the traditionally known design of a
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Fig. 7. Growth rate along the wafer for the case where the inlet diameter is equal to the susceptor diameter.
shows similar growth rate and efficiency to the case with an entry length of 3d/8 and inlet diameter of 0.375d (Fig. 7). 4.3. Effect of inlet velocity profile We next considered two cases of varying the inlet conditions. In the first case, the inlet velocity profile was prescribed to be parabolic, corresponding to a fully developed laminar flow. This condition may represent a very long inlet pipe. The second case corresponded to the precursor being supplied only over a portion of the inlet duct. The advantage of this may be a higher utilization efficiency of the precursor, albeit at a lower growth rate. Fig. 9 shows the results for the case in which we applied a parabolic velocity profile at the inlet. This distribution enhances the transport of precursor to the surface near the center of the susceptor, and reduces the transport further out. As a result, uniformity is greatly reduced, though efficiency slightly increases since the bulk of the deposit occurs at the center, and less precursor gas is lost as it bypasses the substrate. A similar result is shown in Fig. 10 where the inlet velocity profile is uniform, but precursor is only present in the standard concentration in the center half of the inlet while the outer annulus has only the carrier gas. Under these
pancake reactor. A pancake reactor has a short height, similar to our standard reactor configuration, with the inlet gas flow over the entire susceptor. We have computed three cases with the inlet diameter of the gases equal to 0.375d. Fig. 8 shows the velocity vectors and temperature and concentration contours for the pancake type arrangement. It can be seen that the first case of zero rotation and the case of 1511 rpm rotation have no steady solutions. Only the 1007 rpm case has a solution, which is fairly uniform across the susceptor except at the edges. The 1007 rpm case
Growth Rate Distribution
Fig. 8. Streamlines, concentration (left) and temperature (right) contours and velocity vectors for pancake reactor configuration at 1007 rpm.
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Fig. 9. Growth rates along the wafer for different substrate rotation rates for a parabolic inlet flow in the baseline reactor configuration.
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Fig. 10. Growth rates along the wafer for different substrate rotation rates for inlet diameter of precursor gases = d/8.
conditions, the non-uniform distribution of precursor does lead to non-uniform deposition, with a higher growth rate at the center as compared to the edge. However, efficiency increases greatly, exceeding 50% for the highest rotation rate case.
4.4. Effect of the chamber height The distance between the susceptor and the upper wall is a sensitive parameter that determines the natural convection parameter and thereby affects growth. We have considered two variations to this height. For a gap distance twice that of the baseline case, no steady solutions are observed for any rotation rate. Secondary flows are seen to be extremely strong, and it is likely that any deposit observed under these conditions would be nonuniform. For a reduced gap, uniformity also suffers, but not to the same extent. Fig. 11a and b show the results of a case with a gap distance half the baseline case. The uniformity of the deposit, as shown in Fig. 12, is reduced for all rotation rates. Based on these results, it can be concluded that either too small or too large gap distances can lead to uniformity problems in stagnation flow reactors. Table 1 summarizes the parameters for the various cases, and the observed non-uniformity parameters.
Fig. 11. Streamlines, concentration (left) and temperature (right) contours and velocity vectors for gap height of d/16: (a) O ¼ 0 rpm; (b) O ¼ 1511 rpm:
5. Discussion The results of the baseline case suggest that a high degree of uniformity for CVD deposits at atmospheric pressure can be obtained. However, uniform deposits occur under a much narrower range of conditions at atmospheric pressure than at low pressure. For a given total flow rate (e.g. 10 SLM in this study) and given susceptor diameter, there is evidence that suggests that there are an optimal inlet diameter and gap distance that
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Fig. 12. Growth rates along the wafer for different substrate rotation rates for gap height of d/16.
provide uniform deposition. Our smallest inlet diameter (d/4) produces good uniformity at high rotation rates. Increasing the inlet diameter results in increased uniformity and efficiency but steady solutions do not occur for all rotation rates. The confinement of the flow in the narrower channels results in higher mean velocities, and these appear to convect the buoyant recirculation regions downstream to regions in which there is no effect on the deposition. Increasing the inlet diameter results in a flow that is more nearly that of the ideal stagnation flow solution, and thus uniformity is expected to be higher. However, the bulk flow in the channel does not have sufficient momentum to carry the buoyancy-induced recirculation far enough away from the growth surface, and thus these secondary flows can destabilize the inlet flow field, preventing steady -state from being achieved. Similarly, there appears to be an optimal gap distance. The lack of steady solutions at large gap distances is not surprising in light of the lower bulk velocity of the gas around the substrate. As gap distance is decreased, the flow behaves more like the similarity solution, and the radial velocity increases due to the smaller area. As a result, the flow field is more uniform and secondary flows are effectively swept downstream. However, too small a gap also appears to hurt uniformity. From the velocity profiles, a likely reason for this is that the axial inlet flow develops a radial component at the
exit of the entry length over a finite spatial region. In inviscid potential flow, the inlet flow can turn the corner without such a standoff, and so the smaller the gap distance, the closer the flow approaches the ideal stagnation solution. For real flows, too small a gap distance can result in the boundary layer below the inlet sidewall being squeezed, resulting in an enhanced growth rate at these locations, as observed in the simulations. For cases in which the precursor is evenly distributed along the inlet, precursor utilization efficiency increases linearly with growth rate, since the enhanced growth rates at a fixed mass flow rate of precursor necessarily result in higher efficiency. However, efficiencies are fairly low, typically less than 20%, with the remaining 80% bypassing the substrate and proceeding out the exhaust. Separation and recycling can potentially recover some of this, but only with added cost. An interesting exception is the case where the inlet gases only have the regular precursor concentration in the central portion of the inlet. In this case, the outer annulus of diluent appears to act as a shroud, directing the precursor-laden gases into the substrate. Though uniformity is poor, Zp is significantly enhanced, approaching 50% at the high rotation rate. In cases in which Zp is critical and uniformity is still desired, some variant of these conditions, perhaps with a tailored inlet velocity profile or variable slope on walls, may lead to high Zp with acceptable uniformity. While this study addresses the basic parameters associated with a stagnation flow reactor, there are certainly many other variations that are possible for further fine tuning. These include varying the reactor diameter to susceptor diameter ratio (though Evans and Grief [4] found this to have minimal effect on the flow), tapering or contouring the upper reactor wall, making more extensive variation of the inlet velocity profile, adding multiple inlets that may include purge gas flows, varying the wall temperature boundary conditions, etc. Our study demonstrates, however, that such variations may not be necessary since the appropriate choice of simple reactor parameters can lead to highly uniform films at atmospheric pressure.
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33
Table 1 Growth rates and non-uniformity for the impinging jet CVD reactor at 1 atm and 10 SLM Gr=Re2in
Rotation speed of wafer (rpm)
130.8 130.8 130.8
1.191 1.191 1.191
0 1007 1511
dwafer
87.2 87.2 87.2
2.68 2.68 2.68
dsubstrate
58.4 58.4 58.4
Pancake reactor dwafer
Inlet diameter
d/4 baseline case
Partial opening for precursor gases (d/8)
Parabolic distribution of inlet velocities
Lower chamber height (d/16)
3=2
Gr=Rew
Average growth rate
0 40 000 60 000
— 0.00255 0.00139
44.73 73.87 87.67
4.91 1.21 0.67
9.85 15.99 18.93
0 1007 1511
0 40 000 60 000
— 0.00255 0.00139
--69.90 85.22
--0.64 0.36
--14.76 17.95
5.98 5.98 5.98
0 1007 1511
0 40 000 60 000
— 0.00255 0.00139
--69.36 ---
--0.48 ---
--14.56 ---
87.2
2.68
0
0
—
---
---
---
87.2 87.2
2.68 2.68
1007 1511
40 000 60 000
70.26 ---
0.24 ---
14.83 ---
130.8
1.191
0
0
37.95
12.53
30.96
130.8 130.8
1.191 1.191
1007 1511
40 000 60 000
57.83 65.79
18.64 22.32
46.73 53.05
130.8
1.191
0
0
53.65
16.31
11.76
130.8 130.8
1.191 1.191
1007 1511
40 000 60 000
77.44 90.33
4.69 2.93
16.74 19.49
130.8
0.149
0
0
52.26
9.29
11.30
130.8 130.8
0.149 0.149
1007 1511
40 000 60 000
75.85 89.11
2.07 1.16
16.15 18.94
Inlet Reynolds number (Rein)
Rotation Reynolds number (Rew)
0.00255 0.00139 —
0.00255 0.00139 —
0.00255 0.00139 — 0.00032 0.00017
RMS nonuniformity (%)
Precursor efficiency (%)
Note: - - - means that flow is unsteady. The Grashof number is based on the chamber height. The rotation Reynolds number is based on reactor diameter.
6. Conclusions Several conclusions can be reached as a result of this work: (1) For an atmospheric pressure, mass-transfer limited, stagnation flow reactor operating at reasonable flow rates (0.5 SLM/cm2) in a standard reactor configuration, film unifor-
mity at the sub-percent level can be achieved at moderate rotation rates with careful choice of reactor parameters. (2) Rotation is necessary to achieve sub-percent level uniformity in such a reactor design, though rotation rates of 1000–1500 rpm are sufficient. While this is on the high end of current reactor designs, it is by no means impractical.
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(3) In the vicinity of our baseline reactor configuration, the ratio of inlet diameter to susceptor diameter has a significant effect on film uniformity with larger ratios leading to more uniform films in general. However, larger ratios do not support steady solutions for all rotation rates. (4) There appears to also be an optimal gap distance associated with a balance between generating enough radial momentum to convect secondary flows downstream and maintaining enough gap distance for the flow to turn the corner without excessively compressing the boundary layer. (5) Precursor utilization efficiency can be dramatically improved by the use of an inert gas shroud, though our study shows a decrease in uniformity for the one configuration we investigated. There are other possible options within the parameter space of potential configurations that can exploit this enhanced efficiency without a dramatic penalty in uniformity.
Acknowledgements This work was supported in part by the National Science Foundation Division of Manufacturing and Industrial Innovation under Contract DMI-00-99748.
References [1] S.P. Vanka, G. Luo, N.G. Glumac, Numerical study of mixed convection flow in an impinging jet CVD reactor for atmospheric pressure deposition of thin films, J. Heat Transfer, 2003, in print. [2] C. Houtman, D.B. Graves, K.F. Jensen, J. Electrochem. Soc. 133 (1987) 963.
[3] M.E. Coltrin, R.J. Kee, J.A. Miller, J. Electrochem. Soc. 133 (1987) 1206. [4] G.H. Evans, R. Greif, Trans. ASME 109 (1987) 928. [5] G.H. Evans, R. Greif, Numer. Heat Transfer 12 (1987) 243. [6] C.A. Wang, S. Patnaik, J.W. Caunt, R.A. Brown, J. Crystal Growth 93 (1988) 228. [7] S. Patnaik, R.A. Brown, C.A. Wang, J. Crystal Growth 96 (1989) 153. [8] D.I. Fotiadis, A.M. Kremer, D.R. McKenna, K.F. Jensen, J. Crystal Growth 85 (1987) 154. [9] D.I. Fotiadis, S. Kieda, K.F. Jensen, J. Crystal Growth 102 (1990) 441. [10] P.N. Gadgil, J. Crystal Growth 134 (1993) 302. [11] M. Kondo, et al., J. Crystal Growth 124 (1992) 265. [12] A.H. Dilawari, J. Szekely, J. Crystal Growth 108 (1991) 491. [13] W.K. Cho, D.H. Choi, M.-U. Kim, Int. J. Heat Mass Transfer 42 (1999) 1141. [14] W.K. Cho, D.H. Choi, M.-U. Kim, Int. J. Heat Mass Transfer 42 (1999) 4143. [15] R.P. Pawlowski, C. Theodoropoulos, A.G. Salinger, T.J. Mountziaris, H.K. Moffat, J.N. Shadid, E.J. Thrush, J. Crystal Growth 221 (2000) 622. [16] C. Theodoropoulos, T.J. Mountziaris, H.K. Moffat, J. Han, J. Crystal Growth 217 (2000) 65. [17] H. van Santen, C.R. Kleijn, H.E.A. van den Akker, Int. J. Heat Mass Transfer 44 (2001) 659. [18] H. van Santen, C.R. Kleijn, H.E.A. van den Akker, Int. J. Heat Mass Transfer 43 (2000) 1523. [19] H. van Santen, C.R. Kleijn, H.E.A. van den Akker, J. Crystal Growth 212 (2000) 311. [20] D.W. Snyder, P.J. Sides, E.I. Ko, J. Crystal Growth 121 (1992) 631. [21] H.N. Najm, P.S. Wyckoff, O.M. Knio, J. Comput. Phys. 143 (1998) 381. [22] B.J. Boersma, Direct simulation of a jet diffusion flame, Annual Research Briefs, Center for Turbulence Research, Stanford, CA, (1998), pp. 47–56. [23] Database of the Thermophysical Properties of Gases Used in the Semiconductor Industry. Retrieved June 7, 2002 from http://properties.nist.gov/SemiProp/Gases/Index.html. [24] G. Luo, Study of Buoyancy-induced flows in a prototypical CVD reactor, Ph.D.Thesis, University of Illinois, Urbana-Champaign, IL, 2003.
Journal of Crystal Growth 267 (2004) 22–34
Parametric effects on thin film growth and uniformity in an atmospheric pressure impinging jet CVD reactor S.P. Vanka*, G. Luo, N.G. Glumac Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, 1206 West Green Street, Urbana, IL 61801, USA Received 13 August 2003; accepted 15 March 2004 Communicated by J. J. Derby
Abstract A systematic parametric study has been performed to study the effects of various geometrical parameters on the growth rate and growth rate uniformity in a jet impingement chemical vapor deposition reactor operated at atmospheric pressure. A previously validated two-dimensional axisymmetric computational model is used to numerically solve the equations governing variable density flow, and energy and species transport. Buoyancy-induced secondary flows, which are greatly enhanced at elevated pressure, are found to strongly compromise the deposit uniformity for conditions that typically lead to uniform films at lower pressures. However, for appropriate choices of inlet flow rate, substrate rotation rate, and reactor dimensionless lengths, these detrimental effects can be effectively suppressed, leading to highly uniform deposits at atmospheric pressure. In addition, the observed growth rate and efficiency of precursor utilization are significantly improved over low-pressure reactors. These results suggest that uniformity may not necessarily have to be sacrificed in cost-effective, atmospheric pressure reactors. r 2004 Elsevier B.V. All rights reserved. PACS: 47.20; 81.15; 82.20 Keywords: A1. Convection; A1. Fluid flows; A1. Heat transfer; A1. Mass transfer; A3. Metalorganic chemical vapor deposition
1. Introduction Chemical vapor deposition (CVD) remains the most widely used deposition technique in many fields, especially for depositing thin films of optical and electronic materials. Most CVD processes are performed in a reduced pressure environment in order to achieve uniformity of the deposit, even *Corresponding author. Tel.: +1-2172448388; fax: +12172446534. E-mail address: [email protected] (S.P. Vanka).
though growth rate is often small. At low pressures, rapid diffusion minimizes spatial concentration gradients, leading to enhanced uniformity. In addition, buoyancy-induced flows are minimized since the Grashof number is low. The Grashof number Gr ¼ gbDTL3 r2 =m2 ; scales with the density squared, and thus buoyancy effects should increase rapidly with increasing pressure. Due to the high capital and operating costs associated with vacuum system infrastructure, it is nevertheless desirable to operate a deposition system at atmospheric pressure, which may allow
0022-0248/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jcrysgro.2004.03.039
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for a significant reduction in process cost in some applications. Indeed atmospheric pressure CVD (APCVD) is a rapidly growing field. In general, however, films produced by APCVD do not meet the uniformity requirements of some of the more stringent CVD applications, where percent level or better uniformity over large wafers is required. The stagnation flow geometry has been widely applied to CVD, primarily at low pressure. The reactor design involves an axisymmetric chamber with an inlet of uniformly distributed flow impinging upon a susceptor. Under appropriate conditions (i.e. large susceptor radius as compared to inlet-to-susceptor distance, low Reynolds number, negligible buoyancy effects), the flow field resembles that predicted by the similarity solution for a stagnation flow in which radial gradients in concentration and temperature disappear. In practice, however, the inlet-to-susceptor distance and susceptor diameter are at least of the same order, and buoyancy effects are present except at very low pressures. In order to mitigate these effects, susceptor rotation has been widely applied to enhance uniformity and suppress buoyancy effects. Success at low pressure in suppressing buoyancy-induced flow has been great, as evidenced by the wide use of the stagnation flow geometry in research as well as in commercial reactors. Both upflow and downflow stagnation reactor configurations have been used and several variants of this reactor have been successfully implemented. However, rarely is the stagnation flow reactor used at elevated pressures since rotation alone cannot counteract buoyancy effects above 100 Torr or so. In a previous study [1], we explored the performance of a new impingement jet reactor geometry in which the inlet gases entered the reactor geometry through a narrow inlet and impinged on the substrate. Also, the height of the top boundary was lowered such that the natural convection is significantly weakened. The momentum of the inlet jet counteracted the natural convection flow, producing uniform and high growth rates of the deposit under the assumption of mass transfer limited deposition. The performance of the geometry was compared with the traditional stagnation flow geometry, and
23
it was observed that the proposed configuration overcomes the negative effects of atmospheric pressure operation, while also producing high growth rates. This study led us to investigate if the geometry can be further optimized by changing the various dimensions. The results of such a study are reported in this paper. Currently, the investigation has been only computational. The governing Navier–Stokes equations, along with the equations for energy and species transport are numerically solved using a finite volume procedure. The effects of variable density and buoyancy forces are fully taken into account. Several parameters are varied and their effects on the growth rate and deposit uniformity are studied. In addition, the precursor utilization efficiency is computed for each case to evaluate the extent to which the precursor is incorporated into the film as opposed to being exhausted from the reactor. The results of this study are useful to future experiments which can provide corroborative evidence of an optimized atmospheric CVD reactor geometry.
2. Previous work A significant amount of previous research on the stagnation flow CVD reactor geometry has appeared in the literature, though mostly at reduced pressure. Houtman et al. [2] and Coltrin et al. [3] performed some of the first detailed computations of CVD in stagnation flows. Evans and Grief [4,5] presented a detailed two-dimensional simulation of a stagnation flow reactor and showed that buoyancy-induced flows could be mitigated by substrate rotation and/or increased inlet velocity over a limited range of conditions. They suggested 3=2 that the key parameter was the ratio Gr=Rew ; where Rew is the rotational Reynolds number. 3=2 Values of Gr=Rew > 3 lead to strong buoyancyinduced secondary flows. It was seen that increasing the reactor inlet velocity can reduce the buoyancy effect and result in more uniform heat transfer. Compared to an adiabatic wall, the cooled isothermal wall boundary conditions allow a larger value of the Grashof number to be employed without recirculation. Wang et al. [6] investigated a vertical rotating-disk metal organic
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CVD (MOCVD) reactor operating at reduced pressure (0.2 atm) using both computations and experiments. They focused on eliminating buoyancy-induced effect and found, in agreement with Evans and Grief, that susceptor rotation is a critical parameter. Further work from the same group [7] involved a parametric study of the effects of reactor parameters on thin film uniformity. It was found that the secondary flows caused by buoyancy effects, reactor shape, forced convection, and substrate rotation can be eliminated by appropriate choice of operating pressure, gas flow and substrate rotation rate, albeit still in a vacuum environment. Fotiadis et al. [8, 9] established through computational studies that the effects of the geometry of the reactor on the deposit uniformity were significant in stagnation flow reactors. They suggest inverting the reactor, shortening distance between inlet and susceptor, introducing baffles, and reshaping reactor wall to mitigate buoyancy effects. Although they looked at several pressures, they were only able to predict uniform films for pressures much less than atmospheric. The study of Gadgil [10] reached similar conclusions in an experimental study that demonstrated through flow visualization that secondary flows were strongly influenced by the gas inlet configuration though no growth measurements were made. Other experimental work was performed by Kondo et al. [11] in a study that systematically varied several key reactor parameters to assess their effect on the low-pressure CVD environment. Dilawari and Szekely [12] presented numerical results for a modified stagnation point flow reactor. The major difference between their modified reactor and classical vertical stagnation reactor is that the reactor is inverted and the distance between the inlet showerhead and wafer was reduced to low values. They found that the inverted reactor is helpful in minimizing thermal natural convection and the inlet-wafer distance is critical in obtaining good spatial uniformity of deposition rate in their design. The inlet to wafer distance of 10 mm was seen to provide good spatial uniformity for a diameter of the reactor tube of 200 mm. They argue that the small inlet- to wafer distance reduces the ability of the carrier gases to
entrain fluid from the surroundings, thus preventing the formation of the secondary flows. Cho et al. [13] studied the optimization of inlet concentration profile of the reactant gas on the uniformity of the growth rate. Their results showed that the film uniformity could be significantly improved by enforcing an optimum inlet concentration distribution. However, they noted that controlling the inlet concentration is not easy. To make the optimization procedure more practical, Cho et al. [14] also devised a procedure to find the optimum inlet velocity profile. These calculations showed that a properly arranged inlet velocity profile can suppress buoyancy-driven recirculation, thus improving the growth rate uniformity. Pawlowski et al. [15] and Theodoropoulos et al. [16] also investigated the effect of inlet velocity configuration in the stagnation flow reactor at pressures up to 0.2 atm. They found that uniformity was sensitive to the inlet geometry used, as well as to inlet velocity and inlet-to-susceptor distance. Most previous simulations of stagnation flow CVD reactors invoke the axisymmetric assumption, though this assumption is not always valid, as shown in a series of papers by van Santen et al. [17–19]. Those works suggest that asymmetric flows do arise under conditions that are commonly used in CVD reactors, though sufficiently high inlet flow and rotation of the wafer guarantees a perfectly axisymmetric flow, and a decrease in distance between wafer and inlet can also suppress asymmetry. In a recent paper [1], we had demonstrated that uniform thin films can be grown under atmospheric conditions using a certain combination of geometric parameters of a stagnation flow-type reactor. This reactor, named an impinging jet reactor, carefully balanced the inlet jet momentum with the natural convection flow, to obtain a uniform mass transfer rate. However, this study did not explore the influence of the various parameters on the growth rate and its uniformity. Early computational work on a similar impinging jet configuration, where the inlet diameter is smaller than that of the susceptor, was performed by Snyder et al. [20] in a CdTe reactor, and they
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demonstrated that fairly uniform deposits were possible at 0.1 atm, though radial growth rate nonuniformities were typically several percent or more. Thus, there is an emerging consensus on viable techniques for suppression of buoyancy-induced secondary flows. However, most studies address reduced pressure reactors where such effects are reduced in the first place. Mitigation schemes used in low-pressure flows, such as increasing Rew to 3=2 maintain low values of Gr=Rew ; are not practical at elevated pressures since the required rotation rates would exceed practical values. Thus, attaining uniform deposition at atmospheric pressure will likely require careful simultaneous selection of many reactor parameters to attain highly uniform deposition. Our approach attempts to build upon these previous works to attempt to isolate a reactor configuration and set of conditions that lead to uniform deposition at atmospheric pressure, as well as to examine the effect of reactor parameters on deposit uniformity in the vicinity of such a solution. In addition, we examine the effect of reactor parameters on precursor utilization efficiency Zp, that is the fraction of the relevant precursor atoms or molecules that are incorporated into the film, which has received significantly less attention than growth rate or uniformity as a process characteristic. However, with the high expense of some metalorganic precursors, often exceeding several hundred dollars per gram, precursor costs can constitute a significant fraction of the process cost. Thus, optimizing Zp may result in substantial cost savings.
3. Governing equations and numerical procedure 3.1. Governing equations The velocities encountered in a typical CVD reactor are small. Hence, the flow can be treated essentially as incompressible. However, the density variations in the fluid are significant to the extent that the Boussinesq approximation cannot be considered to be accurate. Hence, the local density variations must be accounted for in the convective terms, in addition to the gravitational term. We
25
consider here the non-dimensional equations obtained by using the scales d (diameter of the reactor), V (inlet velocity), rref V 2 ; DTc ðTwafer Tinlet Þ; Yinlet ; and d/V for length, velocity, pressure, temperature, concentration, and time, respectively. The governing equations for mass, momentum, energy, and species concentration can be stated as [19]: @r þ = ðruÞ ¼ 0; ð1Þ @t @ru þ = ðruuÞ @t 1 ¼ =p þ =fm½=u þ ð=uÞT 23ð=uÞ I g Re " # Y 12 Gr þ 2 ex ; Re Y 12 Ga þ 1 Cp
@rY 1 þ Cp = ðruYÞ ¼ = ðk=YÞ; @t Re Pr
@rY 1 þ = ðruY Þ ¼ = ðrDAB =Y Þ; @t Re Sc
ð2Þ
ð3Þ ð4Þ
where u is the velocity vector, I is the unit tensor, ex is the unit vector with component only in the x direction (x positive direction points upwards), p is pressure, Y is the temperature, Y is the mass fraction of precursor gas, and t is the time. The superscript T on ru refers to the transpose of the tensor. All variables are non-dimensional. The material properties, density r, dynamic viscosity m, thermal conductivity k, heat capacity Cp, and the mass diffusivity DAB are made dimensionless with their value at the reference temperature Tref ¼ ðTwafer þ Tinlet Þ=2: The Dufour and Soret diffusion are assumed to be small for the particular gases considered here and hence neglected. The Reynolds (Re), Prandtl (Pr), Schmidt (Sc), Grashof (Gr), and Gay–Lusac (Ga) numbers appearing in the above equations are defined as Re ¼ rref Vd=mref ; Pr ¼ mref Cpref =kref ; Gr ¼
Sc ¼ mref =ðrref Dref Þ; 2 grref d 3 ðTwafer Tinlet Þ=ðm2ref Tref Þ;
ð5Þ
Ga ¼ ðTwafer Tinlet Þ=Tref ; where g is the acceleration due to gravity, Twafer and Tinlet represent dimensional temperatures at
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the wafer and at the inlet. Reference values denoted by the subscript ref are taken at reference temperature. Expansion effects caused by density changes with heating of the gas phase are modeled by ideal gas law. This gives the following dimensionless relation. 1 r ¼ Y 12 Ga þ 1 : ð6Þ The current study assumed axisymmetric flow because of the computational simplicity provided, and the large number of parametric computations that were planned. However, natural convection flows do become three-dimensional in some parameter ranges. There is currently no information on the parameter space in which the flow becomes three-dimensional, as the forced flow can make an originally three-dimensional flow to become axisymmetric (as in Refs. [17–19]). For the low heights considered here, the natural convection cells are swept away by the forced flow. When a steady axisymmetric solution is found, there is a high probability that the flow is indeed twodimensional. However, when a time-dependent solution was found, the flow may have also transitioned to be three-dimensional. To fully validate the axisymmetric assumptions threedimensional calculations are needed. These need to be performed in future for selected parameter combinations. The spatial terms in the governing equations are discretized using a second-order finite volume method on a non-staggered cylindrical polar grid. The time integration is performed using a predictor–corrector method similar to that used by Najm et al. [21] and Boersma [22]. 2.2. Boundary conditions At the top surface, the velocities and concentration values corresponding to the inflow gases are prescribed as Dirichlet conditions. At the wafer, the temperature is fixed at 900 K, and the nondimensional concentration is prescribed to be zero. The normal and radial velocities are also prescribed to be zero at the wafer surface with the tangential velocity prescribed by the rotation rate. At the outlet of the reactor, the normal derivatives of normal velocities and the scalar variables are
prescribed to be zero. Also, the outflow boundary is sufficiently far away from the wafer surface that its boundary conditions should not influence the deposition profiles on the wafer. The temperature at the outer wall is an important aspect for the operation of the reactor. It is necessary to select this in such a way that there is no deposit on the outer wall, but at the same time the buoyancy forces due to the cold outer walls are mitigated. In this study, we considered two different boundary conditions to understand the effect of outer wall thermal boundary condition on the flow inside the reactor. The first condition considered was an adiabatic outer wall. The second condition was an isothermal wall, implying some form of external cooling to maintain the walls at the temperature of the inlet gases. This second condition was used in most of the calculations reported in this paper. On the pedestal side wall, a linear temperature variation from the wafer surface temperature to the ambient of 300 K was prescribed. We believe that this condition will not affect the deposition patterns on the wafer; hence, other conditions appropriate to an industrial setting may also be considered. 2.3. Properties and deposition parameters The present simulations have been performed with argon and acetone as the carrier and precursor gases, respectively. The dynamic viscosity, specific heat, and conductivity of the carrier gas are obtained from database of National Institute of Standards and Technology (NIST) [23]. Binary diffusion coefficients are calculated from the Chapman-Enskog theory. For details, see Ref. [24]. For the present study, the rate of deposition is assumed to be limited by the rate of mass transfer, implying fast chemical kinetics. Thus, the growth rate is taken to be proportional to the gradient of the concentration normal to the wafer surface Growth ratepSh ¼ @Y =@xwafer : Here the growth rate is derived in a non-dimensional sense, as the inlet concentration is fixed at a nondimensional value of unity. The growth rate is given by the product of the local density, diffusion coefficient and the concentration gradient. In our
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study, the variations of density and diffusion coefficients are small because of the dilute concentrations of the precursor and uniform wafer temperature. When the deposition rate is limited by the kinetics of the reaction, it is necessary to include the specific kinetic mechanisms before actual film deposition rates are estimated. By appropriately specifying a value of the inlet concentration, a dimensional value can be then obtained. Hence the units for current growth rates are arbitrary. The non-uniformity and usage are defined as follows: Non-uniformity ¼
Z
% Sh Sh
2
% 2 Awafer dA=Sh
1=2 ;
Awafer
ð7Þ R % where Sh ¼ Awafer Sh dA=Awafer is the average growth rate and Awafer is the area of the wafer. R rDAB ð@Y =@xÞwafer dA A : ð8Þ Usage ¼ wafer R Ainlet rVYinlet dA 2.4. Computational domain and parameters The computational domain is shown in Fig. 1, and the important lengths are identified. All relevant lengths are scaled to the reactor diameter
27
d (13.5 cm). For our baseline configuration, the inlet entry length is 3d/8, the gap distance (between the exit plane of the entry length and the susceptor surface is d/8, and the susceptor diameter is 0.56d. The spatial distribution of the inlet gases in the baseline configuration is uniform. We systematically varied reactor dimensions and other reactor parameters while keeping the pressure fixed at 1 atm and the flow rate of the precursor and carrier gas fixed at 10 SLM. For each configuration, we examined three rotation rates: 0, 1007, and 1511 rpm which span the range of typical rotation rates seen in stagnation flow CVD reactors. A non-uniform cylindrical grid with finite volume cells only in the computational domain was used. The total number of cells in the domain was in excess of 18 000. The computations were performed on a high-end personal computer and typically required about one day of CPU time per calculation when the flow was steady. The gridindependency of the solution was checked by quadrupling the total number of cells. It was found that the maximum difference in local growth rate between the coarse and fine grids was less than 0.5%.
4. Results
3d/8
d/4
d/8
Inlet
Wafer
4.1. Baseline configuration
d/2
0.375 d
0.56 d Outlet d=13.5 cm
Fig. 1. Schematic of a modified impinging jet CVD reactor.
There are three geometrical parameters that describe the present configuration: (a) the height of the cover plate from the susceptor plate; (b) the diameter of the inlet jet; and (c) the diameter of the inlet jet of the species (which can be different from the jet of carrier gas). These dimensions are nondimensionalized with the diameter (d) of the reactor chamber. The baseline configuration corresponds to our previous work in which a series of calculations were made for a configuration with a jet diameter of (d/4) and height of d/8. The precursor and carrier gases both were supplied through the entire inlet diameter (d/4). The base line case was studied for three rotation rates of 0, 1007 and 1511 rpm. Figs. 2a and b show velocity vectors, contours of stream function, temperature and concentration
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Growth Rate Distribution
28
100.0
100.0
90.0
90.0
80.0
80.0
70.0
70.0
60.0
60.0
50.0
50.0
40.0
40.0 rpm Ω=0 Ω = 1007 rpm Ω = 1511 rpm
30.0 20.0 10.0 0.0
30.0 20.0 10.0
0.25 0.2 0.15 0.1 0.05 r
0
0.05 0.1 0.15 0.2 0.25 r
0.0
Fig. 3. Growth rates along the wafer for different substrate rotation rates for baseline configuration.
Fig. 2. Streamlines, concentration (left) and temperature (right) contours and velocity vectors for baseline configuration: (a) O = 0 rpm, (b) O = 1511 rpm.
for the zero rotation and 1511 rpm cases. Fig. 3 shows the corresponding growth rate distribution along the substrate. The growth rate is in arbitrary units, based on the gradient at the substrate and an inlet non-dimensional concentration of unity. The pressure in the reactor is atmospheric. It can be seen that in contrast with what is seen in conventional stagnation flow reactors, there are no vortices due to natural convection. A vortex is formed at the edge of the substrate due to the flow turning and rotation of the substrate. We have
assumed that deposition occurs over the complete substrate. It can be seen that the deposition is nonuniform at zero rotation rate with dips and peaks. However, when rotation is included, deposition becomes uniform except at the edges where a local peak is observed. This region can be neglected for practical CVD depositions because the substrate typically does not extend to the susceptor edge. The growth rate increases with rotation because of the viscous pumping caused by the rotational forces and the resulting thinning of the boundary layer. The growth rate at 1511 rpm is nearly twice that of the rate at zero rotation. In addition, precursor utilization efficiency also increases with rotation rate, beginning at around 10% for zero rotation, and nearly doubling to 19% at 1511 rpm. This baseline configuration represents our initial guess of a reactor configuration that showed enhanced uniformity at atmospheric pressure, based on the work of others and on our initial simulations. This configuration actually performs fairly well in these simulations, and the 1511 rpm case would likely meet some of the more stringent uniformity requirements for a substrate that was up to 75% the diameter of the substrate. However, other combinations of the parameters may give results superior to these results, and are next explored.
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4.2. Effect of the inlet diameter
29 Ω =0 rpm Ω = 1 007 rpm Ω = 1 511 rpm
100.0
Growth Rate Distribution
90.0
Our attempts to investigate how reactor parameters affect uniformity first focused on the diameter of the gas inlet. Fig. 4 shows the flow pattern for the case in which the inlet diameter is increased to 66% of the susceptor diameter, and the growth rate distribution is shown in Fig. 5. The zero rotation case converges to a periodic solution, and the time-averaged growth rate, shown in Fig. 5, has a non-uniformity of 32.08%. However, with rotation, the uniformity is improved slightly over the baseline case, with only a very slight reduction in efficiency. The dip in the center is reduced over the baseline case. Fig. 6 shows the case where the inlet diameter has been further increased all the way to the to the susceptor diameter. The growth rates and profiles are shown in Fig. 7. Under these conditions, neither the zero rotation nor the 1511 rpm case converges to a steady-state solution. Only the 1007 rpm case has a steady solution, and uniformity continues to improve over the narrower inlet lengths. Thus, while widening the inlet does appear to improve uniformity with small efficiency penalties, the range of parameter space over which stable solutions is observed is greatly reduced. Since we integrated the time-dependent governing equations, we are able to capture periodic time-dependent solutions. However, the
100.0 90.0
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10.0
10.0
0.0
0.25 0.2 0.15 0.1 0.05 r
0
0.05 0.1 0.15 0.2 0.25 r
0.0
Fig. 5. Growth rates along the wafer for different substrate rotation rates for inlet diameter of 0.66 of susceptor.
Fig. 6. Streamlines, concentration (left) and temperature (right) contours and velocity vectors for inlet diameter equal to susceptor diameter at 1007 rpm.
Fig. 4. Streamlines, concentration (left) and temperature (right) contours and velocity vectors for inlet diameter of 0.66 of susceptor at 1007 rpm.
flow may be even three-dimensional [17–19], which our current method is unable to capture. Since we are not interested in such time-dependent solutions, further study of such cases is not considered. For these unsteady solutions, the instantaneous flow fields are observed to be very complex, with multiple vortices located on the susceptor. These vortices are certainly not conducive to obtaining uniform deposition rates, even in the limit of large amounts of ensemble averaging of the flow fields. The present configurations may also be compared with the traditionally known design of a
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Growth Rate Distribution
30 100.0
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90.0
90.0
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50.0 Ω =1007 rpm
40.0 30.0
40.0 30.0
20.0
20.0
10.0
10.0 0.0
0.0 0.25 0.2 0.15 0.1 0.05 r
0
0.05 0.1 0.15 0.2 0.25 r
Fig. 7. Growth rate along the wafer for the case where the inlet diameter is equal to the susceptor diameter.
shows similar growth rate and efficiency to the case with an entry length of 3d/8 and inlet diameter of 0.375d (Fig. 7). 4.3. Effect of inlet velocity profile We next considered two cases of varying the inlet conditions. In the first case, the inlet velocity profile was prescribed to be parabolic, corresponding to a fully developed laminar flow. This condition may represent a very long inlet pipe. The second case corresponded to the precursor being supplied only over a portion of the inlet duct. The advantage of this may be a higher utilization efficiency of the precursor, albeit at a lower growth rate. Fig. 9 shows the results for the case in which we applied a parabolic velocity profile at the inlet. This distribution enhances the transport of precursor to the surface near the center of the susceptor, and reduces the transport further out. As a result, uniformity is greatly reduced, though efficiency slightly increases since the bulk of the deposit occurs at the center, and less precursor gas is lost as it bypasses the substrate. A similar result is shown in Fig. 10 where the inlet velocity profile is uniform, but precursor is only present in the standard concentration in the center half of the inlet while the outer annulus has only the carrier gas. Under these
pancake reactor. A pancake reactor has a short height, similar to our standard reactor configuration, with the inlet gas flow over the entire susceptor. We have computed three cases with the inlet diameter of the gases equal to 0.375d. Fig. 8 shows the velocity vectors and temperature and concentration contours for the pancake type arrangement. It can be seen that the first case of zero rotation and the case of 1511 rpm rotation have no steady solutions. Only the 1007 rpm case has a solution, which is fairly uniform across the susceptor except at the edges. The 1007 rpm case
Growth Rate Distribution
Fig. 8. Streamlines, concentration (left) and temperature (right) contours and velocity vectors for pancake reactor configuration at 1007 rpm.
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30.0 20.0 10.0
0.0
0.0 0.25 0.2 0.15 0.1 0.05 r
0
0.05 0.1 0.15 0.2 0.25 r
Fig. 9. Growth rates along the wafer for different substrate rotation rates for a parabolic inlet flow in the baseline reactor configuration.
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S.P. Vanka et al. / Journal of Crystal Growth 267 (2004) 22–34 100.0
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31
20.0 10.0 0.0
0.25 0.2 0.15 0.1 0.05 r
0
0.05 0.1 0.15 0.2 0.25 r
Fig. 10. Growth rates along the wafer for different substrate rotation rates for inlet diameter of precursor gases = d/8.
conditions, the non-uniform distribution of precursor does lead to non-uniform deposition, with a higher growth rate at the center as compared to the edge. However, efficiency increases greatly, exceeding 50% for the highest rotation rate case.
4.4. Effect of the chamber height The distance between the susceptor and the upper wall is a sensitive parameter that determines the natural convection parameter and thereby affects growth. We have considered two variations to this height. For a gap distance twice that of the baseline case, no steady solutions are observed for any rotation rate. Secondary flows are seen to be extremely strong, and it is likely that any deposit observed under these conditions would be nonuniform. For a reduced gap, uniformity also suffers, but not to the same extent. Fig. 11a and b show the results of a case with a gap distance half the baseline case. The uniformity of the deposit, as shown in Fig. 12, is reduced for all rotation rates. Based on these results, it can be concluded that either too small or too large gap distances can lead to uniformity problems in stagnation flow reactors. Table 1 summarizes the parameters for the various cases, and the observed non-uniformity parameters.
Fig. 11. Streamlines, concentration (left) and temperature (right) contours and velocity vectors for gap height of d/16: (a) O ¼ 0 rpm; (b) O ¼ 1511 rpm:
5. Discussion The results of the baseline case suggest that a high degree of uniformity for CVD deposits at atmospheric pressure can be obtained. However, uniform deposits occur under a much narrower range of conditions at atmospheric pressure than at low pressure. For a given total flow rate (e.g. 10 SLM in this study) and given susceptor diameter, there is evidence that suggests that there are an optimal inlet diameter and gap distance that
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32 100.0
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10.0 0.0
30.0
0.25 0.2 0.15 0.1 0.05 r
0
0.05 0.1 0.15 0.2 0.25 r
0.0
Fig. 12. Growth rates along the wafer for different substrate rotation rates for gap height of d/16.
provide uniform deposition. Our smallest inlet diameter (d/4) produces good uniformity at high rotation rates. Increasing the inlet diameter results in increased uniformity and efficiency but steady solutions do not occur for all rotation rates. The confinement of the flow in the narrower channels results in higher mean velocities, and these appear to convect the buoyant recirculation regions downstream to regions in which there is no effect on the deposition. Increasing the inlet diameter results in a flow that is more nearly that of the ideal stagnation flow solution, and thus uniformity is expected to be higher. However, the bulk flow in the channel does not have sufficient momentum to carry the buoyancy-induced recirculation far enough away from the growth surface, and thus these secondary flows can destabilize the inlet flow field, preventing steady -state from being achieved. Similarly, there appears to be an optimal gap distance. The lack of steady solutions at large gap distances is not surprising in light of the lower bulk velocity of the gas around the substrate. As gap distance is decreased, the flow behaves more like the similarity solution, and the radial velocity increases due to the smaller area. As a result, the flow field is more uniform and secondary flows are effectively swept downstream. However, too small a gap also appears to hurt uniformity. From the velocity profiles, a likely reason for this is that the axial inlet flow develops a radial component at the
exit of the entry length over a finite spatial region. In inviscid potential flow, the inlet flow can turn the corner without such a standoff, and so the smaller the gap distance, the closer the flow approaches the ideal stagnation solution. For real flows, too small a gap distance can result in the boundary layer below the inlet sidewall being squeezed, resulting in an enhanced growth rate at these locations, as observed in the simulations. For cases in which the precursor is evenly distributed along the inlet, precursor utilization efficiency increases linearly with growth rate, since the enhanced growth rates at a fixed mass flow rate of precursor necessarily result in higher efficiency. However, efficiencies are fairly low, typically less than 20%, with the remaining 80% bypassing the substrate and proceeding out the exhaust. Separation and recycling can potentially recover some of this, but only with added cost. An interesting exception is the case where the inlet gases only have the regular precursor concentration in the central portion of the inlet. In this case, the outer annulus of diluent appears to act as a shroud, directing the precursor-laden gases into the substrate. Though uniformity is poor, Zp is significantly enhanced, approaching 50% at the high rotation rate. In cases in which Zp is critical and uniformity is still desired, some variant of these conditions, perhaps with a tailored inlet velocity profile or variable slope on walls, may lead to high Zp with acceptable uniformity. While this study addresses the basic parameters associated with a stagnation flow reactor, there are certainly many other variations that are possible for further fine tuning. These include varying the reactor diameter to susceptor diameter ratio (though Evans and Grief [4] found this to have minimal effect on the flow), tapering or contouring the upper reactor wall, making more extensive variation of the inlet velocity profile, adding multiple inlets that may include purge gas flows, varying the wall temperature boundary conditions, etc. Our study demonstrates, however, that such variations may not be necessary since the appropriate choice of simple reactor parameters can lead to highly uniform films at atmospheric pressure.
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Table 1 Growth rates and non-uniformity for the impinging jet CVD reactor at 1 atm and 10 SLM Gr=Re2in
Rotation speed of wafer (rpm)
130.8 130.8 130.8
1.191 1.191 1.191
0 1007 1511
dwafer
87.2 87.2 87.2
2.68 2.68 2.68
dsubstrate
58.4 58.4 58.4
Pancake reactor dwafer
Inlet diameter
d/4 baseline case
Partial opening for precursor gases (d/8)
Parabolic distribution of inlet velocities
Lower chamber height (d/16)
3=2
Gr=Rew
Average growth rate
0 40 000 60 000
— 0.00255 0.00139
44.73 73.87 87.67
4.91 1.21 0.67
9.85 15.99 18.93
0 1007 1511
0 40 000 60 000
— 0.00255 0.00139
--69.90 85.22
--0.64 0.36
--14.76 17.95
5.98 5.98 5.98
0 1007 1511
0 40 000 60 000
— 0.00255 0.00139
--69.36 ---
--0.48 ---
--14.56 ---
87.2
2.68
0
0
—
---
---
---
87.2 87.2
2.68 2.68
1007 1511
40 000 60 000
70.26 ---
0.24 ---
14.83 ---
130.8
1.191
0
0
37.95
12.53
30.96
130.8 130.8
1.191 1.191
1007 1511
40 000 60 000
57.83 65.79
18.64 22.32
46.73 53.05
130.8
1.191
0
0
53.65
16.31
11.76
130.8 130.8
1.191 1.191
1007 1511
40 000 60 000
77.44 90.33
4.69 2.93
16.74 19.49
130.8
0.149
0
0
52.26
9.29
11.30
130.8 130.8
0.149 0.149
1007 1511
40 000 60 000
75.85 89.11
2.07 1.16
16.15 18.94
Inlet Reynolds number (Rein)
Rotation Reynolds number (Rew)
0.00255 0.00139 —
0.00255 0.00139 —
0.00255 0.00139 — 0.00032 0.00017
RMS nonuniformity (%)
Precursor efficiency (%)
Note: - - - means that flow is unsteady. The Grashof number is based on the chamber height. The rotation Reynolds number is based on reactor diameter.
6. Conclusions Several conclusions can be reached as a result of this work: (1) For an atmospheric pressure, mass-transfer limited, stagnation flow reactor operating at reasonable flow rates (0.5 SLM/cm2) in a standard reactor configuration, film unifor-
mity at the sub-percent level can be achieved at moderate rotation rates with careful choice of reactor parameters. (2) Rotation is necessary to achieve sub-percent level uniformity in such a reactor design, though rotation rates of 1000–1500 rpm are sufficient. While this is on the high end of current reactor designs, it is by no means impractical.
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(3) In the vicinity of our baseline reactor configuration, the ratio of inlet diameter to susceptor diameter has a significant effect on film uniformity with larger ratios leading to more uniform films in general. However, larger ratios do not support steady solutions for all rotation rates. (4) There appears to also be an optimal gap distance associated with a balance between generating enough radial momentum to convect secondary flows downstream and maintaining enough gap distance for the flow to turn the corner without excessively compressing the boundary layer. (5) Precursor utilization efficiency can be dramatically improved by the use of an inert gas shroud, though our study shows a decrease in uniformity for the one configuration we investigated. There are other possible options within the parameter space of potential configurations that can exploit this enhanced efficiency without a dramatic penalty in uniformity.
Acknowledgements This work was supported in part by the National Science Foundation Division of Manufacturing and Industrial Innovation under Contract DMI-00-99748.
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