Dissolution Kinetics for Atomic, Molecular, and

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wafer surface which includes first-order kinetics for the dissolution ..... probably not independent, since both species are involved in com-. D. C x k e kke e.
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Journal of The Electrochemical Society, 146 (9) 3522-3526 (1999) S0013-4651(99)02-050-9 CCC: $7.00 © The Electrochemical Society, Inc.

Dissolution Kinetics for Atomic, Molecular, and Ionic Contamination from Silicon Wafers during Aqueous Processing Ian Ivar Suni,a,* Glenn W. Gale,b,c,* and Ahmed A. Busnainab,* aDepartment of Chemical Engineering, and bMicrocontamination Research Laboratory, Clarkson University, Potsdam, New York 13699-5705 USA

Experimental measurements have been made by total reflection X-ray fluorescence spectroscopy of dissolution of K and Cl from p-type silicon wafers by deionized water. The dissolution rate of these ions is initially rapid, then slows dramatically and the surface coverage appears to reach equilibrium at approximately 6 3 1012 and 2 3 1012 atom/cm2 for K and Cl, respectively. These results and others have been fit to a general model for contaminant removal during aqueous processing of silicon wafers. For a twodimensional wafer cleaning geometry, the convective diffusion equation is solved, including the effects of first-order contaminant deposition and dissolution, which enter as a surface boundary flux condition. Results are presented of simulations for diffusion only, for convection of continuously renewed process solution, and for convection of recirculated, contaminated process solution. The results demonstrate the importance of convection in transporting contaminants away from the wafer surface, thus preventing redeposition. These calculations predict that contaminant removal can vary by an order of magnitude across the wafer surface due to high solution-phase contaminant concentrations in the downstream direction. These results are supported by recent studies which report a dependence of contaminant dissolution rate on the cleanliness of the bulk process solution. © 1999 The Electrochemical Society. S0013-4651(99)02-050-9. All rights reserved. Manuscript received February 11, 1999.

Currently one of the leading sources of yield loss in the microelectronics industry is some form of surface contamination. Such contamination may arise ex situ in the cleanroom environment, may be generated in situ by processes such as chemical vapor deposition and chemical mechanical polishing, or may exist on the wafer as received. Although most research efforts have focused on particle contamination, various types of atomic, molecular, and ionic contamination can also be problematic. For example, the metal contamination tolerance level for 16 MB dynamic random access memory (DRAM) devices has been widely quoted as 1010 metal atom/cm2. 1-3 Metal surface contamination, particularly deposition from aqueous HF, has been thoroughly investigated.4-17 In addition, ionic surface contamination by active metals and by anions such as Cl2 may produce charged species which are mobile in an electric field or at elevated temperatures, causing unpredictable operation, device drift, and other instabilities.18-20 Organic surface contamination, which may prevent effective removal of metal and ionic contamination,18 may arise from cleanroom air or from vapors emitted by plastic storage containers.21-24 Atomic and molecular contaminants are commonly removed during initial wafer preparation by aqueous solutions, including H2SO4/H2O2, HF, NH4OH/H2O2 (SC-1), and HCl/H2O2 (SC-2). Additional aqueous cleaning processes may be employed for specific manufacturing steps such as Si epitaxy, photoresist removal, and chemical mechanical polishing. Despite the broad interest in replacing aqueous with dry wafer processing methods,25-27 dry methods still suffer from a variety of shortcomings. Perhaps the most serious difficulty to date is the inability to effectively remove particle contaminants. The future of wafer processing is unclear, but the continued utility of aqueous processing seems certain, with dry methods likely to supplement, rather than supplant, aqueous processing.28 While the various chemistries of aqueous processing have been extensively researched, the transport of contaminants has been largely neglected as an area of study.29 Tonti has presented a simple model for cleaning, from which he concludes that contaminated process solution is typically transferred with the boundary layer during emersion and rinsing.30 Christenson has presented a simple model for contaminant transport and compared different process geometries, demonstrating that a centrifugal geometry may be advantageous if performed as a series of batch processes.31 However, neither of these models includes convective transport. Here, contam* Electrochemical Society Active Member. c Present address: IBM Microelectronics, Essex Junction, Vermont 05452, USA.

inant removal during aqueous processing is modeled by solution of the convective diffusion equation with a boundary condition at the wafer surface which includes first-order kinetics for the dissolution and deposition reactions. Experimental Ionic salt contamination experiments were performed in a class 10 cleanroom at Clarkson University. 125 mm p-type Si(100) wafers were immersed for 3 s in saturated KCl solution and then dried in a spin dryer. The dryer was thoroughly cleaned at this point to remove excess salt residue. Contaminated wafers were placed in a cassette and immersed in a room temperature filtered, deionized water bath for a prescribed time. A stainless steel tank without convection was employed, and the bath temperature was set to 258C. At various times the wafers were removed, dried again in the spin dryer, placed in a storage box, and sealed in a plastic bag. The wafers were analyzed at IBM by total X-ray fluorescence spectroscopy (TXRF), which has a detection limit near 1011 atom/cm2 for K and Cl. Between experiments, the apparatus were thoroughly cleaned with deionized water in order to prevent cross contamination. Mathematical Model The mathematical model discussed here has been briefly described.32 Mass transfer in a wafer cleaning tank is modeled considering only the region between two adjacent wafers, as shown in Fig. 1. Flow upward between parallel plates is assumed, with the wafers taken to be infinite in the third dimension. For laminar flow the z velocity nz is  x2  n z 5 u0  1 2 2  d  

[1]

where u0 is the maximum velocity and d the wafer spacing. Typically u0 is 1.5 cm/s and d 0.5 cm. The transition region at the inlet near the bottom of the wafer in which the parabolic velocity profile develops has been neglected, since calculations show that this region develops in approximately the first centimeter out of a 20 cm diam wafer.33 Near the wafer edges, this transition region will likely be significant, since the interaction length across this chord will be considerably less than 20 cm. The convective diffusion equation can be written ∂C 1 u0 ∂t

  ∂2C x 2  ∂C ∂2C  1 2 2  ∂z 5 D  2 1 2  d  ∂z    ∂x

[2]

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Here a was taken as e3-1. Applying transformation 9 to the dimensionless convective diffusion Eq. 7 yields  ∂2C ∂C ∂C ∂C  ∂2C 1 f1 ( X ) 5 f2 ( X )  2 1 1a  ∂T ∂Z ∂X  ∂Z 2  ∂X

[10]

where  1 2 e ln(11a )2X  f1 ( X ) 5 1 2 1 1  a  

2

[11]

and f2 ( X ) 5 a 2 e 2 X

Figure 1. Two-dimensional geometry employed for convection-diffusionreaction model.

One can define dimensionless groups, including the Peclet number (Pe), according to X5

x d

[3]

T5

Dt d2

[4]

Pe 5

du0 D

[5]

Z5

z dPe

[6]

where t is the time and D the diffusivity. Now the convective diffusion equation can be written in dimensionless form ∂C ∂C ∂2C ∂2C 1 (1 2 X 2 ) 5 1a 2 ∂T ∂Z ∂X ∂Z 2

[7]

2

[8]

In order to increase the permissible step size during finite difference solution, a variable grid spacing is employed using the following transformation34,35 3 2 X 5 ln[1 1 a(1 2 X )]

[9]

[12]

Using the alternating direction implicit (ADI) method, where half-steps are taken alternately in the x and z directions, the convective diffusion Eq. 10 can be solved by a finite difference approach.36,37 The Peclet number as defined above is of the order 105, so backward difference has been employed for the convective term. Without taking boundary conditions into account, the resulting finite difference equations are of the implicit Crank-Nicholson type, yielding a readily solvable tridiagonal system. At the plane of symmetry at x 5 0 in Fig. 1, the flux in the x direction must be zero. The boundary flux at the wafer surface at x 5 d is determined by the relative rates of surface dissolution and deposition determined from standard electrochemical kinetics. Since almost all neutrals metals dissolve into an ionic species involving only one metal atom, the reaction order for dissolution might be expected to be one. The dissolution of Cu, Au, and other metals from Si into aqueous solutions appears to commonly follow first-order kinetics, as shown by linear semilogarithmic plots of surface coverage as a function of time.18,38 It should be noted that in some cases, such as Cr dissolution into acidic solutions,39 association of metal species as in Cr2O722 might suggest a second-order dissolution. Of course, complex multistep dissolution processes might yield dissolution kinetcs with lower reaction orders. First-order deposition kinetics have been assumed in the current model. The boundary conditions in the z direction have been handled in two different ways. In one case, the grid has been extended to quite large positive and negative dimensions and the boundary values fixed at zero. This is equivalent to modeling a cleaning process in which the process solution is constantly renewed so that uncontaminated solution enters the bottom of the cleaning tank continuously. Alternatively, periodic boundary conditions have also been employed so that recycling of contaminated process solutions is realistically modeled. This is more representative of typical process conditions. For this case the size of the system in the z direction was chosen so that the average fluid element is recirculated every 120 s. The fundamental kinetic processes which occur during dissolution and redeposition of ionic salts and organic species from silicon wafers are as yet unclear. However, the present assumptions of firstorder dissolution and deposition processes seem reasonable and are consistent with available measurements. For first-order dissolution and first-order deposition, the standard rate equation for the change in surface concentration of contaminant C (GC) is ∂G 5 2 k1GC 1 k2 Cn ∂t

where C is the concentration and  D  1 a5  5  du0  Pe 2

2 2 ln(11a )

[13]

where Cn is the concentration of contaminant in solution just above the wafer surface. One might expect that the second term in Eq. 13 should contain the factor 1-u to account for site occupancy as for Langmuir kinetics. This has not been included because the contaminant layer will not generally be a smooth film one atomic layer thick. For example, metals which deposit onto Si surfaces from process solutions typically form three-dimensional nanostructures.4-7,40-42 Regardless, for the contaminant species discussed here, the average surface coverage drops well below one atomic layer quite rapidly.

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Journal of The Electrochemical Society, 146 (9) 3522-3526 (1999) S0013-4651(99)02-050-9 CCC: $7.00 © The Electrochemical Society, Inc.

Equation 13 can be integrated and set equal to the surface flux to yield the flux boundary condition  ∂C  2k t 0 2k t D  5 k1GC e 1 1 k1k2 e 1  ∂x  n

t

∫e

k1t ′

0

Cn d ′t 2 k2 Cn [14]

where GC0 is the initial surface concentration of contaminant. A Taylor series expansion at the boundary is employed to approximate the derivative in Eq. 14 and the derivative at the plane of symmetry.43 The Taylor series expansions for the derivatives in the x direction alter the linear matrix to be diagonalized from a tridiagonal to a band diagonal system. Efficient numerical algorithms are available for band diagonal systems.44 An iterative solution can be obtained by assuming a value for Cn in Eq. 14, solving the set of linear equations, and using the solution for Cn as a new estimate. The main innovation of the current study is the fundamental approach to incorporating the surface kinetic processes which occur during contaminant removal into an otherwise relatively straightforward problem in mass transfer. This gives rise to a nonlinear boundary flux condition. For simplicity, the effective diffusivity was taken as 1025 cm2/s in all of the simulations reported here. The values of k2 which are obtained depend strongly on the value chosen for the effective diffusivity, which has not been measured for most combinations of contaminants and process solutions. Ongoing research includes development of a complete solution of the governing momentum and mass transport conservation equations and coupled convective diffusion equation for a realistic three-dimensional wafer tank geometry, including a surface boundary condition which accounts for dissolution and redeposition. A similar finite-difference approach is taken for the three-dimensional problem, solving the mass, momentum, energy, and chemical species conservation equations in the conservative form. Second-order skew-upwind differencing and a flux-corrected transport algorithm will be employed to mitigate numerical diffusion and eliminate numerical dispersion.45-47 Results and Discussion The experimental results for removal of K and Cl from silicon wafers are shown in Fig. 2 and 3 along with the best fit obtained from the above mathematical model. Since the experiments were performed without convection, u0 was set to an extremely low value. The surface contamination level of these ions initially drops quite rapidly with time, then plateaus, and appears to reach equilibrium. This is similar to the behavior seen for removal of relatively noble metals such as Cu, Au, and Cr by a variety of aqueous solutions.18 The best fit constants for K removal are k1 5 0.12 s21 and k2 5 7.0 3 1025 cm/s, while the best fit constants for Cl removal are k1 5 0.085 s21 and k2 5 1.6 3 1025 cm/s. These sets of rate constants are probably not independent, since both species are involved in com-

Figure 2. Experimental results and best fit model for K removal in room temperature deionized water.

Figure 3. Experimental results and best fit model for Cl removal in room temperature deionized water.

plex equilibria involving charged species in solution, charged species adsorbed on the surface, and electronic surface states. In order to illustrate the generality of the proposed model, Fig. 4 shows experimental results for Cr removal from Si by aqueous H2O2 at 958C 18 along with the best numerical fit, which yields k1 5 2.0 3 1022 s21 and k2 5 3.6 3 1024 cm/s, omitting convection. It should be noted that the precise cleaning geometry is not indicated in Ref. 18, so the numerical fit given here is approximate. Figure 4 also shows for comparison two simulations, with and without recirculation of the process solution, which include convection with u0 5 1.5 cm/s. One can see that complete removal of Cr is only possible due to the convective mass transfer of contaminants away from the silicon wafers. In addition, Fig. 4 demonstrates that contaminant removal is greatly facilitated if the process solution is continuously cleaned so that uncontaminated solution always enters the bottom of the wafer cleaning tank. This conclusion is supported by recent results at Sony Corporation for Cu and Fe removal in SC-1 process solutions, where metal removal was slowed significantly by the presence of the same metal ions in solution.48 Dissolution kinetics have in general not been as thoroughly studied as deposition kinetics in electrochemical systems. However, electrochemical dissolution studies of Cu-Ni alloys demonstrate that both surface electron transfer and bulk diffusion

Figure 4. Data from Ref. 18 for Cr removal in aqueous H2O2 at 958C along with model predictions. The solid line represents the fit for diffusion only, the dashed line represents results for convection without recirculation, and the dotted line illustrates results for convection with recirculation.

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can be rate-limiting in different experimental regimes.49 The results shown in Fig. 4 are consistent with this expectation. When convection is included in the numerical simulations of contaminant dissolution and transport, a potentially important effect arises in overflow tanks due to the reversibility of the dissolution reactions and the convective transport of dissolved contaminants downstream. After dissolution begins, the amount of dissolved contaminant in the solution phase remains low in the upstream direction, while increasing rapidly in the downstream direction. Thus, the high solution-phase contaminant concentrations at the wafer/solution interface in the downstream direction slow the rate of removal. In other words, high levels of dissolved contaminant affect the local quasi equilibrium at the wafer surface. These effects are illustrated in Fig. 5, which shows the average contamination level as a function of position on the wafer surface after 600 s of Cr removal with k1 5 2.0 3 1022 s21, k2 5 3.6 3 1024 cm/s, and u0 5 1.5 cm/s. This simulation has been performed with contaminated process solution continuously recirculated through the wafer cleaning tank. These results predict differences of an order of magnitude in removal effectiveness across the wafer surface. Simulation results demonstrate that such effects will only be observable for cases in which the removal efficiency is extremely low. Thus, these effects are more likely observable in the highly dilute aqueous process solutions that are currently under development. Figure 6 shows the solution-phase concentration at the wafer/solution interface for the same simulation after 600 s. Clearly the interfacial concentration of Cr ions differs by more than an order of magnitude across the wafer surface. The only potentially restrictive electrochemical assumptions made here are simple first-order dissolution and deposition kinetics. Thus, Eq. 13 implicitly assumes that the rate constants for both dissolution and redeposition are independent of the degree of surface contamination. For the case of contamination in the form of metal clusters, one might expect the electrochemical properties of the clusters to depend on cluster size. For this reason, the surface reaction model given above must be considered somewhat phenomenological. However, even for the case of metal clusters, first-order dissolution and deposition reactions seem probable, although the associated rate constants will likely vary somewhat with cluster size during dissolution. Another complication that has not been included in the present model is the effect of bubbles, which may form in aqueous process solutions at elevated temperatures. The effect of bubbles, which can be generated at the surface50-53 or introduced externally,54 on mass transfer in electrochemical systems has been well documented.

Figure 6. Variation along wafer surface of solution-phase interfacial concentration of Cr ion after 600 s of cleaning in aqueous H2O2 at 958.

Conclusions Removal of K and Cl from silicon wafers by room temperature deionized water has been measured by total reflection X-ray fluorescence spectroscopy as a function of time. Contaminant removal is initially rapid but eventually slows down, appearing to reach equilibrium at approximately 6 3 1012 and 2 3 1012 atom/cm2 for K and Cl, respectively. These results and others have been fit to a simple kinetic model for contaminant removal during aqueous processing of silicon wafers which allows for first-order dissolution and first-order deposition of contaminants. In order to model all the physical processes occurring during contaminant dissolution and transport, these surface kinetic relationships are incorporated as a boundary condition into solution by finite difference methods of the convective diffusion equation. The results show the importance of convective transport, which improves removal rates by reducing the solution phase concentration of contaminant just above the wafer surface, thus slowing redeposition. Contamination gradients on the wafer surface of an order of magnitude are predicted to arise from the interaction of convection, diffusion, and surface reaction in highly dilute process solutions. Acknowledgments This research has been funded by NSF grant ECS-9634058. Thanks to Shankar Subramanian for helpful discussions. Clarkson University assisted in meeting the publication costs of this article.

References

Figure 5. Variation along wafer surface of Cr surface contamination after 600 s of cleaning in aqueous H2O2 at 958C.

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