An Optical Method for Monitoring Metal Contamination during Aqueous Processing of Silicon Wafers Dinesh Chopra and Ian Ivar Suni* Department of Chemical Engineeering, Clarkson University, Potsdam, New York 13699-5 705, USA ABSTRACT

An optical technique based on simple absorption spectroscopy has been demonstrated for monitoring metal contaminant deposition from aqueous processing solutions widely employed during microelectronics fabrication. Cu deposition from 0.15 and 0.25% HF solutions contaminated with 3.5 ppm Cu has been observed as a decrease in the absorption of a HeNe laser reflected at glancing incidence from a Si wafer. This is caused by the depletion of Cu2 from the mass-transfer boundary layer, providing direct evidence that Cu deposition is rate-limited by diffusion. This technique allows determination of which metallic species can deposit onto Si wafers in diffusion-limited processes during various aqueous processing steps in microelectronics manufacture. In addition, Cu deposition is seen to coincide with the completion of Si07 dissolution, confirming that Cu2 is reduced by an electroless process involving simultaneous Si oxidation. The decrease in absorption is consistent with a mass-transfer boundary layer thickness of about 335(20) lim. The optical absorption returns to its original value about 2 mm after the onset of deposition, consistent with diffusion-limited deposition of one monolayer of Cu, which is followed by a transition to a slowe surface rate-limited process. Aqueous processing of semiconductors has been widely employed for removing residual metals, organics, and particles from the silicon substrates on which microelectronic devices are fabricated. A typical cleaning sequence may include a HF etch, immersion in SC-i and SC-2 cleaning solutions, and deionized water rinses. The purpose of the HF etch is to remove the native oxide (5i03), which often

has significant contamination arising from cutting and

polishing as well as transport and storage. Various formulations exist for the SC-i (H30-H707-NH,) and SC-2 (H,OH30,-HC1) solutions, with recent trends suggesting that more dilute solutions will be employed in the future.' The oxidizing action of H202 decomposes organics and other species, while the strongly complexing Cl- solvates metal contaminants.2 However, the degree of surface metal contamination depends strongly on the effectiveness of wet cleaning and the purity of the reagents employed. Since

the direction of equilibrium can lie in either direction, each of these aqueous solutions may either deposit or dissolve a trace metal contaminant. Thus Fe can deposit from

surface contamination. Metal contaminants are usually detected by total reflection X-ray fluorescence spectroscopy (TXRF), which has a sensitivity limit of about 10" atom/cm2. 17,28 However, TXRF must be employed ex situ, sometimes leading to sample contamination by repeated exposure to the TXRF apparatus." Recently, surface photovoltage has also been proposed for the detection of surface metal contamination.2' This technique is capable of detecting metallic contamination in the Si07 insu-

lating layer, but may not detect contamination at the Si/5i03 interface. This report describes a new method to indirectly monitor metal deposition by measuring the concentration depletion of metal ions in the mass-transfer

boundary layer during diffusion-limited deposition. Absorption spectroscopy of the mass-transfer boundary

layer has been performed previously by several groups.71-2'

Experimental

A schematic diagram of the experimental setup is shown in Fig. 1. The Melles-Griot model 05-STP-901 HeNe laser,

SC-i and Al from SC-2 solutions,4 with deposition of noble metals such as Cu from HF-based etch solutions a

intensity stabilized to 0.1%, is reflected from the silicon

particularly common problem.56 Metal contamination during aqueous processing has recently been the object of intense research,3-" since metal surface contamination can decrease yield in semiconductor

layer. The laser mirror, which rejects 99.9% of the HeNe laser, limits the photon flux reaching the detector while minimizing the possibility of thermal lensing. The achromatic lens expands the laser beam by approximately 15 times in order to use the entire detector, a Princeton Instruments model RY-1024 photodiode array (PDA) with

manufacturing by causing a variety of electrical prob-

lems.3'678 A striking example of the sensitivity to metal contamination is the limit of 1010 metal atom/cm2 that has been widely quoted as the tolerance level for 16 megabyte (MB) dynamic random access memory (DRAM) devices.'2'4 Num-

erous metal deposition mechanisms have been suggested,6'8'13"5 including precipitation from a supersaturated cleaning solution, incorporation into the silicon dioxide layer during oxide regrowth, and the most problematic, a proposed electroless process whereby metal ion reduction and silicon oxidation occur simultaneously0 In a F-contaming solution Si is a strong reducing agent, since the following half-reaction can occur Si' + 6F - SiFt + 4e [1] with a standard oxidation potential E' of 1.2 V. 16 The ther-

modynamics of electroless deposition might then be expected to obey the Nernst equation, so that below a given contaminant level deposition would not occur.6 According to this theory only metals with reduction potentials more noble than hydrogen evolution should deposit. Surprisingly the Nernst equation has failed to quantitatively account for deposition of Fe, Ni, and Zn from dilute HF:H70. 6

Studies of metallic contamination during aqueous processing are limited in part by the difficulty of monitoring *

Electrochemical Society Active Member.

1688

surface at 3.5° incidence to ensure that a significant portion of the laser path (7%) traverses the mass-transfer boundary

1024 diodes (2.5 mm X 25 p.m), which is employed for con-

ventional absorption spectroscopy The laser line filter placed before the PDA eliminates background light. In addition, the experiments were performed in the dark, so that on the experimental time scale there is no detectable background light from any source. All experiments were performed at room temperature. The sample cell shown in Fig. 2 is mounted on manipulators capable of two angular and one Cartesian adjustment.

P

U A

Laser Liae Filter Si Wafer

Fig. 1. Experimental setup for detection of copper depletion from the mass-transfer boundary layer.

J. Electrochem. Soc., Vol. 145, No. 5, May 1998 The Electrochemical Society, Inc.

Downloaded 26 Aug 2008 to 128.153.14.161. Redistribution subject to ECS license or copyright; see http://www.ecsdl.org/terms_use.jsp

1689

J. Electrochem. Soc., Vol. 145, No. 5, May 1998 The Electrochemical Society, Inc.

The silicon substrate is a 0.013 111 cm n-type 2 in. Si(iii) wafer purchased from Valley Design, Inc. The silicon sample is epoxied to the Teflon piston in the main cell body using TorrSeal, a highly chemically inert epoxy. To prevent corrosion by HF, the materials of construction have been carefully chosen and include a virgin Teflon cell body and piston, Chemraz o-rings, and sapphire optical windows. These materials have been soaked in both concentrated and dilute aqueous HF for 24 h without visible deterioration. Ultralarge scale integration (ULSI) grade reagents are used exclusively In between experiments, Cu was removed from the surface by immersion in SC-i (including megasonic agitation) HF, and SC-2 cleaning solutions. The sample was also changed periodically. In order to increase the experimental sensitivity, the HF

etch solutions also included iO M Na4EDTA, which

increases the molar absorptivity of dilute solutions of Cu2 at 632 nm from about 2 to 36.7 M1 cm* In order to ensure that the measured absorbance in the boundary layer can

be directly related to the concentration of CuEDTA2,

spectrophotometry experiments were performed to compare the absorption spectra of aqueous solutions containing Cu504, HF, Na2SiF6, and Na4EDTA. The absorbance in

the entire visible region of the spectrum with and without Na4EDTA was unaffected by the presence of Na2SiF6, indicating that the SiF anion is noncomplexing. In addition, the presence of HF did not affect the spectrum of solutions containing Na4EDTA, not an unexpected result considering the much stronger complexing strength of EDTA4 rel-

ative to F. Thus the transmitted light intensity can be

related to the concentration of CuEDTA2 using a modification of the Beer-Lambert law. Results and Discussion Deposition from a 3.5 ppm Cu contaminant in dilute (0.15 and 0.25%) aqueous HF was studied in order to clearly separate the time scales during which 5i07 dissolution and Cu deposition occur. This allows a direct in situ test of the pre-

diction that Cu deposition does not begin until after Si07 dissolution is complete. Figures 3 and 4 show the evolution of the total integrated intensity reaching the PDA as a function of time for both HF concentrations. At a time of approximately i25 s for 0.15% HF and 70 s for 0.25% HF, an increase in the total transmitted intensity is observed, reflecting a decrease in the absorbance integrated along the path length as a result of CuEDTA2 depletion from the boundary layer. As discussed later, the subsequent drop in the transmitted intensity reflects formation of about one monolayer of Cu at the Si surface, at which point deposi-

1.116

1.117

a 0

0

.0

1.116

1.115

1.114

1.112

0

200

400

300

500

Time (sec)

Fig. 3. Temporal evolution of total light intensity transmitted through a 0.15% HF solution.

tion becomes surface rate-limited. According to the Nernst

equation, the higher HF concentrations which are commonly used industrially should promote Si oxidation. However, since deposition is in the present case diffusion-

limited, higher HF concentrations should not affect the results other than by decreasing the induction time before Cu deposition begins. The experimental results shown in Fig. 3 and 4 are in all respects consistent with the simple physical picture of diffusion-limited deposition of about one monolayer of Cu following dissolution of the chemical 5i02 layer. The etch rates of thermal 5i02 in 0.15 and 0.25% HF/H20 can be estimated as 5 and 8.5 A/mm, respectively.20 Thus, the times seen for onset of CuEDTA2 depletion from the boundary layer suggest that the 5i02 layer is about 10 A thick. This is in the range of oxide thicknesses that has been obtained by ellipsometry measurements after wet cleaning.2 However, the etch rates given above are for thick thermal oxides, which are compositionally and morphologically different from the

relevant ultrathin chemical oxides.27 As discussed elsewhere, the present technique can also be employed to monitor the dissolution of the chemical oxide Si02 formed during aqueous cleaning.28 The coincidence of the onset of Cu deposition with the completion of 5i02 dissolution provides strong confirming evidence that Cu deposits by an electroless process, whereby Cu2 reduction occurs simultaneously with Si oxidation. Thus the following two half-reactions occur at the silicon surface

Window

Virgin Teflon Cap

100

Si° + 6F -* SiF + 4e

[2]

CuEDTA2 + 2e -. Cu + EDTA4

[31

,,,73ire

\\sSSSS\

1.309

1.309

Sapphire Window

Sapphire

7ndow

/

Silicon Wafer

1.306

1.304

Virgin Teflon Piston

Fig. 2. Teflon cell for aqueous HF experiments,

0

100

200

300

Time (set)

Fig. 4. Temporal evolution of total light intensity transmitted through a 0.25% HF solution.

Downloaded 26 Aug 2008 to 128.153.14.161. Redistribution subject to ECS license or copyright; see http://www.ecsdl.org/terms_use.jsp

1690

J. Electrochem. Soc., Vol. 145, No. 5, May 1998 The Electrochemical Society, Inc.

According to mixed potential theory, the potential at the

addition, the rate of any surface reaction would likely

tions be equal and opposite.29 At a metal surface, if elec-

depend quite strongly on surface preparation, so the results could vary between different investigators. As long as diffusion either initially or eventually becomes rate-limiting, the

wafer surface is determined by the condition that the anodic and cathodic currents from these two haif-reac-

tron transfer is rate-limiting, then the current density i arising from each half-reaction can be related to the potential according to the Butler-Volmer equation3°

i = i0 [e

E—E0)F/RT + e5(1_07T]

[4]

where i9 is the exchange current density, 3 the symmetry factor; E the potential, and E° the standard reduction potential. However; when diffusion is rate-limiting, the current density for a given half-reaction is

=

-nFD -nFD6 dx

[5]

where a is the number of electrons transferred, F is Faraday's constant, D is the diffusivity, C7 is the bulk concentration, x is the distance from the surface, and 6 is the

thickness of the mass-transfer boundary layer Although the Butler-Volmer equation has generally been found to describe electron transfer at metal surfaces, its applicability to semiconductor surfaces is questionable, in part due to the effect on band bending of the applied potential. Recent experiments on n-and p-type Si(lOO) illustrate the difficulties in obtaining reliable electrochemical measurements on semiconductor electrodes.31 Although these measurements

demonstrated that the Butler-Volmer equation is valid within a few hundred millivolts of the mixed potential,

such a result may not be general.31 Both the cathodic and anodic currents arise from the lower of the two values from Eq. 4 and 5. An additional complication is the likely coexistence of other faradaic processes such as corrosion. This in situ technique should be capable of determining which combinations of metal, solvent, and experimental conditions can contaminate silicon wafers in diffusion-limited processes during aqueous cleaning. However; its general applicability requires careful consideration. Kinetic lim-

itations during metal contamination are still uncertain. Both atomic force microscope (AFM) studies32 and the present results provide evidence for diffusion rate-limitation.

Other studies of Cu deposition from a buffered oxide

etchant (BOE) found a deposition rate proportional to bulk concentration,1 which might suggest a first-order surface reaction rate-limited process. However; using a boundary layer thickness of 350 p.m and a Cu3 diffusivity of 6 X 10-6 cm2/s, approximate calculations for the diffusion flux closely match the deposition fluxes reported in Ref. 5. The relatively high activation energies (39, 19 kJ/mol) obtained3 are close to the apparent activation energy of 22 kcal/mol reported for Cu2 diffusion.33 On the other hand, evidence against diffusion limitation is provided by measurements showing that the rate of Cu deposition may depend upon illumination.3437 It has been suggested that while diffusion limitation might be reasonable at metal contamination levels in the part per million range, which is relatively high by current industrial standards, diffusion limitation should not be extrapolated to the parts per billion range.31'38 Without further refinement, this idea is inconsistent with both traditional surface chemistry and electrochemistry, which conclude that mass-transfer limitation of heterogeneous reactions is more likely at low reactant concentrations. The apparently contradictory evidence might be reconciled by the following hypothesis. At extremely low cover-

age, deposition might be surface reaction rate-limited,

while at slightly higher coverage deposition becomes diffusion rate-limited as metal nuclei form and catalyze further

deposition. Support for this idea can be found from the practice of electroless metal deposition onto semiconductors and insulators, which usually requires activation by a predeposited metal seed layer.395 The seed layer provides nucleation sites and also affects the deposit morphology. This hypothesis is difficult to test for several reasons. If correct, at relatively high contaminant levels the surface reaction-limited period might be too short to easily detect. In

current method is capable of studying metal deposition

from various aqueous reagents as a function of temperature, flow velocity, process chemistry, etc. Such knowledge can

aid solvent manufacturers by indicating which metal ions must be removed during purification. Since electroless baths often contain EDTA as a complexing agent, it is interesting to compare the present diffusionlimited rates to those obtained for electroless Cu deposition. The mechanism of electroless Cu deposition from an EDTA complex has been thoroughly studied, and rate-limitation

by hydrogen abstraction from the formaldehyde reducing agent has been reported.46 Electroless Cu deposition from a

formaldehyde-based bath can occur at rates equivalent to 3.4-5.4 mA/cm2. Assuming a 335 p.m thick mass-transfer boundary layer; Eq. 5 yields an equivalent current density of 1.8 x l0 mA/cm2 for the current study. By comparison, diffusion rate-limited electrodeposition of Cu from CuSO4 electrolytes has been observed at current densities ranging from 0.6 to 36.9 mA/cm2, 48 suggesting that diffusion-limited electroless Cu deposition might be reasonable. Since Si is a considerably stronger reducing agent than formaldehyde, the surface reaction rate during Cu deposition onto Si from

HF solutions should not be rate-limiting except perhaps at extremely low surface coverages, as discussed above. The effects of the chelating species EDTA4 on the experimental results should not be very important. Without this chelating agent, the surface reaction rate can only be increased, so the overall reaction in the present case would certainly remain diffusion-limited. The thickness of the mass-transfer boundary layer can be obtained from the transmittance peak to ensure that it is reasonable. For the case where the solution absorbance (A) varies along the path length of the laser

r /2 A = €$ C(z)dz

[6]

J—1012

where A is the absorbance, is the molar absorptivity, C is

the concentration of CuEDTA2, and z is the distance along the laser path length. The total path length is 1, with the z origin taken at the point where the laser contacts the

silicon wafer. Now the laser path can be divided into

regions where the laser traverses either the bulk solution or the boundary layer; taking the concentration inside the boundary layer as C(z) = C0

ri 6/sin3.5°

[7]

The ratio between the intensity (fr) at the PDA after boundary layer development to that prior to Cu deposition (4) can easily be found from piecewise integration of Eq. 6 after substituting from Eq. 7 = e'711"31'

[8]

12

The ratios fl/fl from Fig. 3 and 4 are 1.00115 and 1.00108,

respectively, and yield a mass-transfer boundary layer thickness of about 335(20) p.m.

Another interesting aspect of the data in Fig. 3 and 4 is the decrease in the transmitted intensity observed 2 mm after the onset of deposition, which is consistent with deposition of about one monolayer of Cu. During the period when the absorption decreases, a boundary layer is formed, exists at steady state, and then collapses. Inspection of Fig. 3 and 4 suggests that the steady-state condition is relatively short-lived. Accurate treatment of the boundary layer development is complex, since both the boundary layer thickness and surface CuEDTA3 concentration change with time. Additional complications are suggested by interferometric studies of the boundary layer which suggest

Downloaded 26 Aug 2008 to 128.153.14.161. Redistribution subject to ECS license or copyright; see http://www.ecsdl.org/terms_use.jsp

1691

J. Electrochem. Soc., Vol. 145, No. 5, May 1998 The Electrochemical Society, Inc.

that its collapse may not occur reproducibly.48 For these rea-

sons the deposition flux J is approximated from Fick's first law as

J = -D.dx

-D

Taking the diffusivity of CuEDTA2 as 6 x

[9] 10-6

one obtains a deposition flux of 6.0 X 1012 atom/cm2 s. Since the density of sites on Si(11l) is about 7.8 X 1014 atom/cm2,

the widths of the absorption peaks in Fig. 3 and 4 correspond to deposition of about one monolayer of Cu. It should

be noted that one could envision further Cu deposition

beyond one monolayer, which if surface rate-limited would

not support a boundary layer and be undetectable by the present experimental technique. Since further Si oxidation can occur only at defect sites and by diffusion to the second

layer of Si atoms, surface rate-limitation is unsurprising.

Separate TXRF experiments demonstrate that further

deposition of Cu does occur at a lower rate. Other investigators have reported Cu deposition rates which either saturate or slow down markedly with time,7'836'5° although in only one case was the saturation coverage consistent with exactly one monolayer of Cu.7 The sensitivity and generality of the reported results deserve comment. Theoretically, if one could eliminate the source instability and background scattered light, the detector could be operated in the shot noise limit. Then the minimum detectable absorbance (Am,) compared to a reference beam is5112 mm

Acknowledgments

cm2/s and

the boundary layer thickness of 335 p.m obtained above,

A.

original value about 2 mm later, consistent with deposition of one monolayer of Cu on Si(111) followed by a transition to a slower surface rate-limited deposition regime. These results demonstrate the particular utility of this technique for monitoring transient phenomena. The authors thank Ahmed A. Busnaina for helpful dis-

cussions. This research has been supported by NSF grant ECS-9634058. Manuscript submitted June 25, 1997; revised manuscript received January 31, 1998.

Clarkson University assisted in meeting the publication costs of this article. REFERENCES 1. P. Singer; Semicond. Inter., 18(11), 88 (1995). 2. W. K. Puotinen and D. A. Puotinen, RCA Rev., 31, 187 (1970).

3. 0. J. Anttila, N. V. Tilli, M. Schaekers, and C. L. Claeys, J. Electrochem. Soc., 139, 1180 (1992). 4. G. J. Slusser and L. MacDowell, J. Vac. Sci. Technol., A5, 1649 (1987). 5. K. K. Yoneshige, H. G. Parks, S. Raghavan, J. B. Hiskey, and P J. Resnick, J. Electrochem. Soc., 142, 671 (1995).

6. F. Kern, M. Itano, I. Kawanabe, M. Miyashita, R.

Rosenberg, and T Ohmi, in Proceedings, Ultra Clean Society 11th Workshop on ULSI Ultraclean Technology, p. 23, Tokyo, Japan, June 6, 1991.

7.

H. Morinaga, M. Suyama, and T. Ohmi, J. Electrochem. Soc., 141, 2834 (1994).

8. T. Ohmi, T. Imaoka, I. Sugiyama, and T. Kezuka, J. Elect rochem. Soc., 139, 3317 (1992).

9. M. Kniffin, T. Beerling, and C. R. Helms, J. Elec—log 1— flNsat

[10]

where N,6 is the number of photons which will saturate a detector element and n is the number of detector elements. Calculations for the current detector setup yield a value of Amjn of 8 X i0. However, the noise level in Fig. 3 and 4 suggests that the current experimental setup has a detection limit Ammn of 2 x i0. Clearly additional sources of noise are present, almost certainly due to laser instability. Dual beam spectrophotometry should allow the experimental sensitivity to approach the theoretical limit more closely, although care must be taken to ensure nearly identical optical paths. In addition, the source stability can be improved by the use of an extended source such as an arc lamp, with the disadvantage of potentially increasing the background due to scattered light. Since most transition metal complexes have strong charge-transfer spectra in the range 200-300 nm, an arc lamp in series with a monochromator could be used as a tunable ultraviolet source

capable of detecting a variety of metallic species. The stronger ultraviolet absorption would improve the sensitivity, as would use of a charge-coupled device (CCD), which has a larger total well capacity.12 The authors expect

an ultimate detection limit in the range 10-100 ppb for contaminant depletion from the boundary layer. Conclusions A new optical technique based on simple absorption spectroscopy was demonstrated for monitoring metal contaminant deposition from aqueous processing solutions. Cu deposition from 0.15 and 0.25% HF solutions contaminated with 3.5 ppm Cu has been observed by changes in absorption of a HeNe laser which passes through the mass-transfer boundary layer near a Si wafer. This is caused by the depletion of Cu2 from the boundary layer; providing direct evidence that

Cu deposition is rate-limited by diffusion. This technique may allow the determination of which metallic species can deposit on Si wafers during various aqueous processing steps in microelectronics manufacture. In addition, Cu deposition is seen to coincide with the completion of 5i02 disso-

lution, confirming that Cu is reduced by an electroless process involving simultaneous Si oxidation. Following a decline in absorption, the transmitted intensity returns to its

trochem. Soc., 139, 95

(1992).

10. 0. J. Anttila and M. V. Tilli, J.

1751 11.

Electrochem. Soc., 139,

(1992).

Cleaning Technology in Semiconductor Device Manu-

facturing, J. Ruzyllo and R. E. Novak, Editors, PV

94-7, The Electrochemical Society Proceedings Series, Pennington, NJ (1994).

12. L. Mouche, F Tardif, and J. Derrien, J. Electrochem. Soc., 142, 2395 (1995).

13. J. Ryuta, T. Yoshimi, H. Kondo, H. Okuda, and Y. Shimanuki, Jpn. J. Appl. Phys., 31, 2338 (1992). 14.

T. Ohmi, T. Imaoka, T. Kezuka, J. Takano, and M. Kogure, J. Elect rochem. Soc., 140, 811 (1993) and ref-

erences therein. 15. H. Morinaga, M. Suyama, and T. Ohmi, J. Electrochem. Soc., 141, 2834 (1994). 16. W. Latimer; The Oxidation States of the Elements and Their Potentials in Aqueous Solution, 2nd ed., Prentice-Hall, Englewood Cliffs, NJ (1952).

17. G. Toig and R. Klockenkamper, Spectrochim. Acta, B48, 111 (1993).

18.

S. Verhaverbeke, C. Werkhoven, M. Meuris, H. Schmidt, K. Dillenbeck, P. Mertens, M. Heyns, and A. Philipossian, in Proceedings, IES 39th Annual Technical Meeting, p. 423, Las Vegas, NV, May 2—7, 1993.

19. P C. Pankratz and D. Hymes, in Microcontamination '94 Conference Proceedings, p. 476, San Jose, CA (1994).

20.

K. Nauka and D. A. Gomez, J. Electrochem. Soc., 142, L98

(1995) and references therein; H. Shimizu and C.

Munakata, Appl.

Phys. Lett., 64, 3598 (1994) and references therein. 21. R. Pruksma and R. L. McCreery, Anal. Chem., 51, 2253 (1979).

22, Y. Fukunaka, K. Denpo, M. Iwata, K. Muruoka, and Y. Kondo, J. Elect rochem. Soc., 130, 2492 (1983). 23. J. F. Tyson and T. S. West, Talanta,

27, 335

(1980).

24. A. L. Deputy, H. P Wu, and R. L. McCreery, J.

Chem., 94, 3620

(1990). 25. J. Posdorfer, M. Olbrich-Stock, and R. Z. Phys. Chem., 171, S33 (1991).

Phys.

N. Schindler,

T. Yabune, N. Miki, J. Takano, and T. Ohmi, J. Electrochem. Soc.,

26. H. Kikuyama, M. Waki, M. Miyashita, 141,

366 (1994).

27. E. P. Guxev, H. C. Lu, T. Gustafsson, and E. Garfunkel, Phys. Rev., B52, 1759 (1995).

28. D. Chopra and I. I. Suni, Thin Solid Films, In press. 29. P Bindra and J. Roldan, J. Appl. Elect rochem., 17, 1254 (1987).

Downloaded 26 Aug 2008 to 128.153.14.161. Redistribution subject to ECS license or copyright; see http://www.ecsdl.org/terms_use.jsp

1692

J Electrochem. Soc., Vol. 145, No. 5, May 1998 The Electrochemical Society, Inc.

30. A. J. Bard and L. H. Faulkner, Electrocheinjcal Methods, John Wiley & Sons, New York (1980). 31. V. Bertagna, C. Plougonven, F Rouelle, and M. Chemla, J. Elect roanal. Chem., 422, 115 (1997) and references

therein. 32. 0. M. R. Chyan, J. J. Chen, H. Y. Chien, J. Sees, and L. Hall, J. Electrochem. Soc., 143, 92 (1996). 33. L. J. J. Janssen and J. U. Wijers, J. AppI. Electrochem.,

Vandenhout, J. Elect rochem. Soc., 142, 519 (1995).

42. A. G. Schrott, B. Braren, F. J. M. O'Sullivan, H. F

Saraf, P Bailey, and J. Holdan, J. Electrochem. Soc., 142, 944 (1995).

43. M. J. DeSilva and Y. Shacham-Diamond, J. Etectrochem. Soc., 143, 3512 (1996).

44. V. M. Dubin, Y. Shacham-Diamond, B. Zhao, P K. Vasudev, and C. H. Ting, J. Electrochem. Soc., 144,

19, 823 (1989).

34. I. Teerlnick, P. W. Mertens, H. F Schmidt, M. Meuris, and M. M. Heyns, J. Electrochem. Soc., 143, 3323 (1996).

35. G. J. Norga, M. Piatero, K. A. Black, A. J. Reddy, J. Michel, and L. C. Kimmerling, J. Electrochem. Soc., 144, 2801 (1997). 36. G. Li, F. A. Kneer, B. Vermeire, H. G. Parks, S. Raghavan, and J. S. Jeon, J. Elect rochem. Soc., 145, 241 (1998).

37. X. Cheng, G. Li, F. A. Kneer, B. Vermeire, H. G. Parks,

S. Raghavan, and J. S. Jeon, J. Electrochem. Soc., 145, 352 (1998).

38. G. J. Norga and L. C. Kimmerling, J. Electron. Mater., 24, 397 (1995).

39. V. M. Dubin, J. Electrochem. Soc., 139, 1289 (1992).

40. H. Yoshiki, K. Hashimoto, and A. Fujishima, J. Electrochem. Soc., 142, 428 (1995). 41. F. P Boonekamp, J. J. Kelly, L. G. J. Fokkink, and W E.

898 (1997).

45. P Gorostiza, H. Diaz, J. Servat, F Sanz, and J. H.

Morante, J. Electrochem. Soc., 144, 909 (1997). 46. H. Schumacher, J. J. Pesek, and 0. H. Melroy, J. Phys. Chem., 89, 4338 (1995).

47. V M. Dubin, Y. Shacham-Diamond, B. Zhao, P K. Kasudev and C. H. Ting, J. Electrochem. Soc., 144, 898 (1997).

48. A. Tvarusko and L. S. Watkins, Elect rochim. Acta, 14, 1109 (1969).

49. D. G. Leaist and L. Hao, J. Chain. Soc., Faraday flans., 90, 135 (1994).

50. J. S. Jeon, S. Haghavan, H. G. Parks, J. K. Lowell, and I. All, J. Elect rochem. Soc., 143, 2870 (1996). 51. H. B. Bilhorn, P M. Epperson, J. V Sweedler, and M. B. Denton, Appl. Spectrosc., 41, 1125 (1987). 52. H. S. Pomeroy, M. E. Baker, M. Bonner Denton, and A. G. Dickson, Appl. Spectrosc., 49, 1729 (1995).

Segregation of Oxygen at a Solid/Liquid Interface in Silicon Koichi Kakimoto and Hiroyuki Owe institute of Advanced Material Study, Kyushu University, Kasuga 816, Japan ABSTRACT

The incorporation of oxygen into silicon single crystals from the melt is examined in terms of an experiment and a model on a transient solidification. A transient analysis offered an effective segregation coefficient of oxygen in silicon and a diffusion constant of oxygen In the melt almost independently. The analysis estimated these values of effective segregation coefficient of oxygen in silicon and diffusion constant of oxygen in the melt. Introduction

A knowledge of the segregation coefficient of oxygen at an interface between solid and liquid silicon, and of the diffusion constant of oxygen in the melt is of considerable interest in crystal growth studies, since the values are of great interest and importance for the control of oxygen concentration in solid silicon. Several papers6 on the segregation coefficient of oxygen at the solid/liquid interface have been reported in the last three decades, however, the reported values range from 0.13 to 1.25. Additionally, a diffusion constant for oxygen atoms in the melt has not been reported. These values are important for carrying out the estimation of impurity distribution in the melt and solid, since the numerical simulation technique is going to be a great tool for investigating impurity distribution in the melt using heat and mass-transfer equations. Impurity distribution in the crystals is determined by segregation with time-dependent impurity transfer at a solid/liquid interface. Hurle et al.78 reported an analytical study on impurity distribution using sinusoidal temperature fluctuation in the melt, with the Taylor expansion technique, to estimate how impurities incorporate into the crystals. This analysis was performed by solving the concentration-diffusion and heat-conduction equations for both solid and liquid phases in a linear approximation. Burton et al.9 also described an analysis on melt flow, and the incorporation of solute elements into single crystals using sinusoidal analysis. These analyses imposed some parameters such as an effective segregation coefficient and diffusion constant of impurity in the melt. Accordingly, in this paper we investigate the effect of

the abrupt change of growth velocity on the impurity

profile in crystals and melt by taking into account transient segregation. The transient analysis contained only solidification and diffusion; therefore, melt flow was suppressed in the present experiment using vertical magnetic fields. Results are

presented which show how impurity distribution in the crystals is modified and how an abrupt change of growth speed affects diffusion boundary layers in the melt.

Transient Analysis The concentration-diffusion equation describing a solid/

liquid interface moving with velocity v along the a axis can be written as 32C 3z

+

v&C — = l&C Ddz Ddt

[1]

where C, v, D, and t are impurity concentration, growth velocity, diffusion constant of impurities and oxygen in this study, and time, respectively. Two coordinate systems are employed in this analysis. One is a moving coordinate system with the same velocity

of a solid/liquid interface, while the other is a stationary coordinate system, which is fixed in space. A one-dimensional analysis is employed, since experimental data has only a one-dimensional distribution of oxygen concentration in the grown crystal. Boundary conditions at a solid/liquid interface can be represented by Eq. 2, since the total mass of oxygen, which

is incorporated into crystals and excluded from the melt, should be conserved at the solid/liquid interface liz)

= —C (1 - k7) D

[21

Downloaded 26 Aug 2008 to 128.153.14.161. Redistribution subject to ECS license or copyright; see http://www.ecsdl.org/terms_use.jsp