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Received March 8, 2001
Accepted August 8, 2001
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Mathematical Modeling for Chemical Vapor Deposition in a Single-Wafer Reactor: Application to Low-Pressure Deposition of Tungsten
Dept. of Chemical and Environmental Technology, Inha Technical College, Incheon 402-752, Korea
jhpark@true.inhatc.ac.kr
Korean Journal of Chemical Engineering, May 2002, 19(3), 391-399(9), 10.1007/BF02697145
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Abstract
A mathematical model for low pressure chemical vapor deposition in a single-wafer reactor in stagnation point flow has been developed to investigate the reactor performance. The transient transport equations for a simulated reactor include continuity, momentum, energy, and gaseous species balances. The model equations are simultaneously solved by using a numerical technique of orthogonal collocation on finite element method. Simulation studies have been performed to gain an understanding of tungsten low pressure chemical vapor deposition process. The model is then used to optimize the deposition rate and uniformity on a wafer, and the effects of operating conditions on deposition rate are studied to examine how system responses are affected by changes in process parameters. Deposition rate and uniformity calculated at the steady state are observed to be very sensitive to both temperature and total pressure. In addition, the model predictions for tungsten deposition from hydrogen reduction of tungsten hexafluoride have been compared with available experimental data in order to demonstrate the validity of the model.
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References
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Riely PE, Clark TE, J. Electrochem. Soc., 138(10), 3008 (1991)
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Smith GC, Blumenthal R, "Tungsten and Other Advanced Metals for ULSI Applications in 1990," MRS Publishers, Pittsburgh, PA (1991)
Suwondo E, Pibouleau L, Domenech S, Riba JP, Chem. Eng. Commun., 102, 161 (1991)
Svehla RA, "Estimated Viscosities and Thermal Conductivities of Gases at High Temperatures," NASA Tech. Report R-132, Lewis Res. Center, Cleveland, OH (1962)
Ulacia F, Howell JIS, Krner H, Werner C, Appl. Surf. Sci., 38, 370 (1989)
vander Putte P, Philips J. Res., 42, 608 (1987)
Werner C, Ulacia FJI, Hopfmann C, Flynn P, J. Electrochem. Soc., 139(2), 566 (1992)
Wong F, Solid State Technol., 32(Oct.), 53 (1989)
Blewer RS, "Tungsten and Other Refractory Metals for VLSI Applications," MRS Publishers, Pittsburg, PA (1986)
Blewer RS, McConica CM, "Tungsten and Other Refractory Metals for VLSI Applications IV," MRS Publishers, Pittsburg, PA (1989)
Broadbent EK, "Tungsten and Other Refractory Metals for VLSI Applications II," MRS Publishers, Pittsburg, PA (1987)
Broadbent EK, Ramiller CL, J. Electrochem. Soc., 131(6), 1427 (1984)
Bryant WA, J. Electrochem. Soc., 125(9), 1534 (1978)
Bullis WM, O'Mara WC, Solid State Technol., 36(4), 59 (1993)
Cale TS, Jain MK, Raupp GB, J. Electrochem. Soc., 137(5), 1526 (1990)
Cale TS, Park JH, Raupp GB, Jain MK, "Impacts of Temperature and Reactant Flow Rate Transients on LPCVD Tungsten Silicide Film Properties," in Rapid Thermal and Integrated Processing, Mat. Res. Soc. Symp. Proc., 224, MRS, 171 (1991)
Cale TS, Park JH, Gandy TH, Raupp GB, Jain MK, Chem. Eng. Commun., 119, 197 (1993)
Cale TS, Raupp GB, Park JH, Jain MK, Rogers BR, "The Inherently Transient Nature of Deposition Processes," in Proceedings of First Intermational Conference of Transport Phenomena in Processing, Guceri, S., ed., Technomic Publishing Co., 127 (1992)
Campbell SA, Knutson KL, Ahn KH, Leighton JD, Liu B, IEEE IEDM Tech. Digest, 921 (1990)
Chase MW, Davies CA, Downey JR, Frurip DJ, McDonald RA, Syverud AN, J. Phys. Chem. Ref. Data, 14 (1985)
Chatterjee S, Trachtenberg I, Edgar TF, J. Electrochem. Soc., 139(12), 3682 (1992)
Dobskin DM, J. Electrochem. Soc., 139(9), 2573 (1992)
Economou DJ, Alkire RC, J. Electrochem. Soc., 135(11), 2786 (1988)
Finlayson BA, "Nonlinear Analysis in Chemical Engineering," McGraw-Hill, Inc., New York (1980)
Fitzjohn JL, Holstein WL, J. Electrochem. Soc., 137(2), 699 (1990)
Hasper A, Holleman J, Middelhoek J, Klejin CR, "W-LPCVD Step Coverage and Modeling in Trenches and Contact Holes," in Tungsten and Other Advanced Metals for VLSI Applications, S.S. Wong and S. Furukawa, eds., MRS Publishers, Pittsburgh, PA, 127 (1990)
Hess DW, Jensen KF, Anderson TJ, Rev. Chem. Eng., 3(2), 97 (1985)
Hirschfelder JO, Curtiss CF, Bird RB, "Molecular Theory of Gases and Liquids," John Wiley & Sons, Inc. (1954)
Jasinski TJ, Kang SS, "Application of Numerical Modeling for CVD Simulation Test Case: Blanket Tungsten Deposition Uniformity," in Tungsten and Other Advanced Metals for ULSI Applications in 1990, G.C. Smith and R. Blumenthal, eds., MRS Publishers, Pittsburgh, PA, 219 (1991)
Jasinski TJ, Harshbarger WR, "Numerical Modeling of Tungsten Disilicide Deposition," in Tungsten and Other Refractory Metals for VLSI Applications IV, R.S. Blewer, C.M. McConica, ed., MRS Publishers, Pittsburgh, PA, 189 (1989)
Jenkinson JP, Pollard R, J. Electrochem. Soc., 131(12), 2911 (1984)
Jensen KF, Chem. Eng. Sci., 42(5), 923 (1987)
Kleijn CR, Hoogendoorn CJ, Hasper A, Holleman J, Middelhock J, J. Electrochem. Soc., 138(2), 509 (1991)
Kleijn CR, vander Meer H, Hoogendoorn CJ, J. Electrochem. Soc., 136(11), 3423 (1989)
Kleijn CR, J. Electrochem. Soc., 138(7), 2190 (1991)
Lam DK, Koch GR, Solid State Technol., 23(9), 99 (1980)
McConica CM, Krishnamani K, J. Electrochem. Soc., 133(12), 2542 (1986)
McConica CM, Churchill S, "Step Coverage Prediction During Blanket CVD Tungsten Deposition," in Tungsten and Other Refractory Metals for VLSI Applications III, V.A. Wells, ed., MRS Publishers, Pittsburgh, PA, 257 (1988)
Moslehi MM, Chapman RA, Wong M, Paranjipe A, Najm HN, Kuehne J, Yekley RL, Davis CJ, IEEE Trans. Electron Devices, 39(1), 4 (1992)
Pankratz LB, "Thermodynamics Properties of Halides," U.S. Bureau of Mines, Bulletin 674 (1984)
Park JH, Korean J. Chem. Eng., 13(2), 105 (1996)
Park JH, J. Ind. Eng. Chem., 2(2), 171 (1996)
Park JH, "Simulation of Low Pressure Chemical Vapor Deposition Using Combined Reactor Scale and Feature Scale Models," Ph.D. Dissertation, Arizona State University, U.S.A. (1992)
Park SK, Economou DJ, J. Electrochem. Soc., 137(8), 2624 (1990)
Pauleau Y, Lami P, J. Electrochem. Soc., 132(11), 2779 (1985)
Rana VVS, Joshi RV, Ohdomari I, "Advanced Metalization for ULSI Applications," MRS Publishers, Pittsburgh, PA (1992)
Reid RC, Prausnitz JM, Poling BE, "The Properties of Gases & Liquids," McGraw-Hill, Inc., New York (1988)
Riely PE, Clark TE, J. Electrochem. Soc., 138(10), 3008 (1991)
Rode EJ, Schmitz JEJ, "Study of Reactor Design by Computational Fluid Dynamics," in Advanced Metallization for ULSI Applications, V.V.S. Rana, R.V. Joshi, and I. Ohdomari, eds., MRS Publishers, Pittsburgh, 105 (1992)
Skelly DW, Lu TM, Woodruff DW, "Metallization Techniques," in VLSI Electronics: Microstructure Science, Academic Press, 15, 101 (1987)
Smith GC, Blumenthal R, "Tungsten and Other Advanced Metals for ULSI Applications in 1990," MRS Publishers, Pittsburgh, PA (1991)
Suwondo E, Pibouleau L, Domenech S, Riba JP, Chem. Eng. Commun., 102, 161 (1991)
Svehla RA, "Estimated Viscosities and Thermal Conductivities of Gases at High Temperatures," NASA Tech. Report R-132, Lewis Res. Center, Cleveland, OH (1962)
Ulacia F, Howell JIS, Krner H, Werner C, Appl. Surf. Sci., 38, 370 (1989)
vander Putte P, Philips J. Res., 42, 608 (1987)
Werner C, Ulacia FJI, Hopfmann C, Flynn P, J. Electrochem. Soc., 139(2), 566 (1992)
Wong F, Solid State Technol., 32(Oct.), 53 (1989)