Modeling of Reactive Diffusion: Mechanism and Kinetics of the Intermetallics Growth in Ag/Ag Interconnections

详细信息    查看全文

• 作者：R. Filipek (1) rof@agh.edu.pl
  K. Szyszkiewicz (12)
  P. Dziembaj (1)
  P. Skrzyniarz (3)
  A. Wierzbicka-Miernik (3)
  P. Zieba (3)
• 关键词：intermetallics – ; joining – ; modeling processes
• 刊名：Journal of Materials Engineering and Performance
• 出版年：2012
• 出版时间：May 2012
• 年：2012
• 卷：21
• 期：5
• 页码：638-647
• 全文大小：760.5 KB
• 参考文献：1. A.J. Chorin and J.E. Marsden, A Mathematical Introduction to Fluid Mechanics, Springer-Verlag, New York, 2000 (corrected fourth printing)
  2. W. Nernst, Die elektromotorische Wirksamkeit der Jonen, Z. Phys. Chem., 1889, 4(2), p 129–181
  3. M. Planck, 脺ber die Potentialdifferenz zwischen zwei verd眉nnten L枚sungen bin盲rer Elektrolyte, Ann. Phys. Chem., 1890, 40, p 561–576
  4. J.S. Kirkaldy and D.J. Young, Diffusion in the Condensed State, The Institute of Metals, London, 1987
  5. R. Filipek, Interdiffusion in Non-Ideal Systems, Arch. Metall. Mater., 2004, 49(2), p 201–218
  6. G.E. Murch, Diffusion Kinetics in Solids, Phase Transformations in Materials, G. Kostorz, Ed., Wiley-VCH, Weinheim, 2001, p 171–239
  7. M. Danielewski and M. Wakihara, Kinetic Constraints in Diffusion, Defect Diffus.Forum, 2005, 237-240, p 151–156
  8. C.D. Levermore, Relating Eddington Factors to Flux Limiters, J. Quant. Spectrosc. Radiat. Transf., 1984, 31, p 149–160
  9. M. Zakari and D. Jou, Nonequilibrium Lagrange Multipliers and Heat-Flux Saturation, J. Non-Equilib. Thermodyn., 1995, 20, p 342–349
  10. E.M. Epperlein, G.J. Rickard, and A.R. Bell, Two-Dimensional Nonlocal Electron Transport in Laser-Produced Plasmas, Phys. Rev. Lett., 1988, 61, p 2453–2456
  11. G.J. Rickard, A.R. Bell, and E.M. Epperlein, 2D Fokker-Planck Simulations of Short-Pulse Laser-Plasma Interactions, Phys. Rev. Lett., 1989, 62, p 2687–2690
  12. A.M. Anile and S. Pennisi, Thermodynamic Derivation of the Hydrodynamical Model for Charge Transport in Semiconductors, Phys. Rev. B, 1992, 46, p 13186–13193
  13. J. Stefan, 脺ber einige Probleme der Theorie der W盲rmeleitung, Sitzungsberichte der Mathematisch-Naturwissenschaftliche der Kaiserlichen Adad, Der Wissenschaften, 1889, 98, p 473–484
  14. J. Dantzig and M. Rappaz, Solidification (Engineer Sciences: Materials), EFPL Press, Lausanne, 2009
  15. W.D. Murray and F. Landis, Numerical and Machine Solutions of Transient Heat Conduction Problems Involving Melting and Freezing, Trans. ASME C J. Heat Transf., 1959, 81, p 106–112
  16. L.S. Darken, Diffusion of Carbon in Austenite with a Discontinuity in Composition, Trans. AIME, 1948, 180, p 430–438
  17. J.W. Thomas, Numerical Partial Differential Equations—Finite Difference Methods, Springer-Verlag, New York, 1995, p 5–40
  18. E. Hairer, S.P. Norsett, and G. Wanner, Solving Ordinary Differential Equations I: Nonstiff Problems, 2nd ed., Springer, Berlin, 2002
  19. E. Hairer and G. Wanner, Stiff Differential Equations Solved by Radau Methods, J. Comput. Appl. Math., 1999, 111, p 93–111
  20. P. Skrzyniarz, A. Sypień, J. Wojewoda-Budka, R. Filipek, and P. Zięba, Microstructure and Kinetics of Intermetallic Phases Growth in Ag/Sn/Ag Joint Obtained as the Result of Diffusion Soldering, Arch. Metall. Mater., 2010, 5(5), p 123–130
  21. S. Bader, W. Gust, and H. Hieber, Rapid Formation of Intermetallic Compound by Interdiffusion in the Cu-Sn and Ni-Sn Systems, Acta Metall. Mater., 1995, 43, p 329–337
  22. T.L. Su, L.C. Tsao, S.Y. Chang, and T.H. Chuang, Morphology and Growth Kinetics of Ag3Sn During Soldering Reaction Between Liquid Sn and an Ag Substrate, J. Mater. Eng. Perform., 2002, 11, p 365–368
  23. D.R. Flanders, E.G. Jacobs, and R.F. Pinizzotto, Activation Energies of Intermetallic Growth of Sn-Ag Eutectic Solder on Copper Substrates, J. Electron. Mater., 1967, 26, p 883–887
• 作者单位：1. Faculty of Materials Science and Ceramics, Interdisciplinary Centre of Materials Modeling, AGH University of Science and Technology, 30 Mickiewicza Av., 30-059 Krak贸w, Poland2. Faculty of Computer Sciences, WSB-NLU, Zielona 27, 33-300 Nowy S膮cz, Poland3. Institute of Metallurgy and Materials Science, Polish Academy of Sciences, 25 Reymonta St., Krak贸w, Poland
• 刊物类别：Chemistry and Materials Science
• 刊物主题：Chemistry
  Characterization and Evaluation Materials
  Materials Science
  Tribology, Corrosion and Coatings
  Quality Control, Reliability, Safety and Risk
  Engineering Design
  
• 出版者：Springer New York
• ISSN：1544-1024

文摘

The phenomenological model describing the growth of intermetallic phases in multi-component systems is presented. Full time-dynamics approach is applied without the often-used simplifications such as flux constancy. General form of the species flux is considered, which consists of chemical potential gradient as a driving force for diffusion with additional drift term. Stefan-type (moving) boundary conditions are applied. In the present form, the model assumes local equilibrium at each interface and that the process of growth of intermediate phases is controlled by diffusion of reagents through the layers and/or chemical reactions at the boundaries. The model is solved in its full generality. Numerical method for the solution of the problem has been developed. Specially selected change of dependent variables transforms the moving boundary problem into an equivalent fixed boundary problem. Such problem has been treated using the method of lines which converts partial differential equations into a system of ordinary differential equations, which is subsequently solved numerically. The obtained solution was tested and compared with analytic ones available in special cases, showing satisfactory agreement. The growth of intermetallic phases in Ag/Sn/Ag system has been modeled and compared with experimental results.