Article

Journal of Materials Engineering and Performance

, Volume 21, Issue 5, pp 638-647

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

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

  • R. FilipekAffiliated withFaculty of Materials Science and Ceramics, Interdisciplinary Centre of Materials Modeling, AGH University of Science and Technology Email author 
  • , K. SzyszkiewiczAffiliated withFaculty of Materials Science and Ceramics, Interdisciplinary Centre of Materials Modeling, AGH University of Science and TechnologyFaculty of Computer Sciences, WSB-NLU
  • , P. DziembajAffiliated withFaculty of Materials Science and Ceramics, Interdisciplinary Centre of Materials Modeling, AGH University of Science and Technology
  • , P. SkrzyniarzAffiliated withInstitute of Metallurgy and Materials Science, Polish Academy of Sciences
  • , A. Wierzbicka-MiernikAffiliated withInstitute of Metallurgy and Materials Science, Polish Academy of Sciences
  • , P. ZiebaAffiliated withInstitute of Metallurgy and Materials Science, Polish Academy of Sciences

Abstract

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.

Keywords

intermetallics joining modeling processes