, Volume 21, Issue 5, pp 638-647,
Open Access This content is freely available online to anyone, anywhere at any time.
Date: 11 Feb 2012

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


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.

This article is an invited submission to JMEP selected from presentations at the Symposia “Wetting, soldering and brazing” and “Diffusion bonding and characterization” belonging to the Topic “Joining” at the European Congress and Exhibition on Advanced Materials and Processes (EUROMAT 2011), held September 12-15, 2011, in Montpellier, France, and has been expanded from the original presentation.