Modeling the solid-state reaction between Sn-Pb solder and a porous substrate coating

Solder joints in hybrid microelectronic circuit electronics are formed between the solder alloy and the noble metal thick film conductor that has been printed and fired onto the ceramic. Although the noble metal conductors provide excellent solderability at the time of manufacture, they are susceptible to solid-state reactions with Sn or other constituents of the solder. The reaction products consist of one or more intermetallic compounds (IMC). The integrity of these solder joints can be jeopardized by formation of IMC layers, which can have thermal and mechanical properties that are substantially different from the solder and substrate and which can consume the conductor layer by solid-state reaction. Analytical models predicting IMC growth for a variety of conditions are needed to improve predictions of long-term joint reliability and manufacturing processes. Unfortunately, because of the inherent porosity of thick film conductors, IMC growth in conductors cannot be well predicted by simply applying growth kinetics to a quasi-one-dimensional layer geometry. Rather, IMC growth involves a complicated geometry in which the interfaces between solid-state phases grow, intersect, and coalesce. In such geometries, explicit boundary tracking, which is normally done in one-dimensional models, is impractical. In heat transfer analyses, an implicit approach, referred to as the enthalpy method, has been used to address multidimensional problems in which interface displacement is controlled by an energy flux. However, an analogous general approach has not been available for mass transfer and reaction analyses. This paper discusses initial 2-D results from a coupled experimental and computational effort to develop a mathematical model and computer code that will ultimately predict 3-D intermetallic growth in porous substrate-solder systems. The numerical model is based on an implicit interface tracking approach developed for diffusion-reaction analyses in complicated geometries. To illustrate the implicit approach with a "real" system, the 2-D calculations were based on the reaction couple formed between 63Sn-37Pb solder and 76Au-21Pt-3Pd substrates. Physical constants in the model were evaluated from experimental data. Consumption of the thick film was predicted as a function of time and compared with data from independent experiments.