A study of microstructural change of lead-containing and lead free solders

摘要

This paper presents experiments and a detailed numerical simulation of the coarsening phenomenon observed in microelectronic solder materials that are subjected to high homologeous temperatures in combination with thermo-mechanical stresses. The type of experiments performed include preparation of eutectic SnPb and SnAg solder specimens subjected to well defined thermal aging and microstructural analysis by optical microscopy and SEM. The simulations are based on a phase field model which, for simplicity, is explicitly formulated for a binary alloy. To this end, the thermomechanical stresses originating within a Representative Volume Element (RVE) of the solder material are calculated first. This is achieved by means of a closed-form solution of the Navier equations resulting in explicit expressions for the displacements of an anisotropic, heterogeneous, thermally stressed elastic medium in discrete Fourier space. Inverse discrete Fourier transforms are then applied to these expressions in order to obtain the local stresses in real space. These in turn are then inserted into an extended expression for the diffusion flux, which, in addition to the classical driving force of a concentration gradient takes the influence of different surface tensions between the solder phases as well as the local strain energy into account. The equations are evaluated numerically for the exemplary case of eutectic SnPb solder, for which all material constants re known explicitly. A comparison with aging experiments is performed.