A Multi-Scale Homogenization Technique Applied to the Elastic Properties of Solders

Abstract

In modern microelectronic systems solder materials are frequently used. Consequently, it is of great importance to predict their lifetime and stability. In order to perform such an analysis, material properties are required. Since electronic devices and therefore the amounts of used materials become smaller and smaller, the influence of a changing microstructure on the mechanical properties must be examined. First, some analytical methods will be presented leading to upper and lower bounds for standard solder alloys. They also allow for an examination of the influence of certain micro-geometries. Second, a multi-scale approach is used in order to perform a more general analysis of different micro-structures. The constitutive equations are stated and a homogenization technique for elastic properties of arbitrary structures is derived. The resulting equations are solved numerically and the results are presented. For lamellar-type of structures, closed-form formulas are derived and the results will be compared to the numerical ones.