Finite Element Modeling of Three-Dimensional Solder Joint Geometry in SMT

Abstract

The three-dimensional geometry of a solder joint associated with a surface mount electronic packaging process is modeled by employing a height function, z = ζ(x, y), and applying the finite element solution procedure. A rigorous formulation based on the variational methodologies is derived in two-dimensional integral form so that the standard numerical techniques for plane problems can be applied. The appropriate finite element formulation and corresponding solution procedures are devised. Numerical examples representing circular and rectangular pads are tested for validation of the developed simulator and illustration of its overall capability. The method presented in this paper shows a remarkable alternative method to the complete three-dimensional finite element approach. The developed method eliminates the difficulties associated with setting up three-dimensional brick meshes or adjusting the shape of the joint body to determine the equilibrium geometry of a soldering joint.