Master curve synthesis by effective viscoelastic plastic material modeling

Finite Element Simulations of highly integrated and large electronics packages with detailed elastic-plastic material modeling of thousands of solder balls are still challenging tasks for today's computation systems. The complex geometry and mesh and the usage of time consuming creep laws for solder materials makes it nearly impossible to calculate different geometries or process parameters. This paper describes a method to reduce the complexity of the mesh in the region of the solder balls and surrounding underfill with one simple block physically described as a viscoelastic material. Therefore a viscoelastic/plastic behavior of a complex unit cell was modeled in a temperature dependent harmonic frequency sweep or relaxation simulation. The reaction of the unit cell was utilized to synthesize the master curve, Prony coefficients and shift function to an effective material model. Finally an error estimation of the unit cell approach was carried out. Therefore a reliability simulation was modeled replacing the solder balls and the surrounding underfill by the effective material. A flip chip on FR4 model with underfill was used to benchmark the effective material model approach against detailed models without any complexity reduction. The results show that the introduced effective material approach can be used to cut down computation time significantly without losing accuracy in life time prediction.