An Inverse Procedure for Estimating the Anand Viscoplastic Constitutive Model Parameters for Copper Free-Air Ball

Due to its superior mechanical and electrical properties, as well as low cost, Cu is gradually replacing Au as wire bonding material. However, since copper is a stiffer material, it requires greater bonding force, which in turn increases risk of bond pad cratering and inter-layer dielectric (ILD) fracture. A critical challenge to numerically modeling the pad cratering or ILD fracture is the availability of appropriate constitutive models for the Cu free-air balls (FAB). In this work we first present rate and temperature dependent force-displacement response of micron-sized Cu FAB characterized using a custom-built high-precision microtester. From the experimental force-displacement data, Anand viscoplastic constitutive model parameters are obtained using an inverse finite element analysis procedure, where the material parameters are iterated through an automated procedure until the finite element and experimental force-displacement responses match. The constitutive model parameters to describe the FAB behavior at low and intermediate strain rates and at high temperatures are obtained and reported in this paper.