Nonlinear finite element simulation of thermoviscoplastic deformation of C4 solder joints in high density packaging under thermal cycling

A nonlinear finite element model has been used to simulate the thermally induced viscoplastic deformation of the controlled collapse chip connections (C4) solder joints in a high density single chip module (SCM). The dependence of solder joint deformation on the tin content was demonstrated for various lead-rich lead-tin alloys with the tin content varying from 2 wt.% to 10 wt.%. A thermoviscoplasticity theory was introduced for modeling the inelastic stress-strain response of the Pb-Sn alloys. In the theory, the creep and plasticity were separately considered and formulated. The Garofalo hyperbolic sine law was used to model the creep behavior, while the Prandtl-Reuss equation was used for the rate independent plastic deformation. The modeled SCM consists of a 5-mm silicon chip attached to a 50-mm alumina substrate by an array of C4 with diameter of 0.1 mm on a 0.2-mm I/O pitch. A cyclic temperature load of 0-100°C at a frequency of 3 cycles per hour was applied to the SCM. It is concluded that the decrease of the tin content induces a decrease of the equivalent creep strain and Mises stress, but an increase of the equivalent plastic strain for the edge C4 in the SCM