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

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Abstract
A nonlinear finite element model has been used to simulate the thermally induced viscoplastic deformation of the controlled collapse chip connection (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 Pb-Sn alloys with the tin content varying from 2 wt% to 10 wt%. A thermoviscoplasticity theory was introduced for modeling inelastic stress-strain response of the Pb-Sn alloys. In the theory, the creep and plasticity were separately considered and formulated. The Garafalo 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 50 mm alumina substrate by an array of C4 with diameter of O.1 mm on a 0.2 mm I/O pitch. A cyclic temperature load of 0 to 100°C at frequency of 3 cycles per hour was applied to the SCM, and a nonlinear finite element program ABAQUS was used to numerically study the effect of the tin content on the stress-strain response of the C4. 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

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