Residual compression in area array packages induced by underfill shrinkage
Abstract A non-linear finite element model is developed to investigate underfill shrinkage as a possible source for obtaining beneficial residual compression in solder grid array interconnects. The axisymmetrical model geometry consists of a unit cell of concentric cylinders, the inner with properties representative of solder and the outer with properties representative of underfill, having an outer radius of half the array pitch. The solder, which is assumed to be eutectic, is modeled as an elastic–plastic material that exhibits creep behavior. The elastic modulus and Poisson’s ratio of the underfill material, Eu and νu, as well as the percentage of unconstrained linear shrinkage, ϕ, are varied to determine the influence these parameters have on the final steady-state stresses in the solder connections. To represent the underfill materials in common use, Eu ranged from 0.5 to 8.0 GPa, νu ranged from 0.2 to 0.4, and ϕ ranged from 0.2% to 1.0%. Upon shrinkage of the underfill during curing, the model predicts that the interconnect initially experiences residual compression in the axial direction. Due to tension in the radial direction, however, creep strain causes the axial compressive stress to lessen until a state of hydrostatic stress is reached. For the underfill properties tested, all the residual, steady-state stresses were compressive. The magnitude of this compression is shown in graphical form as a function of Eu, νu, and ϕ. An analytical expression for estimating the magnitude of residual compression as a function of these underfill properties is also included. The potential effect of the residual compression on the fatigue life of a package is discussed in the context of a particular example.