Finite element simulations were used to calculate the rate of whisker growth due to intermetallic formation in a Sn film with columnar grain structure on a Cu substrate. The simulations account for plastic flow by dislocation motion within the grains, as well as diffusion along grain boundaries. Grains with a slightly lower yield stress than their neighbours were shown to act as sinks for material and were progressively extruded from the film. A simple analytical model was developed to estimate the resulting whisker growth rate, and was shown to be in good agreement with experimental measurements.

A Model of Sn Whisker Growth by Coupled Plastic Flow and Grain Boundary Diffusion. E.J.Buchovecky, N.Du, A.F.Bower: Applied Physics Letters, 2009, 94[19], 191904