Evaluation of tin-whisker growth during thermal-cycle testing using stress- and mass-diffusion analysis

To evaluate tin-whisker growth during thermal cycling tests, a simulation technique for calculating the change in atomic-density distribution of tin caused by a change in temperature, which induces a stress gradient in polycrystalline tin plating, was developed. This technique uses the finite-element method (FEM), molecular-dynamics (MD) simulation, and X-ray diffraction (XRD). Specifically, an FEM model was used to simulate stress-induced diffusion, including grain-boundary diffusion, in a tin coating on copper leads by using the stress- and mass-diffusion-analysis function of commercial FEM software. The stress analysis model considered elasticity anisotropy, thermal-expansion anisotropy, and crystal orientation of β-tin. Crystal orientations were assigned to tin grains in the model according to reference XRD measurements. Diffusion coefficients for the mass-diffusion analysis were calculated by MD simulation. Two models with different crystal-orientation distributions were evaluated. Samples with a higher tin atomic density were found to be more likely to have longer tin whiskers and higher whisker density. It is concluded from these results that the tin-atomic-density distribution calculated with this model can be used as an effective indicator of the propensity to form tin whiskers.