Modeling the Diffusion-Driven Growth of a Pre-Existing Gas Bubble in Molten Tin

Finite element method is utilized to solve the diffusion equation and model the diffusion driven growth of a pre-existing spherical gas bubble in molten tin at the solder/substrate interface for reflow time of 120 s and temperature of 250 degrees C. The gibbs free energy change required for determining the equilibrium concentration at liquid solder/gas bubble boundary was calculated using the thermodynamic polynomial coefficients. The rate of change of radius, as function of concentration flux, is calculated using the lagrangian mesh update methodology. With an initial diameter of 20 mu m, the bubble growth is calculated as a function of contact angle. When the wetting angle is varied from a value of 30 degrees to 135 degrees, the numerical calculation has yielded the final sizes for the bubble to change from 62.87 mu m to 82.8 mu m respectively. The effect of wetting transition in the growth of bubble was studied by the in-situ observation of bubble dynamics through synchrotron radiation imaging technique. The scanning electron microscopy images of the morphologies of intermetallic compounds influenced by growing bubble in Sn/Cu solder joint and bubble pictures obtained through synchrotron radiation are utilized to get the experimental size of the bubble. The mean experimental bubble diameter has been obtained as 76.39 mu m. The growing bubble inhibits the growth of intermetallic compound at its vicinity and thereby reduces the strength of solder joints.