Concurrent electromigration and creep in lead-free solder

When electric current flows in a solder bump, electromigration generates stress, but creep relaxes it. After some time, the bump develops a steady-state stress field. We present a theory to show that the two processes — electromigration and creep — set an intrinsic length. When the intrinsic length is large compared to the height of the bump, electromigration is fast relative to creep and the steady-state stress field is linearly distributed in the bump. When the intrinsic length is small compared to the height of the bump, electromigration is slow relative to creep and the steady-state stress field nearly vanishes in the bump, except in a thin layer along the boundary of the bump. We further show that a critical electric current exists, below which the bump can sustain the steady-state stress field without forming voids. Theoretical predictions are compared with existing experimental observations.