Electromigration damage mechanics of lead-free solder joints under pulsed DC: A computational model

Abstract

A numerical method for studying migration of voids driven by pulse electric current and thermal gradient in 95.5Sn–4Ag–0.5Cu (SAC405) solder joints is developed. The theoretical model involves coupling electron wind force, chemical potential, joule heating and stress gradient driving mass diffusion processes. Entropy based damage criteria is adopted to characterize the mass transportation mechanism, which utilize irreversible entropy production rate as a measure of material degradation. The pulse current induced EM damage results were compared with DC EM response under otherwise the same conditions. It is observed that increasing duty factor, current density and frequency leads to a faster damage accumulation. A mean time to failure (MTF) equation for solder joints under pulse current loadings is proposed which incorporates both thermomigration (TM) and EM damage. The failure mechanism is verified by our experimental results. It is observed that MTF is inversely proportional to rm, fp, and jn, where duty factor exponent m equals to 1.1, frequency exponent p equals to 1.43 and current density exponent is 1.96. This equation is effective only when pulse period is below thermal relaxation time, commonly in μs range.