Line length dependence of threshold current density and driving force in eutectic SnPb and SnAgCu solder electromigration

The relationship between the threshold current density and the critical line length in eutectic SnPb and SnAgCu electromigrations were examined using solder lines with the various lengths ranging from 100to1000μm. When the electron wind-force was balanced by the back-stress gradient force, the net flux of electromigration is zero, at which the current density and line length are defined as the threshold current density and the critical length, respectively. It was found that in SnAgCu electromigration, the 1∕L dependence on the threshold current density showed good agreement, whereas the threshold current densities of the eutectic SnPb deviated from the 1∕L dependence. The balance between the electron wind-force and the back-stress gradient force was the main factor determining the threshold product of SnAgCu electromigration. On the other hand, in the case of eutectic SnPb, the chemical driving force is contributed as a back-flux force in addition to the back-stress gradient force. The existence of the chemical driving force was caused by the nonequilibrium Pb concentration inside the Pb-rich phases between the cathode and anode during the electromigration procedure.