Equilibrium current density balancing two atomic flows in coupled problems of electromigration and thermomigration in unpassivated gold film

This work studies the coupled problems of electromigration (EM)- and thermomigration (TM)-induced anomalous atomic flows through experiments for demonstrating EM and TM tests and the theoretical formulation describing the atomic behavior. A two-dimensional unpassivated Au interconnect, having a protrusion nose area where atoms are accumulated, was used for observing hillock formation under current stressing and heating of the substrates. The hillock formation locations depend on the experimental conditions, including current density and temperature involved with the driving forces of EM and TM. The relationship between coupling the EM- and TM-induced driving forces was clarified through the experimental observation of the hillock formation location and the proposition of the equilibrium current density. Considering the magnitude relationship of the EM- and TM-induced driving forces, it was proved that an equilibrium current density, below or above which EM or TM is dominant, respectively, exists. The theoretical equilibrium current density was formulated to estimate the equilibrium state of EM and TM, deducing the behavior of hillock formations by EM and TM. Hillocks form at the nose edge due to EM-induced forward flow in the case of lower current density and higher temperature. Conversely, hillocks form at an area slightly away from the nose end due to TM-induced backward flow in the case of higher current density and lower temperature.