Competition between dislocation nucleation and void formation as the stress relaxation mechanism in passivated Cu interconnects

We perform systematic calculations to study the competition between the dislocation nucleation and void formation as stress relaxation mechanism in Cu interconnects under thermal stress, which is related to the aspect ratio (ratio of the film thickness to width) of the Cu lines. It is quantitatively found from both elastic-perfectly plastic model and kinematic strain hardening model that there exists a critical aspect ratio, below and above which the stress relaxation is dominated by the dislocation nucleation and void formation, respectively. The critical aspect ratio is revealed to modulate by both the length scale of the interconnects and the interfacial strength between the Cu lines and surroundings, suggesting potential application to achieve artificial controlling on stress relaxation mechanism in Cu lines. Calculations are in good agreement with available experiments.