Mixed-mode singularity and temperature effects on dislocation nucleation in strained interconnects

Dislocations can be nucleated from sharp geometric features in strained interconnects due to the thermal expansion coefficient mismatch, lattice mismatch, or stresses that arise during material processing. The asymptotic stress fields near the edge root can be described by mixed-mode singularities, which depend on the dihedral angle and material properties, and a transverse T-stress, which depends on how residual stress is realized in the interconnects. The critical condition for stress nucleation can be determined when an appropriate measure of the stress intensity factors (SIFs) reaches a critical value. This method, however, does not offer an explicit picture of the dislocation nucleation process so that it has difficulties in studying complicated structures, mode mixity effects, and more importantly the temperature effects. Using the Peierls concept, a dislocation can be described by a continuous slip field, and the dislocation nucleation occurs when the total potential energy reaches a stationary state. Through implementing this ad hoc interface model into a finite element framework, it is found that dislocation nucleation becomes more difficult with the increase of mode mixity, or the decrease of the T-stress, or the decrease of the length-to-height ratio of the surface pad, while the shape of the surface pad, being a square or a long line, plays a less important role. The Peierls dislocation model also allows us to determine the activation energy, which is the energy needed for the thermally activated, mechanically assisted dislocation nucleation when the applied load is lower than the athermal critical value. The calculated saddle point configuration agrees well with the molecular simulations in literature. Suggestions on making immortal strained interconnects are made.