Stress Migration Modeling Using Probabilistic Physics of Failure

It is now well accepted that the unbiased isothermal resistance drift and latent open-via failures in Al and Cu metal interconnects is due to the formation and growth of stress induced voids (SIVs). While the basic description of SIV was established early on, it remains an important task to characterize process and design variations and their impacts on reliability. The physics-of-failure arises from the geometrical confinement and the mismatch in coefficients of thermal expansion of the back-end of line (BEOL) materials with subsequent diffusive relaxation. The basic physics must be updated to include the effects of patterned structural features, microstructure, elastic anisotropy, adhesion, and nonlocal interactions. Also, due to the relaxation of the stress with time, it is found that the failure rate diminishes as the driving force reduces, leading to a probabilistic immortality very similar to the Blech effect in electro-migration. However, in some cases, the approach to this saturation is very slow and some failures may "heal." At great age, the cumulative failure (hazard) saturates the value which is proportional to the void initiation density. With the assumption of a non-zero surface energy, the observed reverse resistance drift can be modeled as well as the open failure recovery as a void sintering effect. From the probabilistic physics of the failure model for SIV, we can derive predictions of the failure-free lifetime and immortal fraction as well as scaling laws for linewidth, microstructure, film and via adhesion, and via-size. The model also provides some insight on the physics behind the super-redundancy effect of additional via placement. The model is fit to standard high-temperature storage (125 °C to 200 °C) data, as well as long-term (>3 years) data at 30 °C, from a 110-nm Cu/Ta/TaN/low-k BEOL process.