This paper presents a hybrid modelling approach that combines physics-based electromigration modelling (PEM) and statistical methods to evaluate the electromigration (EM) limits of nano-interconnects in mesh networks. The approach, which is also compatible with standard Place and Route (P&R) tools and practices, takes into account the positive impact of network redundancy on EM current limits. The study shows that conventional methods underestimate the EM current limits of a power delivery network (PDN) unit-cell by 80% due to their lack of consideration for redundancy. Additionally, the time-to-failure (TTF) distributions of a PDN unit-cell adhered to a lognormal distribution, where the lognormal sigma, σlogn, exhibits a 55% reduction compared to that of the single constituent interconnects. The study also found the negative voltage (i.e. ground or Vss) grid to be more susceptible to EM than the positive voltage, i.e. Vdd grid. In the examined grid unit-cell design, both the number of interconnect sites prone to voiding and also the magnitude of the peak tensile stress within the nano-interconnects were found to be 2-folds as high in the Vss case compared to Vdd. lognormal sigma of TFF for the grid unit-cells, σ_(logn-tile), show a marked reduction compared to the lognormal sigma of the constituent single interconnects, σ_logn, with a 50% and 66% decrease compared to single interconnects, for downstream (Vss) and upstream (Vdd), respectively. In addition, σ_(logn-tile) was 3-folds higher for downstream (Vss) compared to upstream (Vdd), whilst, in contrast this difference was only 2-folds at single interconnect level. 4.13-folds higher TTF50% was observed at grid unit-cell level for upstream compared to downstream operation which was also more pronounced than in the single interconnect level where the difference was only 2-folds. This research provides valuable insights into EM aging of nano-interconnects in mesh networks and could pragmatically enhance the accuracy of EM compliance evaluation methods.

The phenomena of electrical conductivity and electromigration in metallic systems are related, since in both cases the basic physical process is the scattering of conduction electrons by metal ions. Numerous searches have been made for equations connecting the conductivity with electromigration. In the case of a liquid metal, when using the Drude-Sommerfeld (DS) conduc-tivity equation, it was not possible to obtain a quantitative relationship between these phenomena, which would be correct. Attempts to find such a relationship when taking into ac-count the N. Mott correction (g - factor) in the DS equation were unsuccessful. This article proposes a different correction (b - factor) to the DS equation, which takes into account the pos-sibility of varying the momentum transferred by the conduction electron to a metal ion during the scattering. This correction allows to establish a quantitative relationship between conductivity and electromigration, as well as between electromigration in various binary systems with common components, in agreement with experiment. The proposed theory describes well, in particular, two- and multi-component metal systems of any concentration (the consistency rule for triangles A-B, B-C, C-A). The value of b - factor smoothly changes depending on the heat of vaporization of the metal, per unit volume.

This paper presents a comprehensive simulation framework for the investigation of electromigration (EM) in nano-interconnects, with a primary focus on unravelling the influential role of microstructure. To this end, a novel approach to generate conductor metal’s microstructures is presented, whereby a predefined statistical distribution of grain sizes obtained from experimental texture analyses can be incorporated into the developed EM modelling framework. The framework considers the impact of diffusion heterogeneity through the metal texture and interfaces. As such, the intricate interplay between microstructural/interfacial properties, and the resulting atomic flux and stress distribution within nanointerconnects could be investigated. Additionally, the study advances beyond the state of the art by comprehensively simulating all stages of electromigration, including stress evolution, void nucleation, and void dynamics while considering the impact of microstructure. Specifically, the model was employed to study the impact of trench dimensions on dual damascene copper texture and its subsequent impact on electromigration aging, where the model findings were corroborated by comparing to available experimental findings. A nearly linear augmentation in normalized lifetime was detected for aspect ratios equal to or greater than 1. However, a saturation is detected for wider lines with no effective enhancement in lifetime. An aspect ratio of 1 seems to maximize EM lifetime for each cross-sectional area by fostering a bamboo-like structure, where about 2-fold of increase is estimated when going from aspect ratio 2 to 1.