Studying the eﬀect of Cu microstructure on electromigration reliability using statistical simulation
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Electromigration (EM) describes the mass transport in a metal driven by the momentum transfer from electron scattering with metal ions. This can develop into a degradation process due to void growth for on-chip interconnects when subjected to high electric current densities and eventual interconnect line failure. The mass transport occurs in decreasing order of magnitude along interfaces grain boundaries and in bulk. The diffusivities along interfaces and grain boundaries are determined by crystallographic orientation. Diffusion discontinuities can create flux divergent sites that control void growth kinetics and failure characteristics. Most of the earlier studies of EM modeling have assumed an averaged diffusivity measured across the underlying crystallographic microstructure. The objective of this thesis is to study the effect of microstructure on EM reliability by modeling of the diffusivity corresponding to grain orientation at the interface and to project the EM lifetime and the standard deviation (sigma) of the failure statistics. The simulation consists of two parts. First, the microstructure is generated using a Monte Carlo algorithm based on the Potts model. In the second stage, the void formation and growth induced by electromigration is modeled until a maximum time elapsed. During the void growth, the electrical resistance is monitored to search for EM failure subjected to a 400% (5 times the initial value) resistance increase failure criterion. The simulated electromigration lifetimes were found to follow a log-normal distribution. The computations were carried out on a parallel computer, simulating a population of 100 interconnect segments with random microstructure configurations. In this way, the 100 interconnect segments form the basis for statistical analysis of a special simulation run. Simulation runs were carried out with microstructures varying over a range of grain sizes and diffusivity for the top interface. In the simulation, four cases were studied and compared to results from EM experiments. These four cases were large and small grains combined with slow and fast diffusing top interfaces. Results from the simulation revealed a consistent trend in that large grains prolong the electromigration lifetime, especially for the case of a slow diffusing top interface. This trend is also consistent with the experimental results where the lifetime was found to increase in the order of small grain/fast interface, large grain/fast interface, small grain/slow interface and large grain/slow interface. The overall agreement, however, is only qualitative. For instance, the EM experiment showed a lifetime improvement of more than 100 fold whereas the simulation only showed an improvement of 6 fold from fast to slow interface for large grains.