Inadequacy of Markov Model in Modeling of Electromigration-Induced Resistance Degradation

Electromigration-induced resistance change carries lot of information about the failure phenomenon and is an important aspect of the degradation process. Hence modeling electromigration-induced resistance degradation is of paramount importance, especially for submicron dual-damascene Cu interconnects. On the other hand, Markov model is extensively used in reliability engineering. This study focuses on the nature of the time-domain discrete states in the failure process. We argue about the memoryless discrete states in Markovian model to predict the electromigration-induced resistance degradation. The physics behind the electromigration failure does not support the application of Markovian model in electromigration and the inadequacy of such application is described. In contrast to the memoryless states, the resistance change behavior can be better explained by considering very generic and dependent discrete states. Whenever required, simulations are performed to obtain the resistance change behaviors. Our findings are concurrence with the experimental observations.