New electromigration modeling and analysis considering time-varying temperature and current densities

Electromigration (EM) is projected to be the major reliability issue for current and future VLSI technologies. However, existing EM models and assessment techniques are mainly based on the constant current density and temperature. Such models will not work well at the system level as the current density (power) and temperature are changing with time due to different tasks (their loans) applied at run time. Existing EM approaches using average current density or temperature, however, will lead to significant errors as shown in this work. In this paper, we propose a new physics-based EM model considering time-varying temperature and current density, which reflects a more practical chip working conditions especially for multi-core and emerging 3D ICs. We study the impacts of the time-varying current densities and temperature profiles on EM-induced lifetime of a wire for both nucleation phase and growth phase. We propose a fast stress calculation method for given time-varying temperature and current densities for the nucleation phase. We further develop new formulae to compute the resistance changes in growth phase due to changing temperature and current densities. Experimental results show that the proposed method shows an excellent agreement with the detailed numerical analysis but with much improved efficiency.