Simulations of stress evolution and the current density scaling of electromigration-induced failure times in pure and alloyed interconnects

Abstract

An electromigration model is developed to simulate the reliability of Al and Al–Cu interconnects. A polynomial expression for the free energy of solution by Murray [Int. Met. Rev. 30, 211 (1985)] was used to calculate the chemical potential for Al and Cu while the diffusivities were defined based on a Cu-trapping model by Rosenberg [J. Vac. Sci. Technol. 9, 263 (1972)]. The effects of Cu on stress evolution and lifetime were investigated in all-bamboo and near-bamboo stud-to-stud structures. In addition, the significance of the effect of mechanical stress on the diffusivity of both Al and Cu was determined in all-bamboo and near-bamboo lines. The void nucleation and growth process was simulated in 200 μm, stud-to-stud lines. Current density scaling behavior for void-nucleation-limited failure and void-growth-limited failure modes was simulated in long, stud-to-stud lines. Current density exponents of both n=2 for void nucleation and n=1 for void growth failure modes were found in both pure Al and Al–Cu lines. Limitations of the most widely used current density scaling law (Black’s equation) in the analysis of the reliability of stud-to-stud lines are discussed. By modifying the input materials properties used in this model (when they are known), this model can be adapted to predict the reliability of other interconnect materials such as pure Cu and Cu alloys.