Modeling electromigration-induced stress evolution and drift kinetics with a stress-dependent diffusivity

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Clement and Thompson have justified that it is necessary to take into account the stress dependence of atomic mobility when describing stress evolution in a metal conductor caused by electromigration [J. J. Clement and C. V. Thompson, J. Appl. Phys. 78, 900 (1995)]. In the present contribution the role of this dependence is considered in more detail, leading to qualitatively new results concerning stress evolution and drift kinetics. The stationary stress distribution over the length of the elastic zone of the conductor was shown to be nonlinear and asymmetrical at superthreshold conditions, with the zone of compressive stress being more extended than that of tensile stress. This also results in an asymmetrical pattern for plastic deformation, the hillocking zone being more extended than the voiding region at the cathode. The drift rate was shown to achieve its maximum value during the nonstationary stage of stress evolution and then to drop down to its stationary value. The duration of the nonstationary stage of stress evolution is proportional to the conductor length and inversely proportional to the current density. This is essentially different from the result obtained in all previous works. Our model also predicts that for conductors with a length much longer than the critical one, the nonstationary stage of stress evolution corresponds to a quasistationary stage for drift kinetics, during which a constant drift rate is observed. Finally, we will consider the consequences of taking into account the stress dependence of mobility when describing the effects of passivation and thermal stress on drift kinetics.