By solving the Laplace equation for the electric field, using a relaxation method, the current direction and the local current density were determined. A 2-dimensional Lennard-Jones monocrystalline structure, in contact with an insulator, was assumed. Periodic boundary conditions on both the current and mass flows were set up in the direction of the applied voltage. The simulations showed that the generation of vacancies, their movement and disappearance, could occur in areas with a high current density. The diffusion coefficient was greatest when the current direction lay along the direction of closest atomic packing. The results suggested the existence of voltage and temperature thresholds for the metal line lifetime.

T.Ohkubo, Y.Hirotsu, K.Nikawa: Materials Transactions, 1996, 37[3], 454-7