ON THE THEORY OF STEADY-STATE ELECTROMIGRATION IN THIN-FILMS

Steady-state electromigration along grain boundaries in a monatomic polycrystalline thin film has been analyzed in a two-dimensional model by balancing the (applied) electric and (induced) stress driving forces to achieve a zero flux divergence. The continuity of chemical potential requires a unique stress normal to each of the three boundaries terminating at a given triple point. These stresses and the steady-state fluxes are determined by a set of linear equations subject to boundary conditions at the intersection of grain boundaries with the film edge (edge points). When the normal stress is assumed zero at all edge points, the stress typically attains maxima and minima at triple points, whereas, when the flux is assumed zero at all edge points, the stress typically builds up monotonically in the field direction.