Numerical investigations of the electromigration boundary value problem

The electromigration diffusion boundary value problem with the perfectly blocking diffusion barrier is numerically investigated. Three possible boundary conditions are identified as physically meaningful and the solutions compared at the blocking barrier. It is seen that the solution of M. Shatzkes and J. R. Lloyd [J. Appl. Phys. 59, 3890 (1986)] is a good approximation for the time to failure if the critical vacancy concentration for failure is not too near a steady-state value. A dimensionless parameter is introduced which may be useful in estimating ultimate electromigration performance.