Characteristic length and time in electromigration

A characteristic length can be defined as the distance a vacancy moves under an electromigration force to do thermal work KT. The times for a vacancy to drift and diffuse this characteristic length are equal and thus define a characteristic time. The diffusion coefficient and the drift velocity are unity when these characteristic values are used as units of length and time. Therefore, when these units are used in the absence of vacancy sources and sinks, the vacancy continuity equation contains no parameters. These considerations are used to estimate the length current density threshold, the electromigration failure times, the edge-displacement velocity, and the incubation time. These estimates are consistent with published experimental results.