Diffusional back flows during electromigration

Non-linear drift velocities have been reported when passing electrical currents through short metal lines. The aluminum drift velocity assumes very small Values or disappears completely when metal lines are short. It was proposed that atoms moving by electromigration cause buildup of stress gradients (and in some cases concentration gradients) opposing their flow. Below a critical length there is no flow and above it, the drift velocity changes linearly with additional current. For aluminum lines with vertical grain boundaries it was suggested that the stress gradients are sufficient for calculating the back flow. By measuring the stress gradients in metal lines at or below the critical length, the value of the effective charge for aluminum was deduced. This value is quite low and does not agree with commonly accepted values. An original experiment is revisited, numerical calculations seem to substantiate the low value of the effective charge. Proposals for further experimentation are given. (C) 1998 Acta Metallurgica Inc.