It was recalled that non-linear drift velocities were reported to occur upon passing currents through short metal lines. The Al drift velocity had very small values, or disappeared completely, when the metal lines were short. It was proposed that atoms which moved via electromigration set up stress gradients (and sometimes concentration gradients) which opposed their motion. Below a critical length there was no flow and, above it, the drift velocity changed linearly with additional current. In the case of Al lines with vertical grain boundaries, it was suggested that the stress gradients were sufficient to calculate the back-flow. By measuring the stress gradients in metal lines at (or below) the critical length, the value of the effective charge for Al was deduced. This value was quite low, and did not agree with the usually accepted values.

Diffusional Back Flows During Electromigration I.A.Blech: Acta Materialia, 1998, 46[11], 3717-23