As a high-field voltage sweep proceeds, the post-breakdown I-V characteristic of an ultrathin gate oxide shows abrupt upward and downward steps which are a clear manifestation of the local area character of the associated conduction mechanism. Moreover, the leakage current through the breakdown spots exhibits conductance values very similar to those found in quantum point contacts, indicating that the conductive paths connecting both electrodes have atomic-scale dimensions. In this work, we propose that some of these jumps in the I-V characteristic might be caused by a local rearrangement of atoms or defects due to the high current density forced to flow through the breakdown path. This is a well-known effect in point contacts where the so-called electron wind force encourages the atomic motion.