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Advances in Condensed Matter Physics
Volume 2015 (2015), Article ID 136938, 8 pages
Research Article

Model of Reversible Breakdown in HfO2 Based on Fractal Patterns

Department of Information Engineering, Electronics and Communications, Sapienza University of Rome, Via Eudossiana 18, 00184 Rome, Italy

Received 21 October 2014; Revised 27 December 2014; Accepted 4 January 2015

Academic Editor: Jan A. Jung

Copyright © 2015 P. Lorenzi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We propose a model of the kinetics of reversible breakdown in metal-insulator-metal structures with afnia based on the growth of fractal patterns of defects when the insulator is subject to an external voltage. The probability that a defect is (or is not) generated and the position where it is generated depend on the electric field distribution. The new defect moves accordingly to fractal rules and attach to another defect in a tree branch. When the two electrodes sandwiching the insulating film are connected a conductive filament is formed and the breakdown takes place. The model is calibrated with experiments inducing metastable soft breakdown events in Pt/HfO2/Pt capacitors.