Model of reversible breakdown in HfO2 based on fractal patterns

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.