Single-parameter model for the post-breakdown conduction characteristics of HoTiO_x-based MIM capacitors

The post-breakdown conduction characteristics of holmium titanium oxide (HoTiO_x)-based metal-insulator-metal capacitors fabricated by the atomic layer deposition technique on Si substrates were investigated. Diode-like and power-law models were fitted to the experimental current-voltage (I-V) curves and the results assessed with the aim of detecting any possible correlation among the model parameters. It was found that the number of parameters involved can be reduced in both cases and that for the power-law model a single parameter is solely required to approximate the I-V curves in a wide current range (from 10^-11 to 10^-4 A). This property, which has also been observed in a variety of material systems, was used to simulate the bipolar switching behavior exhibited by the I-V characteristics. The connection with the physics of electron transport through atom-sized constrictions is discussed.