Percolation conductivity in hafnium sub-oxides

In this study, we demonstrated experimentally that formation of chains and islands of oxygen vacancies in hafnium sub-oxides (HfO_x, x<2) leads to percolation charge transport in such dielectrics. Basing on the model of Éfros-Shklovskii percolation theory, good quantitative agreement between the experimental and theoretical data of current-voltage characteristics was achieved. Based on the percolation theory suggested model shows that hafnium sub-oxides consist of mixtures of metallic Hf nanoscale clusters of 1-2nm distributed onto non-stoichiometric HfO_x. It was shown that reported approach might describe low resistance state current-voltage characteristics of resistive memory elements based on HfO_x.