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 \'{E}fros-Shklovskii percolation theory good quantitative agreement between the experimental and theoretical data of current-voltage characteristics were achieved. Based on the percolation theory suggested model shows that hafnium sub-oxides consist of mixtures of metallic Hf nanoscale clusters of 1-2 nm 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$_x$. 
D. R. Islamov (1 and 2), V. A. Gritsenko (1 and 2), C. H. Cheng (3),   A. Chin (4) ((1) Rzhanov Institute of Semiconductor P...
cond-mat.mes-hall cond-mat.mtrl-sci