The Poole-Frenkel laws and a pathway to multi-valued memory

We revisit the mechanism of Poole-Frenkel nonohmic conduction in materials of nonvolatile memory. Percolation theory is shown to explain both the Poole and Frenkel dependencies corresponding to the cases of small and large samples compared to the correlation radii of their percolation clusters, respectively. The applied bias modifies a limited number of microscopic resistances forming the percolation pathways. That understanding opens a pathway to multivalued nonvolatile memory and related neural network applications.