Localized Conduction Channels in Memristors

Since the early 2000s, the impending end of Moore's scaling, as the physical limits to shrinking transistors have been approached, has fueled interest in improving the functionality and efficiency of integrated circuits by employing memristors or two-terminal resistive switches. Formation (or avoidance) of localized conducting channels in many memristors, often called "filaments", has been established as the basis for their operation. While we understand some qualitative aspects of the physical and thermodynamic origins of conduction localization, there are not yet quantitative models that allow us to predict when they will form or how large they will be. Here we compile observations and explanations of channel formation that have appeared in the literature since the 1930s, show how many of these seemingly unrelated pieces fit together, and outline what is needed to complete the puzzle. This understanding will be a necessary predictive component for the design and fabrication of post-Moore's-era electronics.