Isothermal Switching and Detailed Filament Evolution in Memristive Systems

The steady-state solution of filamentary memristive switching may be derived directly from the heat equation, modelling vertical and radial heat flow. This solution is shown to provide a continuous and accurate description of the evolution of the filament radius, composition, heat flow, and temperature during switching, and is shown to apply to a large range of switching materials and experimental time-scales.