Physics-based memristor models

In order to utilize memristors in circuits, one needs high-quality predictive models that can be used for simulations to act as a design aid. Whenever possible, we base our models on the known physics of the memristors we are using. To that end, we perform a wide range of materials characterizations and electronic measurements on which to base the model. However, given the complexity of the physical processes that occur in the devices, such as drift-diffusion-thermophoresis in ion-migration based memristors and Mott transitions in locally active memristors, the corresponding detailed mathematical descriptions are far too complex to solve analytically and numerical solutions are too time consuming to include in a simulation. We thus need to find simpler, analytical approximations that can match the measured behavior of the memristors over many orders of magnitude in time and a wide range of applied voltage. We present some new models that we have developed and describe how they are derived.