Analysis of a drift-diffusion model with Fermi–Dirac statistics for memristive devices

Abstract

Memristors can be seen as nonlinear resistors with memory. This makes them a promising device in neuromorphic computing, as they show a resistive switching behaviour, thus being ideal candidates to build artificial neurons or synapses. Perovskite solar cells have emerged as a groundbreaking technology, due to the perovskite materials’ outstanding optical and electronical properties. These perovskite materials exhibit a memristive behaviour, which naturally leads to their use in memristors. We analyze a drift-diffusion model for memristors including Fermi–Dirac statistics for the electrons and holes and Blakemore statistics for the oxygen vacancies, coupled to a Poisson equation for the electric potential. Using a-priori estimates obtained from the related free energy functional we prove the existence of weak solutions to the system. Additionally we show the uniform-in-time boundedness of solutions in three space dimensions.