Closed-form analytical solution for on-switching dynamics in a TaO memristor

For the first time, the model of a physical nano-scale memristor is integrated analytically. A closed-form expression for the time evolution of the device memristance during the turn-on process is mathematically derived. The complexity of the inverse imaginary error function-based analytical formula clearly reflects the high degree of nonlinearity in the nano-device switching kinetics, which may typically span several orders of magnitude and is critically dependent on input and initial condition. The excellent agreement between the analytical solution and numerical simulation results clearly demonstrates the correctness of the theoretical derivation. The introduction of this formula represents the first step towards a systematic approach to circuit design with memristors.