Mathematical Model of Metal–Oxide Memristor Resistive Switching based on Full Physical Model of Heat and Mass Transfer of Oxygen Vacancies and Ions

Herein, a 1D mathematical model of memristor resistive switching that includes a full physical model of steady‐state heat and mass transfer is developed. The model considers ions and vacancies generation, recombination, and drift in an electric field in the memristor structure with dominant charge transport mechanism of electron tunnel hopping through vacancies. The distributions of vacancy concentration depending on the applied voltage and the given temperature of the memristor are found by numerical simulation. A good agreement is obtained between the part of the simulated current–voltage characteristics and the experimental one. There is no noticeable temperature gradient in a forming‐free nonfilament memristor. Therefore, the calculation of the vacancy concentration and the current–voltage characteristics in a forming‐free memristor with constant temperature over the film is appropriate. It is shown that the ion‐vacancy recombination can be neglected at temperatures over 600 K. In that case, the equation for ions, as well as the recombination term in the equation for vacancies can be neglected. The developed model at the same time consider all the processes occurring in the oxide layer and allow to reduce the computational complexity without significant loss of accuracy. The proposed model can be used to model large memristor arrays.