Mathematical modeling of memristor resistive switching based on mass transfer full model of oxygen vacancies and ions

About the authors:

Abdulla H. Ebrahim, Cand. Sci. (Phys.-Math.), Junior Researcher, Memristive Materials Laboratory, Center for Nature-Inspired Engineering, University of Tyumen, Tyumen, Russia; abdulla.ybragim@mail.ru, https://orcid.org/0000-0002-1709-9882

Alexander N. Busygin, Cand. Sci. (Phys.-Math.), Associate Professor, Department of Applied and Technical Physics, School of Natural Sciences, University of Tyumen, Tyumen, Russia; Senior Researcher, Memristive Materials Laboratory, Center for Nature-Inspired Engineering, University of Tyumen, Tyumen, Russia; a.n.busygin@utmn.ru, https://orcid.org/0000-0002-3439-8067

Sergey Yu. Udovichenko, Dr. Sci. (Phys.-Math.), Professor, Department of Applied and Tech­nical Physics, School of Natural Sciences, University of Tyumen, Tyumen, Russia; Scientific Director of the Memristive Materials Laboratory, Center for Nature-Inspired Engineering, University of Tyumen, Tyumen, Russia; udotgu@mail.ru, https://orcid.org/0000-0003-3583-7081

Abstract:

A relatively simple mathematical model of dynamic switching of a memristor has been created based on a fairly complete physical model of the processes of stationary mass transfer of oxygen vacancies and ions, considering their generation, recombination and diffusion in electric field in the “metal-oxide-metal” structure with the dominant transport mechanism of electron tunneling through oxygen vacancies.

The results of numerical simulation of mass transfer of oxygen vacancies along thickness of the oxide layer of the memristor are presented. The distributions of vacancy concentration during their diffusion in an electric field are found, taking into account the processes of generation and recombination with ions, depending on the applied voltage to the electrodes and on the temperature of the memristor. A good coincidence of the volt-ampere characteristics part found as a result of numerical simulation and a series of experiments is obtained.

It is shown that under conditions of more than 600 K memristor temperature, it is possible to neglect the process of ion-vacancy recombination and significantly simplify the procedure for mathematical modeling of memristor resistive switching by eliminating the oxygen mass transfer equation, as well as the recombination term in the stationary equation of oxygen vacancies mass transfer.

The developed mathematical model of memristor dynamic switching, including a system of stationary ordinary differential equations, is designed to simulate the operation of large memristor arrays in neuromorphic computing devices and may be preferable in relation to known circuit models that include a certain set of fitting parameters to match the simulation results with the memristor experimental characteristics.

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