Mathematical modeling of resistive states and dynamic switching of a metal oxide memristor

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

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 mathematical model of resistive states and dynamic switching of a memristor from a low-conductive to a highly-conductive state is presented. The model based on a physical model of charge transport without taking into account the heat transfer process in the metal-oxide-metal structure with the dominant transport mechanism of electron tunneling through oxygen vacancies migrating under the influence of an inhomogeneous self-consistent electric field. An analytical solution for the oxygen vacancies distribution over the oxide layer was found by the approximation of a constant electric field. The memristor model with inhomogeneous electric field is implemented as a specialized program based on the finite difference method for solving a stationary nonlinear first-order differential equation. This model well describes the physical effect of reduction in the conductivity growth of a thin dielectric layer under the dominant transport mechanism of electron tunneling through oxygen vacancies, which arises as a result of an increase in the concentration of trapped electrons with increasing voltage at the electrodes near the threshold switching voltage. Numerical modeling of discrete resistive states and dynamic resistive switching of a memristor has been carried out. The obtained current-voltage characteristic of the memristor with the help of numerical simulation is in better agreement with the experimental data compared to the analytical simulation. The numerical model can be used in the research and development of memristors with given electrical characteristics. A simple analytical memristor model, which does not require a large amount of computation, is applicable for modeling basic processes such as write operation, signal summation, and associative self-learning that occur in super-large memory and logic matrices of a biomorphic neuroprocessor when memristors are used as synapses of neurons.

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