Nonlinear effects in memristors with mobile vacancies.

I V Boylo,K L Metlov

doi:10.1098/rsos.210677

Abstract

Because local concentration of vacancies in any material is bounded, their motion must be accompanied by nonlinear effects. Here, we look for such effects in a simple model for electric field-driven vacancy motion in a memristor, solving the corresponding nonlinear Burgers’ equation with impermeable nonlinear boundary conditions exactly. We find non-monotonous relaxation of the resistance while switching between the stable (‘on’ and ‘off’) states, and qualitatively different dependencies of switching time (under applied current) and relaxation time (under no current) on the memristor length. Our solution can serve as a useful benchmark for simulations of more complex memristor models.

Highlights

Memristors were proposed by Chua [1] as another building block for electric circuits
We look for such effects in a simple model for electric field-driven vacancy motion in a memristor, solving the corresponding nonlinear Burgers’ equation with impermeable nonlinear boundary conditions exactly
We find non-monotonous relaxation of the resistance while switching between the stable (‘on’ and ‘off’) states, and qualitatively different dependencies of switching time and relaxation time on the memristor length

Summary

Introduction

Memristors were proposed by Chua [1] as another (originally missing) building block for electric circuits. Among different types of memristors, the ones in which oxygen vacancy movement processes play the key role in formation of resistive states have attracted substantial attention [7,8,9,10]. A more detailed description in terms of spatial distribution of the vacancy concentration was developed in many recent modelling works [13,14,15,16,17,18,19,20,21], where the underlying kinetic equations were solved numerically. Inherent nonlinearity in these models can be expressed via the nonlinear diffusion equation, predicting a royalsocietypublishing.org/journal/rsos R. We study a simpler (but exactly solvable) memristor model in strongly nonlinear regime, reducing to Burgers’ equation for vacancy concentration with impermeable nonlinear boundary conditions, which is formulated

Exactly solvable memristor

Driven vacancy motion

Evolution and relaxation of the resistance

Conclusion