Well-Posed Models of Memristive Devices

TL;DR

This paper addresses the mathematical ill-posedness of existing memristive device models by proposing a new modeling approach that ensures physical bounds and well-defined behavior, enabling robust simulation.

Contribution

It introduces a novel modeling framework for memristive devices using continuous primitives, correcting prior models and making them suitable for simulation in various analyses.

Findings

Corrected existing RRAM and memristor models to be well-posed

Developed models that respect physical bounds and exhibit proper DC behavior

Provided implementation in Verilog-A and MATLAB for simulation readiness

Abstract

Existing compact models for memristive devices (including RRAM and CBRAM) all suffer from issues related to mathematical ill-posedness and/or improper implementation. This limits their value for simulation and design and in some cases, results in qualitatively unphysical predictions. We identify the causes of ill-posedness in these models. We then show how memristive devices in general can be modelled using only continuous/smooth primitives in such a way that they always respect physical bounds for filament length and also feature well-defined and correct DC behaviour. We show how to express these models properly in languages like Verilog-A and ModSpec (MATLAB). We apply these methods to correct previously published RRAM and memristor models and make them well posed. The result is a collection of memristor models that may be dubbed "simulation-ready", i.e., that feature the right physical characteristics and are suitable for robust and consistent simulation in DC, AC, transient, etc., analyses. We provide implementations of these models in both ModSpec/MATLAB and Verilog-A.