How Memristors Work: A Step-by-Step Guide to the CALM Model

Abstract

Memristors made of very different materials, halide perovskites, metal oxides and nanofluidic channels, show a common set of dynamical features: two limiting conductances, hysteresis that depends on the scan rate, regular and inverted hysteresis loops, large and negative capacitances and inductive loops in impedance spectra, and potentiation and depression under pulse trains. This tutorial shows how a single minimal model, the conductance-activated quasi-linear memristor (CALM) model, explains all these features with three ingredients: the two conductance states, the rectification function x_eq (u) and the characteristic time tau(u). The tutorial is a slide presentation that the reader can follow alone, with exercises designed to be solved with the help of an AI assistant, reference Python code, and this support text. The text can also be read on its own: Section 4 gives a compact account of the content of the slides, with the main equations and figures, and the solutions to the exercises are given at the end.