## International summer school **MATERIALS 4.0**

**MATERIALS 4.0**

*The Art and Science of Constructing a Physics-Based Memristor Model*

### Dr. Stanley Williams (HP)

Tuesday, Sept. 12th, 16:00 – 17:00

Görgesbau (Helmholtzstr. 9), room 229

**Abstract:** Since the publication of “The Missing Memristor Found” in 2008, there have been many thousands of papers published on the topic of memristors. However, very few of those have featured quantitative compact models of the circuit elements described. This is not a reflection of the maturity of the field but rather the difficulty of constructing an accurate and predictive compact mathematical model for an electronic circuit element that displays memristor behavior. This Lecture will provide a snapshot of the current state of memristor modeling. Such models are essential for designing and simulating complex integrated circuits that contain memristors, and the types of applications being considered are increasing significantly. Although the fundamental equations that specify the device physics may be known, they usually comprise a set of coupled nonlinear integro-differential equations that are extremely challenging to solve in three dimensions, and standard multi-physics solvers may not have all the components needed for an accurate model. A numerical solution of the physics equations can require supercomputers and long execution times, which makes this approach useless for interactive simulation of large circuits that contain many such elements. Thus, the equations must be simplified dramatically, and it is not always clear which terms are the most important for the behavior of the device. On the other hand, a purely black box approach of fitting a set of experimental measurements to a convenient functional form runs the risk of poorly representing the behavior of the device in operating regimes outside the range in which the data were collected. Thus, a hybrid approach is often necessary, in which the mathematical formalism for a memristor provides the framework for the model and knowledge of the device physics defines the state variable(s), operating limits and asymptotic behavior necessary to make the model useful. After describing the challenge, the art and science of constructing a memristor model are illustrated by three examples: a description of a locally active and volatile device based on a thin film of niobium dioxide that undergoes both a thermal instability and an insulator to metal transition because of Joule heating, the original description of a nonvolatile memory device based on titanium dioxide in which the effective width of an electron tunnel barrier is determined by oxygen vacancy drift caused by an applied electric field, and the analysis of a ferromagnetic inductor as a mem-differential element.