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Handbook of Memristor Networks pp 267–285Cite as

The Art and Science of Constructing a Memristor Model: Updated

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Abstract

This chapter is updated from an earlier version [63]. In the few years since that book chapter was written, there have been several thousand papers published on the topic of memristors, but very few new compact memristor models have appeared. 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. Given the rapid advances in the field in general, it is time to provide another snapshot of the state of memristor modeling, even though any such attempt will be incomplete. 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 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 completely rewritten 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 recent detailed examination of the transport properties and identification of the primary state variable for tantalum oxide.

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Authors and Affiliations

  1. Hewlett Packard Labs, Palo Alto, CA, USA

    Suhas Kumar, Gary Gibson, Catherine E. Graves, Matthew D. Pickett, John Paul Strachan & R. Stanley Williams

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  1. Suhas Kumar
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  2. Gary Gibson
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  3. Catherine E. Graves
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  4. Matthew D. Pickett
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  6. R. Stanley Williams
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Correspondence to R. Stanley Williams .

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Editors and Affiliations

  1. Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA, USA

    Leon Chua

  2. Democritus University of Thrace, Xanthi, Greece

    Georgios Ch. Sirakoulis

  3. Department of Computer Science and Creative Technologies, University of the West of England, Bristol, UK

    Andrew Adamatzky

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Kumar, S., Gibson, G., Graves, C.E., Pickett, M.D., Strachan, J.P., Stanley Williams, R. (2019). The Art and Science of Constructing a Memristor Model: Updated. In: Chua, L., Sirakoulis, G., Adamatzky, A. (eds) Handbook of Memristor Networks. Springer, Cham. https://doi.org/10.1007/978-3-319-76375-0_9

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  • DOI: https://doi.org/10.1007/978-3-319-76375-0_9

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