The Art and Science of Constructing a Memristor Model
Constructing an accurate and predictive compact mathematical model for an electronic circuit element that displays memristor behavior is extremely challenging, but it is also essential for designing and modeling complex integrated circuits that contain th
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The Art and Science of Constructing a Memristor Model R. Stanley Williams and Matthew D. Pickett
3.1 Introduction The methods utilized here for constructing a useful model of a memristor [6, 7] are adapted from those described by Prof. Leon O. Chua [8, 9] to illustrate the more general problem of device modeling for any nonlinear circuit elements. The basic reason why creating a device model is so difficult is that one is essentially trying to solve an inverse problem in a complex nonlinear system. Experience has shown that the total time required for analyzing a particular system theoretically to capture the essential device physics, collecting a substantial and robust electrical data set, testing various hypotheses and finally iterating to a model that reproduces the measured nonlinear behavior of a memristor to satisfactory accuracy generally requires more than one year of effort for a small research team. This laborious task is rewarded by having a mathematical representation that provides significant intuition into how the device works the way it does, reveals the most important physical processes that determine its behavior, and can be used in computer programs such as SPICE to successfully design and numerically simulate complex integrated circuits that utilize the device. A nonlinear device model [8, 9] consists of a set of ideal circuit elements appropriately connected together that can replicate the experimentally measured electrical properties of the physical device to a desired accuracy. The ideal elements are defined mathematically and may include nonlinear algebraic, ordinary differential, partial differential and integral equations. These can be thought of as providing the basis set of solutions for the device model and should be chosen from carefully defined relations to be as complete and relevant as possible. For nonlinear devices, Chua has constructed a Circuit-Element-Array [8], also called a
R.S. Williams () • M.D. Pickett Hewlett-Packard Laboratories, Palo Alto, CA, USA e-mail: [email protected]; [email protected] R. Tetzlaff (ed.), Memristors and Memristive Systems, DOI 10.1007/978-1-4614-9068-5__3, © Springer Science+Business Media New York 2014
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R.S. Williams and M.D. Pickett
doubly periodic table of ideal circuit elements [10], that covers the mathematically possible relationships between measurements of current (i) and voltage (v) in a two-terminal device. He has also proven that these elements are independent (no individual element can be emulated by any combination of other two-terminal element types) and any combination of two or more elements of the same type belongs to that type (element closure). A critical realization is that there is no perfect model for any physical device [8]—all models are approximations, and in fact a particular physical device may be described by different models depending on the operating environment. The best guide is parsimony with iteration; find the simplest model that produces satisfactory results, but modify it if new measurements
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