Abstract
This work presents a continuous and differen- tiable approximation of a Tantalum oxide memristor model which is suited for robust numerical simulations in soft- ware. The original model was recently developed at Hewlett Packard labs on the basis of experiments carried out on a memristor manufactured in house. The Hewlett Packard model of the nano-scale device is accurate and may be taken as reference for a deep investigation of the capabilities of the memristor based on Tantalum oxide. However, the model contains discontinuous and piecewise differentiable func- tions respectively in state equation and Ohm's based law. Numerical integration of the differential algebraic equation set may be significantly facilitated under substitution of these functions with appropriate continuous and differentiable ap- proximations. A detailed investigation of classes of possible continuous and differentiable kernels for the approximation of the discontinuous and piecewise differentiable functions in the original model led to the choice of near optimal can- didates. The resulting continuous and differentiable DAE set captures accurately the dynamics of the original model, delivers well-behaved numerical solutions in software, and may be integrated into a commercially-available circuit sim- ulator.
Highlights
The memristor and its applications represent one of the most interesting fields of research
Recent investigations have highlighted the negative impact the presence of discontinuous and/or piecewise differentiable functions may have on the convergence properties of a numerical solver to differential algebraic equations (DAE) sets pertaining to memristor models [21]
This paper proposes an accurate continuous and differentiable approximation of a TaO memristor model [19] suited for robust numerical simulations in software
Summary
The memristor and its applications represent one of the most interesting fields of research. Thanks to the crucial influence of the history of dynamics of the memristor on its current behavior, this device exhibits memory capability. Memristors are much more than ”mere” memory cells They exhibit computing capability as demonstrated in numerous studies [10]. The local activity of these memristors and the complex dynamics which may emerge in circuits employing them (for example the oscillatory behavior of a simple locally active memristor circuit built at NaMLab is investigated in [17]) may lead to the development of new circuits [18] which could outperform state-of-the-art electronic systems or complement their functionalities This wide plethora of interesting applications urgently requires the developments of accurate mathematical models in order to uncover the full potential of memristors in the electronics of the future. A circuit implementation of the continuous and differentiable DAE set, coded in LTspice version IV, and presented in Section 6 in the form of a netlist, may be of interest to the circuit designer eager to explore the design opportunities the HP TaO resistance switching memory [23] may open up in the field of nano electronics
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