Abstract
This paper proposes the introduction of appropriate continuous and differentiable approximations to discontinuous and piecewise differentiable functions respectively adopted in state equation and Ohm’s based law of the mathematical model of an extended memristor recently fabricated at Hewlett Packard labs. The study of this model is particularly timely because the material at the basis of the relative memristor device, i.e. Tantalum oxide, has been recently classified, together with Hafnium oxide, as one of the most plausible candidates for a large-scale manufacturing of memory resistive devices, especially for memory applications. However, recent studies have demonstrated that the adoption of discontinuous and/or piecewise differentiable functions in the differential algebraic equation set describing the complex dynamics of these devices may be the source of serious convergence issues in standard software packages. This calls for an impeding necessity to ameliorate mathematical descriptions of real memristors. In this paper we present a thorough study which aims at deriving the most appropriate set of continuous and differentiable approximants to the discontinuous and piecewise differentiable functions of the TaO memristor model.
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References
Chua, L.O.: Memristor: the missing circuit element. IEEE Trans. Circuit Theory 18(5), 507–519 (1971)
Vontobel, P.O., Robinett, W., Kuekes, P.J., Stewart, D.R., Straznicky, J., Williams, R.S.: Writing to and reading from a nano-scale crossbar memory based on memristors. Nanotechnol. 20, 425204 (2009). doi:10.1088/0957-4484/20/42/425204. 21pp
Mikolajick, T., Slesazeck, S., M\(\ddot{a}\)hne, H., Wylezich, H., Shuai, Y., You, T., Schmidt, H.: Resistive switching: from basic switching mechanisms to device application. In: Workshop on Memristor Science & Technology, European Conference on Design, Automation & Test in Europe (DATE), 2014
Corinto, F., Ascoli, A., Gilli, M.: Nonlinear dynamics of memristor oscillators. IEEE Trans. Circuits Syst.-I 58(6), 1323–1336 (2011). doi:10.1109/TCSI.2010.2097731
Chua, L.O.: Resistance switching memories are memristors. Appl. Phys. A 102, 765–783 (2011). doi:10.1007/s00339-011-6264-9
Strachan, J.P., Torrezan, A.C., Miao, F., Pickett, M.D., Yang, J.J., Yi, W., Medeiros-Ribeiro, G., Williams, R.S.: State dynamics and modeling of tantalum oxide memristors. IEEE Trans. Electron Devices 60(7), 2194–2202 (2013)
Chua, L.O.: If It’s Pinched, It’s a Memristor. Special Issue on Memristive Devices, Semiconductor Science and Technology, September 2014
Ascoli, A., Corinto, F., Tetzlaff, R.: A class of versatile circuits, made up of standard electrical components, are memristors. Int. J. Circuit Theory Appl. 44, 127–146 (2015). doi:10.1002/cta.2067
Biolek, D., Di Ventra, M., Pershin, Y.V.: Reliable SPICE simulations of memristors, memcapacitors and meminductors. Radioengineering 22(4), 945–968 (2013)
Ascoli, A., Tetzlaff, R., Biolek, Z., Kolka, Z., Biolkov\(\acute{a}\), V., Biolek, D.: The art of finding accurate memristor model solutions. IEEE J. Emerg. Sel. Top. Circuits Syst. 5(2), 133–142 (2015). doi:10.1109/JETCAS.2015.2426493
Chua, L.O.: Everything you wish to know about memristors but are afraid to ask. Radioengineering 24(2), 319–368 (2015)
Ascoli, A., Slesazeck, S., M\(\ddot{a}\)hne, H., Tetzlaff, R., Mikolajick, T.: Nonlinear dynamics of a locally-active memristor. IEEE Trans. Circuits Syst.-I 62(4), 1165–1174 (2015). doi:10.1109/TCSI.2015.2413152
Ascoli, A., Corinto, F., Tetzlaff, R.: Generalized boundary condition memristor model. Int. J. Circuit Theory Appl. 44(1), 60–84 (2015). doi:10.1002/cta.2063
Acknowledgements
The authors would like to acknowledge the contribution and the networking support of the EU COST Action IC1401. This work has been partially supported by the Czech Science Foundation under grant No. \(14-19865S\), Czech Republic. The authors sincerely thank J. P. Strachan, J. J. Yang, and S. Williams for insightful discussions on the HP TaO memristor .
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Ascoli, A., Tetzlaff, R., Chua, L. (2017). Continuous and Differentiable Approximation of a TaO Memristor Model for Robust Numerical Simulations. In: Mantica, G., Stoop, R., Stramaglia, S. (eds) Emergent Complexity from Nonlinearity, in Physics, Engineering and the Life Sciences. Springer Proceedings in Physics, vol 191. Springer, Cham. https://doi.org/10.1007/978-3-319-47810-4_6
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DOI: https://doi.org/10.1007/978-3-319-47810-4_6
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