Continuous and Differentiable Approximation of a TaO Memristor Model for Robust Numerical Simulations

  • Alon AscoliEmail author
  • Ronald Tetzlaff
  • Leon Chua
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 191)


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.


Modulus Function Unit Step Function Tantalum Oxide Convergence Issue Hafnium Oxide 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



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 .


  1. 1.
    Chua, L.O.: Memristor: the missing circuit element. IEEE Trans. Circuit Theory 18(5), 507–519 (1971)CrossRefGoogle Scholar
  2. 2.
  3. 3.
    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
  4. 4.
    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), 2014Google Scholar
  5. 5.
    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 MathSciNetCrossRefGoogle Scholar
  6. 6.
    Chua, L.O.: Resistance switching memories are memristors. Appl. Phys. A 102, 765–783 (2011). doi: 10.1007/s00339-011-6264-9 ADSCrossRefzbMATHGoogle Scholar
  7. 7.
    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)ADSCrossRefGoogle Scholar
  8. 8.
    Chua, L.O.: If It’s Pinched, It’s a Memristor. Special Issue on Memristive Devices, Semiconductor Science and Technology, September 2014Google Scholar
  9. 9.
    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 CrossRefGoogle Scholar
  10. 10.
    Biolek, D., Di Ventra, M., Pershin, Y.V.: Reliable SPICE simulations of memristors, memcapacitors and meminductors. Radioengineering 22(4), 945–968 (2013)Google Scholar
  11. 11.
    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
  12. 12.
    Chua, L.O.: Everything you wish to know about memristors but are afraid to ask. Radioengineering 24(2), 319–368 (2015)CrossRefGoogle Scholar
  13. 13.
    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
  14. 14.
    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 CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institut für Grundlagen der Elektrotechnik und ElektronikTechnische Universität DresdenDresdenGermany
  2. 2.Department of Electrical Engineering and Computer SciencesUniversity of California BerkeleyBerkeleyUSA

Personalised recommendations