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Five non-volatile memristor enigmas solved

A Correction to this article was published on 11 March 2019

This article has been updated

Abstract

Numerous publications on non-volatile memristors made from disparate materials (from inorganic to organic) share many qualitatively similar memory switching and unique v–i phenomena that have hitherto defied a unified physical explanation. This paper selects five, among many, such unexplained mysteries and presents rigorous mathematical proof of the nonlinear dynamical mechanisms responsible for these mysteries. Since no quantum mechanical or chemical concepts are invoked, our resolution of these enigmas does not depend on the material or structure of the memristors.

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Change history

  • 11 March 2019

    The author of the original version of this article makes the following corrections:

Notes

  1. 1.

    The Knowm memristor is currently the only commercially available memristor that is ideal for students and researchers that wish to develop hands-on experience with real-world memristors. It can be ordered from : https://knowm.org/.

  2. 2.

    The proof must hold for all nth-order extended memristors, n > 1.

References

  1. 1.

    T.W. Hickmott, Low frequency negative resistance in thin oxide films. J. Appl. Phys. 33, 2669–2682 (1962). https://doi.org/10.1063/1.1702530

    ADS  Article  Google Scholar 

  2. 2.

    J.F. Gibbons, W.E. Beadle, Switching properties of thin NiO films. Solid-State Electron. 7, 785–797 (1964). https://doi.org/10.1016/0038-1101(64)90131-5

    ADS  Article  Google Scholar 

  3. 3.

    J.G. Simmons, R.R. Verderber, New conduction and reversible memory phenomena in thin insulating films. Proc. Roy. Soc. A. 301, 77–102 (1967). https://doi.org/10.1098/rspa.1967.0191

    ADS  Article  Google Scholar 

  4. 4.

    Y.G. Kriger, N.F. Yudanov, I.K. Igumenov, S.B. Vashchenko, Study of test structures of a molecular memory element. J. Struct. Chem. 34, 966–970 (1993). https://doi.org/10.1007/BF00752875

    Article  Google Scholar 

  5. 5.

    A. Beck, J.G. Bednorz, C.H. Gerber, C. Rossel, D. Widmer, Reproducible switching effect in thin oxide films for memory applications. Appl. Phys. Lett. 77, 139–141 (2000). https://doi.org/10.1063/1.126902

    ADS  Article  Google Scholar 

  6. 6.

    C.J. O’Kelly, H.N.M. Abunahla, M.A. Jaoude, D. Homouz, Subthreshold continuum conductance change in NbO Pt memristor interfaces. J. Phys. Chem. C 120, 18971–18976 (2016). https://doi.org/10.1021/acs.jpcc.6b05010

    Article  Google Scholar 

  7. 7.

    L.O. Chua, Memristor—the missing circuit element. IEEE Trans. Circuit Theory. 18, 507–519 (1971). https://doi.org/10.1109/TCT.1971.1083337

    Article  Google Scholar 

  8. 8.

    D.B. Strukov, G.S. Snider, D.R. Stewart, R.S. Williams, The missing memristor found. Nature. 453, 80–83 (2008). https://doi.org/10.1038/nature06932

    ADS  Article  Google Scholar 

  9. 9.

    L. Chua, If it’s pinched it’s a memristor. Semicond. Sci. Technol. 29, 104001-1–104001-42 (2014). https://doi.org/10.1088/0268-1242/29/10/104001

    ADS  Article  Google Scholar 

  10. 10.

    L. Chua, Everything you wish to know about memristors but are afraid to ask. Radioengineering. 24, 319–368 (2015). https://doi.org/10.13164/re.2015.0319

    Article  Google Scholar 

  11. 11.

    A.L. Hodgkin, A.F. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 117, 500–544 (1952). https://doi.org/10.1113/jphysiol.1952.sp004764

    Article  Google Scholar 

  12. 12.

    L. Chua, V. Sbitnev, H. Kim, Hodgkin–Huxley axon is made of memristors. Int. J. Bifurc. Chaos. 22, 1230011-1–1230011-48 (2012). https://doi.org/10.1142/S021812741230011X

    Article  MATH  Google Scholar 

  13. 13.

    L. Chua, V. Sbitnev, H. Kim, Neurons are poised near the edge of chaos. Int. J. Bifurc. Chaos. 22, 1250098-1–1250098-49 (2012). https://doi.org/10.1142/S0218127412500988

    Article  Google Scholar 

  14. 14.

    T. Zhang, M. Yin, X. Lu, Y. Cai, Y. Yang, R. Huang, Tolerance of intrinsic device variation in fuzzy restricted Boltmann machine network based on memristive nano-synapses. Nano Futures. 1, 015003-1-015003-8 (2017). https://doi.org/10.1088/2399-1984/aa678b

    ADS  Article  Google Scholar 

  15. 15.

    L. P. Shilnikov, A. L. Shilnikov, D. V. Turaev, L. O. Chua, Methods of Qualitative Theory in Nonlinear Dynamics Part-I, (World Scientific Series on Nonlinear Science Series A., 1998). https://doi.org/10.1142/3707. ISBN:978-981-4496-42-1(ebook)

  16. 16.

    Z.I. Mannan, H. Choi, V. Rajamani, H. Kim, L. Chua, Chua corsage memristor: phase portraits, basin of attraction, and coexisting pinched hysteresis loops. Int. J. Bifurc. Chaos. 27(1), 173001-1–1730011-36 (2017). https://doi.org/10.1142/S0218127417300117).

    MathSciNet  Article  MATH  Google Scholar 

  17. 17.

    L. Chua, Introduction to Nonlinear Theory (McGraw-Hill, New York, 1969)

    Google Scholar 

  18. 18.

    K.H. Kim, S.H. Jo, S. Gaba, W. Lu, Nanoscale resistive memory with intrinsic diode characteristics and long endurance. Appl. Phys. Letters, 96, 053106-1–053106-3 (2010). https://doi.org/10.1063/1.3294625

    ADS  Article  Google Scholar 

  19. 19.

    R. Ascoli, L.O. Tetzlaff, J.P. Chua, R.S. Strachan, Williams, History erase effects in a non-volatile memristor. IEEE Trans. Circuits Syst. I. 63, 389–400 (2016). https://doi.org/10.1109/TCSI.2016.2525043

    MathSciNet  Article  Google Scholar 

  20. 20.

    E.R. Kandel, J.H. Schwartz, T.M. Jessel, S.A. Siegelbaum, A.J. Hudspeth, Principle of Neural Science (McGraw-Hill, New York, 2000)

    Google Scholar 

  21. 21.

    T. Chang, S.H. Jo, K.H. Kim, P. Sheridan, S. Gaba, W. Lu, Synaptic behaviors and modelling of a metal oxide memristive device. Appl. Phys. A. 102, 857–863 (2011). https://doi.org/10.1007/s00339-011-6296-1

    ADS  Article  Google Scholar 

  22. 22.

    H.J. Carlin, D.C. Youla, Network synthesis with negative resistors. Proc. IRE. 49, 907–920 (1961). https://doi.org/10.1109/JRPROC.1961.287934

    MathSciNet  Article  Google Scholar 

  23. 23.

    W. Gerstner, W.M. Kistler, R. Naud, L. Paninski, Neuronal Dynamics (Cambridge University Press, Cambridge, 2014)

    Book  Google Scholar 

  24. 24.

    L.O. Chua, C.A. Desore, E.S. Kuh, Linear and Nonlinear Circuits (McGraw-Hill, New York, 1987)

    Google Scholar 

  25. 25.

    S. Yu, Y. Wu, R. Jeyasingh, D. Kuzum, H.S.P. Wong, An electronic synapse device based on metal oxide resistive switching memory for neuromorphic computation. IEEE Trans. Electron Devices 58, 2729–2737 (2011). https://doi.org/10.1109/TED.2011.2147791

    ADS  Article  Google Scholar 

  26. 26.

    S.H. Jo, T. Chang, I. Ebong, B.B. Bhadviya, P. Maxumder, W. Lu, Nanoscale memristor as synapse in neuromorphic systems. Nano Lett. 10, 1297–1301 (2010). https://doi.org/10.1021/nl904092h

    ADS  Article  Google Scholar 

  27. 27.

    L.P. Shilnikov, A.L. Shilnikov, D.V. Turaev, L.O. Chua, Methods of Qualitative Theory in Nonlinear Dynamics Part-II, (World Scientific Series on Nonlinear Science Series A., 2001). https://doi.org/10.1142/4221. ISBN:978-981-4494-29-8(ebook)

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Acknowledgements

This work is supported by the USA Air Force office of Scientific Research under Grant number FA9550-18-1-0016. The author would like to thank Professor Yuchao Yang from Peking University for providing the DRM in Fig. 23, Professor Wei Lu from University of Michigan for the equations describing the memristor in Fig. 24, Professor Qiangfei Xia from the University of Massachusetts for the slides in the concluding section measured from his latest Ta/HfO2 memristor devices, and Professor Kris Campbell from the Boise State University for many constructive discussions. He also wishes to thank Professor Ronald Tetzlaff and Dr. Alon Ascoli from the Technical University of Dresden for providing Figs. 25, 35, and 36. Last but not least, he wishes to thank Professor Hyongsuk Kim, Zubaer Mannan, and Dr. Vetriveeran Rajamani for drawing most of the colorful figures in this paper.

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Chua, L. Five non-volatile memristor enigmas solved. Appl. Phys. A 124, 563 (2018). https://doi.org/10.1007/s00339-018-1971-0

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