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If It’s Pinched It’s a Memristor

  • Leon ChuaEmail author
Chapter

Abstract

This paper presents an in-depth review of the memristor from a rigorous circuit-theoretic perspective, independent of the material the device is made of. From an experimental perspective, a memristor is best defined as any 2-terminal device that exhibits a pinched hysteresis loop in the voltage-current plane when driven by any periodic voltage or current signal that elicits a periodic response of the same frequency. This definition greatly broadens the scope of memristive devices to encompass even non-semiconductor devices, both organic and inorganic, from many unrelated disciplines, including biology, botany, brain science, etc. For pedagogical reasons, the broad terrain of memristors is partitioned into 3 classes of increasing generality, dubbed Ideal Memristors, Generic Memristors, and Extended Memristors. Each class is distinguished from the others via unique fingerprints and signatures. This paper clarifies many confusing issues, such as non-volatility, DC V-I curves, high-frequency v-i curves, local activity, as well as nonlinear dynamical and bifurcation phenomena that are the hallmarks of memristive devices. Above all, this paper addresses several fundamental issues and questions that many memristor researchers do not comprehend but are afraid to ask.

Keywords

Ideal memristors Generic memristors Extended memristors Pinched hysteresis loop Local activity Local passivity Nonlinear dynamical Bifurcation phenomena 

Notes

Acknowledgements

The author would like to thank Prof. Hyongsuk Kim, and his colleagues Dr. Maheshwar Pd. Sah, and Ram Kaji Budhathoki for their indispensable assistance in the preparation of this paper.

He also wishes to acknowledge financial support from the USA Air force office of Scientific Research under Grant number FA9550-13-1-0136 and from the European Commission Marie Curie Fellowship

References

  1. 1.
    Chua, L.O.: Memristor-the missing circuit element. IEEE Trans. Circuit Theory 18(5), 507–519 (1971)CrossRefGoogle Scholar
  2. 2.
    Chua, L.: Resistance switching memories are memristors. Appl. Phys. A: Mater. Sci. Process 102(4), 765–783 (2011)CrossRefzbMATHGoogle Scholar
  3. 3.
    Chua, L.O.: Introduction to Nonlinear Network Theory, vol. 19, McGraw-Hill, New York (1969)Google Scholar
  4. 4.
    Chua, L.O.: Chua, L. O. (2012). The fourth element. Proc. IEEE 100(6), 1920–1927 (2012)CrossRefGoogle Scholar
  5. 5.
    Chua, L.O., Kang, S.M.: Section-wise piecewise-linear functions: Canonical representation, properties, and applications. Proc. IEEE 65(6), 915–929 (1977)CrossRefGoogle Scholar
  6. 6.
    Adhikari, S.P., Sah, M.P., Kim, H., Chua, L.O.: Three fingerprints of memristor. Trans. Circuits and Systems I 60(11), 3008–3021 (2013)CrossRefGoogle Scholar
  7. 7.
    Davy, H.: Nicholson’s J. Nat. Philos. Chem. Arts 4, 326 (1801)Google Scholar
  8. 8.
    Davy, H.: Elements of Chemical Philosophy: Part 1. vol. 1 JohnSon, London (1812)Google Scholar
  9. 9.
    Lin, D., Hui, R., Chua, L.: Gas discharge lamps are volatile memristors. IEEE Trans. Circuits and Systems I 61(7), 2066–2073 (2014)CrossRefGoogle Scholar
  10. 10.
    Francis, V.J.: Fundamentals of Discharge Tube Circuits. Methuen, London (1948)Google Scholar
  11. 11.
    Hickmott, T.W.: Low‐frequency negative resistance in thin anodic oxide films. J. Appl. Phys. 33(9), 2669–2682 (1962)CrossRefGoogle Scholar
  12. 12.
    Argall, F.: Switching phenomena in titanium oxide thin films. Solid State Electron. 11(5), 535–541 (1968)CrossRefGoogle Scholar
  13. 13.
    Strukov, D.B., Snider, G.S., Stewart, D.R., Williams, R.S.: The missing memristor found. Nature 453(7191), 80 (2008)CrossRefGoogle Scholar
  14. 14.
    Pi, S., Lin, P., Xia, Q.: J. Vacuum Sci. Technol. B 31, 06FAQ2–1 (2013)Google Scholar
  15. 15.
    Kikuchi, M., Saito, M., Okushi, H.: Polarized (letter ‘8’) memory in CdSe point contact diodes. Solid State Commun. 9(10), 705–707 (1971)CrossRefGoogle Scholar
  16. 16.
    Henisch, H.K.: Amorphous semiconductor switching. Nature 236(5344), 205–207 (1972)CrossRefGoogle Scholar
  17. 17.
    Beck, A., Bednorz, J.G., Gerber, Ch., Rossel, C., Widmer, D.: Reproducible switching effect in thin oxide films for memory applications. Appl. Phys. Lett. 77(1), 139–141 (2000)CrossRefGoogle Scholar
  18. 18.
    Johnson, S.L., Sundararajan, A., Hunley, D.P., Strachan, D.R.: Memristive switching of single-component metallic nanowires. Nanotechnology 21(12), 125204 (2010)CrossRefGoogle Scholar
  19. 19.
    Waser, R.: Resistive non-volatile memory devices. Microelectron. Eng. 86(7–9), 1925–1928 (2009)Google Scholar
  20. 20.
    Chanthbouala, A., Garcia, V., Cherifi, R.O., Bouzehouane, K., Fusil, S., Moya, X., Xavier, S., Yamada, H., Deranlot, C., Mathur, N.D., Bibes, M., Barthélémy, A., Grollier, J.: A ferroelectric memristor. Nat. Mater. 11(10), 860 (2012)CrossRefGoogle Scholar
  21. 21.
    Nardi, F., Balatti, S., Larentis, S., Gilmer, D.C., Ielmini, D.: Complementary switching in oxide-based bipolar resistive-switching random memory. IEEE Trans. Electron Devices 60(1), 70–77 (2012)CrossRefGoogle Scholar
  22. 22.
    Sakamoto, T., Sunamura, H., Kawamura, H., Hasegawa, T., Nakayama, T., Aono, M.: Nanometer-scale switches using copper sulfide. Appl. Phys. Lett. 82(18), 3032–3034 (2003)CrossRefGoogle Scholar
  23. 23.
    Kim, T.H., Jang, E.Y., Lee, N.J., Choi, D.J., Lee, K.J., Jang, J., Choi, J., Moon, S.H., Jinwoo, C.: Nanoparticle assemblies as memristors. Nano Lett. 9(6), 2229–2233 (2009)CrossRefGoogle Scholar
  24. 24.
    Yang, Y., Sheridan, P., Lu, W.: Complementary resistive switching in tantalum oxide-based resistive memory devices. Applied Physics Letters 100(20), 203112 (2012)CrossRefGoogle Scholar
  25. 25.
    Szot, K., Rogala, M., Speier, W., Klusek, Z., Besmehn, A., Waser, R.: TiO2—a prototypical memristive material. Nanotechnology 22(25), 254001 (2011)CrossRefGoogle Scholar
  26. 26.
    Hino, T., Hasegawa, T., Terabe, K., Tsuruoka, T., Nayak, A., Ohno, T., Aono, M.: Atomic switches: atomic-movement-controlled nanodevices for new types of computing. Sci. Technol. Adv. Mater. 12(1), 013003 (2011)CrossRefGoogle Scholar
  27. 27.
    Jo, S.H., Kim, K., Lu, W.: Programmable resistance switching in nanoscale two-terminal devices. Nano Lett. 9(1), 496–500 (2009)CrossRefGoogle Scholar
  28. 28.
    Pickett, M.D., Medeiros-Ribeiro, G., Williams, R.S.: A scalable neuristor built with Mott memristors. Nat. Mater. 12(2), 114 (2013)CrossRefGoogle Scholar
  29. 29.
    Pickett, M.D., Strukov, D.B., Borghetti, J.L., Yang, J.J., Sinder, G.S., Stewart, D.R., Williams, R.S.:  Switching dynamics in titanium dioxide memristive devices. J. Appl. Phys. 106(7) 074508 (2009)CrossRefGoogle Scholar
  30. 30.
    MacVittie, K., Katz, E.: Electrochemical system with memimpedance properties. J. Phy. Chem. 117(47), 24943–24947 (2013)CrossRefGoogle Scholar
  31. 31.
    Sah, M.P., Yang, C., Kim, H., Muthuswamy, B., Jevtic, J., Chua, L.: A generic model of memristors with parasitic components. Trans. Circuits and Syst. I 62(3), 891–898 (2014)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Martinsen, O.G., Grimnes, S., Lutken, C.A., Johnsen, G.K.: Memristance in human skin. J. Phys Conf. Ser. 224(1), 012071 (2010)Google Scholar
  33. 33.
    Johnsen, G.K., Lutken, C.A., Martinsen, O.G., Grimnes, S.: Memristive model of electro-osmosis in skin. Phys. Rev. E 83(3), 031916 (2011)Google Scholar
  34. 34.
    Gale, E., Mayne, R., Adamatzky, A., Costello, B.: Drop-coated titanium dioxide memristors. Mater. Chem. Phys. 143, 524 (2014)CrossRefGoogle Scholar
  35. 35.
    Volkov, A.G., Tucket, C., Reedus, J., Volkova, M.I., Markin, V.S., Chua, L.: J. Memristors in plants. Plant Signal. Behav. 9(3), e28152–1 (2014)CrossRefGoogle Scholar
  36. 36.
    Liu, K., Cheng, C., Suh, J., Tang-Kong, R., Fu, D., Lee, S., Zhou, J., Chua, L.O., Wu, J.: Powerful, multifunctional torsional micromuscles activated by phase transition. Adv. Mater. 26(11), 1746–1750 (2014)CrossRefGoogle Scholar
  37. 37.
    Georgiou, P.S., Barahona, .M, Yaliraki, S.N., Drakakis, E.M.: Phy. Rev. Appl. (Under Review) (2014)Google Scholar
  38. 38.
    Hodgkin, A.L., Huxley, A.F.: This Week's Citation Classic. J. Physiol. 117, 500–544 (1952)Google Scholar
  39. 39.
    Cole, K.S.: Membranes, Ions and Impulses: a chapter of classical biophysics. vol. 1, University of California Press, Berkeley (1972)Google Scholar
  40. 40.
    Chua, L.: Memristor, Hodgkin–Huxley, and edge of chaos. Nanotechnology 24(38), 383001 (2013)CrossRefGoogle Scholar
  41. 41.
    Sah, M.P., Kim, H., Chua, L.: Brains are made of memristors. IEEE Circuits Syst. Mag. 14(1), 12–36 (2014)CrossRefGoogle Scholar
  42. 42.
    Chua, L., Sbitnev, V., Kim, H.: Int. J. Bifurc. Hodgkin–Huxley axon is made of memristors. Chaos 22(03), 1230011 (2012)zbMATHCrossRefGoogle Scholar
  43. 43.
    Chua, L.O.: Device modeling via nonlinear circuit elements. IEEE Trans. Circuits Syst. 27(11), 1014–1044 (1980)MathSciNetzbMATHCrossRefGoogle Scholar
  44. 44.
    Chua, L.O.: Nonlinear circuit foundations for nanodevices. IEEE Proceedings 91(11), 1830–1859 (2003)Google Scholar
  45. 45.
    Kew, J.N., Davies, C.H.: Ion channels: from structure to function. Oxford University Press, Oxford (2010)Google Scholar
  46. 46.
    Ashcroft, F.M.: Ion Channels and Disease. Academic Press, London (1999)Google Scholar
  47. 47.
    Carlin, H.J., Youla, D.C.: Network synthesis with negative resistors. Proc. IRE 49(5), 907–920 (1961)MathSciNetCrossRefGoogle Scholar
  48. 48.
    Chua, L.O., Desoer, C.A., Kuh, E.S.: Linear and Nonlinear Circuits. MCGraw-Hill, New Yorks (1987)Google Scholar
  49. 49.
    Linn, E., Rosezin, R., Kügeler, C., Waser, R.: Complementary resistive switches for passive nanocrossbar memories. Nat. Mater. 9(5), 403 (2010)CrossRefGoogle Scholar
  50. 50.
    Waser, R., Aono, M.: Nat. Mater. 6, 833 (2007)Google Scholar
  51. 51.
    Strogatz, S.H.: Nonlinear Dynamics And Chaos. Westview Press, Boulder (2001)Google Scholar
  52. 52.
    Chua, L.O., Kang, S.M.: Memristive devices and systems. Proc. IEEE 64(2), 209–223 (1976)MathSciNetCrossRefGoogle Scholar
  53. 53.
    Corinto, F., Ascoli, A.: Memristive diode bridge with LCR filter. Electron. Lett. 48(14), 824–825 (2012)CrossRefGoogle Scholar
  54. 54.
    Reenstra, A.L.: A low-frequency oscillator using PTC and NTC thermistors. IEEE Trans. Electron Devices, ED-16 544–554 (1969)CrossRefGoogle Scholar
  55. 55.
    Muthuswamy, B., Chua, L.O.: Simplest chaotic circuit. Int. J. Bifurcat. Chaos 20(05), 1567–1580 (2010)CrossRefGoogle Scholar
  56. 56.
    Parker, T.S., Chua, L.O.: Practical Numerical Algorithms for Chaotic Systems, Springer, New York (1989)zbMATHCrossRefGoogle Scholar
  57. 57.
    Marsden, J.E.: The Hopf Bifurcation and Its Applications. Springer, New York (1976)zbMATHCrossRefGoogle Scholar
  58. 58.
    Kim, H., Adhikari, S.P.: Memistor is not memristor [express letters]. IEEE Circuits Syst. Mag. 12(1), 75–78 (2012)CrossRefGoogle Scholar
  59. 59.
    Adhikari, S.P., Kim, H.: Memristor bridge synapse-based neural network and its learning. IEEE Trans. Circuits and Systems I 23(9), 1426–1435 (2012)CrossRefGoogle Scholar
  60. 60.
    Chua, L.: Introduction to memristors. IEEE Expert Now Short Course, CD ROM (http://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=&arnumber=EDP091&queryText%3DIntroduction+to+Memristors) (2009)
  61. 61.
    Pershin, Y.V., Ventra, M.D.: Memory effects in complex materials and nanoscale systems. Adv. Phys. 60(2), 145–227 (2011)CrossRefGoogle Scholar

Copyright information

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Authors and Affiliations

  1. 1.Department of Electrical Engineering and Computer SciencesUniversity of CaliforniaBerkeleyUSA

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