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Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 26))

Abstract

This chapter discusses the main properties of the memristor, a comparison between five recent memristor models, mathematical modeling of the HP memristor with analytical expressions for different excitations, mathematical representations of time-invariant memristor (ideal, generic, and extended), different memristor implementation types, and some memristor-based applications in digital and analog circuits.

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References

  1. Widrow, B., et al.: Adaptive “ADALINE” Neuron Using Chemical “Memistors” (1960)

    Google Scholar 

  2. Kim, H., Adhikari, S.P.: IEEE Circuits Syst. Mag. 12(1), 75 (2012)

    Article  Google Scholar 

  3. Fano, R.M., Chu, L.J., Adler, R.B.: Electromagnetic Fields, Energy, and Forces. MIT Press, Cambridge (1968)

    Google Scholar 

  4. Chua, L.: IEEE Trans. Circuit Theory 18(5), 507 (1971)

    Google Scholar 

  5. Chua, L., Kang, S.: Proc. IEEE 64(2), 209 (1976)

    Article  MathSciNet  Google Scholar 

  6. Strukov, D., Snider, G., Stewart, D., Williams, R.: Nature 453(7191), 80 (2008)

    Article  Google Scholar 

  7. Williams, R.: IEEE Spect. 45(12), 28 (2008)

    Google Scholar 

  8. Williams, R.S.: Memristors and Memristive Systems, pp. 3–16. Springer, New York (2014)

    Book  Google Scholar 

  9. Adhikari, S., Sah, M., Kim, H., Chua, L.: IEEE Trans. Circuits Syst. I: Regul. Pap. 60(11), 3008 (2013). doi:10.1109/TCSI.2013.2256171

  10. Biolek, D., Biolek, Z., Biolkova, V., Kolka, Z.: In: 2013 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 201–204 (2013). doi:10.1109/ISCAS.2013.6571817

  11. Chua, L.: Appl. Phys. A 102(4), 765 (2011)

    Article  Google Scholar 

  12. Lehtonen, E., Laiho, M.: In: 2010 12th International Workshop on Cellular Nanoscale Networks and Their Applications (CNNA), pp. 1–4. IEEE (2010)

    Google Scholar 

  13. Yang, J.J., Pickett, M.D., Li, X., Ohlberg, D.A., Stewart, D.R., Williams, R.S.: Nat. Nanotechnol. 3(7), 429 (2008)

    Article  Google Scholar 

  14. Pickett, M.D., Strukov, D.B., Borghetti, J.L., Yang, J.J., Snider, G.S., Stewart, D.R., Williams, R.S.: J. Appl. Phys. 106(7), 074508 (2009)

    Article  Google Scholar 

  15. Simmons, J.G.: J. Appl. Phys. 34(6), 1793 (1963)

    Article  MathSciNet  Google Scholar 

  16. Abdalla, H., Pickett, M.D.: 2011 IEEE International Symposium on in Circuits and Systems (ISCAS), pp. 1832–1835. IEEE (2011)

    Google Scholar 

  17. Kvatinsky, S., Friedman, E, Kolodny, A., Weiser, U.: IEEE Trans. Circuits Syst. I: Regul. Pap. 60(1), 211 (2013). doi:10.1109/TCSI.2012.2215714

    Article  MathSciNet  Google Scholar 

  18. Strukov, D., Snider, G., Stewart, D., Williams, R.: Nature 459, 1154 (2009)

    Article  Google Scholar 

  19. Joglekar, Y., Wolf, S.: Eur. J. Phys. 30(4), 661 (2009)

    Article  MATH  Google Scholar 

  20. Radwan, A., Zidan, M.A., Salama, K.: In: 2010 International Conference on Microelectronics (ICM), pp. 284–287. IEEE (2010)

    Google Scholar 

  21. Biolek, D., Biolek, Z., Biolkova, V.: In: European Conference on Circuit Theory and Design ECCTD 2009, pp. 249–252. IEEE (2009)

    Google Scholar 

  22. Corinto, F., Ascoli, A.: IEEE Trans. Circuits Syst. I: Regul. Pap. 59(11), 2713 (2012)

    Article  MathSciNet  Google Scholar 

  23. Prodromakis, T., Peh, B.P., Papavassiliou, C., Toumazou, C.: IEEE Trans. Electron Devices 58(9), 3099 (2011)

    Article  Google Scholar 

  24. Yu, J., Mu, X., Xi, X., Wang, S.: Radioengineering 22(4), 969 (2013)

    Google Scholar 

  25. Radwan, A., Zidan, M.A., Salama, K.: In: 2010 53rd IEEE International Midwest Symposium on Circuits and Systems (MWSCAS), pp. 861–864. IEEE (2010)

    Google Scholar 

  26. Di Ventra, M., Pershin, Y., Chua, L.: Proc. IEEE 97(10), 1717 (2009)

    Article  Google Scholar 

  27. Chua, L.: Semicond. Sci. Technol. 29, 1 (2014)

    MathSciNet  Google Scholar 

  28. Argall, F.: Solid-State Electron. 11(5), 535 (1968)

    Article  Google Scholar 

  29. Beck, A., Bednorz, J., Gerber, C., Rossel, C., Widmer, D.: Appl. Phys. Lett. 77(1), 139 (2000)

    Article  Google Scholar 

  30. Genrikh, S., Cho, C.R., Yoo, I.K., Lee, E.H., Cho, S.I., Moon, C.W. et al.: Electrode structure having at least two oxide layers and non-volatile memory device having the same. US Patent 7,417,271 (2008)

    Google Scholar 

  31. Willaims, R., et al.: Electrically actuated switch. WO Patent 2,008,108,822 (2008)

    Google Scholar 

  32. Kriegerand, J., Spitzer, S.M.: In: Non-Volatile Memory Technology Symposium, pp. 121–124. IEEE (2004)

    Google Scholar 

  33. Erokhin, V., Fontana, M.P.: (2008) arXiv preprint arXiv:0807.0333

  34. Berzina, T., Smerieri, A., Bernabò, M., Pucci, A., Ruggeri, G., Erokhin, V., Fontana, M.: J. Appl. Phys. 105(12), 124515 (2009)

    Article  Google Scholar 

  35. Moll, J., Tarui, Y.: IEEE Trans. Electron Devices. 10(5), 338 (1963)

    Google Scholar 

  36. Chanthbouala, A., Garcia, V., Cherifi, R.O., Bouzehouane, K., Fusil, S., Moya, X., Xavier, S., Yamada, H., Deranlot, C., Mathur, N.D., et al.: Nat. Mater. 11(10), 860 (2012)

    Article  Google Scholar 

  37. Buot, F., Rajagopal, A.: J. Appl. Phys. 76(9), 5552 (1994)

    Article  Google Scholar 

  38. Yilmaz, Y., Mazumder, P.: In: 2012 12th IEEE Conference on Nanotechnology (IEEE-NANO), pp. 1–4. IEEE (2012)

    Google Scholar 

  39. Jeong, H.Y., Kim, J.Y., Kim, J.W., Hwang, J.O., Kim, J.E., Lee, J.Y., Yoon, T.H., Cho, B.J., Kim, S.O., Ruoff, R.S., et al.: Nano Lett. 10(11), 4381 (2010)

    Article  Google Scholar 

  40. Yang, J., Miao, F., Wu, W., Wang, S.Y., Williams, R.S.: Defective graphene-based memristor. US Patent 8,203,171 (2012)

    Google Scholar 

  41. Mehonic, A., Cueff, S., Wojdak, M., Hudziak, S., Jambois, O., Labbé, C., Garrido, B., Rizk, R., Kenyon, A.J.: J. Appl. Phys. 111(7), 074507 (2012)

    Article  Google Scholar 

  42. Wang, X., Chen, Y., Xi, H., Li, H., Dimitrov, D.: IEEE Electron Device Lett. 30(3), 294 (2009)

    Article  Google Scholar 

  43. Chanthbouala, A., Matsumoto, R., Grollier, J., Cros, V., Anane, A., Fert, A., Khvalkovskiy, A., Zvezdin, K., Nishimura, K., Nagamine, Y., et al.: Nat. Phys. 7(8), 626 (2011)

    Article  Google Scholar 

  44. Pershin, Y.V., Di Ventra, M.: Phys. Rev. B 77(7), 073301 (2008)

    Article  Google Scholar 

  45. Talukdar, A., Radwan, A., Salama, K.: Microelectron. J. 43(3), 169 (2012). http://dx.doi.org/10.1016/j.mejo.2011.12.012. http://www.sciencedirect.com/science/article/pii/S002626921100262X

  46. Talukdar, A., Radwan, A., Salama, K.: Microelectron. J. 42(9), 1032 (2011). http://dx.doi.org/10.1016/j.mejo.2011.07.001. http://www.sciencedirect.com/science/article/pii/S0026269211001431

  47. Talukdar, A., Radwan, A., Salama, K.: In: 2010 International Conference on Microelectronics (ICM), pp. 288–291. IEEE (2010)

    Google Scholar 

  48. ElSamman, A., Radwan, A., Madian, A.: In: 2013 International Conference on Communications, Signal Processing and Their Applications (ICCSPA13). IEEE (2013)

    Google Scholar 

  49. Talukdar, A., Radwan, A., Salama, K.: Appl. Nanosci. 143–145 (2011)

    Google Scholar 

  50. ElSamman, A., Radwan, A., Madian, A.: 2014 International Conference on in Microelectronics (ICM). IEEE (2014)

    Google Scholar 

  51. Shin, S., Kim, K., Kang, S.: International Conference on Communications, Circuits and Systems ICCCAS 2009, pp. 948–951. IEEE (2009)

    Google Scholar 

  52. Shin, S., Kim, K., Kang, S.: IEEE Trans. Nanotechnol. 10(2), 266 (2011)

    Article  Google Scholar 

  53. Pershin, Y., Di Ventra, M.: IEEE Trans. Circuits Syst. I: Regul. Pap. 57(8), 1857 (2010)

    Article  MathSciNet  Google Scholar 

  54. Wey, T.A., Jemison, W.D.: IET Circuits, Devices Syst. 5(1), 59 (2011)

    Google Scholar 

  55. Wey, T., Jemison, W.: Analog Integr. Circuits Signal Process. 73(3), 663 (2012)

    Article  Google Scholar 

  56. Berdan, R., Prodromakis, T., Salaoru, I., Khiat, A., Toumazou, C.: Appl. Phys. Lett. 101(24), 243502 (2012)

    Article  Google Scholar 

  57. Driscoll, T., Quinn, J., Klein, S., Kim, H.T., Kim, B., Pershin, Y.V., Di Ventra, M., Basov, D.: Appl. Phys. Lett. 97(9), 093502 (2010)

    Article  Google Scholar 

  58. Kozma, R., Pino, R.E., Pazienza, G.E.: Advances in Neuromorphic Memristor Science and Applications, vol. 4. Springer, New York (2012)

    Book  Google Scholar 

  59. Chew, Z., Li, L.: Electron. Lett. 48(25), 1610 (2012)

    Article  Google Scholar 

  60. Zhao, Y.B., Tse, C.K., Feng, J.C., Guo, Y.C.: Syst. Signal Process. Circuits 32(3), 1013 (2013)

    Google Scholar 

  61. Ananthanarayanan, R., Esser, S.K., Simon, H.D., Modha, D.S.: In: Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis, pp. 1–12. IEEE (2009)

    Google Scholar 

  62. Indiveri, G., Chicca, E., Douglas, R.: IEEE Trans. Neural Netw. 17(1), 211 (2006)

    Google Scholar 

  63. Izhikevich, E.M., Edelman, G.M.: Proc. Nat. Acad. Sci. 105(9), 3593 (2008)

    Google Scholar 

  64. Pershin, Y.V., La Fontaine, S., Di Ventra, M.: Phys. Rev. E 80(2), 021926 (2009)

    Article  Google Scholar 

  65. Jo, S.H., Chang, T., Ebong, I., Bhadviya, B.B., Mazumder, P., Lu, W.: Nano Lett. 10(4), 1297 (2010)

    Article  Google Scholar 

  66. Pershin, Y.V., Di Ventra, M.: Neural Netw. 23(7), 881 (2010)

    Article  Google Scholar 

  67. Pérez-Carrasco, J.A., Zamarreño-Ramos, C., Serrano-Gotarredona, T., Linares-Barranco, B.: In: Proceedings of 2010 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1659–1662. IEEE (2010)

    Google Scholar 

  68. Snider, G.S.: In: IEEE International Symposium on Nanoscale Architectures, NANOARCH, 2008. pp. 85–92. IEEE (2008)

    Google Scholar 

  69. Zomaya, A.Y.: Handbook of Nature-Inspired and Innovative Computing: Integrating Classical Models with Emerging Technologies. Springer, New York (2006)

    Book  Google Scholar 

  70. Itoh, M., Chua, L.O.: Int. J. Bifurc. Chaos 18(11), 3183 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  71. Muthuswamy, B., Chua, L.O.: Int. J. Bifurc. Chaos 20(05), 1567 (2010)

    Article  Google Scholar 

  72. Muthuswamy, B.: Int. J. Bifurc. Chaos 20(05), 1335 (2010)

    Article  MATH  Google Scholar 

  73. Muthuswamy, B., Przybylski, A., Feilbach, C., Mossbrucker, J.: Chaos and Complex Systems, pp. 1–10. Springer (2013)

    Google Scholar 

  74. Bo-Cheng, B., Zhong, L., Jian-Ping, X.: Chin. Phys. B 19(3), 030510 (2010)

    Article  Google Scholar 

  75. Bao, B., Liu, Z., Xu, J.: Electron. Lett. 46(3), 228 (2010)

    Article  Google Scholar 

  76. Messias, M., Nespoli, C., Botta, V.A.: Int. J. Bifurc. Chaos 20(02), 437 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  77. Kyprianidis, I., Volos, C.K., Stouboulos, I.: In: 7th International Conference of the Balkan Physical Union Organized by the Hellenic Physical Society with the Cooperation of the Physics Departments of Greek Universities, vol. 1203, pp. 626–631. AIP Publishing (2010)

    Google Scholar 

  78. Buscarino, A., Fortuna, L., Frasca, M., Gambuzza, L.V.: Chaos: Interdiscip. J. Nonlinear Sci. 22(2), 023136 (2012)

    Google Scholar 

  79. Petráš, I.: IEEE Trans. Circuits Syst. II: Express Br. 57(12), 975 (2010)

    Article  Google Scholar 

  80. Cafagna, D., Grassi, G.: Nonlinear Dyn. 70(2), 1185 (2012)

    Article  MathSciNet  Google Scholar 

  81. Wang, X., Li, C., Huang, T., Duan, S.: Chaos: Interdiscip. J. Nonlinear Sci. 22(4), 043119 (2012)

    Google Scholar 

  82. Sun, J., Shen, Y., Yin, Q., Xu, C.: Chaos: Interdisc. J. Nonlinear Sci. 23(1), 013140 (2013)

    Google Scholar 

  83. Ngouonkadi, E.M., Fotsin, H., Fotso, P.L.: Physica Scripta 89(3), 035201 (2014)

    Article  Google Scholar 

  84. Zhi-Jun, L., Yi-Cheng, Z.: Chin. Phys. B 22(4), 040502 (2013)

    Article  Google Scholar 

  85. Chen, A., Haddad, S., Wu, Y.C., Fang, T.N., Lan, Z., Avanzino, S., Pangrle, S., Buynoski, M., Rathor, M., Cai, W., et al.: In: IEEE International Electron Devices Meeting. IEDM Technical Digest, pp. 746–749. IEEE (2005)

    Google Scholar 

  86. Waser, R., Aono, M.: Nat. Mater. 6(11), 833 (2007)

    Article  Google Scholar 

  87. Jafar, M., Haneman, D.: Phys. Rev. B 49(19), 13611 (1994)

    Article  Google Scholar 

  88. Chen, X., Wu, G., Bao, D.: Appl. Phys. Lett. 93(9), 093501 (2008)

    Article  Google Scholar 

  89. Ho, Y., Huang, G.M., Li, P.: In: IEEE/ACM International Conference on Computer-Aided Design-Digest of Technical Papers, ICCAD 2009, pp. 485–490. IEEE (2009)

    Google Scholar 

  90. Robinett, W., Pickett, M., Borghetti, J., Xia, Q., Snider, G.S., Medeiros-Ribeiro, G., Williams, R.S.: Nanotechnology 21(23), 235203 (2010)

    Article  Google Scholar 

  91. Ho, Y., Huang, G., Li, P.: IEEE Trans. Circuits Syst. I: Regul. Pap. 58(4), 724 (2011)

    Article  MathSciNet  Google Scholar 

  92. Chiu, P.F., Chang, M.F., Wu, C.W., Chuang, C.H., Sheu, S.S., Chen, Y.S., Tsai, M.J.: IEEE J. Solid-State Circuits 47(6), 1483 (2012)

    Article  Google Scholar 

  93. Nandha Kumar, T., Almurib, H., Lombardi, F.: In: 2013 13th IEEE Conference on Nanotechnology (IEEE-NANO), 1, 71–76 (2013). doi:10.1109/NANO.2013.6720802

  94. Borghetti, J., Snider, G.S., Kuekes, P.J., Yang, J.J., Stewart, D.R., Williams, R.S.: Nature 464(7290), 873 (2010)

    Article  Google Scholar 

  95. Kang, S.M.S., Shin, S.: Memristors and Memristive Systems, pp. 301–325 Springer (2014)

    Google Scholar 

  96. Bickerstaff, K., Swartzlander, E.: In: 2010 Conference Record of the Forty Fourth Asilomar Conference on Signals, Systems and Computers (ASILOMAR), pp. 1173–1177. IEEE (2010)

    Google Scholar 

  97. Shaltoot, A., Madian, A.: In: 2012 IEEE 55th International Midwest Symposium on Circuits and Systems (MWSCAS), pp. 298–301. IEEE (2012)

    Google Scholar 

  98. Swartzlander, Jr. E.E. et al.: Memristor Networks, pp. 473–486. Springer (2014)

    Google Scholar 

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Radwan, A.G., Fouda, M.E. (2015). Memristor: Models, Types, and Applications. In: On the Mathematical Modeling of Memristor, Memcapacitor, and Meminductor. Studies in Systems, Decision and Control, vol 26. Springer, Cham. https://doi.org/10.1007/978-3-319-17491-4_2

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