Journal of Computational Electronics

, Volume 16, Issue 4, pp 1154–1166 | Cite as

Stochastic circuit breaker network model for bipolar resistance switching memories

  • S. BrivioEmail author
  • S. Spiga
S.I.: Computational Electronics of Emerging Memory Elements


We present a stochastic model for resistance switching devices in which a square grid of resistor breakers plays the role of the insulator switching layer. The probability of breaker switching between two fixed resistance values, \(R_\mathrm{OFF}\) and \(R_\mathrm{ON}\), is determined by the corresponding voltage drop and thermal Joule heating. The breaker switching produces the overall device resistance change. Salient features of all the switching operations of bipolar resistance switching memories (RRAMs) are reproduced by the model and compared to a prototypical \(\hbox {HfO}_2\)-based RRAM device. In particular, the need of a forming process that leads a fresh highly insulating device to a low resistance state (LRS) is captured by the model. Moreover, the model is able to reproduce the RESET process, which partially restores the insulating state through a gradual resistance transition as a function of the applied voltage and the abrupt nature of the SET process that restores the LRS. Furthermore, the multilevel capacity of a typical RRAM device obtained by tuning RESET voltage and SET compliance current is reproduced. The manuscript analyses the peculiar ingredients of the model and their influence on the simulated current–voltage curves and, in addition, provides a detailed description of the mechanisms that connect the switching of the single breakers and that of the overall device.


RRAM ReRAM Memristor Stochastic model Random circuit breaker 



The work is partially supported by the European Project H2020-ICT-2015 NEUral computing aRchitectures in Advanced Monolithic 3D-VLSI nano-technologies (\(\hbox {NEURAM}^3\), Grant Agreement No. 687299).


  1. 1.
    Jeong, D.S., Thomas, R., Katiyar, R.S., Scott, J.F., Kohlstedt, H., Petraru, A., Hwang, C.S.: Emerging memories: resistive switching mechanisms and current status. Rep. Prog. Phys. 75(7), 076502 (2012). doi: 10.1088/0034-4885/75/7/076502 CrossRefGoogle Scholar
  2. 2.
    Wong, H.S.P., Lee, H.Y., Yu, S., Chen, Y.S., Wu, Y., Chen, P.S., Lee, B., Chen, F.T., Tsai, M.J.: Metal-Oxide RRAM. Proc. IEEE 100(6), 1951 (2012). doi: 10.1109/JPROC.2012.2190369 CrossRefGoogle Scholar
  3. 3.
    Chen, H.Y., Brivio, S., Chang, C.C., Frascaroli, J., Hou, T.H., Hudec, B., Liu, M., Lv, H., Molas, G., Sohn, J., Spiga, S., Teja, V.M., Vianello, E., Wong, H.S.P.: Resistive random access memory (RRAM) technology: from material, device, selector, 3D integration to bottom-up fabrication. J. Electroceramics (2017). doi: 10.1007/s10832-017-0095-9 Google Scholar
  4. 4.
    Chua, L.: Resistance switching memories are memristors. Appl. Phys. A 102(4), 765 (2011). doi: 10.1007/s00339-011-6264-9 CrossRefzbMATHGoogle Scholar
  5. 5.
    Covi, E., Brivio, S., Frascaroli, J., Fanciulli, M., Spiga, S.: (Invited) Analog HfO2-RRAM switches for neural networks. ECS Trans. 75(32), 85 (2017). doi: 10.1149/07532.0085ecst CrossRefGoogle Scholar
  6. 6.
    Covi, E., Brivio, S., Serb, A., Prodromakis, T., Fanciulli, M., Spiga, S.: Analog memristive synapse in spiking networks implementing unsupervised learning. Front. Neurosci. 10, 482 (2016). doi: 10.3389/fnins.2016.00482 CrossRefGoogle Scholar
  7. 7.
    Prezioso, M., Merrikh-Bayat, F., Hoskins, B.D., Adam, G., Likharev, K.K., Strukov, D.: Training and operation of an integrated neuromorphic network based on metal-oxide memristors. Nat. Lett. 521, 61 (2015). doi: 10.1038/nature14441 CrossRefGoogle Scholar
  8. 8.
    Garbin, D., Vianello, E., Bichler, O., Rafhay, Q., Gamrat, C., Ghibaudo, G., DeSalvo, B., Perniola, L.: HfO\(_{\text{2 }}\)-based OxRAM devices as synapses for convolutional neural networks. IEEE Trans. Electron Devices 62(8), 2494 (2015). doi: 10.1109/TED.2015.2440102 CrossRefGoogle Scholar
  9. 9.
    Borghetti, J., Snider, G.S., Kuekes, P.J., Yang, J.J., Steward, D.R., Williams, R.S.: Memristive switches enable stateful logic operations via material implication. Nature 464, 873 (2010). doi: 10.1038/nature08940 CrossRefGoogle Scholar
  10. 10.
    Rosezin, R., Linn, E., Kügeler, C., Bruchhaus, R., Waser, R.: Crossbar logic using bipolar and complementary resistive switches. IEEE Electron Device Lett. 32(6), 710 (2011). doi: 10.1109/LED.2011.2127439 CrossRefGoogle Scholar
  11. 11.
    Chen, P.Y., Yu, S.: Compact modeling of RRAM devices and its applications in 1T1R and 1S1R array design. IEEE Trans. Electron Devices 62(12), 4022 (2015). doi: 10.1109/TED.2015.2492421 MathSciNetCrossRefGoogle Scholar
  12. 12.
    Huang, P., Liu, X.Y., Chen, B., Li, H.T., Wang, Y.J., Deng, Y.X., Wei, K.L., Zeng, L., Gao, B., Du, G., Zhang, X., Kang, J.F.: A physics-based compact model of metal-oxide-based RRAM DC and AC operations. IEEE Trans. Electron Devices 60(12), 4090 (2013). doi: 10.1109/TED.2013.2287755 CrossRefGoogle Scholar
  13. 13.
    Piccolboni, G, Molas, G., Portal, J.M., Coquand, R., Bocquet, M., Garbin, D., Vianello, E., Carabasse, C., Delaye, V., Pellissier, C., Magis, T., Cagli, C., Gely, M., Cueto, O., Deleruyelle, D., Ghibaudo, G., Salvo, B.D., Perniola, L.: Investigation of the potentialities of Vertical Resistive RAM (VRRAM) for neuromorphic applications. In: IEEE International Electron Devices Meeting (IEDM), pp. 17.2.1–17.2.4. (2015). doi: 10.1109/IEDM.2015.7409717
  14. 14.
    Degraeve, R., Fantini, A., Raghavan, N., Goux, L., Clima, S., Govoreanu, B., Belmonte, A., Linten, D., Jurczak, M.: Causes and consequences of the stochastic aspect of filamentary RRAM. Microelectron. Eng. 147, 171 (2015). doi: 10.1016/j.mee.2015.04.025 CrossRefGoogle Scholar
  15. 15.
    Balatti, S., Ambrogio, S., Carboni, R., Milo, V., Wang, Z., Calderoni, A., Ramaswamy, N., Ielmini, D.: Physical unbiased generation of random numbers with coupled resistive switching devices. IEEE Trans. Electron Devices 63(5), 2029 (2016). doi: 10.1109/TED.2016.2537792 CrossRefGoogle Scholar
  16. 16.
    Bill, J., Legenstein, R.: A compound memristive synapse model for statistical learning through STDP in spiking neural networks. Front. Neurosci. 8, 412 (2014). doi: 10.3389/fnins.2014.00412 Google Scholar
  17. 17.
    Gao, B., Liu, L., Kang, J.: Investigation of the synaptic device based on the resistive switching behavior in hafnium oxide. Prog. Nat. Sci. Mater. Int. 25(1), 47 (2015). doi: 10.1016/j.pnsc.2015.01.005 CrossRefGoogle Scholar
  18. 18.
    Padovani, A., Larcher, L., Pirrotta, O., Vandelli, L., Bersuker, G.: Microscopic modeling of HfO\(_x\) RRAM operations: from forming to switching. IEEE Trans. Electron Devices 62(6), 1998 (2015). doi: 10.1109/TED.2015.2418114 CrossRefGoogle Scholar
  19. 19.
    Abbaspour, E., Menzel, S., Jungemann, C.: The role of the interface reactions in the electroforming of redox-based resistive switching devices using KMC simulations. In: 2015 International Conference on Simulation of Semiconductor Processes and Devices (SISPAD) (2015), pp. 293–296. doi: 10.1109/SISPAD.2015.7292317
  20. 20.
    Brivio, S., Frascaroli, J., Spiga, S.: Role of metal-oxide interfaces in the multiple resistance switching regimes of Pt/HfO\(_2\)/TiN devices. Appl. Phys. Lett. 107(2), 023504 (2015). doi: 10.1063/1.4926340 CrossRefGoogle Scholar
  21. 21.
    Frascaroli, J., Brivio, S., Ferrarese Lupi, F., Seguini, G., Boarino, L., Perego, M., Spiga, S.: Resistive switching in high-density nanodevices fabricated by block copolymer self-assembly. ACS Nano 9(3), 2518 (2015). doi: 10.1021/nn505131b CrossRefGoogle Scholar
  22. 22.
    Bersuker, G., Gilmer, D., Veksler, D., Kirsch, P., Vandelli, L., Padovani, A., Larcher, L., McKenna, K., Schluger, A., Iglesias, V., Porti, M., Nafría, M.: Metal oxide resistive memory switching mechanism based on conductive filament properties. J. Appl. Phys. 110(12), 124518 (2011). doi: 10.1063/1.3671565 CrossRefGoogle Scholar
  23. 23.
    Brivio, S., Tallarida, G., Cianci, E., Spiga, S.: Formation and disruption of conductive filaments in a HfO\(_2\)/TiN structure. Nanotechnology 25(38), 385705 (2014). doi: 10.1088/0957-4484/25/38/385705 CrossRefGoogle Scholar
  24. 24.
    Ielmini, D.: Modeling the universal set/reset characteristics of bipolar RRAM by field- and temperature-driven filament growth. IEEE Trans. Electron Devices 58(12), 4309 (2011). doi: 10.1109/TED.2011.2167513 CrossRefGoogle Scholar
  25. 25.
    Brivio, S., Tallarida, G., Perego, D., Franz, S., Deleruyelle, D., Muller, C., Spiga, S.: Low-power resistive switching in Au/NiO/Au nanowire arrays. Appl. Phys. Lett. 101, 223510 (2012). doi: 10.1063/1.4769044 CrossRefGoogle Scholar
  26. 26.
    Indiveri, G., Linares-Barranco, B., Legenstein, R., Deligeorgis, G., Prodromakis, T.: Integration of nanoscale memristor synapses in neuromorphic computing architectures. Nanotechnology 24(38), 384010 (2013). doi: 10.1088/0957-4484/24/38/384010 CrossRefGoogle Scholar
  27. 27.
    Brivio, S., Covi, E., Serb, A., Prodromakis, T., Fanciulli, M.: S. SpigaExperimental study of gradual/abrupt dynamics of HfO2-based memristive devices. Appl. Phys. Lett. 109(13), 133504 (2016). doi: 10.1063/1.4963675 CrossRefGoogle Scholar
  28. 28.
    Chae, S.C., Lee, J.S., Kim, S., Lee, S.B., Chang, S.H., Liu, C., Kahng, B., Shin, H., Kim, D.W., Jung, C.U., Seo, S., Lee, M.J., Noh, T.W.: Random circuit breaker network model for unipolar resistance switching. Adv. Mater. 20(6), 1154 (2008). doi: 10.1002/adma.200702024 CrossRefGoogle Scholar
  29. 29.
    Chang, S.H., Lee, J.S., Chae, S.C., Lee, S.B., Liu, C., Kahng, B., Kim, D.W., Noh, T.W.: Occurrence of both unipolar memory and threshold resistance switching in a NiO film. Phys. Rev. Lett. 102, 026801 (2009). doi: 10.1103/PhysRevLett.102.026801 CrossRefGoogle Scholar
  30. 30.
    Liu, C., Chae, S.C., Lee, J.S., Chang, S.H., Lee, S.B., Kim, D.W., Jung, C.U., Seo, S., Ahn, S.E., Kahng, B., Noh, T.W.: Abnormal resistance switching behaviours of NiO thin films: possible occurrence of both formation and rupturing of conducting channels. J. Phys. D Appl. Phys. 42(1), 015506 (2009). doi: 10.1088/0022-3727/42/1/015506 CrossRefGoogle Scholar
  31. 31.
    Kim, K., Yoon, S.J., Choi, W.Y.: Dual random circuit breaker network model with equivalent thermal circuit network. Appl. Phys. Express 7(2), 024203 (2014). doi: 10.7567/APEX.7.024203 CrossRefGoogle Scholar
  32. 32.
    Xing, J., Li, Q., Tian, X., Li, Z., Xu, H.: A memristor random circuit breaker model accounting for stimulus thermal accumulation. IEICE Electron. Express advpub (2016). doi: 10.1587/elex.13.20160376 Google Scholar
  33. 33.
    Lee, S.B., Lee, J.S., Chang, S.H., Yoo, H.K., Kang, B.S., Kahng, B., Lee, M.J., Kim, C.J., Noh, T.W.: Interface-modified random circuit breaker network model applicable to both bipolar and unipolar resistance switching. Appl. Phys. Lett. 98(3), 033502 (2011). doi: 10.1063/1.3543776 CrossRefGoogle Scholar
  34. 34.
    Li, C., Gao, B., Yao, Y., Guan, X., Shen, X., Wang, Y., Huang, P., Liu, L., Liu, X., Li, J., Gu, C., Kang, J., Yu, R.: Direct observations of nanofilament evolution in switching processes in HfO2-based resistive random access memory by in situ TEM studies. Adv. Mater. (2017). doi: 10.1002/adma.201602976.1602976 Google Scholar
  35. 35.
    Yu, S., Guan, X., Wong, H.S.P.: On the stochastic nature of resistive switching in metal oxide RRAM: Physical modeling, monte carlo simulation, and experimental characterization. In: Electron Devices Meeting (IEDM), IEEE International, 2011, pp. 17.3.1–17.3.4 (2011). doi: 10.1109/IEDM.2011.6131572
  36. 36.
    Yu, S., Chen, Y.Y., Guan, X., Wong, H.S.P., Kittl, J.A.: A Monte Carlo study of the low resistance state retention of HfOx based resistive switching memory. Appl. Phys. Lett. 100(4), 043507 (2012). doi: 10.1063/1.3679610 CrossRefGoogle Scholar
  37. 37.
    Brivio, S., Covi, E., Serb, A., Prodromakis, T., Fanciulli, M., Spiga, S.: Gradual set dynamics in \(\text{HfO }_2\)-based memristor driven by sub-threshold voltage pulses. In Proceedings of IEEE International Conference on Memristive Systems (MEMRISYS), pp. 1–2 (2015). doi: 10.1109/MEMRISYS.2015.7378383
  38. 38.
    Brivio, S., Frascaroli, J., Spiga, S.: Role of Al doping in the filament disruption in \(\text{ HfO }_2\) resistance switches. Nanotechnology (2017). doi: 10.1088/1361-6528/aa8013 Google Scholar
  39. 39.
    Frascaroli, J., Volpe, F.G., Brivio, S., Spiga, S.: Effect of Al doping on the retention behavior of \(\text{ HfO }_2\) resistive switching memories. Microelectron. Eng. 147, 104 (2015). doi: 10.1016/j.mee.2015.04.043 CrossRefGoogle Scholar
  40. 40.
    Spiga, S., Lamperti, A., Wiemer, C., Perego, M., Cianci, E., Tallarida, G., Lu, H., Alia, M., Volpe, F., Fanciulli, M.: Resistance switching in amorphous and crystalline binary oxides grown by electron beam evaporation and atomic layer deposition. Microelectron. Eng. 85(12), 2414 (2008). doi: 10.1016/j.mee.2008.09.018 CrossRefGoogle Scholar
  41. 41.
    Spiga, S., Lamperti, A., Cianci, E., Volpe, F.G., Fanciulli, M.: Transition metal binary oxides for ReRAM applications. ECS Trans. 25(6), 411 (2009). doi: 10.1149/1.3206640 CrossRefGoogle Scholar
  42. 42.
    Knudsen, H.A., Fazekas, S.: Robust algorithm for random resistor networks using hierarchical domain structure. J. Comput. Phys. 211(2), 700 (2006). doi: 10.1016/ MathSciNetCrossRefzbMATHGoogle Scholar
  43. 43.
    Ferragut, R., Dupasquier, A., Brivio, S., Bertacco, R., Egger, W.: Study of defects in an electroresistive Au/La\(_{2/3}\)Sr\(_{1/3}\)MnO\(_3\)/SrTiO\(_3\)(001) heterostructure by positron annihilation. J. Appl. Phys. 110, 053511 (2011). doi: 10.1063/1.3631825 CrossRefGoogle Scholar
  44. 44.
    Traoré, B., Baise, P., Vianello, E., Grampiex, H., Bonnevialle, A., Jalaguier, E., Molas, G., Jeannot, S., Perniola, L., De Salvo, B., Nishi, Y.: Microscopic understanding of the low resistance state retention in HfO\(_2\) and HfAlO based RRAM. In: Proceedings of IEEE International Electron Devices Meeting (IEDM), p. 21.5.1 (2013). doi: 10.1109/IEDM.2014.7047097
  45. 45.
    Zhao, L., Ryu, SW., Hazeghi, A., Duncan, D., Magyari-Köpe, B., Nishi, Y.: Dopant selection rules for extrinsic tunability of HfOx RRAM characteristics: a systematic study. In: 2013 Symposium on VLSI Technology (VLSIT), p. T106 (2013)Google Scholar
  46. 46.
    Zhang, H., Gao, B., Sun, B., Chen, G., Zeng, L., Liu, L., Liu, X., Lu, J., Han, R., Kang, J., Yu, B.: Ionic doping effect in ZrO\(_2\) resistive switching memory. Appl. Phys. Lett. 96(12), 123502 (2010). doi: 10.1063/1.3364130 CrossRefGoogle Scholar
  47. 47.
    Wu, Y., Yu, S., Wong, H.S., Chen, Y.S., Lee , H.Y., Wang, S.M., . Gu, P.Y., Chen, F., Tsai, M.J.: Circuit implementation of spike time dependent plasticity (STDP) for artificial synapse. In: Proceedings of IEEE International Memory Workshop (IMW), pp. 1–4 (2012). doi: 10.1109/IMW.2012.6213663
  48. 48.
    Park, J., Woo, J., Prakash, A., Lee, S., Lim, S., Hwang, H.: Improved reset breakdown strength in a HfOx-based resistive memory by introducing RuOx oxygen diffusion barrier. AIP Adv. 26(5), 055114 (2016). doi: 10.1063/1.4950966 CrossRefGoogle Scholar
  49. 49.
    Russo, U., Ielmini, D., Cagli, C., Lacaita, A.: Self-accelerated thermal dissolution model for reset programming in unipolar resistive-switching memory (RRAM) devices. IEEE Trans. Electron Devices 56(2), 193 (2009). doi: 10.1109/TED.2008.2010584 CrossRefGoogle Scholar
  50. 50.
    Celano, U., Goux, L., Belmonte, A., Giammaria, G., Opsomer, K., Detavernier, C., Richard, O., Bender, H., Irrera, F., Jurczak, M., Vandervorst, W.: Progressive versus abrupt reset behavior in conductive bridging devices: A C-AFM tomography study. In: IEEE International Electron Devices Meeting, pp. 14.1.1–14.1.4 (2014). doi: 10.1109/IEDM.2014.7047048
  51. 51.
    Jana, D., Roy, S., Panja, R., Dutta, M., Rahaman, S.Z., Mahapatra, R., Maikap, S.: Conductive-bridging random access memory: challenges and opportunity for 3D architecture. Nanoscale Res. Lett. 10, 1 (2015). doi: 10.1186/s11671-015-0880-9 CrossRefGoogle Scholar
  52. 52.
    Traoré, B., Blaise, P., Vianello, E., Perniola, L., Salvo, B.D., Nishi, Y.: HfO2-Based RRAM: Electrode Effects, Ti/HfO2 Interface, Charge Injection, and Oxygen (O) Defects Diffusion Through Experiment and Ab Initio Calculations. IEEE Trans. Electron Devices 63(1), 360 (2016). doi: 10.1109/TED.2015.2503145 CrossRefGoogle Scholar
  53. 53.
    Ambrogio, S., Balatti, S., Gilmes, D., Ielmini, D.: Analytical modeling of oxide-based bipolar resistive memories and complementary resistive switches. IEEE Trans. Electron Devices 61(7), 2378 (2014). doi: 10.1109/TED.2014.2325531 CrossRefGoogle Scholar
  54. 54.
    Marchewka, A., Roesgen, B., Skaja, K., Du, H., Jia, C.L., Mayer, J., Rana, V., Waser, R., Menzel, S.: Nanoionic resistive switching memories: on the physical nature of the dynamic reset process. Adv. Electron. Mater. 2(1), 1500233 (2016). doi: 10.1002/aelm.201500233.1500233
  55. 55.
    Kim, S., Du, C., Sheridan, P., Ma, W., Choi, S., Lu, W.D.: Experimental demonstration of a second-order memristor and its ability to biorealistically implement synaptic plasticity. Nano Lett. 15(3), 2203 (2015). doi: 10.1021/acs.nanolett.5b00697 CrossRefGoogle Scholar
  56. 56.
    Vandelli, L., Padovani, A., Larcher, L., Broglia, G., Ori, G., Montorsi, M., Bersuker, G., Pavan, P.: Comprehensive physical modeling of forming and switching operations in HfO\(_{\text{2 }}\) RRAM devices. In: Proceedings of IEEE International Electron Devices Meeting (IEDM), pp. 17.5.1–17.5.4 (2011). doi: 10.1109/IEDM.2011.6131574
  57. 57.
    Menzel, S., Böttger, U., Wimmer, M., Salinga, M.: Physics of the switching kinetics in resistive memories. Adv. Funct. Mater. 25(40), 6306 (2015). doi: 10.1002/adfm.201500825 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Laboratorio MDMIMM - CNRAgrate BrianzaItaly

Personalised recommendations