Multiscale modeling of oxide RRAM devices for memory applications: from material properties to device performance


RRAM devices have been subjected to intense research efforts and are proposed for nonvolatile memory and neuromorphic applications. In this paper we describe a multiscale modeling platform connecting the microscopic properties of the resistive switching material to the electrical characteristics and operation of RRAM devices. The platform allows self-consistently modeling the charge and ion transport and the material structural modifications occurring during RRAM operations and reliability, i.e., conductive filament creation and partial disruption. It allows describing the electrical behavior (current, forming, switching, cycling, reliability tests) of RRAM devices in static and transient conditions and their dependence on external conditions (e.g., temperature). Thanks to the kinetic Monte Carlo approach, the inherent variability of physical processes is properly accounted for. Simulation results can be used both to investigate material properties (including atomic defect distributions) and to optimize stack and bias pulses for optimum device performances and reliability.

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  1. 1.

    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), 1951–1970 (2012)

    Article  Google Scholar 

  2. 2.

    Nauenheim, C., et al.: Nano-crossbar arrays for nonvolatile resistive RAM (RRAM) applications. In: NANO ’08 8th IEEE Conference on Nanotechnology, pp. 464–467 (2008)

  3. 3.

    Chen, A.: Ionic Memory Technology, in Solid State Electrochemistry II: Electrodes, Interfaces and Ceramic Membranes, First Edition (ed V. V. Kharton). Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim (2011). doi:10.1002/9783527635566.ch1

  4. 4.

    Govoreanu, B., et al.: 10x10nm2 Hf/HfOx crossbar resistive RAM with excellent performance, reliability and low-energy operation. In: IEDM Tech. Dig, Washington (2011)

  5. 5.

    Lee, S.L., et al.: Multi-level switching of triple-layered \({\rm TaO}_{x}\) RRAM with excellent reliability for storage class memory. In: Symposium on VLSI Technology (VLSIT), pp. 71–72 (2012)

  6. 6.

    Lee, H.Y., et al.: Low power and high speed bipolar switching with a thin reactive Ti buffer layer in robust \(\text{HfO}_{2}\) based RRAM. In: IEDM Tech. Dig, San Francisco (2008)

  7. 7.

    Butcher, B., et al.: High endurance performance of 1T1R \(HfO_{x}\) based RRAM at low (\(<20\mu \text{ A }\)) operative current and elevated (\(150^{\circ }\text{ C }\)) temperature. In: IEEE International Integrated Reliability Workshop Final Report (IRW), pp. 146–150 (2011)

  8. 8.

    Hsu, C.W., et al.: Self-rectifying bipolar \(\text{ TaO }_{{\rm x}}/\text{ TiO }_{2}\) RRAM with superior endurance over \(10^{12}\) cycles for 3D high-density storage-class memory. In: Symposium on VLSI Technology, pp. 166–167 (2013)

  9. 9.

    Burr, G.W., Kurdi, B.N., Scott, J.C., Lam, C.H., Gopalakrishnan, K., Shenoy, R.S.: Overview of candidate device technologies for storage-class memory. IBM J. Res. Dev. 52(4.5), 449–464 (2008)

    Article  Google Scholar 

  10. 10.

    Singha, A., et al.: Analog memristive time dependent learning using discrete nanoscale RRAM devices. In: Int. Joint Conf. Neural Netw., pp. 2248–2255 (2014)

  11. 11.

    Ielmini, D.: Modeling the universal set/reset characteristics of bipolar RRAM by field- and temperature-driven filament growth. IEEE Trans. Electron Devices 58(12), 4309–4317 (2011)

    Article  Google Scholar 

  12. 12.

    Raghavan, N., Pey, K.L., Wu, X., Liu, W., Bosman, M.: Percolative model and thermodynamic analysis of oxygen-ion-mediated resistive switching. IEEE Electron Device Lett. 33(4), 712–714 (2012)

    Article  Google Scholar 

  13. 13.

    Miranda, E., Jiménez, D., Suñé, J.: The quantum point-contact memristor. IEEE Electron Device Lett. 33(10), 1474–1476 (2012)

    Article  Google Scholar 

  14. 14.

    Long, S., Lian, X., Cagli, C., Perniola, L., Miranda, E., Liu, M., Suñé, J.: A model for the set statistics of RRAM inspired in the percolation model of oxide breakdown. IEEE Electron Device Lett. 34(8), 999–1001 (2013)

    Article  Google Scholar 

  15. 15.

    Villena, M.A., Jimenez-Molinos, F., Roldan, J.B., Suñe, J., Long, S., Lian, X., Gamiz, F., Liu, M.: An in-depth simulation study of thermal reset transitions in resistive switching memories. J. Appl. Phys. 114(14), 144505 (2013)

    Article  Google Scholar 

  16. 16.

    Villena, M.A., González, M.B., Jimenez-Molinos, F., Campabadal, F., Roldan, J.B., Suñe, J., Romera, E., Miranda, E.: Simulation of thermal reset transitions in resistive switching memories including quantum effects. J. Appl. Phys. 115(21), 214504 (2014)

    Article  Google Scholar 

  17. 17.

    Szot, D.R., Speier, W., Waser, R.: Nanoscale resistive switching in SrTiO\(_{3}\) thin films. Phys. Status Solidi Rapid Res. Lett. 1(2), R86–R88 (2007)

    Article  Google Scholar 

  18. 18.

    Lin, M.-H., Wu, M.-C., Huang, C.-Y., Lin, C.-H., Tseng, T.-Y.: High-speed and localized resistive switching characteristics of double-layer SrZrO\(_{3}\) memory devices. J. Phys. D Appl. Phys. 43(29), 295404 (2010)

    Article  Google Scholar 

  19. 19.

    Kwon, D.-H., Kim, K.M., Jang, J.H., Jeon, J.M., Lee, M.H., Kim, G.H., Li, X.-S., Park, G.-S., Lee, B., Han, S., Kim, M., Hwang, C.S.: Atomic structure of conducting nanofilaments in TiO\(_{2}\) resistive switching memory. Nat. Nanotechnol. 5(2), 148–53 (2010)

    Article  Google Scholar 

  20. 20.

  21. 21.

    Larcher, L., Puglisi, F.M., Padovani, A., Vandelli, L., Pavan, P.: Multiscale Modeling of electron-ion interactions for engineering novel electronic devices and materials. In: 26th International Workshop on Power and Timing Modeling, Optimization and Simulation (PATMOS), pp. 296–300 (2016)

  22. 22.

    Padovani, A., Larcher, L., Pirrotta, O., Vandelli, L., Bersuker, G.: Microscopic modeling of HfOx RRAM operations: from forming to switching. IEEE Trans. Electron Devices 62(6), 1998–2006 (2015)

    Article  Google Scholar 

  23. 23.

    Muñoz Ramo, D., Gavartin, J.L., Shluger, A.L., Bersuker, G.: Spectroscopic properties of oxygen vacancies in monoclinic HfO\(_{2}\) calculated with periodic and embedded cluster density functional theory. Phys. Rev. B 75, 205336 (2007)

    Article  Google Scholar 

  24. 24.

    Capron, N., Broqvist, P., Pasquarello, A.: Migration of oxygen vacancy in \(\text{ HfO }_{2}\) and across the \(\text{ HfO2/SiO }_{2}\) interface: a first-principles investigation. Appl. Phys. Lett. 91, 192905 (2007)

    Article  Google Scholar 

  25. 25.

    Foster, A.S., Shluger, A.L., Nieminen, R.M.: Mechanism of interstitial oxygen diffusion in Hafnia. Phys. Rev. Lett. 89(22), 225901 (2012)

    Article  Google Scholar 

  26. 26.

    Vandelli, L., Padovani, A., Larcher, L., Southwick III, R.G., Knowlton, W.B., Bersuker, G.: A physical model of the temperature dependence of the current through \(\text{ SiO }_{2}/\text{ HfO }_{2}\) stacks. IEEE Trans. Electron Devices 58(9), 2878–2887 (2011)

    Article  Google Scholar 

  27. 27.

    Zhang, M., Huo, Z., Yu, Z., Liu, J., Liu, M.: Unification of three multi-phonon trap-assisted tunneling mechanisms. J. Appl. Phys. 110, 114108 (2011)

    Article  Google Scholar 

  28. 28.

    Vandelli, L., et al.: Comprehensive physical modeling of forming and switching operations in \(\text{ HfO }_{2}\) RRAM devices. In: Proceedings o the IEEE International Electron Devices Meeting, pp. 421–424 (2011)

  29. 29.

    Larcher, L., Padovani, A., Pirrotta, O., Vandelli, L., Bersuker, G.: Microscopic understanding and modeling of \(\text{ HfO }_{2}\) RRAM device physics. In: Proceedings o the IEEE International Electron Devices Meeting, pp. 474–477 (2012)

  30. 30.

    Padovani, A., Larcher, L., Bersuker, G., Pavan, P.: Charge transport and degradation in \(\text{ HfO }_{2}\) and \(\text{ HfO }_{{\rm x}}\) dielectrics. IEEE Electron Device Lett. 34(5), 680–682 (2013)

    Article  Google Scholar 

  31. 31.

    Puglisi, F.M., Larcher, L., Bersuker, G., Padovani, A., Pavan, P.: An empirical model for RRAM resistance in low- and high-resistance states. IEEE Electron Device Lett. 34, 387–389 (2013)

    Article  Google Scholar 

  32. 32.

    Larcher, L., Puglisi, F.M., Pavan, P., Padovani, A., Bersuker, G.: A compact model of program window in HfOx RRAM devices for conductive filament characteristics analysis. IEEE Trans. Electron Devices 61(8), 2668–2673 (2014)

    Article  Google Scholar 

  33. 33.

    Huang, K., Rhys, A.: Theory of light absorption and non-radiative transition in F-centres. Proc. R. Soc. London 204A, 406–423 (1950)

    Article  MATH  Google Scholar 

  34. 34.

    Henry, C.H., Lang, D.V.: Non radiative capture and recombination by multiphonon emission in GaAs and GaP. Phys. Rev. B 15(2), 989–1016 (1977)

    Article  Google Scholar 

  35. 35.

    Pirrotta, O., et al.: Leakage current through the poly-crystalline \(\text{ HfO }_{2}\): trap densities at grains and grain boundaries. J. Appl. Phys. 114, 134503 (2013)

    Article  Google Scholar 

  36. 36.

    Vandelli, L., Padovani, A., Larcher, L., Bersuker, G.: Microscopic modeling of electrical stress-induced breakdown in poly-crystalline hafnium oxide dielectrics. IEEE Trans. Electron Devices 60(5), 1754–1762 (2013)

    Article  Google Scholar 

  37. 37.

    Padovani, A., Raghavan, N., Larcher, L., Pey, K.L.: Identifying the first layer to fail in dual layer \(\text{ SiO }_{{\rm x}}/\text{ HfSiON }\) gate dielectric stacks. IEEE Electron Device Lett. 34(10), 1289–1291 (2013)

    Article  Google Scholar 

  38. 38.

    McKenna, K.P., Blumberger, J.: Crossover from incoherent to coherent electron tunneling between defects in MgO. Phys. Rev. B 86, 245110 (2012)

    Article  Google Scholar 

  39. 39.

    Marcus, R.A.: Rev. Mod. Phys. 65, 599–610 (1993)

    Article  Google Scholar 

  40. 40.

    Padovani, A., Gao, D.Z., Shluger, A.L., Larcher, L.: A microscopic mechanisms of dielectric breakdown in \(\text{ SiO }_{2}\) films: an insight from multi-scale modeling. J. Appl. Phys. 121(15), 155101 (2017)

  41. 41.

    Gao, D.Z., El-Sayed, Al-Moatasem, Shluger, A.L.: A mechanism for Frenkel defect creation in amorphous \(\text{ SiO }_{2}\) facilitated by electron injection. Nanotechnology 27, 505207 (2016)

    Article  Google Scholar 

  42. 42.

    Bradley, S.R., Shluger, A.L.: Electron-injection-assisted generation of oxygen vacancies in monoclinic \(\text{ HfO }_{2}\). Phys. Rev. B 4, 064008 (2015)

    Google Scholar 

  43. 43.

    McPherson, J., Kim, J.Y., Shanware, A., Mogul, H.: Thermochemical description of dielectric breakdown in high dielectric constant materials. Appl. Phys. Lett. 82(13), 2121–2123 (2003)

    Article  Google Scholar 

  44. 44.

    Manceau, J.-P., Bruyerel, S., Jeannot, S., Sylvestre, A., Gonon, P.: Leakage current variation with time in Ta\(_{2}\)O\(_{5}\) MIM and MIS capacitors. In: IIRW Final Report, p. 129 (2006)

  45. 45.

    Bersuker, G., et al.: Grain boundary-driven leakage path formation in \(\text{ HfO }_{2}\) dielectrics. Solid State Electron. 65–66, 146–150 (2011)

    Article  Google Scholar 

  46. 46.

    Ramprasad, R.: First principles study of oxygen vacancy defects in tantalum pentoxide. J. Appl. Phys. 94, 5609 (2003)

    Article  Google Scholar 

  47. 47.

    Padovani, A., Woo, J., Larcher, L., Hwang, H.: Understanding and optimization of pulsed SET operation in \(\text{ HfO }_{{\rm x}}\)-based RRAM devices for neuromorphic computing applications. (submitted to IEEE Electron Device Lett)

  48. 48.

    Woo, J., Padovani, A., Moon, K., Kwak, M., Larcher, L., Hwang, H.: Linking conductive filament properties and evolution to synaptic behavior of RRAM devices for neuromorphic applications. IEEE Electron Device Lett. 38(9), 1–4 (2017)

    Article  Google Scholar 

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Correspondence to Luca Larcher.

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Larcher, L., Padovani, A. Multiscale modeling of oxide RRAM devices for memory applications: from material properties to device performance. J Comput Electron 16, 1077–1084 (2017).

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  • RRAM
  • \(\hbox {HfO}_{2}\)
  • Forming
  • Trap-assisted tunneling
  • Conductive filament (CF)
  • Resistive switching
  • Set
  • Reset