Stochastic circuit breaker network model for bipolar resistance switching memories

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 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 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 Chua, L.: Resistance switching memories are memristors. Appl. Phys. A 102(4), 765 (2011). doi:10.1007/s00339-011-6264-9 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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/j.jcp.2005.06.007 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 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 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) 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 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 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 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 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 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 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 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 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 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 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 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