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Thousands of conductance levels in memristors integrated on CMOS

Nature volume 615, pages 823–829 (2023)Cite this article

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Abstract

Neural networks based on memristive devices1,2,3 have the ability to improve throughput and energy efficiency for machine learning4,5 and artificial intelligence6, especially in edge applications7,8,9,10,11,12,13,14,15,16,17,18,19,20,21. Because training a neural network model from scratch is costly in terms of hardware resources, time and energy, it is impractical to do it individually on billions of memristive neural networks distributed at the edge. A practical approach would be to download the synaptic weights obtained from the cloud training and program them directly into memristors for the commercialization of edge applications. Some post-tuning in memristor conductance could be done afterwards or during applications to adapt to specific situations. Therefore, in neural network applications, memristors require high-precision programmability to guarantee uniform and accurate performance across a large number of memristive networks22,23,24,25,26,27,28. This requires many distinguishable conductance levels on each memristive device, not only laboratory-made devices but also devices fabricated in factories. Analog memristors with many conductance states also benefit other applications, such as neural network training, scientific computing and even ‘mortal computing’25,29,30. Here we report 2,048 conductance levels achieved with memristors in fully integrated chips with 256 × 256 memristor arrays monolithically integrated on complementary metal–oxide–semiconductor (CMOS) circuits in a commercial foundry. We have identified the underlying physics that previously limited the number of conductance levels that could be achieved in memristors and developed electrical operation protocols to avoid such limitations. These results provide insights into the fundamental understanding of the microscopic picture of memristive switching as well as approaches to enable high-precision memristors for various applications.

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Fig. 1: High-precision memristor for neuromorphic computing.
Fig. 2: Direct observation of the evolution of conduction channels in the denoising process using C-AFM.
Fig. 3: Trapped-charge-induced conductance change in incomplete conduction channels.
Fig. 4: Mechanism of denoising using subthreshold voltage, identified using C-AFM measurements and phase-field theory simulations.

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Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Code availability

The algorithm for memristor high-precision programming is included in the Supplementary Information. The code for physical modelling and simulations is available at GitHub (https://github.com/htang113/HfO2-memristor-denoise/tree/main).

References

  1. Chua, L. O. Memristor—the missing circuit element. IEEE Trans. Circuit Theory 18, 507–519 (1971).

    Article  Google Scholar 

  2. Valov, I., Waser, R., Jameson, J. R. & Kozicki, M. N. Electrochemical metallization memories—fundamentals, applications, prospects. Nanotechnology 22, 254003 (2011).

    Article  ADS  PubMed  Google Scholar 

  3. Yang, Y. & Huang, R. Probing memristive switching in nanoionic devices. Nat. Electron. 1, 274–287 (2018).

    Article  Google Scholar 

  4. Wen, W., Wu, C., Wang, Y., Chen, Y. & Li, H. Learning structured sparsity in deep neural networks. In Advances in Neural Information Processing Systems 29 (eds Lee, D. D., et al.), 2082–2090 (Curan Associates, 2016).

  5. Wan, W. et al. A compute-in-memory chip based on resistive random-access memory. Nature 608, 504–512 (2022).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  6. Kumar, S., Wang, X., Strachan, J. P., Yang, Y. & Lu, W. D. Dynamical memristors for higher-complexity neuromorphic computing.Nat. Rev. Mater. 7, 575–591 (2022).

    Article  ADS  Google Scholar 

  7. Xue, C.-X. et al. A CMOS-integrated compute-in-memory macro based on resistive random-access memory for AI edge devices. Nat. Electron. 4, 81–90 (2021).

    Article  CAS  Google Scholar 

  8. Lanza, M. et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication. Science 376, eabj9979 (2022).

    Article  CAS  PubMed  Google Scholar 

  9. Yao, P. et al. Fully hardware-implemented memristor convolutional neural network. Nature 577, 641–646 (2020).

    Article  ADS  CAS  PubMed  Google Scholar 

  10. Zhang, W. et al. Neuro-inspired computing chips. Nat. Electron. 3, 371–382 (2020).

    Article  ADS  Google Scholar 

  11. Ielmini, D. & Wong, H.-S. P. In-memory computing with resistive switching devices. Nat. Electron. 1, 333–343 (2018).

    Article  Google Scholar 

  12. Zidan, M. A., Strachan, J. P. & Lu, W. D. The future of electronics based on memristive systems. Nat. Electron. 1, 22–29 (2018).

    Article  Google Scholar 

  13. Yu, S. Neuro-inspired computing with emerging nonvolatile memorys. Proc. IEEE 106, 260–285 (2018).

    Article  CAS  Google Scholar 

  14. Jung, S. et al. A crossbar array of magnetoresistive memory devices for in-memory computing. Nature 601, 211–216 (2022).

    Article  ADS  CAS  PubMed  Google Scholar 

  15. Sangwan, V. K. & Hersam, M. C. Neuromorphic nanoelectronic materials. Nat. Nanotechnol. 15, 517–528 (2020).

    Article  ADS  CAS  PubMed  Google Scholar 

  16. Burr, G. W. A role for analogue memory in AI hardware. Nat. Mach. Intell. 1, 10–11 (2019).

    Article  Google Scholar 

  17. Chen, S. et al. Wafer-scale integration of two-dimensional materials in high-density memristive crossbar arrays for artificial neural networks. Nat. Electron. 3, 638–645 (2020).

    Article  CAS  Google Scholar 

  18. Fuller, E. J. et al. Parallel programming of an ionic floating-gate memory array for scalable neuromorphic computing. Science 364, 570–574 (2019).

    Article  ADS  CAS  PubMed  Google Scholar 

  19. Choi, C. et al. Reconfigurable heterogeneous integration using stackable chips with embedded artificial intelligence.Nat. Electron. 5, 386–393 (2022).

    Article  Google Scholar 

  20. Lim, D.-H. et al. Spontaneous sparse learning for PCM-based memristor neural networks. Nat. Commun. 12, 319 (2021).

    Article  ADS  MathSciNet  CAS  PubMed  PubMed Central  Google Scholar 

  21. Xu, X. et al. Scaling for edge inference of deep neural networks. Nat. Electron. 1, 216–222 (2018).

    Article  Google Scholar 

  22. Sun, Y. et al. A Ti/AlOx/TaOx/Pt analog synapse for memristive neural network. IEEE Electron Device Lett. 39, 1298–1301 (2018).

    Article  ADS  CAS  Google Scholar 

  23. Stathopoulos, S. et al. Multibit memory operation of metal-oxide bi-layer memristors. Sci. Rep. 7, 17532 (2017).

    Article  ADS  PubMed  PubMed Central  Google Scholar 

  24. Kim, H., Mahmoodi, M. R., Nili, H. & Strukov, D. B. 4K-memristor analog-grade passive crossbar circuit. Nat. Commun. 12, 5198 (2021).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  25. Zidan, M. A. et al. A general memristor-based partial differential equation solver. Nat. Electron. 1, 411–420 (2018).

    Article  Google Scholar 

  26. Li, C. et al. Analogue signal and image processing with large memristor crossbars. Nat. Electron. 1, 52–59 (2018).

    Article  Google Scholar 

  27. Mackin, C. et al. Optimised weight programming for analogue memory-based deep neural networks. Nat. Commun. 13, 3765 (2022).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  28. Choi, S. et al. SiGe epitaxial memory for neuromorphic computing with reproducible high performance based on engineered dislocations. Nat. Mater. 17, 335–340 (2018).

    Article  ADS  CAS  PubMed  Google Scholar 

  29. Yao, P. et al. Face classification using electronic synapses. Nat. Commun. 8, 15199 (2017).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  30. Hinton, G. The forward–forward algorithm: some preliminary investigations. Preprint at https://arxiv.org/abs/2212.13345 (2022).

  31. Yan, Z., Hu, X. S. & Shi, Y. SWIM: Selective write-verify for computing-in-memory neural accelerators. Preprint at https://arxiv.org/abs/2202.08395 (2022).

  32. Chen, B. et al. A memristor-based hybrid analog-digital computing platform for mobile robotics. Sci. Robot. 5, eabb6938 (2020).

    Article  PubMed  Google Scholar 

  33. Choi, S., Yang, Y. & Lu, W. Random telegraph noise and resistance switching analysis of oxide based resistive memory. Nanoscale 6, 400–404 (2014).

    Article  ADS  CAS  PubMed  Google Scholar 

  34. Ielmini, D., Nardi, F. & Cagli, C. Resistance-dependent amplitude of random telegraph-signal noise in resistive switching memories. Appl. Phys. Lett. 96, 053503 (2010).

    Article  ADS  Google Scholar 

  35. Puglisi, F. M., Pavan, P., Padovani, A., Larcher, L. & Bersuker, G. Random telegraph signal noise properties of HfOx RRAM in high resistive state. In 2012 Proc. European Solid-State Device Research Conference (ESSDERC), 274–277 (IEEE, 2012).

  36. Lee, J.-K. et al. Extraction of trap location and energy from random telegraph noise in amorphous TiOx resistance random access memories. Appl. Phys. Lett. 98, 143502 (2011).

    Article  ADS  Google Scholar 

  37. Puglisi, F. M., Padovani, A., Larcher, L. & Pavan, P. Random telegraph noise: measurement, data analysis, and interpretation. In 2017 IEEE 24th International Symposium on the Physical and Failure Analysis of Integrated Circuits (IPFA), 1–9 (IEEE, 2017).

  38. Puglisi, F. M., Zagni, N., Larcher, L. & Pavan, P. Random telegraph noise in resistive random access memories: compact modeling and advanced circuit design. IEEE Trans. Electron Devices 65, 2964–2972 (2018).

    Article  ADS  CAS  Google Scholar 

  39. Yang, Y. et al. Probing nanoscale oxygen ion motion in memristive systems. Nat. Commun. 8, 15173 (2017).

    Article  ADS  PubMed  PubMed Central  Google Scholar 

  40. Puglisi, F. M. Noise in Nanoscale Semiconductor Devices (ed. Grassor, T.), 87–133 (Springer, 2020).

  41. Hui, F. & Lanza, M. Scanning probe microscopy for advanced nanoelectronics. Nat. Electron. 2, 221–229 (2019).

    Article  Google Scholar 

  42. Celano, U. et al. Three-dimensional observation of the conductive filament in nanoscaled resistive memory devices. Nano Lett. 14, 2401–2406 (2014).

    Article  ADS  CAS  PubMed  Google Scholar 

  43. Du, H. et al. Nanosized conducting filaments formed by atomic-scale defects in redox-based resistive switching memories. Chem. Mater. 29, 3164–3173 (2017).

    Article  CAS  Google Scholar 

  44. Puglisi, F. M., Larcher, L., Padovani, A. & Pavan, P. A complete statistical investigation of RTN in HfO2-based RRAM in high resistive state. IEEE Trans. Electron Devices 62, 2606–2613 (2015).

    Article  ADS  CAS  Google Scholar 

  45. Ambrogio, S. et al. Statistical fluctuations in HfOx resistive-switching memory: part II—random telegraph noise. IEEE Trans. Electron Devices 61, 2920–2927 (2014).

    Article  ADS  CAS  Google Scholar 

  46. Becker, T. et al. An electrical model for trap coupling effects on random telegraph noise. IEEE Electron Device Lett. 41, 1596–1599 (2020).

    Article  ADS  CAS  Google Scholar 

  47. Brivio, S., Frascaroli, J., Covi, E. & Spiga, S. Stimulated ionic telegraph noise in filamentary memristive devices. Sci. Rep. 9, 6310 (2019).

    Article  ADS  PubMed  PubMed Central  Google Scholar 

  48. Miao, F. et al. Anatomy of a nanoscale conduction channel reveals the mechanism of a high‐performance memristor. Adv. Mater. 23, 5633–5640 (2011).

    Article  CAS  PubMed  Google Scholar 

  49. Zhou, Y. et al. The effects of oxygen vacancies on ferroelectric phase transition of HfO2-based thin film from first-principle. Comput. Mater. Sci. 167, 143–150 (2019).

    Article  ADS  CAS  Google Scholar 

  50. Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758–1775 (1999).

    Article  ADS  CAS  Google Scholar 

  51. Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169–11186 (1996).

    Article  ADS  CAS  Google Scholar 

  52. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).

    Article  ADS  CAS  PubMed  Google Scholar 

  53. Monkhorst, H. J. & Pack, J. D. Special points for Brillouin-zone integrations. Phys. Rev. B 13, 5188–5192 (1976).

    Article  ADS  MathSciNet  Google Scholar 

  54. Lyons, J. L., Janotti, A. & Van de Walle, C. G. The role of oxygen-related defects and hydrogen impurities in HfO2 and ZrO2. Microelectron. Eng. 88, 1452–1456 (2011).

    Article  CAS  Google Scholar 

  55. Monaghan, S., Hurley, P. K., Cherkaoui, K., Negara, M. A. & Schenk, A. Determination of electron effective mass and electron affinity in HfO2 using MOS and MOSFET structures. Solid State Electron. 53, 438–444 (2009).

    Article  ADS  CAS  Google Scholar 

  56. Zhao, X. & Vanderbilt, D. First-principles study of structural, vibrational, and lattice dielectric properties of hafnium oxide. Phys. Rev. B 65, 233106 (2002).

    Article  ADS  Google Scholar 

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Acknowledgements

J.J.Y., W.S. and Y.Z. were partially supported by a subcontract (GR1055585 53-4502-0003) from the University of Massachusetts Amherst, with the sponsor being TetraMem. R.M., Q.X. and J.J.Y. were partially supported by the Air Force Office of Scientific Research through the Multidisciplinary University Research Initiative programme under contract no. FA9550-19-1-0213, the US Air Force Research Laboratory (prime contract nos. FA8650-21-C-5405 and FA8750-22-1-0501) and by the National Science Foundation under contract no. 2023752. J.W. and H.W. acknowledge the support by the Army Research Office (grant no. W911NF2120128) and the National Science Foundation (grant no. CMMI-2240407). H.T. and J.L. acknowledge the support by the National Science Foundation (grant no. CMMI-1922206). We thank A. Tan for proofreading the manuscript.

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Author notes

  1. These authors contributed equally: Mingyi Rao, Hao Tang, Jiangbin Wu, Wenhao Song

Authors and Affiliations

  1. TetraMem, Fremont, CA, USA

    Mingyi Rao, Max Zhang, Wenbo Yin, Xiangqi Jiang, Mingche Wu, Miao Hu, Qiangfei Xia, Ning Ge & J. Joshua Yang

  2. Department of Electrical and Computer Engineering, University of Massachusetts, Amherst, MA, USA

    Mingyi Rao, Fatemeh Kiani, Benjamin Chen, Rivu Midya, Fan Ye, Hao Jiang, Zhongrui Wang, Qiangfei Xia & J. Joshua Yang

  3. Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA

    Hao Tang & Ju Li

  4. Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, CA, USA

    Jiangbin Wu, Wenhao Song, Ye Zhuo, Hefei Liu, Hung-Yu Chen, Han Wang & J. Joshua Yang

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Contributions

J.J.Y. and M.R. conceived the concept. J.J.Y. and Q.X. supervised the entire project. J.J.Y., M.R., Q.X., H.T., J.W. and W.S. designed the experiments and simulations. M.R., M.Z., R.M. and H.J. fabricated the devices. M.R., W.S., Y.Z., B.C., X.J. and Z.W. carried out the electrical measurements. H.T., M.R. and J.L. designed and carried out the simulation. J.W., M.R., H.L., H.-Y.C. and H.W. designed and carried out the C-AFM studies. W.Y., F.K., F.Y., Z.W., M.W., M.H., Q.X., N.G. and J.J.Y. helped with experiments and data analysis. M.R., H.T. and J.J.Y. wrote the paper. All authors discussed the results and implications and commented on the manuscript at all stages.

Corresponding author

Correspondence to J. Joshua Yang.

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Competing interests

J.J.Y. and Q.X. are co-founders and paid consultants of TetraMem.

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Nature thanks Yiyu Shi, Ilia Valov and Yuchao Yang for their contribution to the peer review of this work. Peer reviewer reports are available.

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Supplementary information

Supplementary Information

This file contains Supplementary Figs. 1–15, a discussion on the probable RTN-responsible defect and an analysis of electronic and atomic noise effects.

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Rao, M., Tang, H., Wu, J. et al. Thousands of conductance levels in memristors integrated on CMOS. Nature 615, 823–829 (2023). https://doi.org/10.1038/s41586-023-05759-5

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