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Low-power linear computation using nonlinear ferroelectric tunnel junction memristors


Analogue in-memory computing using memristors could alleviate the performance constraints imposed by digital von Neumann systems in data-intensive tasks. Conventional linear memristors typically operate at high currents, potentially limiting power efficiency and scalability in practical applications. Here, we show that nonlinear ferroelectric tunnel junction memristors can perform linear computation at ultralow currents. Using logarithmic line drivers, we demonstrate that analogue-voltage-amplitude vector–matrix multiplication (VMM) can be performed in selectorless ferroelectric tunnel junction crossbars by exploiting a device nonlinearity factor that remains constant for multiple conductive states. We also show that our ferroelectric tunnel junction crossbars have the attributes required to scale analogue VMM-intensive applications, such as neural inference engines, towards energy efficiencies above 100 tera-operations per second per watt.

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Fig. 1: FTJ device characteristics and selectorless crossbar programming.
Fig. 2: FTJ pulse write and IV fits for different device states.
Fig. 3: Linear effective conductance of FTJ memristors by logarithmic line biasing.
Fig. 4: Linear VMM with nonlinear FTJ crossbars and logarithmic line drivers.
Fig. 5: Performance metrics and comparison of VMM engines implemented by FTJ crossbars.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.


  1. 1.

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

    Article  Google Scholar 

  2. 2.

    Yoo, H.-J. Intelligence on silicon: from deep-neural-network accelerators to brain mimicking AI-SOCs. In IEEE International Solid-State Circuits Conference (ISSCC) 20–26 (IEEE, 2019).

  3. 3.

    Song, J. et al. An 11.5TOPS/W 1024-MAC butterfly structure dual-core sparsity-aware neural processing unit in 8 nm flagship mobile SoC. In IEEE International Solid-State Circuits Conference (ISSCC) 130–131 (IEEE, 2019).

  4. 4.

    Yue, J. et al. A 65nm 0.39-to-140.3TOPS/W 1-to-12b unified neural-network processor using block-circulant-enabled transpose-domain acceleration with 8.1× higher TOPS/mm2 and 6T HBST-TRAM-based 2D data-reuse architecture. In IEEE International Solid-State Circuits Conference (ISSCC) 138–139 (IEEE, 2019).

  5. 5.

    Sayal, A., Fathima, S., Nibhanupudi, S. S. T. & Kulkarni, J. P. All-digital time-domain CNN engine using bidirectional memory delay lines for energy-efficient edge computing. In IEEE International Solid-State Circuits Conference (ISSCC) 228–229 (IEEE, 2019).

  6. 6.

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

    Article  Google Scholar 

  7. 7.

    Xia, Q. & Yang, J. J. Memristive crossbar arrays for brain-inspired computing. Nat. Mater. 18, 309–323 (2019).

    Article  Google Scholar 

  8. 8.

    Krestinskaya, O., James, A. P. & Chua, L. O. Neuro-memristive circuits for edge computing: a review. IEEE Trans. Neural Netw. Learn. Syst. 1, 1–20 (2019).

    Google Scholar 

  9. 9.

    Ambrogio, S. et al. Equivalent-accuracy accelerated neural-network training using analogue memory. Nature 558, 60–67 (2018).

    Article  Google Scholar 

  10. 10.

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

    Article  Google Scholar 

  11. 11.

    Wang, Z. et al. Reinforcement learning with analogue memristor arrays. Nat. Electron. 2, 115–124 (2019).

    Article  Google Scholar 

  12. 12.

    Cai, F. et al. A fully integrated reprogrammable memristor-CMOS system for efficient multiply-accumulate operations. Nat. Electron. 2, 290–299 (2019).

    Article  Google Scholar 

  13. 13.

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

    Article  Google Scholar 

  14. 14.

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

    Article  Google Scholar 

  15. 15.

    Sun, Z. Solving matrix equations in one step with cross-point resistive arrays. Proc. Natl Acad. Sci. USA 116, 4123–4128 (2019).

    MathSciNet  Article  Google Scholar 

  16. 16.

    Prezioso, M. et al. Spike-timing-dependent plasticity learning of coincidence detection with passively integrated memristive circuits. Nat. Commun. 9, 5311 (2018).

    Article  Google Scholar 

  17. 17.

    Wang, Z. et al. Fully memristive neural networks for pattern classification with unsupervised learning. Nat. Electron. 1, 137–145 (2018).

    Article  Google Scholar 

  18. 18.

    Hu, M. et al. Memristor-based analog computation and neural network classification with a dot product engine. Adv. Mater. 30, 1705914 (2018).

    Article  Google Scholar 

  19. 19.

    Merrikh Bayat, F. et al. Implementation of multilayer perceptron network with highly uniform passive memristive crossbar circuits. Nat. Commun. 9, 2331 (2018).

    Article  Google Scholar 

  20. 20.

    Li, Y., Wang, Z., Midya, R., Xia, Q. & Yang, J. J. Review of memristor devices in neuromorphic computing: material sciences and device challenges. J. Phys. D 51, 503002 (2018).

    Article  Google Scholar 

  21. 21.

    Shimeng, Yu. Neuro-inspired computing with emerging non-volatile memorys. Proc. IEEE 106, 260–285 (2018).

    Article  Google Scholar 

  22. 22.

    He, K., Zhang, X. Ren & Sun, J. Deep residual learning for image recognition. In Conference on Computer Vision and Pattern Recognition (CVPR) 770–778 (IEEE, 2016).

  23. 23.

    Simonyan, K. & Zisserman, A. Very deep convolutional neural networks for large-scale image recognition. Preprint at (2014).

  24. 24.

    Szegedy, C. et al. Going deeper with convolutions. In Conference on Computer Vision and Pattern Recognition (CVPR) 1–9 (IEEE, 2015).

  25. 25.

    Krizhevsky, A., Sutskever, I. & Hinton, G. E. ImageNet classification with deep convolutional neural networks. Comm. ACM 60, 84–90 (2012).

    Article  Google Scholar 

  26. 26.

    Choi, S., Shin, J. H., Lee, J., Sheridan, P. & Lu., W. Experimental demonstration of feature extraction and dimensionality reduction using memristor networks. Nano Lett. 17, 3113–3118 (2017).

    Article  Google Scholar 

  27. 27.

    Garcia, V. & Bibes, M. Ferroelectric tunnel junctions for information storage and processing. Nat. Commun. 5, 4289 (2014).

    Article  Google Scholar 

  28. 28.

    Maksymovych, P. et al. Polarization control of electron tunnelling into ferroelectric surfaces. Science 12, 1421–1425 (2009).

    Article  Google Scholar 

  29. 29.

    Chanthbouala, A. et al. A ferroelectric memristor. Nat. Mater. 11, 860–864 (2012).

    Article  Google Scholar 

  30. 30.

    Kim, D. J. et al. Ferroelectric tunnel memristor. Nano Lett. 12, 5697–5702 (2012).

    Article  Google Scholar 

  31. 31.

    Hu, Z. et al. Ferroelectric memristor based on Pt/BiFeO3/Nb-doped SrTiO3 heterostructure. Appl. Phys. Lett. 102, 102901 (2013).

    Article  Google Scholar 

  32. 32.

    Mises, R. V. & Pollaczek-Geiringer, H. Praktische verfahren der gleichungsauflösung. Z. Angew. Math. Mech. 9, 152–164 (1929).

    Article  Google Scholar 

  33. 33.

    Fujii, S., Saitoh, M., Schroeder, U., Hwang, C. S. and Funakubo, H. Ferroelectricity in Doped Hafnium Oxide: Materials, Properties and Devices 437–449 (Elsevier, 2019).

  34. 34.

    Fujii, S. et al. First demonstration and performance improvement of ferroelectric HfO2-based resistive switch with low operation current and intrinsic diode property. In Symposium on VLSI Technology 1–2 (IEEE, 2016).

  35. 35.

    Zidan, M. A., Fahmy, H. A. H., Hussain, M. & Salama, K. N. Memristor-based memory: the sneak paths problem and solutions. Microelectron. J. 44, 176–183 (2013).

    Article  Google Scholar 

  36. 36.

    Serb, A., Redman-White, W., Papavassiliou, C. & Prodromakis, T. Practical determination of individual element resistive states in selectorless RRAM arrays. IEEE Trans. Circuits Syst. I 63, 827–835 (2016).

    MathSciNet  Article  Google Scholar 

  37. 37.

    Ota, K. et al. Performance maximization of in-memory reinforcement learning with variability-controlled Hf1−xZrxO2 ferroelectric tunnel junctions. In International Electron Devices Meeting (IEDM) 6.2.1–6.2.4 (IEEE, 2019).

  38. 38.

    Simmons, J. G. Generalised formula for the electric tunnel effect between similar electrodes separated by a thin insulating film. J. Appl. Phys. 34, 1793 (1963).

    Article  Google Scholar 

  39. 39.

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

    Article  Google Scholar 

  40. 40.

    Zidan, M. A. et al. Single-readout high-density memristor crossbar. Sci. Rep. 6, 18863 (2016).

    Article  Google Scholar 

  41. 41.

    Xia, L. et al. Technological exploration of RRAM crossbar array for vector-matrix multiplication. J. Comp. Sci. Tech. 31, 3–19 (2016).

    Article  Google Scholar 

  42. 42.

    Xiao, H., Rasul, K. & Vollgraf, R. Fashion-MNIST: a novel image dataset for benchmarking machine learning algorithms. Preprint at (2017).

  43. 43.

    Khodabandehloo, G., Mirhassani, M. & Ahmadi, M. Analog implementation of a novel resistive-type sigmoidal neuron. IEEE Trans. Very Large Scale Integr. VLSI Syst. 20, 750–754 (2012).

    Article  Google Scholar 

  44. 44.

    Mochida, R. et al. A 4M synapses integrated analog ReRAM based 66.5 TOPS/W neural-network processor with cell current controlled writing and flexible network architecture. In Symposium on VLSI Technology 175–176 (IEEE, 2018).

  45. 45.

    Böscke, T. S., Müller, J., Bräuhaus, D., Schröder, U. & Böttger, U. Ferroelectricity in hafnium oxide thin films. Appl. Phys. Lett. 99, 102903 (2011).

    Article  Google Scholar 

  46. 46.

    Polakowski, P. & Müller, J. Ferroelectricity in undoped hafnium oxide. Appl. Phys. Lett. 106, 232905 (2015).

    Article  Google Scholar 

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We thank K. Nomura, S. Miyano and F. Tachibana for fruitful and insightful discussions. We also thank K. Mizushima for his kind feedback during the writing of this paper.

Author information




R.B. conceived the idea, performed the experiments and analysed the results. T.M and Y.N. validated the measurements and simulations. K.O., M.Y., M.S. and S.F. manufactured the devices and contributed to the characterization. J.D. assisted in the estimations of system-level performance. All authors discussed the results and contributed to the writing and editing of the paper.

Corresponding author

Correspondence to Radu Berdan.

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Supplementary Information

Supplementary Figs. 1–21, Notes 1–11 and Tables 1–3.

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Berdan, R., Marukame, T., Ota, K. et al. Low-power linear computation using nonlinear ferroelectric tunnel junction memristors. Nat Electron 3, 259–266 (2020).

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