Design of NbO<sub><i>x</i></sub> memristive neuron and its application in spiking neural networks

Gu Ya-Na; Liang Yan; Wang Guang-Yi; Xia Chen-Yang

doi:10.7498/aps.71.20220141

Abstract

NbO_x memristors show great application prospect in neuromorphic computing due to its nanoscale size, threshold switching, and locally active properties. The in-depth analysis and study of NbO_x memristors’s dynamic properties are beneficial to the design and optimization of memristive neuron circuits. In this paper, based on the local active theory, the physical model of NbO_x memristor is studied by using the small signal analysis method, and the region and conditions of the peak oscillation are quantitatively analyzed, and the quantitative relationship between the excitation signal amplitude and the peak frequency is determined. Based on the above theoretical analysis, NbO_x memristor neurons are further designed and combined with the memristive synaptic crisscross array in order to construct a 25×10 spiking neural network (SNN). Finally, the recognitional function of digital 0 to 9 patterns is effectively realized by using frequency coding and time coding respectively.

Keywords:

Authors and contacts

1.
School of Electronic Information, Hangzhou Dianzi University, Hangzhou 310018, China
2.
Jiangsu Provincial Laboratory of Electrical and Automation Engineering for Coal Mining, School of Electrical Engineering, China University of Mining and Technology, Xuzhou 221116, China

Corresponding author: Liang Yan, liangyan@hdu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 62171173) and the Natural Science Foundation of Zhejiang Province, China (Grant No. LY20F010008).

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References

[1]	Chua L O 1971 IEEE Trans. Circuits Syst. 18 5
[2]	Williams R S 2008 IEEE Spectr. 45 12
[3]	Zhou J, Cai F, Wang Q, Chen B, S Gaba, W D Lu 2016 IEEE Electron Device Lett. 37 4 Google Scholar
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[17]	Yi W, Tsang K K, Lam S K, Bai X, Crowell J A, Flores E A 2018 Nat. Commun. 7 9
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[32]	洪庆辉 2019 博士学位论文 (武汉: 华中科技大学) Hong Q H 2019 Ph.D. Dissertation (Wuhan: Huazhong University of Science and Technology) (in Chinese)

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图 1 S型NbO_x LAM响应于1 MHz, 10 MHz, 1 GHz的正弦信号的捏滞曲线

Figure 1. Pinch hysteresis curves of S-type NbO_x LAM in response to sinusoidal signals at 1 MHz, 10 MHz and 1 GHz.

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图 2 NbO_x LAM的直流V-I图　(a) 浅蓝色部分是忆阻器的NDR区; (b) 红色线是负载线, 插图为电压偏置电路

Figure 2. DC V-I plot of NbO_x LAM: (a) The light blue part is the NDR region of the memristor; (b) the red line is the load line and the inset is the bias circuit with DC voltage supply.

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图 3 h (V₀ , T)与温度T的关系图

Figure 3. Relationship between h (V₀ , T) and temperature T.

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图 4 (a) NbO_x-Mott忆阻器在工作点Q (0.008 A, 0.3003 V)处的小信号等效电路模型; (b) R_x对工作点的依赖性; (c) L_x对工作点的依赖性; (d) R_y对工作点的依赖性

Figure 4. (a) Small-signal equivalent circuit model of NbO_x-Mott memristor at the operating point Q (0.008 A, 0.3003 V); (b) the dependence of R_x on the operating point; (c) the dependence of L_x on the operating point; (d) the dependence of R_y on the operating point.

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图 5 (a) I = 0.008 A时的实部虚部的频率响应; (b) 奈奎斯特图

Figure 5. (a) Frequency responses of the real and imaginary parts at I = 0.008 A; (b) Nyquist plot.

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图 6 二阶振荡电路

Figure 6. Second-order oscillator circuit.

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图 7 雅可比矩阵的特征值在0.042 nF < C < 10 nF范围内的变化

Figure 7. Variations of the eigenvalues of the Jacobian matrix for 0.042 nF < C < 10 nF.

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图 8 当I = 0.008 A, C = 0.3 nF时, NbO_x LAM的二阶振荡器的仿真结果　(a)电压v_m、状态变量T和电流i_m的瞬态波形; (b)稳定点的i_m-T相图; 当I = 0.008 A, C = 0.8 nF时, NbO_x LAM的二阶振荡器的仿真结果: (c)电压v_m、状态变量T和电流i_m的瞬态波形; (d) 振荡状态的i_m-T相图

Figure 8. Simulation results of the NbO_x LAM second-order oscillator: (a) The transient waveforms of v_m, T and i_m at I = 0.008 A and C = 0.3 nF; (b) the stable equilibrium on i_m-T phase plane at I = 0.008 A and C = 0.3 nF; (c) the transient waveforms of v_m, T and i_m at I = 0.008 A and C = 0.8 nF; (d) the limit cycle on the i_m-T phase plane at I = 0.008 A and C = 0.8 nF.

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图 9 (a) 输入的直流电流激励取10, 30和 50 mA时, 忆阻器电流的时域图; (b) 不同电流激励对应的尖峰数量关系图

Figure 9. (a) The time-domain waveforms of i_m at different input DC current excitations of 10, 30 and 50 mA; (b) the number of spikes corresponding to different current excitations.

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图 10 基于NbO_x忆阻器的神经元电路

Figure 10. Neuron circuit based on NbO_x memristor.

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图 11 (a) 忆阻突触处于ON状态时, V_i1和v_m时域图; (b) 忆阻突触处于ON状态时, i_m时域图; (c) 忆阻突触处于OFF状态时, V_i1和v_m时域图; (d) 忆阻突触处于OFF状态时, i_m时域图

Figure 11. (a) The time-domain waveforms of V_i1 and v_m when the memristive synapse is at ON state; (b) the time-domain waveforms of i_m at ON state; (c) the time-domain waveforms of V_i1 and v_m when the memristive synapse is at OFF state; (d) the time-domain waveforms of i_m at OFF state.

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图 12 5×5的10种数字模式

Figure 12. 10 digital patterns of 5×5.

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图 13 电压突触电路实现

Figure 13. Implementation of voltage synapse circuit.

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图 14 由25×10的突触阵列以及10个输出神经元构成的尖峰神经网络

Figure 14. A spiking neural network consisting of a 25×10 synaptic array and 10 output neurons.

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图 15 (a) 数字2输入尖峰神经网络, 10个输出神经元的电流i_m输出时域图; (b) 10种模式输入尖峰神经网络时各输出神经元输出电流频率的情况

Figure 15. (a) The time-domain waveforms of i_m of 10 output neurons when “2” mode is input to SNN; (b) the output current frequencies of each output neuron when ten modes are input to the spiking neural network.

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图 16 基于TC SNN的神经元电路

Figure 16. Neuron circuit based on TC SNN.

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图 17 (a) 单尖峰电路的仿真结果图; (b) 未应用单尖峰电路方案的仿真结果

Figure 17. (a) The simulation results with the single-spike circuit; (b) the simulation results without the single-spike circuit.

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图 18 (a)“2”模式输入SNN时, 10个输出神经元的电流时域图; (b) 不同输入模式对应的神经元输出首个脉冲的时间

Figure 18. (a) The time-domain waveforms of i_m of 10 output neurons when “2” mode is input to SNN; (b) the time of outputting the first pulse of neurons corresponding to different input modes.

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map

[1]	Chua L O 1971 IEEE Trans. Circuits Syst. 18 5
[2]	Williams R S 2008 IEEE Spectr. 45 12
[3]	Zhou J, Cai F, Wang Q, Chen B, S Gaba, W D Lu 2016 IEEE Electron Device Lett. 37 4 Google Scholar
[4]	王春华, 蔺海荣, 孙晶如, 周玲, 周超, 邓全利 2020 电子与信息学报 42 795 Google Scholar Wang C H, Lin H R, Sun R J, Zhou L, Zhou C, Deng Q L 2020 J. Electron. Inf. Technol. 42 795 Google Scholar
[5]	Yang J J, Strukov D B, Stewart D R 2013 Nat. Nanotechnol. 8 1 Google Scholar
[6]	Wu H, Zhou J, Chen M, Xu Q, Bao B 2021 Chaos, Solitons Fractals. 154 2022
[7]	Kim S, Du C, Sheridan P, Ma W, Choi S H, Lu W D 2015 ACS Nano 15 3
[8]	Weiher M, Herzig M, Tetzlaff R, Ascoli A, Mikolajick T, Slesazeck S 2019 IEEE Trans. Circuits Syst. 66 7
[9]	Strukov D B 2016 Appl. Phys. A 122 4 Google Scholar
[10]	Kvatinsky S, Ramadan M, Friedman E G, Kolodny A 2015 IEEE Trans. Circuits Syst. Express Briefs. 62 8
[11]	Chua L O 2005 Int. J. Bifurcation Chaos 15 11
[12]	Ruan J Y, Sun K H, Mou J, He S B, Zhang L M 2018 Eur. Phys. J. Plus 133 3 Google Scholar
[13]	Weiher M, Herzig M, Tetzlaff R, Ascoli A, Mikolajick T, Slesazeck S 2019 IEEE Trans. Circuits Syst. Regul. Pap. 66 7
[14]	Liang Y, Wang G Y, Chen G R, Dong Y J, Yu D S, Iu H H C 2020 IEEE Trans Circuits Syst. 67 5139 Google Scholar
[15]	Mannan Z I, Choi H, Kim H, Chua L O 2016 Int. J. Bifurcation Chaos 26 1630009 Google Scholar
[16]	Jin P P, Wang G Y, Liang Y, Iu H H C, Chua L O 2021 IEEE Trans. Circuits Syst. 68 11
[17]	Yi W, Tsang K K, Lam S K, Bai X, Crowell J A, Flores E A 2018 Nat. Commun. 7 9
[18]	Lin H R, Wang C H, Sun Y C, Yao W 2020 Nonlinear Dyn. 100 4
[19]	Wei Q M, Tang J S, Li X Y, Zhong Y N, Gao B, Qian H, Wu H Q 2021 5th IEEE Electron Devices Technology & Manufacturing Conference (EDTM) Chengdu, China, April 8–11, 2021 pp1–3
[20]	Frank D J, Dennard R H, Nowak E, Solomon P M, Taur Y, Wong H S P 2001 Proc. IEEE. 89 3 Google Scholar
[21]	Yeo I, Chu M, Gi S, Hwang H, Lee B 2019 IEEE Trans. Electron Devices 66 7 Google Scholar
[22]	Zhang X M, Wu Z H, Lu J K, et al. 2020 IEEE International Electron Devices Meeting(IEDM) Electr Network, December 12–18, 2020
[23]	Wang Z R, Joshi S, Savel’ ev S, et al. 2018 Nat. Electron. 1 2 Google Scholar
[24]	Sheridan P, Ma W, Lu W 2014 IEEE International Symposium on Circuits and Systems (ISCAS) Melbourne, June 1–5, 2014 pp1078–1081
[25]	Kumar S, Strachan J P, Williams R S 2017 Nature 548 7667
[26]	Lottermoser T, Lonkai T, Amann U, Hohlwein D, Ihringer J, Fiebig M 2004 Nature 430 6999
[27]	Sawicki M, Chiba D, Korbecka A, Nishitani Y, Majewski J A, Matsukura F, Dietl T, Ohno H 2008 Nature 455 7212
[28]	Ascoli1 A, Demirkol1 A S, Tetzlaff R, Slesazeck S, Mikolajick T, Chua L O 2021 Front. Neurosci. 15 651452 Google Scholar
[29]	Liang Y, Zhu Q, Wang G Y, Nath S K, Iu H H C, Nandi S K, Elliman R G 2021 IEEE Trans. Circuits Syst. Regul. Pap. 68 1278 Google Scholar
[30]	徐泠风, 李传东, 陈玲 2016 65 240701 Google Scholar Xu L F, Li C D, Chen L 2016 Acta Phys. Sin. 65 240701 Google Scholar
[31]	Zhang Y, Wang X, Li Y, Friedman E G 2017 IEEE Trans. Circuits Syst. Express Briefs. 64 7
[32]	洪庆辉 2019 博士学位论文 (武汉: 华中科技大学) Hong Q H 2019 Ph.D. Dissertation (Wuhan: Huazhong University of Science and Technology) (in Chinese)

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Design of NbO_x memristive neuron and its application in spiking neural networks

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Corresponding author: Liang Yan, liangyan@hdu.edu.cn

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Design of NbOx memristive neuron and its application in spiking neural networks

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Corresponding author: Liang Yan, liangyan@hdu.edu.cn

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Design of NbO_x memristive neuron and its application in spiking neural networks