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A novel modeling method and implementation of floating memory elements

Zheng Ci-Yan Zhuang Chu-Yuan Li Ya Lian Ming-Jian Liang Yan Yu Dong-Sheng

Liu Dan, Liang Pei, Wang Le, Xu Guo-Tang, Liu Yang, Li Xiao-Yan, Dong Qian-Min, Huang Jie. Low-temperature combustion synthesis and luminescent properties of SrMgAl10O17:Eu2+, Er3+ high brightness blue phosphors. Acta Phys. Sin., 2013, 62(19): 197802. doi: 10.7498/aps.62.197802
Citation: Liu Dan, Liang Pei, Wang Le, Xu Guo-Tang, Liu Yang, Li Xiao-Yan, Dong Qian-Min, Huang Jie. Low-temperature combustion synthesis and luminescent properties of SrMgAl10O17:Eu2+, Er3+ high brightness blue phosphors. Acta Phys. Sin., 2013, 62(19): 197802. doi: 10.7498/aps.62.197802

A novel modeling method and implementation of floating memory elements

Zheng Ci-Yan, Zhuang Chu-Yuan, Li Ya, Lian Ming-Jian, Liang Yan, Yu Dong-Sheng
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  • Memristors, memcapacitors and meminductors are nonlinear circuit components with memory effects and belong to memory element (mem-element) system. Since there are many shortcomings in the existing available commercial memristor chips, and the physical realizations of memcapacitor and meminductor hardware are still in early stages, it is still difficult for researchers to obtain hardware mem-elements for research. In order to solve this problem, it is still necessary to build effective equivalent models of mem-elements to facilitate the research on their characteristics and applications. In this paper, a novel floating mem-element modeling method is proposed by connecting different passive circuit component to a universal interface while keeping the circuit topology unchanged. Compared with other floating universal mem-element models, the model built in this paper has simple structure, high working frequencies, thus making proposed models easier to implement. The feasibility and effectiveness of the mem-elements models based on the universal interface are successfully verified through theoretical analysis, PSPICE simulation results and hardware experimental results.
      PACS:
      78.40.Fy(Semiconductors)
      78.66.Fd(III-V semiconductors)
      78.20.Ci(Optical constants (including refractive index, complex dielectric constant, absorption, reflection and transmission coefficients, emissivity))
      Corresponding author: Li Ya, liya2829@gpnu.edu.cn
    • Funds: Project supported by the Young Scientists Fund of the National Natural Science Foundation of China (Grant Nos. 61801154, 62101142), the Science and Technology Program of Guangzhou, China (Grant Nos. 201904010302, 202102020874), the Featured Innovation Foundation of the Education Department of Guangdong Province, China (Grant Nos. 2021ZDZX1079, 2021KTSCX062), and the Doctoral Scientific Research Startup Fund of Guangdong Polytechnic Normal University, China (Grant No. 2021SDKYA009).

    透射式GaAs光电阴极具有量子效率高、长波响应大的特点, 因而三代像增强器采用GaAs光电阴极[13]. 目前大家更多关注透射式GaAs光电阴极光电发射性能的研究, 对比国内外的研究成果, 国内实验室制备的透射式GaAs光电阴极积分灵敏度为2130 μA/lm, 而美国ITT研制生产的透射式GaAs光电阴极积分灵敏度高达2330 μA/lm. 关于光学性能的研究, 杜晓晴[4]介绍了GaAs光电阴极中发射层吸收系数与量子效率的关系, 张益军[5]在讨论变掺杂GaAs光电阴极相关计算公式时, 提到了对吸收系数的处理方法. 邹继军[6]在推导反射式GaAs光电阴极量子效率公式时研究了电子吸收光子在不同能谷间激发的影响. 关于光电发射性能的研究; 张益军[5]推导了包含GaAs衬底层产生光电子项的反射式指数掺杂GaAs光电阴极量子效率公式, 以及包含GaAlAs窗口层产生光电子项的透射式指数掺杂GaAs光电阴极量子效率公式. 在这些量子效率公式中都将光学性能的影响看作定值, 没有考虑反射率随组件结构、光子波长的变化. 关于光学性能和光电发射性能之间的研究, 赵静[7]对量子效率公式进行了光学性能的修正, 同时分析了表征光学性能的吸收率与表征光电发射性能的量子效率之间的关系, 研究了光学性能对光电发射性能的影响. 但是研究光学性能时, 将窗口层的GaAlAs和发射层的GaAs作为不掺杂的材料考虑, 只是定性地研究了掺杂浓度的影响趋势, 本文对此进行完善, 进一步研究掺杂浓度对光学性能和光电发射性能的影响, 有利于完善透射式GaAs光电阴极光学与光电发射性能的研究.

    本文开展了对GaAs光电阴极光学性能和光电发射性能方面的研究, 考虑光学性能中窗口层的厚度、Al组分以及发射层的厚度、掺杂浓度对阴极量子效率的影响, 对量子效率公式进行修正. 利用光学性能、修正后的量子效率和积分灵敏度的理论模型, 仿真了两者的量子效率曲线, 分析了两者结构参数和性能参数上的差异. 在此研究基础上, 优化阴极组件结构设计, 提高阴极灵敏度.

    透射式GaAs光电阴极结构包括Si3N4增透层、Ga1xAlxAs窗口层、GaAs发射层, 在研究光在各膜层的传播过程中, 考虑到光在每层膜上的吸收、反射、透射, 采用图1所示的矩阵法求解三层膜[7], 图中E+0E0分别表示光在玻璃中入射界面上的正向和反向传播电场分量, E+1E1分别表示光在增透层中入射界面上的正向和反向传播电场分量, E+2E2分别表示光在窗口层中入射界面上的正向和反向传播电场分量, E+3E3分别表示光在发射层中入射界面上的正向和反向传播电场分量, E4表示光在真空中传播电场分量.

    图 1 求解三层膜的矩阵法\r\nFig. 1. Matrix method for solving three film.
    图 1  求解三层膜的矩阵法
    Fig. 1.  Matrix method for solving three film.

    透射式GaAs光电阴极结构中, Si3N4层、Ga1xAlxAs层和GaAs层分别用一个包含该膜层参数的矩阵表示, 在膜层1和2上应用边界条件可以得到

    [E0H0]=[cosδ2iη2sinδ2iη2sinδ2cosδ2][E22H22]. (1)

    在膜层2和3上, 膜层3和4上分别应用边界条件得到

    [E12H12]=[cosδ2iη2sinδ2iη2sinδ2cosδ2][E33H33], (2)
    [E23H23]=[cosδ3iη3sinδ3iη3sinδ3cosδ3][E4H4]. (3)

    这里, H0为玻璃的厚度, E12为增透层材料的弹性模量, H12为增透层的厚度, E22E23为窗口层材料的弹性模量, H22H23为窗口层的厚度, E33为发射层材料的弹性模量, H33为发射层的厚度, H4为真空层的厚度. 由于各膜层上具有连续的切向分量, 即[Ej1,jHj1,j]=[Ej,jHj,j], 经过连续的线性变换, 可得到透射式GaAs光电阴极膜系组合的矩阵方程式:

    [E0H0]={3j=1[cosδjiηjsinδjiηjsinδjcosδj]}[E4H4]. (4)

    由于膜层和基底组合的导纳Y=H0/E0, 且基底中只有正向波, 没有反向波, HK+1/EK+1=ηK+1, 代入(4)式得

    E0[1Y]={3j=1[cosδjiηjsinδjiηjsinδjcosδj]}[1η4]E4. (5)

    可得到上述膜系的特征矩阵为

    [BC]={3j=1[cosδjiηjsinδjiηjsinδjcosδj]}[1η4]=[a11a12a21a22][1η4]=[a11+η4a12a21+η4a22]. (6)

    这里δj为膜层的相位厚度; nj=njikj为膜层光学常数, nj, kj分别是第j层膜的折射率和消光系数; dj是膜层的几何厚度; θj是第j层膜的折射角.

    透射式GaAs光电阴极膜系组合的理论反射率Rthe计算为

    Rthe=(η0BCη0B+C)(η0BCη0B+C)=[η0(a11+η4a12)(a21+η4a22)η0(a11+η4a12)+(a21+η4a22]2. (7)

    由(6)式和(7)式可得, 透射式GaAs光电阴极膜系组合的反射率会随着膜层的几何厚度以及光学常数的变化而变化.

    对均匀掺杂透射式GaAs光电阴极, 其量子效率为[8]

    YTC(hν)=P(1R)a2hνL2D1×{ahνDn+SV(Dn/LD)cosh(Te/LD)+SVsinh(Te/LD)exp(ahνTe)[SVcosh(Te/LD)+(Dn/LD)sinh(Te/LD)](Dn/LD)cosh(Te/LD)+SVsinh(Te/LD)ahνLDexp(ahνTe)}. (8)

    式中SV后界面复合速率; Te为阴极发射层厚度; LD为电子扩散长度; P为电子逸出概率; Dn为电子扩散系数; ahv为阴极对入射光的吸收系数; R为阴极对入射光的反射率, R一般为定值, 取为0.2; h为普朗克常数; ν为光的频率. 然而由文献[8,9]可知, 反射率会随着光电阴极窗口层、发射层以及波长变化, 是个变值. 因而在原先量子效率公式的基础上, 将定值R替换成Rthe(hυ). 此外考虑光子在窗口层的吸收, 加入短波约束因子exp(βhνTw).

    修正后的均匀掺杂透射式GaAs光电阴极量子效率公式可写为

    YTC(hν)=P(1Rthe(hν))exp(βhνTw)a2hνL2D1×{ahνDn+SV(Dn/LD)cosh(Te/LD)+SVsinh(Te/LD)exp(ahνTe)[SVcosh(Te/LD)+(Dn/LD)sinh(Te/LD)](Dn/LD)cosh(Te/LD)+SVsinh(Te/LD)ahνLDexp(ahνTe)}. (9)

    式中, βhν为窗口层的吸收系数, Tw为窗口层的厚度. 从修正后的量子效率公式(9)可知, 若考虑光学性能对量子效率的影响, 则量子效率的影响因素又包括发射层和窗口层的厚度、窗口层的Al组分以及发射层的掺杂浓度, 其中Al组分是通过影响折射率和消光系数来影响光电阴极的量子效率, 掺杂浓度是通过影响吸收系数来影响光电阴极的量子效率.

    图2Ga1xAlxAs层的折射率和消光系数随Al组分的变化. 消光系数和折射率通过影响反射率, 从而对光电阴极的量子效率有影响, 图3为量子效率随Al组分的变化, 可以看出, 随Ga1xAlxAs层Al组分的增加, 400—700 nm波段上的量子效率增加, 870 nm以后波段量子效率不变.

    图 2 $ {{\mathrm{G}}{\mathrm{a}}}_{1-x}{{\mathrm{A}}{\mathrm{l}}}_{x}{\mathrm{A}}{\mathrm{s}} $光学常数随Al组分的变化[10]\r\nFig. 2. Variation of the ${{\mathrm{G}}{\mathrm{a}}}_{1-x}{{\mathrm{A}}{\mathrm{l}}}_{x}{\mathrm{A}}{\mathrm{s}} $ optical constant with the Al component[10].
    图 2  Ga1xAlxAs光学常数随Al组分的变化[10]
    Fig. 2.  Variation of the Ga1xAlxAs optical constant with the Al component[10].
    图 3 量子效率随Al组分的变化\r\nFig. 3. Variation of the quantum efficiency with the Al components.
    图 3  量子效率随Al组分的变化
    Fig. 3.  Variation of the quantum efficiency with the Al components.

    图4为GaAs层掺杂浓度对材料吸收系数的影响. 根据吸收系数ahν与消光系数k的关系ahν=4πk/λ[1113]可知, 掺杂浓度通过影响消光系数从而对光电阴极的量子效率有影响, 其中λ为波长. 图5为量子效率随掺杂浓度的变化, 可以看出, 870 nm之前, 量子效率随着掺杂浓度的增加而减小; 870 nm之后, 量子效率随着掺杂浓度的增加而增大.

    图 4 GaAs层掺杂浓度对材料吸收系数的影响\r\nFig. 4. Effect of GaAs-layer doping concentration on the absorption coefficient of materials.
    图 4  GaAs层掺杂浓度对材料吸收系数的影响
    Fig. 4.  Effect of GaAs-layer doping concentration on the absorption coefficient of materials.
    图 5 量子效率随掺杂浓度的变化\r\nFig. 5. Variation of quantum efficiency with the doping concentration.
    图 5  量子效率随掺杂浓度的变化
    Fig. 5.  Variation of quantum efficiency with the doping concentration.

    考虑影响光谱响应参数的因素, 包括发射层和窗口层的厚度、窗口层的Al组分、发射层的掺杂浓度、电子扩散长度、表面逸出概率以及后界面复合速率. 设计透射式GaAs光电阴极光学结构软件, 通过改变各个光学结构参数得到最大光谱响应值.

    图6为国产和ITT典型GaAs光电阴极的量子效率曲线. 从整个波段可以产出, 国产透射式阴极与ITT之间差距不大, 短波段和长波段略低于ITT, 量子效率峰值略高于ITT, 两条量子效率曲线的具体光谱响应参数对比如表1所列.

    图 6 国产与ITT光电阴极量子效率对比[14,15]\r\nFig. 6. Comparison of domestic and ITT photoelectric cathode quantum efficiency [14,15].
    图 6  国产与ITT光电阴极量子效率对比[14,15]
    Fig. 6.  Comparison of domestic and ITT photoelectric cathode quantum efficiency [14,15].
    表 1  国内外透射式GaAs光电阴极光谱响应参数对比
    Table 1.  Comparison of response parameters of transmitted GaAs photocathode spectrum at home and abroad.
    曲线起始波长/nm截止波长/nm峰值波长/nm量子效率峰值/%积分灵敏度/(μA·lm–1)
    国内450930710452130
    ITT440920660432330
    下载: 导出CSV 
    | 显示表格

    为了进一步研究ITT光电阴极的光学结构, 对其量子效率曲线进行拟合仿真, 仿真过程中考虑光学性能对量子效率的影响因素以及修正后的量子效率公式, 拟合计算得到光电阴极的性能参数, 列入表2中.

    表 2  透射式光电阴极性能参数的对比
    Table 2.  Comparison of the performance parameters of the transmitted photocathode.
    类型表面逸出概率电子扩散长度/μm后界面复合速率/(cm·s–1)发射层厚度/μm窗口层厚度/μm窗口层Al组分阴极灵敏度/(μA·lm–1)
    国内0.522.51000001.50.40.72130
    ITT0.523.5100001.30.41.32330
    下载: 导出CSV 
    | 显示表格

    表2可以看出, ITT电子扩散长度要比国内的大, 电子扩散长度越大, 产生光电子的有效面积越大, 到达阴极表面的光电子数目越多, 量子效率越大[16]. 变掺杂发射层设计会使体内产生内建电场, 可以使电子扩散长度更大[1719]. 在发射层厚度方面, 国内外光电阴极相差不大. 对于不同结构的光电阴极, 存在一个最佳发射层厚度使得量子效率最大. 国内由于设备以及制作工艺不完善, 无法对阴极膜层厚度进行精确控制, 导致了光谱响应短波段的差异. 在后界面复合速率方面, 国内均匀掺杂光电阴极的后界面速率只能达到105 cm/s, 而国外光电阴极后界面复合速率已经达到小于104 cm/s, 国内通过变组分[20]窗口层设计可以使后界面速率降到与ITT同样的数量级水平, 在一定变化范围内后界面复合速率值对量子效率没有太大影响.

    在上述我国与ITT量子效率的对比中, 可以看出两者还存在一定差距, 为了缩短差距, 通过仿真分析发射层厚度和电子扩散长度对透射式GaAs光电阴极积分灵敏度的影响.

    基于阴极修正后的量子效率公式以及光学性能对量子效率的影响因素, 对阴极的理论灵敏度进行研究分析, 从而优化和指导阴极的结构设计. 假设初始的Si3N4层厚度Ta = 0.1 μm, 折射率2.06, Ga1xAlxAs层厚度Tw=0.4 μm, 组分x = 0.7, P = 0.52, SV = 105 cm/s和Dn= 120 cm2/s. 计算时单独改变发射层厚度或电子扩散长度, 研究其对阴极积分灵敏度或量子效率的作用.

    当电子扩散长度一定时, 阴极积分灵敏度随阴极发射层厚度的变化如图7所示. 可以看出, 当电子扩散长度Ld = 3 μm时, 透射式阴极获得最高灵敏度的发射层厚度为1.2 μm, 而当Ld = 4 μm时, 最佳厚度为1.5 μm. 随着电子扩散长度的增加, 阴极达到最高灵敏度的发射层厚度也在增加, 即最佳发射层厚度增加. 这主要是由于电子扩散长度越大, 光电子的有效区域越大, 发射层厚度也就越大.

    图 7 透射式阴极理论灵敏度随Te的变化\r\nFig. 7. Variation of the sensitivity of the transmission cathode theory with Te.
    图 7  透射式阴极理论灵敏度随Te的变化
    Fig. 7.  Variation of the sensitivity of the transmission cathode theory with Te.

    当改变电子扩散长度而保持阴极发射层厚度不变时, 可得到如图8所示的计算结果. 可以看出, 随着电子扩散长度的增加, 透射式阴极的灵敏度也在逐步增加. 电子扩散长度较小时, 阴极发射层厚度越大, 灵敏度越小; 且随着电子扩散长度的增加, 发射层厚度大的阴极增加幅度最大, 灵敏度可达到2800 μA/lm.

    图 8 透射式阴极理论灵敏度随Ld的变化\r\nFig. 8. Variation of the theoretical sensitivity of the transmission cathode with Ld.
    图 8  透射式阴极理论灵敏度随Ld的变化
    Fig. 8.  Variation of the theoretical sensitivity of the transmission cathode with Ld.

    当电子扩散长度一定时, 阴极量子效率随阴极发射层厚度的变化如图9所示. 可以看出, 随着厚度的增加, 短波响应不变, 长波响应不断提高. 厚度增加, 发射层吸收光子增多, 从而激发的光电子也增多, 量子效率提高. 当发射层厚度大于一定值时, 吸收的光子不能激发光电子, 量子效率下降.

    图 9 透射式阴极理论量子效率随Te的变化\r\nFig. 9. Variation of quantum efficiency of transmission cathode theory with Te.
    图 9  透射式阴极理论量子效率随Te的变化
    Fig. 9.  Variation of quantum efficiency of transmission cathode theory with Te.

    当改变电子扩散长度而保持阴极发射层厚度不变时, 可得到如图10所示的计算结果. 可以看出, 随着电子扩散长度的增加, 短波响应不变, 长波响应部分提高. 这是因为电子扩散长度越大, 到达阴极表面的光电子数目将增加, 量子效率也就越大, 量子效率可达50%.

    图 10 透射式阴极理论量子效率随Ld的变化\r\nFig. 10. Variation of quantum efficiency of transmission cathode theory with Ld.
    图 10  透射式阴极理论量子效率随Ld的变化
    Fig. 10.  Variation of quantum efficiency of transmission cathode theory with Ld.

    透射式GaAs光电阴极结构中包含3个膜层, 在研究光在各膜层的传播过程中, 考虑到光在每层膜上的吸收、反射、透射, 通过矩阵法求解三层膜, 得到透射式GaAs光电阴极膜系组合的理论反射率, 基于均匀掺杂透射式GaAs光电阴极量子效率公式, 将定值R替换成变值Rthe, 同时加入短波约束因子, 对量子效率公式进行修正, 得到修正后的均匀掺杂透射式GaAs光电阴极量子效率公式. 同时也仿真了量子效率随Al组分和掺杂浓度的变化而变化, 可得到量子效率值最大时的Al组分值和掺杂浓度. 在此基础上, 为了缩短与国外之间的差距, 研究了国产以及ITT透射式光电阴极的光学性能以及光电发射特性. 国内阴极灵敏度能达到2130 μA/lm, 而国外能达到2330 μA/lm, 通过对美国ITT公司量子效率曲线的拟合, 反推出ITT阴极组件的性能参数, 与国内性能参数对比后得出主要是电子扩散长度以及发射层厚度的差距. 设计透射式GaAs光电阴极光学结构软件, 进一步具体分析电子扩散长度和发射层厚度对光电阴极量子效率的影响, 从而优化阴极结构, 结果表明电子扩散长度为7 μm, 发射层厚度为1.5 μm时, 透射式GaAs光电阴极灵敏度能达到2800 μA/lm以上. 然而大的电子扩散长度对阴极材料和制备水平具有很高的要求, 导致我国与国内差距的原因一方面是阴极材料生长工艺不成熟, 另一方面是阴极制备设备的落后. 本文研究了GaAs光电阴极光学性能和光电发射性能之间的关系, 进一步对阴极组件结构设计进行优化, 这对提高阴极量子效率以及像增强器的水平有一定的指导意义.

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    Chua L O 1971 IEEE Trans. Circuit Theory 18 507Google Scholar

    [2]

    Strukov D B, Snider G S, Stewart D R, Williams R S 2008 Nature 453 80Google Scholar

    [3]

    Ventra M D, Pershin Y V, Chua L O 2009 Proc. IEEE 97 1371Google Scholar

    [4]

    Mauro D, Marco M F, Fernando C, Chua L O 2021 IEEE Transactions on Circuits and Systems I: Regular Papers 68 14Google Scholar

    [5]

    Yuan F, Li Y 2019 Chaos 29 101101Google Scholar

    [6]

    Barraj I, Bahloul M A, Masmoudi M 2021 AEU-Inter. J. Electron. C. 132 153664Google Scholar

    [7]

    Wang M, Yu Y, Yang N, Yang C, Ma H 2019 14th IEEE Conference on Industrial Electronics and Applications (ICIEA) Xi'an, China, June 19−21, 2019

    [8]

    Emara A A M, Aboudina M M, Fahmy H A H 2017 Microelectron. J. 64 39Google Scholar

    [9]

    Dalgaty T, Castellani N, Turck C, Harabi K E, Vianello E 2021 Nat. Electron. 4 151Google Scholar

    [10]

    Liu Z, Tang J, Gao B, Yao P, Wu H 2020 Nat. Commun. 11 4234Google Scholar

    [11]

    Corinto F, Marco M, Forti M, Chua L 2019 IEEE T. Cybernetics 50 4758Google Scholar

    [12]

    Yang Y 2020 Nat. Commun. 11 3399Google Scholar

    [13]

    Shang D S, Chai Y C, Cao Z X, Lu J, Sun Y 2015 Chin. Phys. B Sin. 24 68402Google Scholar

    [14]

    申见昕, 尚大山, 孙阳 2018 物理学报 67 127501Google Scholar

    Shen J X, Shang D S, Sun Y 2018 Acta Phys. Sin. 67 127501Google Scholar

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    任宽, 张珂嘉, 秦溪子, 任焕鑫, 朱守辉, 杨峰, 孙柏, 赵勇, 张勇 2021 物理学报 70 078701Google Scholar

    Ren K, Zhang K J, Qin X Z, Ren H X, Zhu S H, Yang F, Sun B, Zhao Y, Zhang Y 2021 Acta Phys. Sin. 70 078701Google Scholar

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    Han J, Song C, Gao S, Wang Y, Chen C, Pan F 2014 ACS Nano 8 10043Google Scholar

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    沈怡然, 李付鹏, 王光义 2020 电子与信息学报 42 844Google Scholar

    Shen Y R, Li F P, Wang G Y 2020 J. Electron. Infor. Technol. 42 844Google Scholar

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    Yuan F, Li Y, Wang G, Dou G, Chen G 2019 Entropy 21 188Google Scholar

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    Vista J, Ranjan A 2019 IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 39 2020Google Scholar

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    Pu Y, Yu B A 2019 IEEE/CAA J. Automat. Sin. 7 237Google Scholar

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    Gupta S, Rai S K 2020 Wireless Pers. Commun. 113 773Google Scholar

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    Yesil A, Babacan Y 2020 IEEE Transactions on Circuits and Systems II: Express Briefs 68 1443Google Scholar

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    Sozen H, Cam U 2020 J. Circuit. Syst. Comput. 29 2050247Google Scholar

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    Pershin Y V, Ventra M 2011 Electron. Lett. 47 243Google Scholar

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    Yu D S, Liang Y, Iu HHC, Hu Y H 2014 Chin. Phys. B 23 070702Google Scholar

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    Fouda M E, Radwan A G 2012 Electron. Lett. 48 1454Google Scholar

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    Liang Y, Yu D S, Chen H 2013 Acta Phys. Sin. 62 158501Google Scholar

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    李志军, 向林波, 肖文润 2017 电子与信息学报 39 1626Google Scholar

    Li Z J, Xiang L B, Xiao W R 2017 J. Electron. Infor. Technol. 39 1626Google Scholar

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    Zhao Q, Wang C, Zhang X 2019 Chaos 29 013141Google Scholar

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    Zheng C Y, Yu D S, Hu HHC, Fernando, T, Sun T T, Eshraghian J K, Guo H D 2019 IEEE T. Circuits I. 66 4793Google Scholar

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    Yu D S, Zhao X, Sun T, Iu HHC, Fernando T 2019 IEEE Transactions on Circuits and Systems II: Express Briefs 67 1334Google Scholar

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    Sharma P K, Ranjan R K, Khateb F, Kumngern M 2020 IEEE Access 8 171397Google Scholar

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    Wang C, Liu X, Hu X 2017 Chaos 27 033114Google Scholar

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    Korneev I A, Semenov V V 2017 Chaos: An Interdisciplinary J. Nonlinear Sci. 27 081104Google Scholar

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    Lin T, Iu HHC, Wang X, Wang X 2015 Int. J. Numer. Model. El. 28 275Google Scholar

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    Wang G, Shi C, Wang X, Yuan F 2017 Math. Probl. Eng. 2017 6504969Google Scholar

    [38]

    Fouda M E, Radwan A G 2014 Circuits, Syst. Signal Process. 33 1573Google Scholar

  • 图 1  通用模拟器设计

    Figure 1.  Design of a universal emulator for building models of mem-elements.

    图 2  忆阻器模型的PSPICE仿真结果 (a) 不同频率激励下的忆阻器vAB-iAB特性曲线; (b) 不同频率激励下的忆阻器忆导值WmvAB的关系图; (c) 在Uo = 1 V, f = 100 kHz下, vAB, iAB, ϕAB(用vC1表示)和Wm的时域波形图

    Figure 2.  Measured simulation results of the proposed memristor emulator: (a) Pinched hysteresis loops under different working frequencies; (b) variation curves of the memductance Wm plotted against the terminal voltage vAB; (c) time-domain wave-forms of vAB, iAB, ϕAB(represented by vC1) and the memductance Wm when Uo = 1 V, f = 100 kHz.

    图 3  忆容器模型的PSPICE仿真结果 (a) 不同频率激励下的忆容器vAB-qAB(用vAB-(vC2)表示)特性曲线; (b)不同频率激励下的忆容器忆容值CmvAB的关系图; (c) 在Uo = 1 V, f= 80 kHz下, vABqAB(用vC2表示)、ϕAB(用vC1表示)和Cm的时域波形图

    Figure 3.  Measured simulation results of the proposed memcapacitor emulator: (a) Pinched hysteresis loops under different working frequencies; (b) variation curves of the memcapacitanceCmplotted against the terminal voltage vAB; (c) time-domain wave-forms of vAB, qAB(represented byvC2), ϕAB(represented byvC1) and the memcapacitance Cmwhen Uo = 1 V, f= 80 kHz.

    图 4  忆感器模型的PSPICE仿真结果 (a) 不同频率激励下的忆感器ϕAB-iAB(用i1-iAB表示)特性曲线; (b)不同频率激励下忆感器的忆感值倒数L1mϕAB(用i1表示)的关系图; (c) 当Uo = 1 V, f= 100 kHz时, iAB, ρAB(用vC1表示)、ϕABL1m的时域波形图

    Figure 4.  Measured simulation results of the proposed meminductor emulator: (a) Pinched hysteresis loops under different working frequencies; (b) variation curves of the inverse meminductance L1m plotted against the fluxϕAB(represented by i1); (c) time-domain wave-forms of iAB, ρAB(represented byvC1), ϕABand the inverse meminductance L1m when Uo = 1 V, f= 100 kHz.

    图 5  通用模拟器硬件实验电路实现

    Figure 5.  Implementation of the universal emulator in hardware experiment.

    图 6  在通用模拟器的Z1Z2接入不同的电阻、电容和电感元件组合, 分别实现忆阻器、忆容器和忆感器模型的硬件实验电路 (a) 忆阻器; (b) 忆容器; (c) 忆感器

    Figure 6.  The experimental breadboard implementation of (a) memristor, (b) memcapacitor, (c) meminductor models based on the universal emulator by connecting different combinations of resistor, capacitor or inductor to Z1 and Z2.

    图 7  忆阻器模型的硬件电路实验结果 (a) 不同频率激励下的忆阻器vAB-iAB(用vAB-(vR3)表示)特性曲线; (b)不同频率激励下的忆阻器忆导值WmvAB的关系图; (c)在Uo = 3 V, f = 100 kHz下, vAB, iAB(用vR3表示)、ϕAB(用vC1表示)和Wm的时域波形图

    Figure 7.  Experimental results of the proposed memristor emulator: (a) Pinched hysteresis loops under different working frequencies; (b) variation curves of the memductance Wm plotted against the terminal voltage vAB; (c) time-domain wave-forms of vAB, iAB(represented byvR3), ϕAB(represented byvC1) and the memductance Wmwhen Uo = 3 V, f = 100 kHz.

    图 8  忆容器模型的硬件实验结果 (a) 不同频率激励下的忆容器vAB-qAB(用vAB-(vC2)表示)特性曲线; (b)不同频率激励下的忆容器忆容值CmvAB的关系图; (c) 在Uo = 3 V, f = 80 kHz下vAB, qAB(用vC2表示)、ϕAB(用vC1表示)和Cm的时域波形图

    Figure 8.  Experimental results of the proposed memcapacitor emulator: (a) Pinched hysteresis loops under different working frequencies; (b) variation curves of the memcapacitance Cm plotted against the terminal voltage vAB; (c) time-domain wave-forms of vAB, qAB(represented by vC2), ϕAB(represented by vC1) and the memcapacitance Cm when Uo = 3 V, f = 80 kHz.

    图 9  忆感器模型的硬件实验结果 (a) 不同频率激励下的忆感器ϕAB-iAB(用(vR1)-(vR2)表示)特性曲线; (b)不同频率激励下忆感器的忆感值倒数L1mϕAB(用vR1表示)的关系图; (c) 在Uo = 3 V, f = 80 kHz下iAB(用vR2表示)、ϕAB(用vR1表示)、ρAB(用vC1表示)和L1m的时域波形图

    Figure 9.  Experimental results of the proposed meminductor emulator: (a) Pinched hysteresis loops under different working frequencies; (b) variation curves of the inverse meminductance L1m plotted against the flux ϕAB(represented byvR1) ; (c) time-domain wave-forms of iAB(represented byvR2), ρAB(represented byvC1), ϕAB(represented byvR1), ρAB(represented by vC1) and the inverse meminductance L1m when Uo = 3 V, f = 80 kHz.

    表 1  基于通用模拟器的记忆元件模型对应特征比较

    Table 1.  Comparison of characteristics of different kinds of mem-element models based on the proposed universal emulator.

    记忆元件类型忆阻器忆容器忆感器
    电路拓扑结构通用模拟器
    阻抗元件Z1电阻R2电阻R2电感L1
    阻抗元件Z2电阻R3电容C2电阻R2
    内部状态变量q-ϕσ-ϕq-ρ
    本构方程W(ϕAB)=α1ϕAB+β1Cm(ϕAB)=α2ϕAB+β2L1m(ρAB)=α3ρAB+β3
    αxα1=R110R22R3C1α2=R1C210R22C1α3=R110L21R2C1
    βxβ1=R110R2R3Vsβ2=R1C210R2Vsβ3=R110L1R2Vs
    DownLoad: CSV
  • [1]

    Chua L O 1971 IEEE Trans. Circuit Theory 18 507Google Scholar

    [2]

    Strukov D B, Snider G S, Stewart D R, Williams R S 2008 Nature 453 80Google Scholar

    [3]

    Ventra M D, Pershin Y V, Chua L O 2009 Proc. IEEE 97 1371Google Scholar

    [4]

    Mauro D, Marco M F, Fernando C, Chua L O 2021 IEEE Transactions on Circuits and Systems I: Regular Papers 68 14Google Scholar

    [5]

    Yuan F, Li Y 2019 Chaos 29 101101Google Scholar

    [6]

    Barraj I, Bahloul M A, Masmoudi M 2021 AEU-Inter. J. Electron. C. 132 153664Google Scholar

    [7]

    Wang M, Yu Y, Yang N, Yang C, Ma H 2019 14th IEEE Conference on Industrial Electronics and Applications (ICIEA) Xi'an, China, June 19−21, 2019

    [8]

    Emara A A M, Aboudina M M, Fahmy H A H 2017 Microelectron. J. 64 39Google Scholar

    [9]

    Dalgaty T, Castellani N, Turck C, Harabi K E, Vianello E 2021 Nat. Electron. 4 151Google Scholar

    [10]

    Liu Z, Tang J, Gao B, Yao P, Wu H 2020 Nat. Commun. 11 4234Google Scholar

    [11]

    Corinto F, Marco M, Forti M, Chua L 2019 IEEE T. Cybernetics 50 4758Google Scholar

    [12]

    Yang Y 2020 Nat. Commun. 11 3399Google Scholar

    [13]

    Shang D S, Chai Y C, Cao Z X, Lu J, Sun Y 2015 Chin. Phys. B Sin. 24 68402Google Scholar

    [14]

    申见昕, 尚大山, 孙阳 2018 物理学报 67 127501Google Scholar

    Shen J X, Shang D S, Sun Y 2018 Acta Phys. Sin. 67 127501Google Scholar

    [15]

    任宽, 张珂嘉, 秦溪子, 任焕鑫, 朱守辉, 杨峰, 孙柏, 赵勇, 张勇 2021 物理学报 70 078701Google Scholar

    Ren K, Zhang K J, Qin X Z, Ren H X, Zhu S H, Yang F, Sun B, Zhao Y, Zhang Y 2021 Acta Phys. Sin. 70 078701Google Scholar

    [16]

    Han J, Song C, Gao S, Wang Y, Chen C, Pan F 2014 ACS Nano 8 10043Google Scholar

    [17]

    沈怡然, 李付鹏, 王光义 2020 电子与信息学报 42 844Google Scholar

    Shen Y R, Li F P, Wang G Y 2020 J. Electron. Infor. Technol. 42 844Google Scholar

    [18]

    Knowm Inc https://knowm.org/downloads/Knowm_Memeistors.pdf [2019-10-6]

    [19]

    Yuan F, Li Y, Wang G, Dou G, Chen G 2019 Entropy 21 188Google Scholar

    [20]

    Vista J, Ranjan A 2019 IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 39 2020Google Scholar

    [21]

    Pu Y, Yu B A 2019 IEEE/CAA J. Automat. Sin. 7 237Google Scholar

    [22]

    Gupta S, Rai S K 2020 Wireless Pers. Commun. 113 773Google Scholar

    [23]

    Yesil A, Babacan Y 2020 IEEE Transactions on Circuits and Systems II: Express Briefs 68 1443Google Scholar

    [24]

    Sozen H, Cam U 2020 J. Circuit. Syst. Comput. 29 2050247Google Scholar

    [25]

    Pershin Y V, Ventra M 2011 Electron. Lett. 47 243Google Scholar

    [26]

    Yu D S, Liang Y, Iu HHC, Hu Y H 2014 Chin. Phys. B 23 070702Google Scholar

    [27]

    Fouda M E, Radwan A G 2012 Electron. Lett. 48 1454Google Scholar

    [28]

    梁燕, 于东升, 陈昊 2013 物理学报 62 158501Google Scholar

    Liang Y, Yu D S, Chen H 2013 Acta Phys. Sin. 62 158501Google Scholar

    [29]

    李志军, 向林波, 肖文润 2017 电子与信息学报 39 1626Google Scholar

    Li Z J, Xiang L B, Xiao W R 2017 J. Electron. Infor. Technol. 39 1626Google Scholar

    [30]

    Zhao Q, Wang C, Zhang X 2019 Chaos 29 013141Google Scholar

    [31]

    Zheng C Y, Yu D S, Hu HHC, Fernando, T, Sun T T, Eshraghian J K, Guo H D 2019 IEEE T. Circuits I. 66 4793Google Scholar

    [32]

    Yu D S, Zhao X, Sun T, Iu HHC, Fernando T 2019 IEEE Transactions on Circuits and Systems II: Express Briefs 67 1334Google Scholar

    [33]

    Sharma P K, Ranjan R K, Khateb F, Kumngern M 2020 IEEE Access 8 171397Google Scholar

    [34]

    Wang C, Liu X, Hu X 2017 Chaos 27 033114Google Scholar

    [35]

    Korneev I A, Semenov V V 2017 Chaos: An Interdisciplinary J. Nonlinear Sci. 27 081104Google Scholar

    [36]

    Lin T, Iu HHC, Wang X, Wang X 2015 Int. J. Numer. Model. El. 28 275Google Scholar

    [37]

    Wang G, Shi C, Wang X, Yuan F 2017 Math. Probl. Eng. 2017 6504969Google Scholar

    [38]

    Fouda M E, Radwan A G 2014 Circuits, Syst. Signal Process. 33 1573Google Scholar

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Metrics
  • Abstract views:  6319
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Publishing process
  • Received Date:  30 May 2021
  • Accepted Date:  13 July 2021
  • Available Online:  17 August 2021
  • Published Online:  05 December 2021

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