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The mathematical model and properties of memristor with border constraint

Zhang Xu Zhou Yu-Ze Bi Qiang Yang Xing-Hua Zu Yun-Xiao

The mathematical model and properties of memristor with border constraint

Zhang Xu, Zhou Yu-Ze, Bi Qiang, Yang Xing-Hua, Zu Yun-Xiao
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  • The properties of memristor as the fourth basic circuit element are studied. The mathematical models in integral form for memristors with and without border constraint are developed. The simulation is done for the memristor with border constraint. The influences of the source frequency and model parameters on the memristor’s properties are analyzed and some conclusions are drawn. The model parameters considered include the doping ratio and the initial doping width, and their influnce on the current, voltage-current relation and flux-charge relation of the memrister are investigaled.
    • Funds:
    [1]

    Chua L O 1971 IEEE trans. on Circuit theory CT-18 507

    [2]

    Chua L O 1976 Proceedings of the IEEE 64 209

    [3]

    Dmitri B S,Gregory S S,Duncan R S, Stanley W 2008 Nature 453 80

    [4]

    James M,He T 2008 Nature 453 42

    [5]

    Gergel H N,Hamadani B,Dunlap B,Suehle J,Richter C, Hacker C, Gundlach D 2009 IEEE 30 706

    [6]

    Wey T A, Benderli S 2009 Electronics Letters 45 1103

    [7]

    Wang X B, Chen Y R,Xi H W,Li H,Dimitrov D 2009 Electron Device Letters of IEEE 30 294

    [8]

    Chen G 2008 Circuits and Systems IEEE 8 55

    [9]

    Shkabko A,Aguirre M H,Marozau I,Lippert T,Weidenkaff A 2009 Applied Physics Letters 95 152109

    [10]

    Di Ventra M,Pershin Y V,Chua L O 2009 Proceedings of the IEEE 97 1717

    [11]

    Driscoll T, Kim H T,Chae B G,Di V M, Basov D N 2009 Applied Physics Letters 95 043503

    [12]

    Smerieri A,Berzina T,Erokhin V, Fontana M. P 2008 Journal of Applied Physics 104 114513

    [13]

    Chen X M, Wu G H,Bao D H 2008 Applied Physics Letters 93 093501

    [14]

    Goknar I C 2008 IEEE of Antennas and Propagation Magazine 50 215

    [15]

    Williams R 2008 IEEE 45 28

    [16]

    Yang X S, Zhao Y 2008 Acta Phys.Sin.57 3188 (in Chinese)[羊新胜、赵 勇 2008 物理学报 57 3188]

    [17]

    He L,Hu X,Yin L,Xu H Y,Xu X L,Guo J D,Li C Y,Yin D L 2009 Acta Phys. Sin.58 417(in Chinese)[贺 丽、胡 翔、尹 澜、许恒毅、徐晓林、郭建栋、李传义、尹道乐 2009 物理学报 58 417]

    [18]

    Su X P,Bao J,Yan S K,Xu X G,Jiang Y 2008 Acta Phys.Sin.57 2509(in Chinese)[苏喜平、包 瑾、闫树科、徐晓光、姜 勇 2008 物理学报 57 2509]

    [19]

    Li B Q,Liu Y H,Feng Y C 2008 Acta Phys.Sin.57 477(in Chinese)[李炳乾、刘玉华、冯玉春 2008 物理学报 57 477]

    [20]

    Jin L,Zhu L,Li L,Xie Z W 2009 Acta Phys.Sin.58 8577(in Chinese)[金 莲、朱 林、李 玲、谢征微 2009 物理学报 58 8577]

    [21]

    Zhu F,Jiao F,Quan S W,Hao J K,Zhao K 2009 Acta Phys.Sin.58 876(in Chinese)[朱 凤、焦 飞、全胜文、郝建奎、赵 夔 2009 物理学报 58 876]

    [22]

    Fan F,Ban C Y,Wang Y,Ba Q X,Cui J Z 2009 Acta Phys.Sin.58 628 (in Chinese)[樊 飞、班春燕、王 洋、巴启先、崔建忠 2009 物理学报 58 68]

    [23]

    Xu X Y,Qian L J,Hu J G 2009 Acta Phys.Sin.58 2023 (in Chinese)[许小勇、钱丽洁、胡经国 2009 物理学报 58 2023]

    [24]

    Cao X,Li X M,Gao X D, Yu W D, Liu X J, Zhang Y W,Chen Lidong, Cheng Xinhong 2009 Journal of Applied Physics 106 073723

    [25]

    Song Y W,Sun H 2008 Acta Phys.Sin.57 7178(in Chinese)[宋亚舞、孙 华 2008 物理学报 57 7178]

    [26]

    Zhang M X,Tian X L,Guo F X 2009 Acta Phys.Sin.58 6080(in Chinese)[张明晓、田学雷、郭风祥 2009 物理学报 58 6080]

    [27]

    Jiang D D,Du J M,Gu Y,Feng Y J 2008 Acta Phys.Sin.57 566(in Chinese)[蒋冬冬、杜金梅、谷 岩、冯玉军 2008 物理学报 57 566]

    [28]

    Xu J F,Fan Y F,Chen W,Zhai Q Y 2009 Acta Phys.Sin.58 644(in Chinese)[徐锦锋、范于芳、陈 娓、翟秋亚 2009 物理学报 58 644]

    [29]

    Peng X D,Zhu T, Wang F W 2009 Acta Phys.Sin.58 3274(in Chinese)[彭先德、朱 涛、王芳卫 2009 物理学报 58 3274]

    [30]

    Feng C W, Cai L, Li Q 2008 Acta Phys.Sin.57 2462(in Chinese)[冯朝文、蔡 理、李 芹 2008 物理学报57 2462]

  • [1]

    Chua L O 1971 IEEE trans. on Circuit theory CT-18 507

    [2]

    Chua L O 1976 Proceedings of the IEEE 64 209

    [3]

    Dmitri B S,Gregory S S,Duncan R S, Stanley W 2008 Nature 453 80

    [4]

    James M,He T 2008 Nature 453 42

    [5]

    Gergel H N,Hamadani B,Dunlap B,Suehle J,Richter C, Hacker C, Gundlach D 2009 IEEE 30 706

    [6]

    Wey T A, Benderli S 2009 Electronics Letters 45 1103

    [7]

    Wang X B, Chen Y R,Xi H W,Li H,Dimitrov D 2009 Electron Device Letters of IEEE 30 294

    [8]

    Chen G 2008 Circuits and Systems IEEE 8 55

    [9]

    Shkabko A,Aguirre M H,Marozau I,Lippert T,Weidenkaff A 2009 Applied Physics Letters 95 152109

    [10]

    Di Ventra M,Pershin Y V,Chua L O 2009 Proceedings of the IEEE 97 1717

    [11]

    Driscoll T, Kim H T,Chae B G,Di V M, Basov D N 2009 Applied Physics Letters 95 043503

    [12]

    Smerieri A,Berzina T,Erokhin V, Fontana M. P 2008 Journal of Applied Physics 104 114513

    [13]

    Chen X M, Wu G H,Bao D H 2008 Applied Physics Letters 93 093501

    [14]

    Goknar I C 2008 IEEE of Antennas and Propagation Magazine 50 215

    [15]

    Williams R 2008 IEEE 45 28

    [16]

    Yang X S, Zhao Y 2008 Acta Phys.Sin.57 3188 (in Chinese)[羊新胜、赵 勇 2008 物理学报 57 3188]

    [17]

    He L,Hu X,Yin L,Xu H Y,Xu X L,Guo J D,Li C Y,Yin D L 2009 Acta Phys. Sin.58 417(in Chinese)[贺 丽、胡 翔、尹 澜、许恒毅、徐晓林、郭建栋、李传义、尹道乐 2009 物理学报 58 417]

    [18]

    Su X P,Bao J,Yan S K,Xu X G,Jiang Y 2008 Acta Phys.Sin.57 2509(in Chinese)[苏喜平、包 瑾、闫树科、徐晓光、姜 勇 2008 物理学报 57 2509]

    [19]

    Li B Q,Liu Y H,Feng Y C 2008 Acta Phys.Sin.57 477(in Chinese)[李炳乾、刘玉华、冯玉春 2008 物理学报 57 477]

    [20]

    Jin L,Zhu L,Li L,Xie Z W 2009 Acta Phys.Sin.58 8577(in Chinese)[金 莲、朱 林、李 玲、谢征微 2009 物理学报 58 8577]

    [21]

    Zhu F,Jiao F,Quan S W,Hao J K,Zhao K 2009 Acta Phys.Sin.58 876(in Chinese)[朱 凤、焦 飞、全胜文、郝建奎、赵 夔 2009 物理学报 58 876]

    [22]

    Fan F,Ban C Y,Wang Y,Ba Q X,Cui J Z 2009 Acta Phys.Sin.58 628 (in Chinese)[樊 飞、班春燕、王 洋、巴启先、崔建忠 2009 物理学报 58 68]

    [23]

    Xu X Y,Qian L J,Hu J G 2009 Acta Phys.Sin.58 2023 (in Chinese)[许小勇、钱丽洁、胡经国 2009 物理学报 58 2023]

    [24]

    Cao X,Li X M,Gao X D, Yu W D, Liu X J, Zhang Y W,Chen Lidong, Cheng Xinhong 2009 Journal of Applied Physics 106 073723

    [25]

    Song Y W,Sun H 2008 Acta Phys.Sin.57 7178(in Chinese)[宋亚舞、孙 华 2008 物理学报 57 7178]

    [26]

    Zhang M X,Tian X L,Guo F X 2009 Acta Phys.Sin.58 6080(in Chinese)[张明晓、田学雷、郭风祥 2009 物理学报 58 6080]

    [27]

    Jiang D D,Du J M,Gu Y,Feng Y J 2008 Acta Phys.Sin.57 566(in Chinese)[蒋冬冬、杜金梅、谷 岩、冯玉军 2008 物理学报 57 566]

    [28]

    Xu J F,Fan Y F,Chen W,Zhai Q Y 2009 Acta Phys.Sin.58 644(in Chinese)[徐锦锋、范于芳、陈 娓、翟秋亚 2009 物理学报 58 644]

    [29]

    Peng X D,Zhu T, Wang F W 2009 Acta Phys.Sin.58 3274(in Chinese)[彭先德、朱 涛、王芳卫 2009 物理学报 58 3274]

    [30]

    Feng C W, Cai L, Li Q 2008 Acta Phys.Sin.57 2462(in Chinese)[冯朝文、蔡 理、李 芹 2008 物理学报57 2462]

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  • Received Date:  23 December 2009
  • Accepted Date:  12 April 2010
  • Published Online:  15 September 2010

The mathematical model and properties of memristor with border constraint

  • 1. School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China

Abstract: The properties of memristor as the fourth basic circuit element are studied. The mathematical models in integral form for memristors with and without border constraint are developed. The simulation is done for the memristor with border constraint. The influences of the source frequency and model parameters on the memristor’s properties are analyzed and some conclusions are drawn. The model parameters considered include the doping ratio and the initial doping width, and their influnce on the current, voltage-current relation and flux-charge relation of the memrister are investigaled.

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