SEMICONDUCTOR DEVICES

Memristor interpretations based on constitutive relations

Wei Wu and Ning Deng

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 Corresponding author: Ning Deng, Email: ningdeng@tsinghua.edu.cn

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Abstract: The attractive memristor is interpreted based on its constitutive relation. The memory property of the memristor is explained, along with the explanation on its three fingerprints: (1) Pinched hysteresis loop; (2) Hysteresis lobe area decreases as frequency increases; (3) Pinched hysteresis loop shrinks to a single-valued function at infinite frequency. Where the magnetic flux is in Strukov’s memristor is also introduced. Resistive elements including the memristor are taken as an example to argue that the constitutive relation determines the electrical property of a circuit element and diagram method is used to distinguish different elements in the resistive element series.

Key words: memristormagnetic fluxconstitutive relationpinched hysteresis loop



[1]
Chua L O. Memristor–The missing circuit element. IEEE Trans Circuit Theory, 1971, 18(5): 507 doi: 10.1109/TCT.1971.1083337
[2]
Strukov D, Snider G, Stewart D, et al. The missing memristor found. Nature, 2008, 453: 80 doi: 10.1038/nature06932
[3]
Ho P W C, Almurib H A F, Kumar T N. Memristive SRAM cell of seven transistors and one memristor. J Semicond, 2016, 37(10): 104002 doi: 10.1088/1674-4926/37/10/104002
[4]
You Z Q, Hu F, Huang L M, et al. A long lifetime, low error rate RRAM design with self-repair module. J Semicond, 2016, 37(11): 115004 doi: 10.1088/1674-4926/37/11/115004
[5]
Kokate P P. Memristor-based chaotic circuits. IETE Techn Rev, 2009, 26(6): 417 doi: 10.4103/0256-4602.57827
[6]
Jo S H, Chang T, Ebong I, et al. Nanoscale memristor device as synapse in neuromorphic systems. Nano Lett, 2010, 10(4): 1297 doi: 10.1021/nl904092h
[7]
Kim H, Sah M P, Yang C, et al. Neural synaptic weighting with a pulse-based memristor circuit. IEEE Trans Circuits Syst I, 2012, 59-I(1): 148
[8]
Shinde S S, Dongle T D. Modelling of nanostructured TiO2-based memristors. J Semicond, 2015, 36(3): 034001 doi: 10.1088/1674-4926/36/3/034001
[9]
Biolek Z, Biolek D, Biolkova V. SPICE model of memristor with nonlinear dopant drift. Radioengineering, 2009, 18(2): 210
[10]
Kumar A, Baghini M S. Experimental study for selection of electrode material for ZnO-based memristors. Electron Lett, 2014, 50(21): 1547 doi: 10.1049/el.2014.1491
[11]
Ho P W C, Hatem F O, Almurib H A F, et al. Comparison between Pt/TiO2/Pt and Pt/TaOX/TaOY/Pt based bipolar resistive switching devices. J Semicond, 2016, 37(6): 064001 doi: 10.1088/1674-4926/37/6/064001
[12]
Adhikari S P, Sah M P, Kim H, et al. Three fingerprints of memristor. IEEE Trans Circuits Syst I, 2013, 60(11): 3008 doi: 10.1109/TCSI.2013.2256171
[13]
Chua L O. Nonlinear circuit foundations for nanodevices I: the four-element torus. Proc IEEE, 2003, 9(11): 1830 doi: 10.1109/JPROC.2003.818319
[14]
Wang F Z. A triangular periodic table of elementary circuit rlements. IEEE Trans Circuits Syst I, 2013, 60(3): 616 doi: 10.1109/TCSI.2012.2209734
[15]
Kuzum D, Yu S, Wong H S. Synaptic electronics: materials, devices and applications. Nanotechnology, 2013, 24(38): 382001 doi: 10.1088/0957-4484/24/38/382001
Fig. 1.  A triangular periodic table of elementary circuit elements, with resistive elements series, capacitive elements series and inductive elements series.

Fig. 2.  Diagram of a non-linear resistor. A pinched hysteresis loop can also be generated in dv/dt–di/dt diagram.

Fig. 3.  The change of resistance under a frequency-dependent sinusoidal current excitation. Red curve indicates the working section of the memristor. The resistance becomes constant when the frequency is infinite because the red curve shrinks to a dot.

Fig. 4.  (Color online) An imaginary black box and closed loop with current i and voltage v. The charge q can be seen as the charge flows into the black box and the magnetic flux φ can be seen as the flux in the open space to generate the voltage source.

Fig. 5.  (Color online) Generating the pinched hysteresis loop in terms of constitutive relation under different excitations. A sinusoidal current excitation and a square wave current excitation are taken as examples.

Fig. 6.  Odd symmetric relation and non-odd symmetric relation of a resistive element. (a) In odd symmetric relation case, the constitutive relation is not fixed. (b) In non-odd symmetric relation case, the constitutive relation is fixed.

Fig. 7.  Different kinds of non-odd symmetric vi curve. (a) Single-value function. (b) A pinched hysteresis loop. (c) An open multi-value curve

[1]
Chua L O. Memristor–The missing circuit element. IEEE Trans Circuit Theory, 1971, 18(5): 507 doi: 10.1109/TCT.1971.1083337
[2]
Strukov D, Snider G, Stewart D, et al. The missing memristor found. Nature, 2008, 453: 80 doi: 10.1038/nature06932
[3]
Ho P W C, Almurib H A F, Kumar T N. Memristive SRAM cell of seven transistors and one memristor. J Semicond, 2016, 37(10): 104002 doi: 10.1088/1674-4926/37/10/104002
[4]
You Z Q, Hu F, Huang L M, et al. A long lifetime, low error rate RRAM design with self-repair module. J Semicond, 2016, 37(11): 115004 doi: 10.1088/1674-4926/37/11/115004
[5]
Kokate P P. Memristor-based chaotic circuits. IETE Techn Rev, 2009, 26(6): 417 doi: 10.4103/0256-4602.57827
[6]
Jo S H, Chang T, Ebong I, et al. Nanoscale memristor device as synapse in neuromorphic systems. Nano Lett, 2010, 10(4): 1297 doi: 10.1021/nl904092h
[7]
Kim H, Sah M P, Yang C, et al. Neural synaptic weighting with a pulse-based memristor circuit. IEEE Trans Circuits Syst I, 2012, 59-I(1): 148
[8]
Shinde S S, Dongle T D. Modelling of nanostructured TiO2-based memristors. J Semicond, 2015, 36(3): 034001 doi: 10.1088/1674-4926/36/3/034001
[9]
Biolek Z, Biolek D, Biolkova V. SPICE model of memristor with nonlinear dopant drift. Radioengineering, 2009, 18(2): 210
[10]
Kumar A, Baghini M S. Experimental study for selection of electrode material for ZnO-based memristors. Electron Lett, 2014, 50(21): 1547 doi: 10.1049/el.2014.1491
[11]
Ho P W C, Hatem F O, Almurib H A F, et al. Comparison between Pt/TiO2/Pt and Pt/TaOX/TaOY/Pt based bipolar resistive switching devices. J Semicond, 2016, 37(6): 064001 doi: 10.1088/1674-4926/37/6/064001
[12]
Adhikari S P, Sah M P, Kim H, et al. Three fingerprints of memristor. IEEE Trans Circuits Syst I, 2013, 60(11): 3008 doi: 10.1109/TCSI.2013.2256171
[13]
Chua L O. Nonlinear circuit foundations for nanodevices I: the four-element torus. Proc IEEE, 2003, 9(11): 1830 doi: 10.1109/JPROC.2003.818319
[14]
Wang F Z. A triangular periodic table of elementary circuit rlements. IEEE Trans Circuits Syst I, 2013, 60(3): 616 doi: 10.1109/TCSI.2012.2209734
[15]
Kuzum D, Yu S, Wong H S. Synaptic electronics: materials, devices and applications. Nanotechnology, 2013, 24(38): 382001 doi: 10.1088/0957-4484/24/38/382001
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    Received: 24 February 2017 Revised: 10 April 2017 Online: Accepted Manuscript: 13 November 2017Published: 01 October 2017

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      Wei Wu, Ning Deng. Memristor interpretations based on constitutive relations[J]. Journal of Semiconductors, 2017, 38(10): 104005. doi: 10.1088/1674-4926/38/10/104005 W Wu, N Deng. Memristor interpretations based on constitutive relations[J]. J. Semicond., 2017, 38(10): 104005. doi: 10.1088/1674-4926/38/10/104005.Export: BibTex EndNote
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      Wei Wu, Ning Deng. Memristor interpretations based on constitutive relations[J]. Journal of Semiconductors, 2017, 38(10): 104005. doi: 10.1088/1674-4926/38/10/104005

      W Wu, N Deng. Memristor interpretations based on constitutive relations[J]. J. Semicond., 2017, 38(10): 104005. doi: 10.1088/1674-4926/38/10/104005.
      Export: BibTex EndNote

      Memristor interpretations based on constitutive relations

      doi: 10.1088/1674-4926/38/10/104005
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      • Corresponding author: Email: ningdeng@tsinghua.edu.cn
      • Received Date: 2017-02-24
      • Revised Date: 2017-04-10
      • Published Date: 2017-10-01

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