J. Semicond. > 2018, Volume 39 > Issue 12 > 124009, doi: 10.1088/1674-4926/39/12/124009
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SEMICONDUCTOR DEVICES

Analysis and parameter extraction of memristive structures based on Strukov’s non-linear model

A. Avila Garcia and L. Ortega Reyes

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 Corresponding author: A. Avila Garcia, Email: aavila@cinvestav.mx

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Abstract: Diverse models have been proposed for explaining the electrical performance of memristive devices. In principle, the behavior of internal variables associated to each one could be extracted from experimental results. In a former work, thermally grown TiOx memristive structures were built and characterized to obtain the constitutive relationship (magnetic flux versus charge). The aim of this work is to continue that analysis by determining the microscopic parameters within the frame of a simple model. We use the already obtained memristance dependence of time and the basic expressions from the non-linear model proposed by Strukov et al. to compute the state-variable, the mobility of the doping species, the speed of the boundary between the doped and the undoped regions, the voltages and the electric fields on the distinct regions. The power dissipation and its time evolution are also presented. Moreover, a quite different window function from those formerly proposed, which was estimated from experimental data, is also determined. This information provides a straightforward picture of the ionic transport during one cycle of a square voltage waveform within the framework of this simple model. Finally, a quality factor is proposed as the key parameter for actual memristors viewed under the same model.

Key words: memristors, parameter extraction, non-linear model, experimental window function



[1]
Strukov D B, Snider G S, Stewart D R, et al. The missing memristor found. Nature, 2008, 453: 80 doi: 10.1038/nature06932
[2]
Lehtonen E, Laiho M. CNN using memristors for neighborhood connections. 2010 12th International Workshop on Cellular Nanoscale Networks and Their Applications (CNNA) IEEE, 2010: 1
[3]
Pickett M D, Strukov D B, Borghetti J L, et al. Switching dynamics in titanium dioxide memristive devices. J Appl Phys, 2009, 106(7): 074508 doi: 10.1063/1.3236506
[4]
Kvatinsky S, Friedman E, Kolodny A, et al. TEAM: ThrEshold adaptive memristor model. IEEE Trans Circuits Syst I, 2013, 60(1): 211 doi: 10.1109/TCSI.2012.2215714
[5]
Avila G A, Ortega R L, Romero-Paredes G, et al. Memristive structures based on thermally oxidized TiOx. JMSA, 2017, 3(6): 94
[6]
Messerschmitt F, Kubicek M, Schweiger S, et al. Memristor kinetics and diffusion characteristics for mixed anionic-electronic SrTiO 3-δ bits: the memristor-based cottrell analysis connecting material to device performance. Adv Funct Mater, 2014 doi: 10.1002/adfm.201402286
[7]
Yang J J, Pickett M D, Li X, Ohlberg D A A, et al. Memristive switching mechanism for metal/oxide/metal nanodevices. Nat Nanotech, 2008, 3: 429 doi: 10.1038/nnano.2008.160
[8]
Yang J J, Miao F, Pickett M D, et al. The mechanism of electroforming of metal oxide memristive switches. Nanotechnology, 2009, 20: 215201 doi: 10.1088/0957-4484/20/21/215201
[9]
Bersuker G, Gilmer D C, Veksler D, et al. Metal oxide resistive memory switching mechanism based on conductive filament properties. J Appl Phys, 2011, 110: 124518 doi: 10.1063/1.3671565
[10]
Buckwell M, Montesi L, Mehonic A, et al. Microscopic and spectroscopic analysis of the nature of conductivity changes during resistive switching in silicon-rich silicon oxide. Phys Status Solidi C, 2015, 12(1/2): 211
[11]
Joglekar Y N, Wolf S J. The elusive memristor: properties of basic electrical circuits. Eur J Phys, 2009, 30: 661 doi: 10.1088/0143-0807/30/4/001
[12]
Biolek Z, Biolek D, Biolkova V. Spice Model of memristor with nonlinear dopant drift. Radioengineering, 2009, 18: 210
[13]
Prodromakis T, Peh B P, Papavassiliou C, et al. A versatile memristor model with nonlinear dopant kinetics. IEEE Trans Electron Devices, 2011, 58(9): 3099 doi: 10.1109/TED.2011.2158004
[14]
Kavehei O, Kim Y S, Iqbal A et al. The fourth element: insights into the memristor. IEEE International Conference on Communications, Circuits and Systems ICCCAS, 2009: 921
[15]
McDonald N R, Pino R E, Rozwood P J et al. Analysis of dynamic linear and non-linear memristor device models for emerging neuromorphic computing hardware design. Neural Networks (IJCNN), The 2010 International Joint Conference, 2010: 18
Fig. 1.  (Color online) Data obtained from Chua’s analysis of the experimental data in Ref. [5]. This is the starting point for the analysis in this work.

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Fig. 3.  (Color online) The product ημd on a broken vertical axis with a linear scale in the lower part, plotted as a function of time. The break was introduced to emphasize the details around the zero crossings. The step at the middle of the cycle (17 s) results from the numerical calculation of the derivative used in Eq. (3).

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Fig. 5.  (Color online) (a) Partial memristances of the doped and undoped regions. (b) Voltage drops in each region considered and total voltage across the structure. (c) Magnitude of the average electric field strength across the doped and undoped regions, all of them as functions of time.

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Fig. 6.  (Color online) Time dependence of the instantaneous power dissipated by the doped and undoped regions. The total power is also plotted. Two local maxima in the total power exist, one for each semi-cycle.

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Fig. 7.  (Color online) Time dependences of the state variable, the total instantaneous and the cumulative powers dissipated by the structure.

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Fig. 8.  (Color online) The product ημd as a function of the state variable x = w/wmax. Breaks in the axes are introduced to emphasize detailed features close to x = 1 on the graph. Note the different scales in both horizontal and vertical axes and the magnification of the tip in the neighborhood of x = 1, which is showed in the inset.

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Fig. 4.  (Color online) (a) the magnitude of the ημd product and the normalized position of the boundary (state-variable) as functions of time. (b) velocity of the boundary on linear and logarithmic scales for better appreciating both its sign and magnitude. The +/− signs indicate those of the boundary velocity during each period.

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Fig. 2.  Schematic cross-section of a conducting filament, illustrating the region where the length of such a filament changes from w = 0 to w = wmax under some specific voltage waveform, so defining wmax as the maximum w value under the bias considered. When w = 0 the total resistance becomes the maximum Roff and when w = wmax, the resistance becomes Ron. The polarity is defined by the connections as indicated.

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Fig. 9.  Resistance modulation index as a function of the state variable.

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Table 1.   The sign of the parameter η in Eq. (2), related to the boundary movement.

Current (or Voltage) sign η > 0 η < 0
Negative vd < 0, Shortening Period II vd > 0, Enlargement Most of Period I
Positive vd > 0, Enlargement Period III vd < 0, Shortening Period IV
DownLoad: CSV

Table 2.   Coefficients obtained from fitting a quadratic polynomial to our (η μd) versus x data during the periods already observed in Fig. 3. The polynomials are of the form ημd (x) = B0 + B1x + B2x2.

Coefficient Period I Period II Period III Period IV
B0 −3.4582 × 10−14 3.27856 × 10−14 1.13749 × 10−14 −1.39974 × 10−14
B1 6.8698 × 10−14 −6.51576 × 10−14 −2.23865 × 10−14 2.75294 × 10−14
B2 −3.41166 × 10−14 3.23726 × 10−14 1.10131 × 10−14 −1.35324 × 10−14
DownLoad: CSV

Table 3.   Ionic mobility pre-factor determined from a least square fitting to quadratic and cubic polynomials. These polynomials yield the window functions of the samples in this work.

Period Type/x range μd0 ( \setlength{\voffset}{0pt}$\frac{{{\rm m^2}}}{{\rm {V\cdot s}}}$ )
I Quadratic (x ≤ 0.9969) 3.4582 × 10−14
Cubic (x ≥ 0.9999) 1.59684 × 10−7
II Quadratic (x ≤ 0.9638) 3.27856 × 10−14
Cubic (x ≥ 0.985) 9.19605 × 10−13
III Quadratic (x ≤ 0.9511) 1.13749 × 10−14
Cubic (x ≥ 0.9606) 1.1308 × 10−13
IV Quadratic (x ≤ 0.992) 1.39974 × 10−14
Cubic (x ≥ 0.9982) 5.33136 × 10−10
DownLoad: CSV
[1]
Strukov D B, Snider G S, Stewart D R, et al. The missing memristor found. Nature, 2008, 453: 80 doi: 10.1038/nature06932
[2]
Lehtonen E, Laiho M. CNN using memristors for neighborhood connections. 2010 12th International Workshop on Cellular Nanoscale Networks and Their Applications (CNNA) IEEE, 2010: 1
[3]
Pickett M D, Strukov D B, Borghetti J L, et al. Switching dynamics in titanium dioxide memristive devices. J Appl Phys, 2009, 106(7): 074508 doi: 10.1063/1.3236506
[4]
Kvatinsky S, Friedman E, Kolodny A, et al. TEAM: ThrEshold adaptive memristor model. IEEE Trans Circuits Syst I, 2013, 60(1): 211 doi: 10.1109/TCSI.2012.2215714
[5]
Avila G A, Ortega R L, Romero-Paredes G, et al. Memristive structures based on thermally oxidized TiOx. JMSA, 2017, 3(6): 94
[6]
Messerschmitt F, Kubicek M, Schweiger S, et al. Memristor kinetics and diffusion characteristics for mixed anionic-electronic SrTiO 3-δ bits: the memristor-based cottrell analysis connecting material to device performance. Adv Funct Mater, 2014 doi: 10.1002/adfm.201402286
[7]
Yang J J, Pickett M D, Li X, Ohlberg D A A, et al. Memristive switching mechanism for metal/oxide/metal nanodevices. Nat Nanotech, 2008, 3: 429 doi: 10.1038/nnano.2008.160
[8]
Yang J J, Miao F, Pickett M D, et al. The mechanism of electroforming of metal oxide memristive switches. Nanotechnology, 2009, 20: 215201 doi: 10.1088/0957-4484/20/21/215201
[9]
Bersuker G, Gilmer D C, Veksler D, et al. Metal oxide resistive memory switching mechanism based on conductive filament properties. J Appl Phys, 2011, 110: 124518 doi: 10.1063/1.3671565
[10]
Buckwell M, Montesi L, Mehonic A, et al. Microscopic and spectroscopic analysis of the nature of conductivity changes during resistive switching in silicon-rich silicon oxide. Phys Status Solidi C, 2015, 12(1/2): 211
[11]
Joglekar Y N, Wolf S J. The elusive memristor: properties of basic electrical circuits. Eur J Phys, 2009, 30: 661 doi: 10.1088/0143-0807/30/4/001
[12]
Biolek Z, Biolek D, Biolkova V. Spice Model of memristor with nonlinear dopant drift. Radioengineering, 2009, 18: 210
[13]
Prodromakis T, Peh B P, Papavassiliou C, et al. A versatile memristor model with nonlinear dopant kinetics. IEEE Trans Electron Devices, 2011, 58(9): 3099 doi: 10.1109/TED.2011.2158004
[14]
Kavehei O, Kim Y S, Iqbal A et al. The fourth element: insights into the memristor. IEEE International Conference on Communications, Circuits and Systems ICCCAS, 2009: 921
[15]
McDonald N R, Pino R E, Rozwood P J et al. Analysis of dynamic linear and non-linear memristor device models for emerging neuromorphic computing hardware design. Neural Networks (IJCNN), The 2010 International Joint Conference, 2010: 18

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    Received: 10 April 2018 Revised: 13 October 2018 Online: Accepted Manuscript: 05 November 2018Uncorrected proof: 07 November 2018Published: 13 December 2018

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      Article Navigation >  Journal of Semiconductors  > 2018  >  39(12): 124009
      A. Avila Garcia, L. Ortega Reyes. Analysis and parameter extraction of memristive structures based on Strukov’s non-linear model[J]. Journal of Semiconductors, 2018, 39(12): 124009. doi: 10.1088/1674-4926/39/12/124009 A A Garcia, L O Reyes, Analysis and parameter extraction of memristive structures based on Strukov’s non-linear model[J]. J. Semicond., 2018, 39(12): 124009. doi: 10.1088/1674-4926/39/12/124009.Export: BibTex EndNote
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      A. Avila Garcia, L. Ortega Reyes. Analysis and parameter extraction of memristive structures based on Strukov’s non-linear model[J]. Journal of Semiconductors, 2018, 39(12): 124009. doi: 10.1088/1674-4926/39/12/124009

      A A Garcia, L O Reyes, Analysis and parameter extraction of memristive structures based on Strukov’s non-linear model[J]. J. Semicond., 2018, 39(12): 124009. doi: 10.1088/1674-4926/39/12/124009.
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      Analysis and parameter extraction of memristive structures based on Strukov’s non-linear model

      doi: 10.1088/1674-4926/39/12/124009

      • Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, Departamento de Ingeniería Eléctrica, Sección de Electrónica del Estado Sólido, México 07360, México

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      • Corresponding author: Email: aavila@cinvestav.mx
      • Received Date: 2018-04-10
      • Revised Date: 2018-10-13
      • Published Date: 2018-12-01

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