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Exploring Memristor Switching Mechanisms: A Comprehensive Study

Delve into the complex world of switching mechanisms in memristors, ranging from inorganic to organic materials. Understand bipolar and unipolar behaviors, filament types, and interface switching mechanisms. Explore memristor modeling, redox processes, and more.

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Exploring Memristor Switching Mechanisms: A Comprehensive Study

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  1. MOOREA Meeting, 02/25/2013 J.E. Lorival, T. Jacquet, C. Maneux

  2. Switching mechanisms Outline • Switching mechanisms. • Switching mechanisms in inorganic materials. • Organic materials classification and switching mechanisms observed. • Switching mechanisms discussions. • Memristor modeling. • Literature models analyses. • Work in progress.

  3. Switching mechanisms Context • Last years, several teams working on memristors. • Ferromagnetic materials. • Organic materials. • Inorganic materials. • Electrolytes, amorphous silicon, binary oxides. • Numerous materials : memristors, top/bottom electrodes. • Substantial state of the art. • Classification. • Material, compound types. • Resistive switching mechanisms.

  4. Switching mechanisms Classification of switching mechanisms Bipolar Unipolar [1] Waser, Nature, 2007 [2] Pan, Natural Science: Materials International 20(2010), 2010 Filament Interface • Switching mechanisms in inorganic materials [1] [2]. • Unipolar and bipolar switching behaviors. • Filament and interface types.

  5. Switching mechanisms Memristors Model Switching mechanisms, filament type [1/4] Sawa, materialstoday, 2008, Vol. 11, no. 6 • Thermal effect : Joule heating → unipolar behavior • Filaments created/restored by voltage breakdowns. • Filaments broken with high currents by thermal dissolution. • Materials: NiO, CuO, ZrO, HfO…

  6. Switching mechanisms Switching mechanisms, filament type [2/4] • Ionic transport / redox processes → bipolar behavior. • Anions migration: • Migration of oxygen vacancies VO+. • Cations migration: electrochemical metallization (ECM). • Migration of metal cations. • Relative mature theory [2]. [2] Pan, Natural Science: Materials International 20(2010), 2010

  7. Switching mechanisms Switching mechanisms, filament type [3/4] Left: Right: [3] Xu, VLSI Technology, 2008 • Ionic transport / redox processes → bipolar behavior • Anions migration : different mechanisms [3]. • (I): Oxygen vacancies VO+ form hopping conduction path (ZnO). • SET: dielectric breakdown. Generation and drift of VO+→ filaments. • RESET: depletion of e- in VO+ along filaments. • Recovery of the electron-depleted VO+ with O2-.

  8. Switching mechanisms Switching mechanisms, filament type [4/4] [4] Waser, Microelectronic Engeneering 86, 2009 • Ionic transport / redox processes → bipolar behavior • Anions migration : different mechanisms [4]. • (II): VO+ acting as dopants making the MO conductive (TiO). • VO+ piling up near the cathode and trapping electrons. • Metal valency reduced → Generated filaments moving up to the anode.

  9. Switching mechanisms Switching mechanisms, interface type [5] J. J. Yang, Nature Nanotechnology, Vol 3, July 2008 • Interface type switching mechanism → bipolar. • Oxygen depleted zone near cathode due to VO+ diffusion (doping) [5]. • Electron injection from electrode modified by barrier height change. • Electrode materials, effects on contact resistance. • Contact resistances control the switching mechanism. • MIM, two interfaces. 1 Ohmic, 1 Schottky-like for switching. • Barrier height: F(applied voltage ; material, electrodes energy bands).

  10. Switching mechanisms Another mechanisms referred • Charge Transfert. • Trapping/DetrappingSpace Charge Limited Current (SCLC). • Insulator-metal transition(IMT). • Electronic charge injection acts as doping. • Induce IMT in perovskite-type oxides : (Pr, Ca)MnO3, SrTiO3:Cr. • Ferroelectric polarization.

  11. Switching mechanisms Organic materials Investigation on the influence of the bottom electrode on the memristor performances (I-V) [BOZANO_2005] Hystereses observed in organic materials based memristors. [6] Campbell Scott, Bozano, ‘Nonvolatile Memory Elements Based on Organic Materials’, Advanced Materials, 2007 • Classification in [6]. • Polymer MIM devices. • Small-molecules MIM devices. • Donor-acceptor complexes. • Electrochemical systems. • Nanoparticle blends.

  12. Switching mechanisms Switching mechanisms in organic materials Two molecules with different conformations. The two molecules can be made identical with a rotation of 180 degree about the central single bond • Organic and inorganic materials. • Some switching mechanisms in common. • => Yet with different driving mechanisms (drivers). [6] Campbell, Bozano, ‘Nonvolatile Memory Elements Based on Organic Materials’, Advanced Materials, 2007 • Some switching mechanisms reported in [6]. • Filament conduction. • Ion transport / redox process. • Trapping- Detrapping SCLC. • Charge Transfer (CT). • Conformational effects.

  13. Switching mechanisms Discussions and debates [1/2] [7] Yang L, Appl. Phys. Lett., 2009 [8] Colle, OrganicElectronics 7, 2006 [9] Yang T, Appl. Phys, 2009 [10] Jeong, Electrochemical and Solid-State Letters, 2007 • Switching mechanisms still under investigations. • For a same switching mechanisms, various drivers. • Driving mechanisms depending on both materials and electrodes. • Electrodes impacts. • Inorganic material: Cu electrodes with TiO2: Cu diffusion in TiO2[7]. • Organic material: Aluminum electrode controls switching, not material [8]. • Changing material state : different switching mechanisms. • ZnO/Cu/ZnO: carriers trapping/detrapping→ redox after RTA [9]. • Several switching mechanisms occurring simultaneously. • TiO2: thermal effects, metallic filament, VO+ migration, E fields. • Unipolarity/bipolarity coexistence depending on CC [10].

  14. Switching mechanisms Discussions and debates [2/2] PCzDPMπ-conjugatedpolylerbearingcarbazolemoieties. Park, J. Chem. Phys. Vol. 114, no. 32, 2010 • Switching mechanisms still under investigations. • Numerous mechanisms observed but few conclusions. • Not enough measurements that go beyond observations. • Are the switching mechanisms observed in structures the right ones ? • Several structure deteriorated after a set of measures. • Fabrication processes currently not enough mature ? • Cases where mechanisms are due to (un)desirable effects ? • Electrode atoms diffusion in material, fabrication defaults, dust… • Reproducibility of switching behaviors ?

  15. Memristor models Outline • Switching mechanisms. • Memristors modeling. • Memristor models present in the literature. • Linear ion drift, “Simmons”, TEAM models. • Window functions for boundary conditions and ion drift profiles. • Literature models analyses. • Work in progress

  16. Memristor models Context • Other types of model found. • Non linear ion drift model [15]. • Simmons tunneling barrier model [16]. • ThrEsholdAdaptative Memristor (TEAM) model [17]. [11] Strukov, Nature, vol 453, 2008 [12] Sharifi, Journal Circuits, Systems ans Computers, Vol 19, no 2, 2010 [13] Batas, IEEE Trans. on Nanotechnology, Vol 10, no 2, 03/2011 [14] Corinto, IEEE Trans. on Circuits and Systems, vol 59, no 11, 11/2012 [15] Chang, Appl. Phys. A, 2011 [16] Pickett, J. Appl. Phys. 106, 2009 [17] Kwatinsky, IEEE Trans. Circuits and systems, 2012 (not published) • Few models present in the literature. • Dedicated to inorganic models. • Most of them are based on the linear ion drift model [11] [12] [13] [14]. • Aims: Test the original model viability or improve/update it. • Ref. [12]: saturation/depletion effects + lifetime. • Ref. [14]: threshold voltages for bipolarity added.

  17. Memristor models Fundamentals w : [set of] state variables • Memristor mathematical definition given by Chua. • Functional relation between charge and flux. • Basic mathematical definition for a current controlled memristor.

  18. Memristor models TiO2 HP memristor [1/2] w : state variable doped (conductive) region length [11] Strukov, Nature, vol 453, 2008 • Memristor behavior recognition at the nanoscale from HP [11]. • TiO2 binary oxide based inorganic memristor. • Proposition of the linear ion drift model.

  19. Memristor models TiO2 HP memristor [2/2] [11] Strukov, Nature, vol 453, 2008 • Memristor behavior recognition at the nanoscale from HP [11]. • Simulations with the model, measurements with a test structure. • Test structure : Pt/TiO2/Pt.

  20. Memristor models Memristor models characteristics [1/2] • In [17]. • Memristor model types listed • Basic version for the linear ion drift model. • TEAM model proposition. [17] Kwatinsky, IEEE Trans. Circuits and systems, 2012 (not published)

  21. Memristor models Memristor models characteristics [2/2] [17] Kwatinsky, IEEE Trans. Circuits and systems, 2012 (not published)

  22. Memristor models Window functions requirement D = 10n ROFF = 16KΩ RON = 100Ω Source: Prodromakis, IEEE Trans. Electron Device, vol 58, no 9, 09/2011 • Window functions. • Fix boundary conditions, w comprised exclusively in [0,D]. • Serve to model ion drift profile in the material. • In model description, boundary conditions needed. • W can be smaller (higher) than 0 (D) → wrong memristor values.

  23. Memristor models Window functions in literature [1/3] [19] [20] [18] [17] Kwatinsky, IEEE Trans. Circuits and systems, 2012 (not published) [18] Joglekar, European Journal of Physics, vol 30, no 4, 2009 [19] Bioleck, radioengineering, vol 18, no 2, Part 2, 2009 [20] Prodromakis, IEEE Trans. Electron Device, vol 58, no 9, 09/2011 Most known window functions listed in [17].

  24. Memristor models Window functions in literature [2/3] Joglekar Biolek Prodromakis • Window functions • Defined with the normalized value of D, w (or x) evolves between [0,1]. • Depend on a “p” parameter. • “p” small : non linear ions drift profile function. • “p” high : linear ions drift profile function. • Linear model + non linear function ≠ non linear model.

  25. Memristor models Window functions in literature [3/3] Joglekar & Biolek Prodromakis • Joglekar window. • When x=0 or x=D, state cannot be changed anymore. • Works only for single-valued memristor. • Biolekwindow. • Controls states for bipolarity behavior. • Discontinuities for boundary conditions for high p. • Works only for multi-valued memristor. • Prodromakiswindow. • Parabolic function like Joglekar. • Window function is scalable : F(x)max different from 1.

  26. Memristor models Simmons tunneling barrier model [1/2] X [21] Pickett, Journal of Appl. Phys, 2009 [22] Simmons, Journal of Appl. Phys, 1963 • HP Team investigates deeper the Pt/TiO2/Pt memristor [21]. • More knowledge regarding the physical process in bipolar switching. • Energy required to switch the device decreases exponentially when increasing current → Pt/TiO2/Pt is non linear. • Model evolution : linear ion drift → Simmons tunneling barrier. • Ions drift profile based on electric tunnel effect between two identical electrodes separated by a thin insulating film [22]. • Bipolarity controlled with threshold currents + boundary conditions.

  27. Memristor models Simmons tunneling barrier model [2/2] • Model can only be applied to TiO2 structures. • High complexity degree → huge convergence problems. • Asymmetric behaviors can be only observed. • Asymmetric behavior when switching states time are different. Kwatinsky et al. worked on a simplified version. TEAM Model Deep knowledge of switching mechanisms in TiO2. Physical model → High accuracy degree.

  28. Memristor models ThrEsholdAdaptative Model (TEAM) [1/3] Simmons model TEAM model • Simplified version of Simmons tunneling barrier model. • Decomposition in two parts of the derivative function. • (I) Bipolar switching controlled by threshold currents. • (II) Window function, TEAM function. • Doping concentration in the material when injecting a current.

  29. Memristor models ThrEsholdAdaptative Model (TEAM) [2/3] dx/dt direction when i<0 dx/dt direction when i>0 aoff aon • Simplified version of Simmons tunneling barrier model. • Decomposition in two parts of the derivative function. • (I) Bipolar switching controlled by threshold currents. • (II) Window function, TEAM function. • Doping concentration in the material when injecting a current.

  30. Memristor models ThrEsholdAdaptative Model (TEAM) [3/3] • or I-V non-linear relationship I-V linear relationship • TEAM model can be described with any window function. • By modifying some parameters in v(t) and dx/dt expressions. • => TEAM model → linear ion drift model. • When TEAM model fits Simmons one. • => Asymmetric behaviors only. • I-V relationship can be defined as linear or not.

  31. Models analyses Outline • Switching mechanims. • Memristor modeling. • Literature models analyses. • Tests on some memristor models to check their robustness and their versatility. • Different versions of the linear ion drift model, TEAM model. • Performed by varying different parameters describing dw/dt and M(w). • Work in progress.

  32. Models analyses Memristor models chosen for test • Current work : test the models robustness and versatility. • Linear ion drift model with “ideal window”(Verilog-A). • Linear model, enhanced version with threshold voltages (ELDO) [14]. • TEAM model fitting Simmons model with “ideal window” (Verilog-A). • TEAM model fitting linear model with ideal “window” (Verilog-A). • Simmons model : converge problems. Work-in-progress. [14] Corinto, IEEE Trans. on Circuits and Systems, vol 59, no 11, 11/2012 [23] Kvatinsky, CCIT (Center for Communication and information Technologies) Reports, 2011 • Some authors provide descriptions with their model. • Kvatinsky : Verilog-A descriptions [23]. • Linear, non-linear, Simmons, TEAM models. • Joglekar, Biolek, Prodromakis, TEAM window functions.

  33. Models analyses Linear ion drift model Roff = 16kΩ w = 0 Roff / Ron = 160 Ron = 100Ω w = 10nm Model configuration. Sinusoidal input voltage Vsin : 500mV, F = 0,1Hz. Ron = 100Ω ; Roff = 16KΩ ; D = 10nm ; µv = 10e-14 m2 s-1 V-1. w(t0) = 0 ; // initial condition dt = 5ms. • “Ideal window” : bipolarity and w comprised in [0, D]. • F(w) = 0 for w = 0 and w = D, 1 otherwise => linear ion drift profile.

  34. Models analyses Linear model, M(w)=f(Vin) Model configuration. Vsin : F = 0,1Hz. Ron = 100Ω ; Roff = 16KΩ; D = 10nm ; µv = 10e-14 m2 s-1 V-1; w(t0) = 0; dt = 5ms. w = 0 →Roff = 16kΩ w = 0,9nm → R= 1,5kΩ Vin = 250mV Roff / Ron = 160 Vin = 125mV w = 0 →Roff = 16kΩ w = 0,29nm → R = 11kΩ Roff / Ron = 160

  35. Models analyses Linear model, M(w)=f(D) Model configuration. Vsin : 500 mV, F = 0,1Hz. Ron = 100Ω ; Roff = 16KΩ; µv = 10e-14 m2 s-1 V-1 ; w(t0) = 0 ; dt = 5ms. w = 0 →Roff = 16kΩ w = 10nm →Ron = 100Ω D = 10nm Roff / Ron = 160 D = 20nm w = 0 →Roff = 16kΩ w = 0,58nm →R = 11,5kΩ Roff / Ron = 160

  36. Models analyses Linear model, behavior on multiple periods Roffdecreases Rmin → Ron • Reproducibility problem due to robustness ? • Does model integrate uncovered defects in TiO2 ? Model configuration. Sinusoïdal input voltage Vsin : 250mV, F = 0,1Hz. Ron = 100Ω ; Roff = 16KΩ; D = 10nm, µv = 10e-14 m2 s-1 V-1. w(t0) = 0 ; dt = 5ms. Source: Yu, IEEE Trans. Electron Device, vol 58, no 8, 08/2011 By applying sinusoidal voltage during several periods (10T).

  37. Models analyses Linear model, impact of Roff/Ron ratio Roff/Ron = 80 Roff/Ron = 120 Roff/Ron = 160 Model configuration. Sinusoïdal input voltage Vsin : 125mV, F = 0,1Hz. Ron = 100Ω ; D = 10nm, µv = 10e-14 m2 s-1 V-1. w(t0) = 0 ; dt = 5ms. Memristor responses when increasing Roff/Ron.

  38. Models analyses Linear model, impact of frequency Roff/Ron = 160 • Like Roff/Ron, when F increases. => ions have lower mobility. => memristor → resistor. • dt : parameter in Verilog-A code [23]. • dt given such as dt = T/1000 at least. Model configuration. Sinusoïdal input voltage Vsin : 250mV, F = 0,1Hz. Ron = 100Ω; Roff= 16KΩ ; D = 10nm ; µv = 10e-14 m2 s-1 V-1. w(t0) = 0 ; dt = 5ms. 5F = 0,5Hz → dt = 2ms. 100F = 10Hz → dt = 100us. Analytical expression Verilog-A translation in [22] [23] Kvatinsky, Kvatinsky, CCIT (Center for Communication and information Technologies) Reports, 2011 Memristor responses when increasing frequency.

  39. Models analyses Linear model robustness Time step: 5ms Time step: 2,5ms Model configuration. Sinusoïdal input voltage Vsin : 250mV, F = 0,1Hz. Ron = 100Ω ; D = 10nm ; µv = 10e-14 m2 s-1 V-1. w(t0) = 0 ; dt = 5ms. dt: 5ms dt: 5ms • “dt” is a sensitive parameter in the model. The results are in agreement with the hystereses behaviors observed in literature when modifying parameters for a given configuration. Time step: 5ms Time step: 5ms dt: 10ms What is the behavior which must be observed for the starting configuration ? dt: 2,5ms Robustness of the model. Impact of the time step.

  40. Models analyses How about the other linear models ? • Enhanced version proposed by [14]. • Window functions (bipolarity + boundary conditions) + (VthOFF, VthON). Window Function Behavioral condition x(t) [14] Corinto, IEEE Trans. on Circuits and Systems, vol 59, no 11, 11/2012 • TEAM Model fitting the linear ion drift model. • Same behaviors observed for the same configurations.

  41. Models analyses Corinto’s linear model enhanced version [1/2] • Enhanced version proposed by [14]. • Window functions (bipolarity + boundary conditions) + (VthOFF, VthON). Model configuration. Vsin : 1V, F = 1Hz. Ron = 100Ω ; Roff = 6KΩ ; D = 10nm ; µv = 10e-14 m2 s-1 V-1; w(t0) = 1nm. Vth(off) = Vth(on) = 0. [14] Corinto, IEEE Trans. on Circuits and Systems, vol 59, no 11, 11/2012

  42. Models analyses Corinto’slinear model enhanced version [2/2] • Enhanced version proposed by [14]. • Window functions (bipolarity + boundary conditions) + (VthOFF, VthON). • Beware of the time step ! Model configuration. Vsin : 1,95V, F = 1Hz. Ron = 100Ω ; Roff = 16KΩ ; D = 10nm ; µv = 10e-14 m2 s-1 V-1; w(t0) = 3,5nm ; Vth(off) = Vth(on) = 0,975V ; α Simulation of 1 period (1s) Below a time step of 500us (2000 points) Simulation of 1 period (1s) Below a time step of 1ms (1000 points) [14] Corinto, IEEE Trans. on Circuits and Systems, vol 59, no 11, 11/2012

  43. Models analyses TEAM model (Simmons), expression of dx/dt foff(x) = fon(x) = F(x) 1 when 0 < x < D F(x) = 0 otherwise Bipolarswitchingcontrolledwith Thresholdcurrentsioff and ion • TEAM model in Simmons configuration + “ideal window”. • Linear and non linear relations exhibit the same behaviors. • X : oxide (undoped) region length.

  44. Models analyses TEAM model (Simmons), hysteresis behavior X : 0 → 0,862. M : 50Ω → 640Ω Model configuration. Sinusoïdal input voltage Vsin : 0,5V, F = 20MHz. Ron = 50Ω; Roff= 1KΩ ; D = 3nm ; Ion = -8,9uA ; Ioff = 115uA ; αon = 10 ; αoff = 10 ; Kon = -4,68e-13 ; Koff = 1,46e-9 ; Xon = 0 ; Xoff = 3nm ; w(t0) = 0 ; dt = 50ps. Simulation on 3T = 150ns for time step = 185ps. Kvatinsky results Asymetric switching: OFF state slower than ON STATE.

  45. Models analyses TEAM model (Simmons), M(x) = f(Vin) Model configuration. Sinusoïdal input voltage : F = 20MHz. Ron = 50Ω; Roff= 1KΩ ; D = 3nm ; Ion = -8,9uA ; Ioff = 115uA ; αon = 10 ; αoff = 10 ; Kon = -4,68e-13 ; Koff = 1,46e-9 ; Xon = 0 ; Xoff = 3nm ; w(t0) = 0 ; dt = 50ps. Simulation on 3T = 150ns for time step = 105ps. Vin = 500mV X : 0 → 0,862. M : 50Ω → 640Ω Vin = 1V X : 0 → 1 M : 50Ω → 1KΩ

  46. Models analyses TEAM model (Simmons), M(x) = f(Roff) Model configuration. Sinusoïdal input voltage : F = 20MHz. Ron = 50Ω ; D = 3nm ; Ion = -8,9uA ; Ioff = 115uA ; αon = 10 ; αoff = 10 ; Kon = -4,68e-13 ; Koff = 1,46e-9 ; Xon = 0 ; Xoff = 3nm ; w(t0) = 0 ; dt = 50ps. Simulation on 3T = 150ns for time step = 187ps. Vin = 1V, ROFF = 1KΩ X : 0 → 1 M : 50Ω → 1KΩ Vin = 1V, ROFF = 5KΩ X : 0 → 0.71 M : 50Ω → 1.3KΩ

  47. Models analyses TEAM model, M(x) regarding the frequency Model configuration. Sinusoïdal input voltage : V = 500mV Ron = 50Ω; Roff= 5KΩ; D = 3nm ; Ion = -8,9uA ; Ioff = 115uA ; αon = 10 ; αoff = 10 ; Kon = -4,68e-13 ; Koff = 1,46e-9 ; Xon = 0 ; Xoff = 3nm ; w(t0) = 0 ; Simulation on 3T = 150ns for time step = 105ps. Evolution of x and M(x) in function of frequency.

  48. Models analyses TEAM model (Simmons), ion and ioff [1/2] Model configuration. Sinusoïdal input voltage Vsin : 1V, F = 20MHz. Ron = 50Ω; Roff= 1KΩ ; D = 3nm ; Ion = -8,9uA ; Ioff = 115uA ; αon = 10 ; αoff = 10 ; Kon = -4,68e-13 ; Koff = 1,46e-9 ; Xon = 0 ; Xoff = 3nm ; w(t0) = 0 ; dt = 50ps. Simulation on 3T = 150ns for time step = 150ps. • Memristor behaviors when modifying threshold currents. • (I) Ioff : 115μA → 1mA.

  49. Models analyses TEAM model (Simmons), ion and ioff [2/2] Model configuration. Sinusoïdal input voltage Vsin : 0,5V, F = 20MHz. Ron = 50Ω; Roff= 1KΩ ; D = 3nm ; Ion = -8,9uA ; Ioff = 115uA ; αon = 10 ; αoff = 10 ; Kon = -4,68e-13 ; Koff = 1,46e-9 ; Xon = 0 ; Xoff = 3nm ; w(t0) = 0 ; dt = 50ps. Simulation on 3T = 150ns for time step = 150ps. • Memristor behaviors when modifying threshold currents. • (II) Ion: -8.9μA → -50 μA.

  50. Models analyses TEAM model (Simmons), robustness • Even if TEAM is simpler: convergence problems (IC-CAP). • Analyses performed for numerous time step when changing (V, F, dt). • Convergence problems more important with TEAM window. • TEAM model : simplified version of Simmons one. • Simmons model presents huge convergence problem. • Simplification through a modification of the expression of dx/dt.

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