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

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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.