MOOREA Meeting, 02/25/2013

J.E. Lorival, T. Jacquet, C. Maneux

MOOREA Feb 25, 2013

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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.

Switching mechanisms

MOOREA Feb 25, 2013

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.

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Switching mechanisms

MOOREA Feb 25, 2013

• Switching mechanisms in inorganic materials [1] [2].– Unipolar and bipolar switching behaviors.

– Filament and interface types.

Classification of switching mechanisms

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[1] Waser, Nature, 2007[2] Pan, Natural Science: Materials International 20(2010), 2010 Filament Interface

Unipolar Bipolar

Switching mechanisms

MOOREA Feb 25, 2013

Switching mechanisms, filament type [1/4]

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• 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…

Sawa, materialstoday, 2008, Vol. 11, no. 6

Memristors ModelSwitching mechanisms

MOOREA Feb 25, 2013

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[2] Pan, Natural Science: Materials International 20(2010), 2010

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].

MOOREA Feb 25, 2013

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• 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-.

[3] Xu, VLSI Technology, 2008

Left:

Right:

Switching mechanisms

Switching mechanisms, filament type [3/4]

MOOREA Feb 25, 2013

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• 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.

[4] Waser, Microelectronic Engeneering 86, 2009

Switching mechanisms

Switching mechanisms, filament type [4/4]

MOOREA Feb 25, 2013

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• 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).

[5] J. J. Yang, Nature Nanotechnology, Vol 3, July 2008

Switching mechanisms

Switching mechanisms, interface type

MOOREA Feb 25, 2013

Another mechanisms referred

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• Charge Transfert.• Trapping/Detrapping Space 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.

Switching mechanisms

MOOREA Feb 25, 2013

Organic materials

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• Classification in [6].– Polymer MIM devices.– Small-molecules MIM devices.– Donor-acceptor complexes.– Electrochemical systems.– Nanoparticle blends.

[6] Campbell Scott, Bozano, ‘Nonvolatile Memory Elements Based on Organic Materials’, Advanced Materials, 2007

Hystereses observed in organic materials based memristors.

Investigation on the influence of the bottom electrode on the memristor

performances (I-V) [BOZANO_2005]

Switching mechanisms

MOOREA Feb 25, 2013

Switching mechanisms in organic materials

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• Some switching mechanisms reported in [6].– Filament conduction.– Ion transport / redox process.– Trapping- Detrapping SCLC.– Charge Transfer (CT).– Conformational effects.

• Organic and inorganic materials.– Some switching mechanisms in common.

=> Yet with different driving mechanisms (drivers).

Two molecules with different conformations. The two molecules can be made identical with a rotation of 180 degree about the central

single bond

[6] Campbell, Bozano, ‘Nonvolatile Memory Elements Based on Organic Materials’, Advanced Materials, 2007

Switching mechanisms

MOOREA Feb 25, 2013

Discussions and debates [1/2]

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• 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].

[7] Yang L, Appl. Phys. Lett., 2009[8] Colle, Organic Electronics 7, 2006[9] Yang T, Appl. Phys, 2009[10] Jeong, Electrochemical and Solid-State Letters, 2007

Switching mechanisms

MOOREA Feb 25, 2013

Discussions and debates [2/2]

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• 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 ?

PCzDPM π-conjugated polyler bearing carbazole moieties. Park, J. Chem. Phys. Vol. 114, no. 32, 2010

Switching mechanisms

MOOREA Feb 25, 2013

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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

Memristor models

MOOREA Feb 25, 2013

Context

• 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.

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[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

• Other types of model found.– Non linear ion drift model [15].– Simmons tunneling barrier model [16].– ThrEshold Adaptative Memristor (TEAM) model [17].

[15] Chang, Appl. Phys. A, 2011[16] Pickett, J. Appl. Phys. 106, 2009[17] Kwatinsky, IEEE Trans. Circuits and systems, 2012 (not published)

Memristor models

MOOREA Feb 25, 2013

Fundamentals

• Memristor mathematical definition given by Chua.– Functional relation between charge and flux.

– Basic mathematical definition for a current controlled memristor.

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Mdqd

),(

),(

iwfdt

dw

iidtMiiwRV

w : [set of] state variables

Memristor models

MOOREA Feb 25, 2013

TiO2 HP memristor [1/2]

• Memristor behavior recognition at the nanoscale from HP [11].– TiO2 binary oxide based inorganic memristor.

• Proposition of the linear ion drift model.

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ti

D

R

dt

tdw

tiD

twR

D

twRtV

ONv

OFFON

1

w : state variable doped (conductive) region length

Memristor models

[11] Strukov, Nature, vol 453, 2008

MOOREA Feb 25, 2013

TiO2 HP memristor [2/2]

• Memristor behavior recognition at the nanoscale from HP [11].– Simulations with the model, measurements with a test structure.

– Test structure : Pt/TiO2/Pt.

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Memristor models

[11] Strukov, Nature, vol 453, 2008

MOOREA Feb 25, 2013

Memristor models characteristics [1/2]

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[17] Kwatinsky, IEEE Trans. Circuits and systems, 2012 (not published)

• In [17].– Memristor model types listed

• Basic version for the linear ion drift model.– TEAM model proposition.

Memristor models

MOOREA Feb 25, 2013

Memristor models characteristics [2/2]

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[17] Kwatinsky, IEEE Trans. Circuits and systems, 2012 (not published)

Memristor models

MOOREA Feb 25, 2013

Window functions requirement

• In model description, boundary conditions needed.– W can be smaller (higher) than 0 (D) → wrong memristor values.

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• Window functions.– Fix boundary conditions, w comprised exclusively in [0,D].– Serve to model ion drift profile in the material.

Source: Prodromakis, IEEE Trans. Electron Device, vol 58, no 9, 09/2011

D = 10nROFF = 16KΩ RON = 100Ω

Memristor models

MOOREA Feb 25, 2013

Window functions in literature [1/3]

• Most known window functions listed in [17].

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)(

1

wftiD

R

dt

tdw

tiD

twR

D

twRtV

ONv

OFFON

[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

[18] [19] [20]

Memristor models

MOOREA Feb 25, 2013

Window functions in literature [2/3]

• 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.

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ProdromakisJoglekar Biolek

Memristor models

MOOREA Feb 25, 2013

Window functions in literature [3/3]

• Joglekar window.– When x=0 or x=D, state cannot be changed anymore.– Works only for single-valued memristor.

• Biolek window.– Controls states for bipolarity behavior.– Discontinuities for boundary conditions for high p.– Works only for multi-valued memristor.

• Prodromakis window.– Parabolic function like Joglekar.– Window function is scalable : F(x)max different from 1.

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Prodromakis

Joglekar & Biolek

Memristor models

MOOREA Feb 25, 2013

Simmons tunneling barrier model [1/2]

• 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.

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[21] Pickett, Journal of Appl. Phys, 2009[22] Simmons, Journal of Appl. Phys, 1963

X

Memristor models

MOOREA Feb 25, 2013

Simmons tunneling barrier model [2/2]

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• Deep knowledge of switching mechanisms in TiO2.

• Physical model → High accuracy degree.

• 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.

Memristor models

TEAM Model

MOOREA Feb 25, 2013

ThrEshold Adaptative Model (TEAM) [1/3]

• 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.

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Memristor models

Simmons model

TEAM model

MOOREA Feb 25, 2013

ThrEshold Adaptative Model (TEAM) [2/3]

• 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.

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Memristor models

dx/dt directionwhen i>0

dx/dt directionwhen i<0

aoff aon

MOOREA Feb 25, 2013

ThrEshold Adaptative Model (TEAM) [3/3]

• I-V relationship can be defined as linear or not.

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Memristor models

• 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.

or

I-V linear relationship I-V non-linear relationship

MOOREA Feb 25, 2013

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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.

Models analyses

MOOREA Feb 25, 2013

Memristor models chosen for test

• Some authors provide descriptions with their model.– Kvatinsky : Verilog-A descriptions [23].

• Linear, non-linear, Simmons, TEAM models.• Joglekar, Biolek, Prodromakis, TEAM window functions.

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Models analyses

• 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

MOOREA Feb 25, 2013

Linear ion drift model

• “Ideal window” : bipolarity and w comprised in [0, D].– F(w) = 0 for w = 0 and w = D, 1 otherwise => linear ion drift profile.

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Models analyses

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 conditiondt = 5ms.

Roff = 16kΩ w = 0

Ron = 100Ω w = 10nm

Roff / Ron = 160

MOOREA Feb 25, 2013

Linear model, M(w)=f(Vin)

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Models analyses

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.

Vin = 250mV

Vin = 125mV

w = 0 →Roff = 16kΩ w = 0,9nm → R= 1,5kΩ

w = 0 →Roff = 16kΩ w = 0,29nm → R = 11kΩ

Roff / Ron = 160

Roff / Ron = 160

MOOREA Feb 25, 2013

w = 0 →Roff = 16kΩ w = 0,58nm →R = 11,5kΩ

Linear model, M(w)=f(D)

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Models analyses

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.

D = 10nm

D = 20nm

w = 0 →Roff = 16kΩ w = 10nm →Ron = 100Ω

Roff / Ron = 160

Roff / Ron = 160

MOOREA Feb 25, 2013

Linear model, behavior on multiple periods

• By applying sinusoidal voltage during several periods (10T).

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Models analyses

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.

Roff decreases

Rmin → Ron

• Reproducibility problem due to robustness ?

Source: Yu, IEEE Trans. Electron Device, vol 58, no 8, 08/2011

• Does model integrate uncovered defects in TiO2 ?

MOOREA Feb 25, 2013

Linear model, impact of Roff/Ron ratio

• Memristor responses when increasing Roff/Ron.

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Models analyses

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.

Roff/Ron = 80

Roff/Ron = 120

Roff/Ron = 160

Roff/Ron 80 120 160

wmin 0 0 0

M(wmin) 8KΩ 12KΩ 16KΩ

wmax 7nm 3,7nm 2,9nm

M(wmax) 2,7KΩ 7KΩ 11KΩ

MOOREA Feb 25, 2013

Linear model, impact of frequency

• Memristor responses when increasing frequency.

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Models analyses

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.

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.

[23] Kvatinsky, Kvatinsky, CCIT (Center for Communication and information Technologies) Reports, 2011

Analytical expression Verilog-A translation in [22]

MOOREA Feb 25, 2013

Linear model robustness

• Robustness of the model. Impact of the time step.

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Models analyses

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.

Time step: 5ms

• “dt” is a sensitive parameter in the model.

Time step: 2,5ms

dt: 5ms

dt: 5ms

dt: 2,5ms

Time step: 5ms

Time step: 5ms

dt: 10ms

The results are in agreement with the hystereses behaviors observed in literature when modifying parameters for a given configuration.

What is the behavior which must be observed for the starting configuration ?

MOOREA Feb 25, 2013

How about the other linear models ?

• TEAM Model fitting the linear ion drift model.– Same behaviors observed for the same configurations.

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Models analyses

[14] Corinto, IEEE Trans. on Circuits and Systems, vol 59, no 11, 11/2012

• Enhanced version proposed by [14].– Window functions (bipolarity + boundary conditions) + (VthOFF, VthON).

Behavioral condition

Window Function

x(t)

MOOREA Feb 25, 2013

Corinto’s linear model enhanced version [1/2]

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Models analyses

[14] Corinto, IEEE Trans. on Circuits and Systems, vol 59, no 11, 11/2012

• 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.

MOOREA Feb 25, 2013

Corinto’s linear model enhanced version [2/2]

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Models analyses

[14] Corinto, IEEE Trans. on Circuits and Systems, vol 59, no 11, 11/2012

• 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 ;

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)

α

MOOREA Feb 25, 2013

TEAM model (Simmons), expression of dx/dt

• TEAM model in Simmons configuration + “ideal window”.– Linear and non linear relations exhibit the same behaviors.

• X : oxide (undoped) region length.

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Models analyses

Bipolar switching controlled with Threshold currents ioff and ion

foff(x) = fon(x) = F(x)

F(x) =1 when 0 < x < D

0 otherwise

MOOREA Feb 25, 2013

TEAM model (Simmons), hysteresis behavior

• Asymetric switching: OFF state slower than ON STATE.

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Models analyses

Kvatinsky results

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.

X : 0 → 0,862.M : 50Ω → 640Ω

MOOREA Feb 25, 2013

TEAM model (Simmons), M(x) = f(Vin)

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Models analyses

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.

X : 0 → 1M : 50Ω → 1KΩ

Vin = 500mV

Vin = 1V

X : 0 → 0,862.M : 50Ω → 640Ω

MOOREA Feb 25, 2013

TEAM model (Simmons), M(x) = f(Roff)

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Models analyses

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.

X : 0 → 1M : 50Ω → 1KΩ

Vin = 1V, ROFF = 1KΩ

Vin = 1V, ROFF = 5KΩ

X : 0 → 0.71M : 50Ω → 1.3KΩ

MOOREA Feb 25, 2013

TEAM model, M(x) regarding the frequency

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Models analyses

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.

Frequency 200K 20MEG 2G

xmin 0 0 0

M(xmin) 50 50 50

xmax 1.8nm 1.95nm 2,1nm

M(xmax) 815Ω 1.2KΩ 1.7KΩ

MOOREA Feb 25, 2013

TEAM model (Simmons), ion and ioff [1/2]

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Models analyses

• Memristor behaviors when modifying threshold currents.– (I) Ioff : 115μA → 1mA.

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.

MOOREA Feb 25, 2013

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Models analyses

• Memristor behaviors when modifying threshold currents.– (II) Ion: -8.9μA → -50 μA.

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.

TEAM model (Simmons), ion and ioff [2/2]

MOOREA Feb 25, 2013

TEAM model (Simmons), robustness

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Models analyses

• TEAM model : simplified version of Simmons one.– Simmons model presents huge convergence problem. – Simplification through a modification of the expression of dx/dt.

• 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.

MOOREA Feb 25, 2013

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Outline

Switching mechanims.

Memristor modeling.

Literature models analyses.

Work in progress.Memristor models.

Database for measurements performed on test structures.

Discussion.

Work in progress

MOOREA Feb 25, 2013

Memristor models investigation [1/3]

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• Two models have hold our attention.– (I) Enhanced version of the linear ion drift model [14].

• Seems more robust than the basic model.• Bipolar switching can be controlled by threshold voltages.• Integrates a functional linear ion drift profile window function.

– (II) TEAM model [23].• Model derived from a real accurate physical model.

– Bipolar switching can be controlled by threshold currents.– Integrates a doping concentration window function.

– (I) and (II) : used to model the switching behavior in TiO2 structure.

Work in progress

[14] Corinto, IEEE Trans. on Circuits and Systems, vol 59, no 11, 11/2012[23] Kvatinsky, Kvatinsky, CCIT (Center for Communication and information Technologies) Reports, 2011

MOOREA Feb 25, 2013

Memristor models investigation [2/3]

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• Next steps concerning these models.– (I) Enhanced version of the linear ion drift model [14].

• Only few analyses have been realized.=> deeper investigation of the model.

– (II) TEAM model.• Convergence problems => find a way to resolve them.

– Other ways to express the analytical relations of dx/dt and M(x) ?– Are we also able to run the original model, that says Simmons one ?

Work in progress

[14] Corinto, IEEE Trans. on Circuits and Systems, vol 59, no 11, 11/2012[23] Kvatinsky, Kvatinsky, CCIT (Center for Communication and information Technologies) Reports, 2011

MOOREA Feb 25, 2013

Memristor models investigation [3/3]

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• Present day memristor models are not complete.– Only electrical behavior is taken into account.– Models require to integrate thermal, lifetime effects.– For neuromorphic applications : electrical couplings with environment.

• Impact of parasitive effects on memristor switching behavior ?

Work in progress

• In order to propose accurate models, one must consider :– Theory aspect.– Measurements provided by test structures : realistic data.

– Comparisons simulations/measurements to improve the model.

MOOREA Feb 25, 2013

Measurement files database

• To compare simulations with measurements on IC-CAP.=> A Database is currently under development.

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• Expected achievements with this database.– Classify all the measurements files provided in the Dropbox. – Call a file through a path during DUT definition in ICCAP.

– The file is converted in IC-CAP format.

Work in progress

• Measurement files treatment.– Segmentation and conversion of the measurement files. – Automatic classification.– Permanent update of the database.

MOOREA Feb 25, 2013

Storing method used in database

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Work in progress

MOOREA Feb 25, 2013

Running “Cycle_I-V_WER” files [1/2]

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• Present Day.– Segmentation of a “Cycle_I-V_WER” measurement file in “n” files.

– “n” depends on file length.– nth file → nth I-V cycle (work in progress).

– Files are converted in IC-CAP format.

Work in progress

• To run the measurement files.– Maximum number of measurement points : 50000.– Modify the file heading such that:

Input parameters : Time start ; end ; nb_pts ; time step .

Output parameters : voltage (V) and current (I).

MOOREA Feb 25, 2013

Running “Cycle_I-V_WER” files [2/2]

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• Measured cycles I-V : observation under IC-CAP.– Plot exhibit for numerous cycles V applied and I obtained.

Work in progress

Measurement file illustrated : 2D017-1a-cycles_I-V_WER_Ag-Pt1_15-10-12

MOOREA Feb 25, 2013

Points to discuss about the test devices [1/2]

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• Model orientation depending on developed test structures. Geometrical and technological data require.

• Evolution in the technological process ? Changes in material and/or electrode types ?

• First test structures. – Dispersion observed.

• Reproducibility ? Can we return to the initial condition ?– Switching behavior.

• Unipolar ? Bipolar ? Both.• Symmetric / Asymmetric switching ?

Work in progress

MOOREA Feb 25, 2013

Points to discuss about the test devices [2/2]

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• “Cycle I-V” files.– Signification of V1, V2, I1, I2 ?

• Why most of V2 values are equal to 0 ?– Measurements performed with ramp voltages.

• What is the maximum value reached ?

Work in progress