introduction to the memristor isaac abraham staff engineer (analog), cloud platform division, intel....

Introduction to the Memristor

Isaac Abraham

Staff Engineer (Analog),Cloud Platform Division, Intel.

5/24/2014 1

Introduction to the Memristor Isaac Abraham

The topic is part of a self-funded graduate study at Univ. Washington, Seattle. The presentation is not related to the speaker’s work at Intel, nor does it contain any information, proprietary or otherwise, relating to Cloud Platform Division or Intel.

Presented on 2014/08/05 @ Newcastle Public Library, WA

Acknowledgements

5/24/20142Introduction to the Memristor

Isaac Abraham

Thanks to Mr. Buchanan, IEEE Seattle CAS Chair, for making all the necessary arrangements w.r.t logistics.

Thanks to Dr.Anantram, UW for introducing me to the IEEE-Seattle chapter so I could choose to avail of this opportunity to speak at its monthly meeting.

Many thanks to the attendees many of whom were from afar.

General Q&A


Isaac Abraham

FAQs from HPhttp://www.hpl.hp.com/news/2008/apr-jun/memristor_faq.html

Where and when can I buy a memristor?http://www.theregister.co.uk/2013/11/01/hp_memristor_2018/

Memristor @ NISTMemory with a Twist: NIST Develops a Flexible Memristor

Molecule of TiO2Molecule (right click -> Open hyperlink) for TiO2 and links to reliable online references.

Phase Change vs. Vacancy – MemoryLinks (right click -> Open hyperlink) to PCM tutorials from Micron and IBM.

http://www.hpl.hp.com/news/2008/apr-jun/memristor_faq.html



http://www.theregister.co.uk/2013/11/01/hp_memristor_2018/

http://www.theregister.co.uk/2013/11/01/hp_memristor_2018/

http://www.nist.gov/pml/div683/memristor_060209.cfm

http://www.nist.gov/pml/div683/memristor_060209.cfm

Speaker Bio


Isaac Abraham

Isaac Abraham received his B.Tech in EE from the Govt. College of Engg. Kerala, India 1994 and his MS in VLSI and Control Systems from Wright State University, Dayton OH, in 1998. Since 1998 he has been with Intel Corporation, in the Cloud Platform Division and is currently Staff Engineer (Analog Circuits). He designs high speed analog IOs for proprietary interfaces and industry standard DDR, PCI, PCIX and PCIE. His area of specialization is the design of receivers, impedance compensated transmitters, on-die power supplies and generally analog circuit design down to the 14nm technology node and into the 10GHz range.

Isaac’s interest in memristors is part of his graduate level research work at UW, and spans modeling, digital and analog circuit applications. He enjoys good mathematics, circuit modeling and studying useful positive feedback applications.

Positive Feedback


Isaac Abraham

Regenerative, Super-regenerative Radio

Active Negative Components

Abraham, “A Novel Analytical Negative Resistor Compact Model”, IEEE, MWSCAS 2013

Table of Contents


Isaac Abraham

INTRODUCTIONSTRUCTURE AND BASIC OPERATIONMEMRISTOR MODELS IN VOGUEELECTRICAL PROPERTIESCIRCUIT APPLICATIONSCHALLENGESCLASSIFICATIONALTERNATE MODELING STUDIESMEMRISTANCE IN NATURESUMMARY

Estimated Duration55 – 70 minutes

Introduction


Isaac Abraham

What is the memristor?

A resistor that retains a memory of its last programmed state (resistance) is a memory-resistor.


Isaac Abraham

Phenomena


Isaac Abraham

A large variety of physical phenomena can lead to memristance.

Micro/Nano scale effects -> relevant to EEMacro scale effects -> observable

A memristive device will exhibit at least two resistance “states”

Mechanisms


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Ions discharge at electrodes causing “filaments”. (Electro chemical Mechanism, ECM)Visualize: Electrolysis

Vacancies move between endplates. (Valence Change Mechanism, VCM)Visualize: Sedimentation

Stoichiometry changes due to heat. (Thermo Chemical Mechanism, TCM)Visualize: O3 (cold air)

Amorphous to crystalline (Phase Change Mechanism, PCM)Waser, “Redox based…”, Wiley Inter Sci, DOI 10.1002/adma.200900375

Phase Change Memory (PCM)


Isaac Abraham

A Phase change memory uses heat to change a chalcogenide(elements in Group 16 of periodic table) from amorphous (high resistance) to crystalline (low resistance) state.

The vacancy dynamics based memristors rely on changing the concentration of “defect” structures at various locations in the device, to change the resistance.

Below are readable links about PCM from industry leaders.

http://www.micron.com/about/innovations/pcm

http://www.research.ibm.com/labs/zurich/sto/pcm/





Silver filaments


Isaac Abraham

Waser, “Redox based…”, Wiley Inter Sci, DOI 10.1002/adma.200900375, page 2636

Silver dendrites (Pt/H2O/Ag)


Isaac Abraham

Memristive devices for computingJ. Joshua Yang, Dmitri B. Strukov and Duncan R. StewartNATURE NANOTECHNOLOGY | VOL 8 | JANUARY 2013 | www.nature.com/naturenanotechnology

History# Year Who Where

0 ?? Unknowns Those who may have observed memristance, while studying thin films.

1 1962 Hickmott “Low Frequency negative resistance in thin anodic oxide films”, J. Appl. Phys. 33, 2669 – 2682

2 1967 Argall “Switching phenomena in Titanium oxide thin films”, Solid State Electronics, vol 11, issue 5, May 1968, pp535-541.

3 1971 Chua “Memristor – the missing circuit element”, IEEE Trans. Circuit Theory, 18, 507 – 517

4 2008 Strukov, et. al.

“The missing memristor found”, Nature 2008, vol. 453, 1 May 2008, pp. 80-83.

5 2014 Many Many papers, References @ the end


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Device Characteristics Two terminals

Can be programmed into a high-or-low resistance o And an infinite number of intermediate resistance

states.

The mechanism that programs the device is the “time-integral” of the voltage applied between the terminals.o In other words, a charge-dependent device.


Isaac Abraham

Electrical Symbol

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Thermistor symbol

“stop bar”

L. O. Chua, “Memristor: The missing circuit element”, IEEE Trans. Circuit Theory, vol. 18, no. 5, pp. 507-519, September 1971.


Scale of things


Isaac Abraham

http://science.energy.gov/bes/news-and-resources/scale-of-things-chart/

Materials

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# Date Author Affiliation Sandwich Dimensions(nm)

1 1968 Argall Ti/ TiO2 / Ti 30 / 100 / 30

1 2008 Williams HP Ti/ TiO2 / Pt 15 / 50 / 15xx / 03 /yy

2 2008 Driscoll UCSD, ETRI ??/ VO / ?? ? / ? / ?

3 2009 George Hackett

NIST Al/ TiO2 / Al 80 / 60 / 80

4 2009 Waser JARA-Germany Pt/ TiO2 / PtPt/ STO / SrTO

10 / 27 /10xx / 500 /yy

In general, dimensions can 10nm < d < 100nm. TiO2 seems to be a popular choice for the thin film among

experimentalists.


Current-Voltage Characteristics


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This tutorial focusses on the bipolar

Waser, “Nanoionics based…”, nature Materials, vol 6, nov 2007, p833

Summary


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M1 M2

sandwich

MEMRISTOR

M1 M2

Filling V

I

RESISTOR

Structure and basic operation


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The HP Concept Sketch

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(a) (b)

R. S. Williams, “How we found the missing memristor”, IEEE Spectrum, Dec. 2008, pp. 29 – 35.

(c)


boundary

Shell Structure


Isaac Abraham

Molecule Plot


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Additional information is available at:

http://ruby.colorado.edu/~smyth/min/tio2.html

Curated data from Wolfram Mathematica



The Chemistry

A common chemical species in the business is Titanium Dioxide.

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O

O

This is an animation.


Ti

Structure Summary


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- +

Low Resistance High Resistance

- +

o Electronic conduction

o Mobile vacancies

Memristor models in vogue


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Memristor States


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Contemporary “Physical” Models

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# Mechanism Source Notes

1 Charge carrier traps T. Fujii et. al, App. Phys. Lett., 86, 012107, 2005

Experimental, verbose.

Expresses the idea that the vacancies/ions are e-traps.

2 Electro-chemical migration of oxygen ions

Nishi & Jameson, Device Research Conference, 2008, (Stanford)

Article, Verbose.

3 A unified physical model

Gao et. al, Oxide based RRAM, Symp. On VLSI Tech. Digest of Tech. Papers.

Experimental, Verbose.

4 A two-variable resistor model

Kim & Choi, “A Comprehensive Study of Resistive Switching Mechanism…”, IEEE Trans. Electron Dev., 2009

Experimental, Verbose.


The Modeling Effort

Find an equation to model the movement of the boundary.


Isaac Abraham

Williams, Spectrum, 2008

Charge Traps

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M1 M2

M1 M2

Distributed charge traps (~ rumble-strips)

A large charge trap (~ speed bump)



The Common Denominator in Modeling

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Under the action of an external electric field,

Vacancies distribute throughout the device volume, to create a low-resistance.

Vacancies evolve and accumulate to an end plate to create high-resistance.


Accumulation Boundary


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Need two equations(1) Resistance w.r.t boundary(2) Boundary w.r.t time


Contemporary Rheostat Model:Equations


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# What Chua Strukov & Williams

1 Governing equation

Dual Variable Resistor Model


Isaac Abraham

This model may also be called the dual variable resistor model.


Strukov, “The missing memristor….”, Vol 453, 1 May 2008, doi.10.1038/nature 06932

A Numerical Model


Isaac Abraham

# What Chua Nardi et. al.

1 Governing equation

Larentis, Nardi et.al, “Resistive Switching by Volage…”, IEEE Transactions on Electron Devices, Vol. 59, no.9, Sep 2012

Modeling Summary


Isaac Abraham

Analytical Numerical

Strukov & Williams’ dual variable resistor

Corinto & Ascoli,“Window function…”

Nardi,Numerical solutions

Electrical Properties


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Cumulative I-V Curve


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Accumulating R

dependence


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Negative Resistance

Lobe size

Circuit Applications


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Isaac Abraham

Visual Aid

High Resistance Low Resistance Dynamic

1 0

-1 0


Crossbar Memory

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Wei Lu et. al, “Two Terminal Resistive Switches (Memristors) for Memory and Logic Applications”, 2011 IEEE.


Crossbar Memory

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Waser et. al, “Redox-Based Resistive…..”, DOI 10.1002, adma 200900375


Plate line

01

10

10

10

“STOP” @ Low R-> Timed pulse-> Opamp sensor

Bit line

Waser, “Redox based…”, Wiley Inter Sci, DOI 10.1002/adma.200900375, page 2632

Memristor Logic - AND


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Memristor Demo Logic - AND


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1

1

R

R R

R

vo

𝑣𝑜=12𝑅

(2𝑅+𝑅2 )

=14 𝑅5𝑅

=0.8

1

0

R

R R

R

vo

𝑣𝑜=1( 2∗1

2+1 )1+( 2∗1

2+1 )=1

23

( 53 )

=25=0.4

0

0 R R

R

vo

0.4V

0.8V

1.0V

00

10, 01

11

uncertainty

Fiedler & Batas, IEEE Nano Tech., vol 10, no. 2, Mar 2011

Memristor Oscillator


Isaac Abraham

vn

vp

0.5V

1

1

0

1

1

1

O

O

O

O

O

t 0 1 2 3 4 5 6

Zidan, “Memristor based …”, Electronics Letters, Vol 47, Issue 22, DOI10.1049/el.2011.2700

Self Adjusting LPF

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Abraham, “Quasi-Linear Vacancy Dynamics Modeling and Circuit Analysis of the Bipolar Memristor”, PLOS 1, submitted May 2014.



Signal Conditioning


Isaac Abraham

I. Abraham, S. Kaya, G. Pennington, “A Closed Form Memristor SPICE Model and Oscillator”, MWSCAS 2012

Switching Speed

2014 Jun 0350Introduction to the Memristor

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quadratic

Simple inverse

Est-ce un peu compliqué?

Challenges


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Challenges : Manufacturing

Integration into CMOS technologies w/ appropriate chemical species

Controlling filament growth through– Generating preferred filament path– High mobility pathways


Isaac Abraham

Challenges : Reliability

Balancing scalability with MIM voltage breakdown rules

Modeling surface potential effects at the MIM interfaces


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Challenges : PerformanceSwitching Speed.– Mobility+ Device length scaling

Heat dissipation in a confined area– Scaling

False transition due to naturally occurring free ions.


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Classification


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Fundamental element?

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# Element

Equation Notes

1

2

3

4


The puzzle


Isaac Abraham

𝑅=𝑑𝑣𝑑𝑖

𝐶=𝑑𝑞𝑑𝑣

𝐿=𝑑∅𝑑𝑖

𝑀=𝑑∅𝑑𝑞

R(t)

R

C

L

Dissipative

Alternate Modeling Approach


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Nonlinear (Vacancy) Transport


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𝑢 (𝑥 , 𝑡 )= 1

1+𝑎𝑒− 𝑓 0❑𝜙 𝜆(𝜙 )

Results


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Vacancy velocity Vacancy concentration

Device resistance

Circuit Model

HP

Memristance in Nature


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Macro Memristance (Analemma)


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http://www.wolfram.com/products/mathematica/newin7/content/DynamicAstronomicalComputation/ComputePositionDependentAnalemmas.html

Summary


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Summary


Isaac Abraham

Memristors are a nascent field holding promise as candidates for

(i) high density memory (ii) Modeling synapse/amoeba (iii) analog encoding and self-tuning

circuits,

while presenting challenges in performance (speed) and basic electrical device reliability (due to ease of scalability).


Some References


Isaac Abraham

1. Waser et.al, “Redox based resistive switching memories – Nanoionic mechanisms, Prospects and Challenges, Adv. Mater. 2009, 21, 2632-2663

2. Nardi, et.al, “Resistive switching by voltage driven ion migration in Bipolar RRAM – Parts I and II”, IEEE Transactions on Electron Devices, vol. 59, no. 9, Sep 2012

3. Corinto & Ascoli, “A boundary condition based approach to the modeling of memristor nanostructurs”, IEEE Transactions on Circuits and Systems, DOI 10.1109/TCSI 2012.2190563

4. Kwon et.al, “Atomic structure of conducting nanofilaments in TiO2 resistive switching memory”, DOI 10.1038/Nano.2009.456

5. http://www.hpl.hp.com/news/2008/apr-jun/memristor_faq.html



Extras


Isaac Abraham

The Idealized Concept Sketch

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M1 : Metal endplate 1

M2 : Metal endplate 2

F1 : Mature filament

F2 : Stubby filament

F3 : “vacancy rich” filling

M1 M2

F2 F1

F3

R. Waser, M. Aono, “Nano-ionics based resistive switching memories”, Nature Materials, vol.6, November 2007, pp 833 -840.


Low and High Resistance


Isaac Abraham

M1 M2

M1 M2

O

V

(a) (b)

Device Polarity

Although both (a) and (b) are high resistance, they have a different “phase”. Hence the device is “pin” sensitive.

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(a) (b)


Shell Structure

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22 protons30 electrons

8 protons4 electrons

2014 Jun 0371Introduction to the Memristor

Isaac Abraham

# Source Equation Notes

1 Fiedler & Batas Simple algebraic derivation in Williams & Strukov, “Exponential Ionic Drift…”, App. Phys. A, (2009) 94: 514- 519

2 Abraham

introduction to the memristor isaac abraham staff engineer (analog), cloud platform division, intel....

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