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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
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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
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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.
Speaker Bio
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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
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Regenerative, Super-regenerative Radio
Active Negative Components
Abraham, “A Novel Analytical Negative Resistor Compact Model”, IEEE, MWSCAS 2013
Table of Contents
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INTRODUCTIONSTRUCTURE AND BASIC OPERATIONMEMRISTOR MODELS IN VOGUEELECTRICAL PROPERTIESCIRCUIT APPLICATIONSCHALLENGESCLASSIFICATIONALTERNATE MODELING STUDIESMEMRISTANCE IN NATURESUMMARY
Estimated Duration55 – 70 minutes
Introduction
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What is the memristor?
A resistor that retains a memory of its last programmed state (resistance) is a memory-resistor.
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Phenomena
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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)
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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
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Waser, “Redox based…”, Wiley Inter Sci, DOI 10.1002/adma.200900375, page 2636
Silver dendrites (Pt/H2O/Ag)
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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.
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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.
Introduction to the Memristor Isaac Abraham
Scale of things
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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.
Introduction to the Memristor Isaac Abraham
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)
Introduction to the Memristor Isaac Abraham
boundary
Shell Structure
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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.
Introduction to the Memristor Isaac Abraham
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.
Introduction to the Memristor Isaac Abraham
The Modeling Effort
Find an equation to model the movement of the boundary.
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Williams, Spectrum, 2008
Charge Traps
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M1 M2
M1 M2
Distributed charge traps (~ rumble-strips)
A large charge trap (~ speed bump)
This is an animation.
Introduction to the Memristor Isaac Abraham
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.
Introduction to the Memristor Isaac Abraham
Accumulation Boundary
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Need two equations(1) Resistance w.r.t boundary(2) Boundary w.r.t time
Williams, Spectrum, 2008
Contemporary Rheostat Model:Equations
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# What Chua Strukov & Williams
1 Governing equation
Dual Variable Resistor Model
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This model may also be called the dual variable resistor model.
This is an animation.
Strukov, “The missing memristor….”, Vol 453, 1 May 2008, doi.10.1038/nature 06932
A Numerical Model
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# 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
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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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Visual Aid
High Resistance Low Resistance Dynamic
1 0
-1 0
This is an animation.
Crossbar Memory
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Wei Lu et. al, “Two Terminal Resistive Switches (Memristors) for Memory and Logic Applications”, 2011 IEEE.
Introduction to the Memristor Isaac Abraham
Crossbar Memory
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Waser et. al, “Redox-Based Resistive…..”, DOI 10.1002, adma 200900375
Introduction to the Memristor Isaac Abraham
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
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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.
Introduction to the Memristor Isaac Abraham
This is an animation.
Signal Conditioning
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I. Abraham, S. Kaya, G. Pennington, “A Closed Form Memristor SPICE Model and Oscillator”, MWSCAS 2012
Switching Speed
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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
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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
Introduction to the Memristor Isaac Abraham
The puzzle
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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
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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).
Williams, Spectrum, 2008
Some References
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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
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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.
Introduction to the Memristor Isaac Abraham
Low and High Resistance
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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)
Introduction to the Memristor Isaac Abraham
Shell Structure
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This is an animation.
Introduction to the Memristor Isaac Abraham
22 protons30 electrons
8 protons4 electrons
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# Source Equation Notes
1 Fiedler & Batas Simple algebraic derivation in Williams & Strukov, “Exponential Ionic Drift…”, App. Phys. A, (2009) 94: 514- 519
2 Abraham