Introduction to the
Memristor
Isaac Abraham
Staff Engineer (Analog),
Cloud Platform Division, Intel.
5/24/2014
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.
Introduction to the Memristor
Isaac Abraham
1
Presented on 2014/08/05 @ Newcastle Public Library, WA
Acknowledgements
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.
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General Q&A
FAQs from HP
http://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 @ NIST
Memory with a Twist: NIST Develops a Flexible Memristor
Molecule of TiO2
Molecule (right click -> Open hyperlink) for TiO2 and links to reliable online
references.
Phase Change vs. Vacancy – Memory
Links (right click -> Open hyperlink) to PCM tutorials from Micron and IBM.
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Speaker Bio
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.
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Positive Feedback
Regenerative, Super-regenerative Radio
Active Negative Components
Abraham, “A Novel Analytical
Negative Resistor Compact Model”,
IEEE, MWSCAS 2013
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Table of Contents
INTRODUCTION
STRUCTURE AND BASIC OPERATION
MEMRISTOR MODELS IN VOGUE
ELECTRICAL PROPERTIES
CIRCUIT APPLICATIONS
CHALLENGES
CLASSIFICATION
ALTERNATE MODELING STUDIES
MEMRISTANCE IN NATURE
SUMMARY
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Estimated Duration
55 – 70 minutes
Introduction to the Memristor
Isaac Abraham
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
A large variety of physical phenomena can lead to
memristance.
Micro/Nano scale effects
Macro scale effects
-> relevant to EE
-> observable
A memristive device will exhibit at least two resistance
“states”
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Mechanisms
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)
Waser, “Redox based…”, Wiley Inter Sci, DOI 10.1002/adma.200900375
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Amorphous to crystalline
(Phase Change
Mechanism, PCM)
Phase Change Memory (PCM)
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/
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Silver filaments
Waser, “Redox based…”, Wiley Inter Sci, DOI 10.1002/adma.200900375, page 2636
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Silver dendrites (Pt/H2O/Ag)
Memristive devices for computing
J. Joshua Yang, Dmitri B. Strukov and Duncan R. Stewart
NATURE NANOTECHNOLOGY | VOL 8 | JANUARY 2013 | www.nature.com/naturenanotechnology
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History
14
# 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
“stop bar”
Thermistor symbol
L. O. Chua, “Memristor: The missing circuit
element”, IEEE Trans. Circuit Theory, vol. 18, no. 5,
pp. 507-519, September 1971.
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Scale of things
17
http://science.energy.gov/bes/news-and-resources/scale-of-things-chart/
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Materials
#
Date
Author
1
1968
1
Affiliation
Sandwich
Dimensions(nm)
Argall
Ti/ TiO2 / Ti
30 / 100 / 30
2008
Williams HP
Ti/ TiO2 / Pt
15 / 50
xx / 03
/ 15
/yy
2
2008
Driscoll
UCSD, ETRI
??/ VO / ??
?
/?
3
2009
George
Hackett
NIST
Al/ TiO2 / Al
80 / 60
4
2009
Waser
JARA-Germany
Pt/ TiO2 / Pt
Pt/ STO / SrTO
10 / 27 /10
xx / 500 /yy
/ ?
 In general, dimensions can 10nm < d < 100nm.
 TiO2 seems to be a popular choice for the thin film among
experimentalists.
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/ 80
Current-Voltage Characteristics
This tutorial focusses on the bipolar
19
Waser, “Nanoionics based…”, nature Materials, vol 6, nov 2007, p833
Introduction to the Memristor
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Summary
M1
M2
sandwich
MEMRISTOR
M1
I
M2
V
Filling
RESISTOR
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Structure and basic operation
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The HP Concept Sketch
(a)
(b)
boundary
(c)
R. S. Williams, “How we found the missing memristor”, IEEE
Spectrum, Dec. 2008, pp. 29 – 35.
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Shell Structure
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Molecule Plot
Additional information is available at:
http://ruby.colorado.edu/~smyth/min/tio2.html
Curated data from Wolfram Mathematica
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The Chemistry

 A common chemical species in the
business is Titanium Dioxide.
O
Ti
O
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This is an animation.
Structure Summary
o Electronic conduction
o Mobile vacancies
-
+
Low Resistance
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-
+
High Resistance
Introduction to the Memristor
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Memristor models in vogue
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Memristor States
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Contemporary “Physical” Models
#
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.
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The Modeling Effort
Find an equation to model the
movement of the boundary.
Williams, Spectrum, 2008
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Charge Traps
M1
M1
M2
Distributed charge traps
(~ rumble-strips)
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
This is an animation.
M2
A large charge trap
(~ speed bump)
Introduction to the Memristor
Isaac Abraham
The Common Denominator in
Modeling
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 highresistance.
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Accumulation Boundary
Williams, Spectrum, 2008
Need two equations
(1) Resistance w.r.t boundary
(2) Boundary w.r.t time
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Contemporary Rheostat Model:
Equations
#
What
1
Governing
equation
34
Chua
5/24/2014
Strukov & Williams
Introduction to the Memristor
Isaac Abraham
Dual Variable Resistor
Model

This is an animation.
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
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A Numerical Model
#
What
Chua
1
Governing
equation
Nardi et. al.
Larentis, Nardi et.al, “Resistive Switching by Volage…”, IEEE Transactions on Electron Devices, Vol. 59, no.9, Sep 2012
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Modeling Summary
Analytical
Numerical
Nardi,
Numerical solutions
Strukov & Williams’
dual variable resistor
Corinto & Ascoli,
“Window function…”
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Electrical Properties
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Cumulative I-V Curve
Accumulating R
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𝒇 & 𝑨 dependence
Lobe size 𝛼 𝑓 −1
Negative Resistance
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Circuit Applications
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Visual Aid
High Resistance
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
Low Resistance
Introduction to the Memristor
Isaac Abraham
This is an animation.
Dynamic
1
0
-1
0
Crossbar Memory
Wei Lu et. al, “Two Terminal Resistive Switches (Memristors) for
Memory and Logic Applications”, 2011 IEEE.
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Crossbar Memory
Waser et. al, “Redox-Based Resistive…..”, DOI 10.1002, adma
200900375
Bit line
Plate line
1
0
0
1
0
1
0
1
“STOP” @ Low R
-> Timed pulse
-> Opamp sensor
Waser, “Redox based…”, Wiley Inter Sci, DOI 10.1002/adma.200900375, page 2632
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Memristor Logic - AND
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Memristor Demo Logic - AND
R
R
vo
1
vo
1
R
R
1
0
vo
0
R
R
R
0
R
R
R
R
1.0V
𝑣𝑜 = 1
2𝑅
𝑅
2𝑅 + 2
=1
4𝑅
= 0.8
5𝑅
2 ∗1
2
+1
𝑣𝑜 = 1
=1
2 ∗1
1+ 2+1
2
= = 0.4
5
2
3
5
3
Fiedler & Batas, IEEE Nano Tech., vol 10, no. 2, Mar 2011
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11
0.8V
uncertainty
10, 01
0.4V
00
Memristor Oscillator
O
vp
vn
O
1
0
1
1
1
1
O
O
O
t
0 1 2 3 4 5 6
0.5V
Zidan, “Memristor based …”, Electronics Letters, Vol 47, Issue 22, DOI10.1049/el.2011.2700
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Self Adjusting LPF

This is an animation.
Abraham, “Quasi-Linear Vacancy Dynamics Modeling and Circuit Analysis
of the Bipolar Memristor”, PLOS 1, submitted May 2014.
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Signal Conditioning
I. Abraham, S. Kaya, G. Pennington, “A Closed Form Memristor SPICE Model
and Oscillator”, MWSCAS 2012
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Switching Speed
Est-ce un peu compliqué?
quadratic
Simple inverse
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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 : Performance
Switching 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?
#
Eleme
nt
Equation
Notes
1
2
3
4
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The puzzle
𝑑𝑣
𝑅=
𝑑𝑖
𝑑𝑞
𝐶=
𝑑𝑣
𝑑∅
𝐿=
𝑑𝑖
𝑀=
𝑑∅
𝑑𝑞
C
R
R(t)
L
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Alternate Modeling Approach
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Nonlinear (Vacancy) Transport
𝑢 𝑥, 𝑡 =
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1
1 + 𝑎 𝑒 −𝑓0
𝜙 𝜆(𝜙)
Introduction to the Memristor
Isaac Abraham
Results
Vacancy concentration
Vacancy velocity
𝑢𝑡 + 𝜐 𝑥, 𝑡 𝑢𝑥 = 0
𝑢 𝑥, 𝑡 =
1
1 + 𝑎 𝑒 −𝑓0
𝜙 𝜆(𝜙)
HP
Device resistance
Circuit Model
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Memristance in Nature
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Macro Memristance (Analemma)
http://www.wolfram.com/products/mathematica/newin7/content/DynamicAstronomica
lComputation/ComputePositionDependentAnalemmas.html
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Summary
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Summary
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
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Some References
1. Waser et.al, “Redox based resistive switching memories – Nanoionic
mechanisms, Prospects and Challenges, Adv. Mater. 2009, 21, 26322663
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
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Extras
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The Idealized Concept Sketch
F3
M1
: Metal endplate 1
M2
: Metal endplate 2
F1
: Mature filament
F2
: Stubby filament
F3
: “vacancy rich” filling
M1
M2
F2 F1
R. Waser, M. Aono, “Nano-ionics based resistive switching memories”, Nature
Materials, vol.6, November 2007, pp 833 -840.
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Low and High Resistance
(a)
(b)
M1
M2
M1
M2
V
O
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Device Polarity
Although both (a) and (b) are high
resistance, they have a different
“phase”. Hence the device is “pin”
sensitive.
(a)
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(b)
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Isaac Abraham
Shell Structure
22 protons
30 electrons
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
This is an animation.
8 protons
4 electrons
Introduction to the Memristor
Isaac Abraham
#
Source
1
Fiedler & Batas
2
Abraham
71
2014 Jun 03
Equation
Notes
Simple algebraic
derivation in Williams &
Strukov, “Exponential
Ionic Drift…”, App. Phys.
A, (2009) 94: 514- 519
Introduction to the Memristor
Isaac Abraham