1. Introduction to the Memristor
Isaac Abraham
Staff Engineer (Analog),
Cloud Platform Division, Intel.
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
5/24/2014
Presented on Newcastle Public Library, WA

2. Introduction to the Memristor Isaac Abraham
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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3. Introduction to the Memristor Isaac Abraham
General Q&A
FAQs from HP
Where and when can I buy a 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 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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5. Introduction to the Memristor Isaac Abraham
Positive Feedback
Regenerative, Super-regenerative Radio
Active Negative Components
Abraham, “A Novel Analytical Negative Resistor Compact Model”, IEEE, MWSCAS 2013
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6. Introduction to the Memristor Isaac Abraham
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
Estimated Duration
55 – 70 minutes
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8. Introduction to the Memristor Isaac Abraham
What is the memristor?
A resistor that retains a memory of its last programmed state (resistance) is a memory-resistor.
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9. Phenomena
A large variety of physical phenomena can lead to memristance.
Micro/Nano scale effects -> relevant to EE
Macro scale effects -> observable
A memristive device will exhibit at least two resistance “states”
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10. Introduction to the Memristor Isaac Abraham
Mechanisms
Ions discharge at electrodes causing “filaments”. (Electro chemical Mechanism, ECM)
Visualize: Electrolysis
Waser, “Redox based…”, Wiley Inter Sci, DOI /adma
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)
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11. 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.
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12. Introduction to the Memristor Isaac Abraham
Silver filaments
Waser, “Redox based…”, Wiley Inter Sci, DOI /adma , page 2636
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13. 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 |
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14. Introduction to the Memristor Isaac Abraham
History #
Year
Who
Where ??
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, pp 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 5
2014
Many
Many papers, the end
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15. Device Characteristics
Two terminals
Can be programmed into a high-or-low resistance
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.
In other words, a charge-dependent device.
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16. Introduction to the Memristor Isaac Abraham
Electrical Symbol
“stop bar”
Thermistor symbol
L. O. Chua, “Memristor: The missing circuit element”, IEEE Trans. Circuit Theory, vol. 18, no. 5, pp , September 1971.
I have not heard anyone describe the parts of the symbol, but it makes sense as a “heating element that stops dissipating heat at some time”.
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17. Introduction to the Memristor Isaac Abraham
Scale of things
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18. Introduction to the Memristor Isaac Abraham
Materials #
Date
Author
Affiliation
Sandwich
Dimensions(nm) 1
1968
Argall
Ti/ TiO2 / Ti
30 / 100 / 30
2008
Williams HP
Ti/ TiO2 / Pt
15 / 50 / 15
xx / 03 /yy 2
Driscoll
UCSD, ETRI
??/ VO / ??
? / ? / ? 3
2009
George Hackett
NIST
Al/ TiO2 / Al
80 / 60 / 80 4
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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19. Current-Voltage Characteristics
This tutorial focusses on the bipolar
Waser, “Nanoionics based…”, nature Materials, vol 6, nov 2007, p833
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20. Introduction to the Memristor Isaac Abraham
Summary M1 M2
sandwich
MEMRISTOR M1 M2
Filling V I
RESISTOR
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21. Structure and basic operation
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The HP Concept Sketch
(a)
(b)
boundary
(c)
The thickness of the sandwich >> the lead-in wires.
R. S. Williams, “How we found the missing memristor”, IEEE Spectrum, Dec. 2008, pp. 29 – 35.
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23. Introduction to the Memristor Isaac Abraham
Shell Structure
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Molecule Plot
Additional information is available at:
Curated data from Wolfram Mathematica
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25. Introduction to the Memristor Isaac Abraham
The Chemistry
This is an animation.
A common chemical species in the business is Titanium Dioxide. O Ti O
2014/07/25 : Inserted vacancy.
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26. Introduction to the Memristor Isaac Abraham
Structure Summary
Electronic conduction
Mobile vacancies - + - +
Low Resistance
High Resistance
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27. Memristor models in vogue
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28. Introduction to the Memristor Isaac Abraham
Memristor States
End sensitive.
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29. Contemporary “Physical” Models#
Mechanism
Source
Notes 1
Charge carrier traps
T. Fujii et. al, App. Phys. Lett., 86, , 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
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The Modeling Effort
Find an equation to model the movement of the boundary.
Williams, Spectrum, 2008
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31. Introduction to the Memristor Isaac Abraham
Charge Traps
This is an animation. M1 M2 M1 M2
Distributed charge traps
(~ rumble-strips)
A large charge trap
(~ speed bump)
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32. 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 high-resistance.
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33. Accumulation Boundary
Williams, Spectrum, 2008
Need two equations
Resistance w.r.t boundary
Boundary w.r.t time
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34. Contemporary Rheostat Model: Equations#
What
Chua
Strukov & Williams 1
Governing equation
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35. 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 /nature 06932
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36. Introduction to the Memristor Isaac Abraham
A Numerical Model #
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
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37. Introduction to the Memristor Isaac Abraham
Modeling Summary
Analytical
Numerical
Nardi,
Numerical solutions
Strukov & Williams’
dual variable resistor
Corinto & Ascoli,
“Window function…”
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38. Electrical Properties
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39. Introduction to the Memristor Isaac Abraham
Cumulative I-V Curve
Accumulating R
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40. Introduction to the Memristor Isaac Abraham
𝒇 & 𝑨 dependence
Lobe size 𝛼 𝑓 −1
Negative Resistance
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41. Introduction to the Memristor Isaac Abraham
Circuit Applications
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42. Introduction to the Memristor Isaac Abraham
Visual Aid
This is an animation.
High Resistance
Low Resistance
Dynamic 1 -1
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43. Introduction to the Memristor Isaac Abraham
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 , adma
Bit line
Plate line 1 1
Low R
-> Timed pulse
-> Opamp sensor
Waser, “Redox based…”, Wiley Inter Sci, DOI /adma , page 2632
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45. Introduction to the Memristor Isaac Abraham
Memristor Logic - AND
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46. Memristor Demo Logic - AND1 R vo
𝑣𝑜=1 2𝑅 2𝑅+ 𝑅 2 =1 4𝑅 5𝑅 =0.8 1 R vo R vo
0.4V
0.8V
1.0V 00
10, 01 11
uncertainty
𝑣𝑜= ∗ ∗ = = 2 5 =0.4
Fiedler & Batas, IEEE Nano Tech., vol 10, no. 2, Mar 2011
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47. Introduction to the Memristor Isaac Abraham
Memristor Oscillator O O vp 1 1 vn 1 1 1 O O O t 1 2 3 4 5 6
0.5V
Zidan, “Memristor based …”, Electronics Letters, Vol 47, Issue 22, DOI /el
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48. Introduction to the Memristor Isaac Abraham
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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49. Introduction to the Memristor Isaac Abraham
Signal Conditioning
I. Abraham, S. Kaya, G. Pennington, “A Closed Form Memristor SPICE Model and Oscillator”, MWSCAS 2012
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50. Introduction to the Memristor Isaac Abraham
Switching Speed
Est-ce un peu compliqué?
quadratic
Simple inverse
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51. Introduction to the Memristor Isaac Abraham
Challenges
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52. 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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53. Challenges : Reliability
Balancing scalability with MIM voltage breakdown rules
Modeling surface potential effects at the MIM interfaces
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54. 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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55. Introduction to the Memristor Isaac Abraham
Classification
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56. Introduction to the Memristor Isaac Abraham
Fundamental element? #
Element
Equation
Notes 1 2 3 4
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57. Introduction to the Memristor Isaac Abraham
The puzzle
𝑅= 𝑑𝑣 𝑑𝑖
𝐶= 𝑑𝑞 𝑑𝑣
𝑀= 𝑑∅ 𝑑𝑞
𝐿= 𝑑∅ 𝑑𝑖 C
Dissipative R
R(t) L
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58. Alternate Modeling Approach
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59. Nonlinear (Vacancy) Transport
𝑢 𝑥,𝑡 = 1 1+𝑎 𝑒 −𝑓 0 𝜙 𝜆(𝜙)
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60. Introduction to the Memristor Isaac Abraham
Results
Vacancy velocity
Vacancy concentration
𝑢 𝑡 + 𝜐 𝑥,𝑡 𝑢 𝑥 =0
𝑢 𝑥,𝑡 = 1 1+𝑎 𝑒 −𝑓 0 𝜙 𝜆(𝜙)
Circuit Model HP
Device resistance
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61. Introduction to the Memristor Isaac Abraham
Memristance in Nature
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62. Macro Memristance (Analemma)
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63. Introduction to the Memristor Isaac Abraham
Summary
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64. Introduction to the Memristor Isaac Abraham
Summary
Memristors are a nascent field holding promise as candidates for
high density memory
Modeling synapse/amoeba
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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65. Introduction to the Memristor Isaac Abraham
Some References
Waser et.al, “Redox based resistive switching memories – Nanoionic mechanisms, Prospects and Challenges, Adv. Mater. 2009, 21,
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
Corinto & Ascoli, “A boundary condition based approach to the modeling of memristor nanostructurs”, IEEE Transactions on Circuits and Systems, DOI /TCSI
Kwon et.al, “Atomic structure of conducting nanofilaments in TiO2 resistive switching memory”, DOI /Nano
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66. Introduction to the Memristor Isaac Abraham
Extras
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67. The Idealized Concept SketchM1 M2 F2 F1 F3
M1 : Metal endplate 1
M2 : Metal endplate 2
F1 : Mature filament
F2 : Stubby filament
F3 : “vacancy rich” filling
It does look like a capacitor. The difference is that we don’t expect filaments to form in a good quality capacitor.
R. Waser, M. Aono, “Nano-ionics based resistive switching memories”, Nature Materials, vol.6, November 2007, pp
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68. Low and High ResistanceM1 M2 V
(a)
(b)
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69. Introduction to the Memristor Isaac Abraham
Device Polarity
Although both (a) and (b) are high resistance, they have a different “phase”. Hence the device is “pin” sensitive.
(a)
(b)
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70. Introduction to the Memristor Isaac Abraham
Shell Structure
This is an animation.
22 protons
30 electrons
8 protons
4 electrons
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71. Introduction 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: 2
Abraham
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