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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
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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. Introduction to the Memristor Isaac Abraham 5/24/2014
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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. Introduction to the Memristor Isaac Abraham 5/24/2014
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Introduction to the Memristor Isaac Abraham
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. Introduction to the Memristor Isaac Abraham 06/25/2014
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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 Introduction to the Memristor Isaac Abraham 06/25/2014
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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 Introduction to the Memristor Isaac Abraham 5/24/2014
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Introduction to the Memristor Isaac Abraham
5/24/2014
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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. Introduction to the Memristor Isaac Abraham 5/24/2014
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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” Introduction to the Memristor Isaac Abraham 5/24/2014
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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) Introduction to the Memristor Isaac Abraham 5/24/2014
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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. Introduction to the Memristor Isaac Abraham 08/06/2014
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Introduction to the Memristor Isaac Abraham
Silver filaments Waser, “Redox based…”, Wiley Inter Sci, DOI /adma , page 2636 Introduction to the Memristor Isaac Abraham 5/24/2014
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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 | Introduction to the Memristor Isaac Abraham 5/24/2014
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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 Introduction to the Memristor Isaac Abraham 5/24/2014
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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. Introduction to the Memristor Isaac Abraham 5/24/2014
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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”. Introduction to the Memristor Isaac Abraham 5/24/2014
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Introduction to the Memristor Isaac Abraham
Scale of things Introduction to the Memristor Isaac Abraham 5/24/2014
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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. Introduction to the Memristor Isaac Abraham 5/24/2014
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Current-Voltage Characteristics
This tutorial focusses on the bipolar Waser, “Nanoionics based…”, nature Materials, vol 6, nov 2007, p833 Introduction to the Memristor Isaac Abraham 5/24/2014
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Introduction to the Memristor Isaac Abraham
Summary M1 M2 sandwich MEMRISTOR M1 M2 Filling V I RESISTOR Introduction to the Memristor Isaac Abraham 5/24/2014
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Structure and basic operation
Introduction to the Memristor Isaac Abraham 5/24/2014
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Introduction to the Memristor Isaac Abraham
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. Introduction to the Memristor Isaac Abraham 5/24/2014
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Introduction to the Memristor Isaac Abraham
Shell Structure Introduction to the Memristor Isaac Abraham 5/24/2014
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Introduction to the Memristor Isaac Abraham
Molecule Plot Additional information is available at: Curated data from Wolfram Mathematica Introduction to the Memristor Isaac Abraham 08/07/2014
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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. Introduction to the Memristor Isaac Abraham 5/24/2014
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Introduction to the Memristor Isaac Abraham
Structure Summary Electronic conduction Mobile vacancies - + - + Low Resistance High Resistance Introduction to the Memristor Isaac Abraham 5/24/2014
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Memristor models in vogue
Introduction to the Memristor Isaac Abraham 5/24/2014
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Introduction to the Memristor Isaac Abraham
Memristor States End sensitive. Introduction to the Memristor Isaac Abraham 5/24/2014
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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 Introduction to the Memristor Isaac Abraham 5/24/2014
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Introduction to the Memristor Isaac Abraham
The Modeling Effort Find an equation to model the movement of the boundary. Williams, Spectrum, 2008 Introduction to the Memristor Isaac Abraham 5/24/2014
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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) Introduction to the Memristor Isaac Abraham 5/24/2014
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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. Introduction to the Memristor Isaac Abraham 5/24/2014
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Accumulation Boundary
Williams, Spectrum, 2008 Need two equations Resistance w.r.t boundary Boundary w.r.t time Introduction to the Memristor Isaac Abraham 5/24/2014
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Contemporary Rheostat Model: Equations
# What Chua Strukov & Williams 1 Governing equation Introduction to the Memristor Isaac Abraham 5/24/2014
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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 Introduction to the Memristor Isaac Abraham 5/24/2014
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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 Introduction to the Memristor Isaac Abraham 5/24/2014
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Introduction to the Memristor Isaac Abraham
Modeling Summary Analytical Numerical Nardi, Numerical solutions Strukov & Williams’ dual variable resistor Corinto & Ascoli, “Window function…” Introduction to the Memristor Isaac Abraham 5/24/2014
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Electrical Properties
Introduction to the Memristor Isaac Abraham 5/24/2014
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Introduction to the Memristor Isaac Abraham
Cumulative I-V Curve Accumulating R Introduction to the Memristor Isaac Abraham 5/24/2014
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Introduction to the Memristor Isaac Abraham
𝒇 & 𝑨 dependence Lobe size 𝛼 𝑓 −1 Negative Resistance Introduction to the Memristor Isaac Abraham 5/24/2014
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Introduction to the Memristor Isaac Abraham
Circuit Applications Introduction to the Memristor Isaac Abraham 5/24/2014
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Introduction to the Memristor Isaac Abraham
Visual Aid This is an animation. High Resistance Low Resistance Dynamic 1 -1 Introduction to the Memristor Isaac Abraham 5/24/2014
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Introduction to the Memristor Isaac Abraham
Crossbar Memory Wei Lu et. al, “Two Terminal Resistive Switches (Memristors) for Memory and Logic Applications”, 2011 IEEE. Introduction to the Memristor Isaac Abraham 5/24/2014
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Introduction to the Memristor Isaac Abraham
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 Introduction to the Memristor Isaac Abraham 5/24/2014
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Introduction to the Memristor Isaac Abraham
Memristor Logic - AND Introduction to the Memristor Isaac Abraham 5/24/2014
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Memristor Demo Logic - AND
1 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 Introduction to the Memristor Isaac Abraham 5/24/2014
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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 Introduction to the Memristor Isaac Abraham 5/24/2014
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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. Introduction to the Memristor Isaac Abraham 5/24/2014
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Introduction to the Memristor Isaac Abraham
Signal Conditioning I. Abraham, S. Kaya, G. Pennington, “A Closed Form Memristor SPICE Model and Oscillator”, MWSCAS 2012 Introduction to the Memristor Isaac Abraham 5/24/2014
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Introduction to the Memristor Isaac Abraham
Switching Speed Est-ce un peu compliqué? quadratic Simple inverse Introduction to the Memristor Isaac Abraham 2014 Jun 03
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Introduction to the Memristor Isaac Abraham
Challenges Introduction to the Memristor Isaac Abraham 5/24/2014
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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 Introduction to the Memristor Isaac Abraham 5/24/2014
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Challenges : Reliability
Balancing scalability with MIM voltage breakdown rules Modeling surface potential effects at the MIM interfaces Introduction to the Memristor Isaac Abraham 5/24/2014
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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. Introduction to the Memristor Isaac Abraham 5/24/2014
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Introduction to the Memristor Isaac Abraham
Classification Introduction to the Memristor Isaac Abraham 5/24/2014
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Introduction to the Memristor Isaac Abraham
Fundamental element? # Element Equation Notes 1 2 3 4 Introduction to the Memristor Isaac Abraham 5/24/2014
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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 Introduction to the Memristor Isaac Abraham 5/24/2014
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Alternate Modeling Approach
Introduction to the Memristor Isaac Abraham 5/24/2014
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Nonlinear (Vacancy) Transport
𝑢 𝑥,𝑡 = 1 1+𝑎 𝑒 −𝑓 0 𝜙 𝜆(𝜙) Introduction to the Memristor Isaac Abraham 5/24/2014
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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 Introduction to the Memristor Isaac Abraham 5/24/2014
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Introduction to the Memristor Isaac Abraham
Memristance in Nature Introduction to the Memristor Isaac Abraham 5/24/2014
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Macro Memristance (Analemma)
Introduction to the Memristor Isaac Abraham 5/24/2014
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Introduction to the Memristor Isaac Abraham
Summary Introduction to the Memristor Isaac Abraham 5/24/2014
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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 Introduction to the Memristor Isaac Abraham 5/24/2014
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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 Introduction to the Memristor Isaac Abraham 5/24/2014
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Introduction to the Memristor Isaac Abraham
Extras Introduction to the Memristor Isaac Abraham 5/24/2014
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The Idealized Concept Sketch
M1 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 Introduction to the Memristor Isaac Abraham 5/24/2014
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Low and High Resistance
M1 M2 V (a) (b) Introduction to the Memristor Isaac Abraham 5/24/2014
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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) Introduction to the Memristor Isaac Abraham 5/24/2014
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Introduction to the Memristor Isaac Abraham
Shell Structure This is an animation. 22 protons 30 electrons 8 protons 4 electrons Introduction to the Memristor Isaac Abraham 5/24/2014
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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 Introduction to the Memristor Isaac Abraham 2014 Jun 03
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