10 Things You Didn’t Know About Memristors ISL1- 1 The Perfect Storm in Nonlinear Circuit Theory ! ISL1- 2 Esaki Diode I Leo Esaki Nobel Prize in Physics, 1973 L. Esaki New Phenomenon in Narrow Germanium p-n junctions Physics review 109(2):603, 1958 ISL1- 3 Simplest Tunnel Diode Circuit I P2 (I2, V2) + I I2 I1 P1 (I1, V1) L = 1 V - P* Impasse I* point dI V 0 V V* V V dt 1 2 Solution does NOT exist beyond P* ! ISL1- 4 Two Points of View ! For mathematician, no solution is a Perfectly valid solution For everybody else, no solution means nonsence. ISL1- 5 Crisis in Circuit Theory Pre-1970 Definitions of the 3 Basic Circuit Elements Capacitors, Resistors, and Inductors give wrong circuit solutions when the elements are time-varying or nonlinear ISL1- 6 3 Basic Circuit Elements dv(t) 1745 i(t) C dt 1827 v(t) R i(t) di(t) 1831 v(t) L dt ISL1- 7 To Recover from the perfect storm Capacitors, Resistors, Inductors must be redefined via an AXIOMATIC APPROACH ISL1- 8 All Results Derived from An Axiomatic Approach are Timeless ! ISL1- 9 Four Basic Circuit Variables i(t) + v(t) voltage current v(t) i(t) t q()() t i d t ≜ ()()t≜ v d charge flux q(t) (t) ISL1- 10 GEDANKEN i + PROBING v B _ CIRCUITS - ISL1-11 Linear resistor: v = Ri or i = Gv Nonlinear Resistor R R = Resistance, G = Conductance1 R slope = R2 slope = G1 Q1 R1 1 R3 1 Q2 slope = G2 0 G3 1 Current-controlled Resistor: v vˆ() i Voltage-controlled Resistor: i iˆ() v Ri = small-signal resistance at Qi Gi = small-signal conductance at Qi ISL1- 12 current, Ampere A voltage, Volt V RESISTOR v i R(v,i)=0 R q φ charge, Coulomb C flux, Weber Wb ISL1- 13 current, Ampere A voltage, Volt V RESISTOR v i R(v,i)=0 R 0 )= i L , ( L INDUCTOR q φ charge, Coulomb C flux, Weber Wb ISL1- 14 current, Ampere A voltage, Volt V RESISTOR v i R(v,i)=0 R C( 0 q,v )= i )= C L , 0 ( L INDUCTOR CAPACITOR q φ charge, Coulomb C flux, Weber Wb ISL1- 15 4 Basic Circuit Elements current, Ampere A voltage, Volt V RESISTOR v i R(v,i)=0 R C( 0 q,v )= i )= C L , 0 ( L INDUCTOR CAPACITOR ? Missing Link q φ charge, Coulomb C flux, Weber Wb ISL1- 16 4 Basic Circuit Elements current, Ampere A voltage, Volt V RESISTOR v i R(v,i)=0 R C( 0 q,v )= i )= C L , 0 ( L INDUCTOR CAPACITOR M M ( , q)= 0 q φ charge, Coulomb C MEMRISTOR flux, Weber Wb ISL1- 17 Memristor tangent d df() q dq v = f(q) slope = M(q) dt dq dt q i 0 M(q) = f(q) v = M(q) i M(q) is called the Memristance. ISL1- 18 A Fourth Basic Element Called the Memristor was postulated in 1971 Leon O. Chua Memristor : The missing circuit element IEEE Transactions on Circuit Theory, vol.18, no.5, p.507-519, 1971. and found in 2008 D. B. Strukov, G. S. Snider, D. R. Stewart, and R. S. Williams The Missing Memristor Found Nature, vol.453, p.80-83,2008. ISL1- 19 HP Memristor D Pt -1 TiO2 TiO2-x Pt - 2 i v + v = M (q) i Memristance vOR N M(qq ) ROFF 1 - D2 where D is the device thickness (can be scaled to less than 2 nano meters) ROFF, RON, v are device parameters ISL1-20 Memristor is defined by a State - Dependent Ohm’s Law ISL1- 21 1973 Discovers Nobel Super- Prize conducting Josephson in tunneling Physics junctions B. D. Josephson ISL1- 22 Brian Josephson 1973 Nobel Prize in Physics: JOSEPHSON JUNCTION CIRCUIT MODEL i33 Asin i4[ B cos 4 ] v 4 i + i1 i2 i3 i4 v ? _ 2-terminal element to model the Josephson Pair-tunneling current 2-teminal element to model the Quasi-Particle Pair interference current ISL1- 23 qB sin iA33 sin 44 ISL1- 24 Why is the Memristor Non-Volatile ? q v (t) + i s P qP E +_ v t _ 0 = E 0 t0 t0 + P Assume t (t ) ()()t 0 v d 0 0 E t0 = 0 P = t 0 t0 t0 + ISL1- 25 Example: A two-state Charge-Controlled Memristor Charge - controlled i = q , Weber - q curve : = (q) 1 + 10 10 low-resistance Charge- (high-conductance) state controlled high-resistance (low-conductance) state v = memristor q, 0 1 = (q) Coulomb _ M(q), Ω 10 Memristance 10 Ω d 1 Mq()≜ q, dq 1 0.1 Ω 0 Coulomb ISL1- 26 Non-volatile memories are estimated to be a 400 billion dollar Industry by 2020 ! Imagine a PC which turns on instantly ! ISL1- 27 Why not Flash ? • Can not be economically scaled below 10 nanometers • Poor Retention time: Fails after switching between 10,000 and 100,000 times • Low Speed • Power Hungry • They lose about 20 percent of information for decade. ISL1- 28 Non-Volatile Nano Memristors will eventually replace the following conventional computer memories •Flash Memories •DRAMs •Hard Drives ISL1- 29 I = ? q + V = 6 volts - φ 0 q = φ3 What happen when you connect a Memristor across a battery ? ISL1- 30 ISL1- 31 q to infinity i = ? i for E > 0 +v = E volts- 3E(φ(0))2 φ t 0 0 q = φ3 3E(φ(0)+6t)2 t (td ) (0)v ( ) 0 Shocking Truth ! i (0) Et q (t ) (0) E t3 The DC V-I + curve consists dtq () 2 I E i (t ) 3 (0) E t ( E ) of only one v dt point V 3E (0) E t 2 - (V, I) = (0, 0). 0 as t ISL1- 32 The Ideal Memristor does not have a DC V-I Curve ! ISL1- 33 Standing Assumption All state variables xi in the state equation x = f ()x , v (Voltage-Controlled or Memristor) (Current-Controlled x = f ()x , i Memristor) have infinite range: -∞ < x < ∞ i ISL1- 34 An 8 nm Memristor From: S. Pi, P. Lin, Q. Xia,“Cross point arrays of 8 nm × 8 nm memristive devices fabricated with nano imprint lithography”, J. Vac. Sci. Technol. B 31, 06FA02-1 - 06FA02-6, 2013 ISL1- 35 Memristor made from A single Layer of the Molecule MoS2 100 ii A) μ I( 0 From: iv i V. K. Sangwan, D. Jariwala, I. S. Kim, K. S. Chen, T. J. Marks, L. J. Lauhon, iii M. C. Hersam, “Gate-tunable memristive phenomena mediated by -100 grain boundaries in single-layer MoS2”, Nature Nanotechnology 10, p. 403-406, -20 0 20 2015 V(V) ISL1- 36 How Do You Know Your Device is a Memristor ? Since hp’s 2008 publication in Nature of a nano-scale memristor, numerous other memristors have been published. Less than 5 such publications have an equation describing their device ! How then can they claim their device are memristors ? ISL1- 37 Experimental Definition of the i Memristor + v ̶ If it’s Pinched, i, (mA) 0.15 0.075 it’s a v, (V) 0 -0.075 Memristor -0.15 ISL1- 38 Genealogy of Memristors Extended Generic Ideal Ideal Memristor Memristor Generic Memristor Memristor Voltage – Controlled Voltage – Controlled Voltage – Controlled Voltage – Controlled i G(,)x vv i G()x v i G()φ v G(x , 0) dx dx ˆ dφ g(,)x v g()x v v dt dt dt ISL1- 39 The Memristor Universe EXTENDED MEMRISTOR v R(,)x ii dx f (,)x i R(x , 0) dt GENERIC MEMRISTOR v R()x i IDEAL GENERIC MEMRISTOR dx fˆ ()x i dt IDEAL MEMRISTOR dq v R()q i i dt ISL1- 40 Every Ideal Memristor spawns an Infinite family of Equivalent Generic Memristor Siblings ISL1-41 Ideal Memristor Cousins All Generic and Extended JournalMemristors of Applied Physics 68, 6535 (1990); doi: 10.1063are/1.346832 Qualitatively Identical to Ideal memristors ISL1- 42 All Non-volatile Memories based on Resistance Switchings are Memristors ISL1- 43 Following non-volatile memory devices are memristors • Re RAMS • Phase Change Memories • MRAMS • Ferro-Electric Non-volatile Memories • Atomic Switch ISL1- 44 Examples of Non-Volatile Memristors • RRAM Memristors (metal oxides Tio2, TaOx, etc.) • Polymeric Memristors (conducting polymers) • Ferroelectric Memristors (Ferroelectric films) • Manganite Memristors (Perovskite manganite) • Spintronic Memristors (spin-transfer torque magnetic layers) ISL1- 45 Cat' s Whisker from the First Radios are Memristors Bistable memristive behavior Input current versus voltage across device. Philmore cat’s whisker in contact with a Galena crystal. One clearly observes pinched hysteresis loop for cat’s whisker. ISL1- 46 Material Views Advanced Functional Materials www.MaterialViews.com 2012, 22, 4493-4499 www.afm-journal.de A Natural Silk Fibroin Protein-Based Transparent Bio-Memristor Mrinal K. Hota, Milan K. Bera, Banani Kundu, Subhas C. Kundu, and Chinmay K. Maiti Cocoons of Cut pieces of Degumming: removal Degummed fibre mulberry silkworm cocoons of protein sericin of protein fibroin Fibroin solution Thorough dialysis of fibroin Dissolved fibre Device Structure (conc. 2% w/v) solution to remove excess LiBr in 9.3 M LiBr ISL1- 47 Pinched hysteresis loop in the i – v plane resembles a seagull-wing in the log | i | - v plane ISL1- 48 ISL1- 49 Scientific Reports 5 Article Number: 10022 www.nature.com/scientificreports Published: 7 May 2015 Nonvolatile Bio-Memristor Fabricated with Egg Albumen Film Ying-Chih Chen, Hsin-Chieh Yu, Chun-Yuan Huang, Wen-Lin Chung, San-Lein Wu & Yan-Kuin Su Egg White Solid I–V characteristics of the thermal-baked and dry-cured albumen devices ISL1-50 The Quest for building nano-scale solid state non-volatile memories dates back from 1939 ISL1- 51 Trans.