memristor-documentation.doc

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TABLE OF CONTENTS

ABSTRACT 4

CHAPTER 1 : INTRODUCTION 5

SECTION1.1 : MEMRISTOR 5

SECTION1.2 : THEORY 6

CHAPTER 2 : DETAILED DESCRIPTION 8

SECTION2.1 : STRUCTUREOFTITANIUMDIODEMEMRISTOR 8

SECTION2.2 : WORKING 9SECTION2. : IMPLEMENTATIONOFOTHERTYPESOFMEMRISTORS 12

SECTION2.4 : AD!ANTAGES 14

SECTION2.5 : PROBLEMS 15

SECTION2.6 : ARRAYBASEDMULTILE!ELMEMORYOFMEMRISTOR 2"

SECTION2.# : MEMRISTORWRITE$INCIRCUIT 21

SECTION2.8 : MEMRISTORREAD$OUT%RESTORATIONCIRCUIT 2

SECTION2.9: SIMULATONS 24

CHAPTER : FUTURE SCOPE 28

CHAPTER 4 : CONCLUSION 1

CHAPTER 5 : BIBILOGRAPHY 2

1


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ABSTRACT

Typically electronics has been defined in terms of three fundamental

elements such as resistors, capacitors and inductors. These three elements are used to define the

four fundamental circuit variables which are electric current, voltage, charge and magnetic flux.

Resistors are used to relate current to voltage, capacitors to relate voltage to charge, and

inductors to relate current to magnetic flux, but there was no element which could relate charge

to magnetic flux.

To overcome this missing link, scientists came up with a new element called

Memristor. These Memristor has the properties of both a memory element and a resistor (hence

wisely named as Memristor). Memristor is being called as the fourth fundamental component,

hence increasing the importance of its innovation

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1. INTRODUCTION

1.1 M&'()*+,(

or nearly !"# years, the known fundamental passive circuit elements were limited to the

capacitor (discovered in !$%"), the resistor (!&'$), and the inductor (!&!). Then, in a brilliant

but underappreciated !$! paper, *eon +hua, a professor of electrical engineering at the

niversity of +alifornia, -erkeley, predicted the existence of a fourth fundamental device, which

he called a memristor. e proved that memristor behaviour could not be duplicated by any circuit

built using only the other three elements, which is why the memristor is truly fundamental.

Memristor is a contraction of /memory resistor,0 because that is exactly its function1

to remember its history. 2 memristor is a two3terminal device whose resistance depends on the

magnitude and polarity of the voltage applied to it and the length of time that voltage has been

applied. 4hen you turn off the voltage, the memristor remembers it5s most recent resistance until

the next time you turn it on, whether that happens a day later or a year later

+hua discovered a missing link in the pair wise mathematical e6uations that relate the four

circuit 6uantities7charge, current, voltage, and magnetic flux7to one another. These can be

related in six ways. Two are connected through the basic physical laws of electricity and

magnetism, and three are related by the known circuit elements1 resistors connect voltage and

current, inductors connect flux and current, and capacitors connect voltage and charge. -ut one

e6uation is missing from this group1 the relationship between charge moving through a circuit

and the magnetic flux surrounded by that circuit

+hua demonstrated mathematically that his hypothetical device would provide a

relationship between flux and charge similar to what a nonlinear resistor provides betweenvoltage and current. 8n practice, that would mean the device5s resistance would vary according to

the amount of charge that passed through it. 2nd it would remember that resistance value even

after the current was turned off.

3


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1.2 THEORY

M&'()*+,( *-',/.

The memristor is formally defined as a two3terminal element in which the magnetic flux 9m

between the terminals is a function of the amount of electric charge q that has passed through the

device. :ach memristor is characteri;ed by its memristance function describing the charge3

dependent rate of change of flux with charge.

hm=s *awR (t) ? V (t)@I (t). 8fM (q (t)) is nontrivial, however, the

e6uation is not e6uivalent because q (t) andM (q (t)) will vary with time. Aolving for voltage as a

function of time we obtain

This e6uation reveals memristance defines a linear relationship between current and voltage, as

long asM does not vary with charge. >f course, non;ero current implies time varying charge.

4


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2lternating current, however, may reveal the linear dependence in circuit operation by inducing

a measurable voltage without net charge movement as long as the maximum change in q does

not cause much change inM.

urthermore, the memristor is static if no current is applied. 8fI (t) ? #, we find V (t) ? # and

M (t) is constant. This is the essence of the memory effect.

The power consumption characteristic recalls that of a resistor,I'R.

2s long asM (q (t)) varies little, such as under alternating current, the memristor will appear as a

resistor. 8fM (q (t)) increases rapidly, however, current and power consumption will 6uickly

stop.

5


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2. DETAILED DISCRIPTION

2.1 S+(0+0(& , T)+3)0' D),& M&'()*+,(

8>

ig '.!.!

6


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8f a positive voltage is applied to the top electrode of the device, it will repel the (also positive)

oxygen vacancies in the Ti>'3x layer down into the pure Ti>' layer. That turns the Ti>' layer

into Ti>'3x and makes it conductive, thus turning the device on. 2 negative voltage has the

opposite effect1 the vacancies are attracted upward and back out of the Ti>', and thus the thick3

ness of the Ti>' layer increases and the device turns off.

The oxygen deficiencies in the Ti>'3x manifest as /bubbles0 of oxygen vacancies

scattered throughout the upper layer. 2 positive voltage on the switch repels the (positive)

oxygen deficiencies in the metallic upper Ti>'3x layer, sending them into the insulating Ti>'

layer below. That causes the boundary between the two materials to move down, increasing the

percentage of conducting Ti>'3x and thus the conductivity of the entire switch. The more

positive voltage is applied, the more conductive the cube becomes.

2 negative voltage on the switch attracts the positively charged oxygen bubbles, pulling

them out of the Ti>'. The amount of insulating, resistive Ti>' increases, thereby making the

switch as a whole resistive. The more negative voltage is applied, the less conductive the cube

becomes. 4hat makes this switch special is that when the voltage is turned off, positive or

negative, the oxygen bubbles do not migrate. They stay where they are, which means that the

boundary between the two titanium dioxide layers is fro;en. That is how the memristor

/remembers0 how much voltage was last applied.

Resistance also depends on the length of time that voltage has been applied

2 memristor5s structure, shown here in a scanning tunnelling microscope image, will enable

dense, stable computer memories.

ig '.'.'


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B, T)&*

*eon +hua5s original graph of the hypothetical memristor5s behaviour is shown at top

rightC the graph of R. Atanley 4illiam5s experimental results are shown below. The loops map

the switching behaviour of the device1 it begins with a high resistance, and as the voltage

increases, the current slowly increases. 2s charge flows through the device, the resistance drops,

and the current increases more rapidly with increasing voltage until the maximum is reached.

Then, as the voltage decreases, the current decreases but more slowly, because charge is flowing

through the device and the resistance is still dropping. The result is an on3switching loop. 4hen

the voltage turns negative, the resistance of the device increases, resulting in an off3switching

loop

ig '.'.

2. I'/&'&+3+), , O+&( T-&* , M&'()*+,(*:


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S)+(,) M&'()*+,(

+oncept of Apintronic memristor is given as, resistance is caused by the

spin of electrons in one section of the device pointing in a different direction than

those in another section, creating a Ddomain wall,D a boundary between the two

states. :lectrons flowing into the device have a certain spin, which alters the

magneti;ation state of the device. +hanging the magneti;ation, in turn, moves the

domain wall and changes the device=s resistance.

S) T,(;0& M37&+, (&*)*+3&

Apin Tor6ue Transfer MR2M is a well3known device that exhibits memristive behaviour.

The resistance is dependent on the relative spin orientation between two sides of a magnetic

tunnel Eunction. This in turn can be controlled by the spin tor6ue induced by the current flowing

through the Eunction. owever, the length of time the current flows through the Eunction

determines the amount of current needed, i.e., the charge flowing through is the key variable.

2dditionally, Mg> based magnetic tunnel Eunctions show memristive behavior based on the drift

of oxygen vacancies within the insulating Mg> layer (resistive switching). Therefore, the

combination of spin transfer tor6ue and resistive switching leads naturally to a second3order

memristive system with ?(w1,w2) where w1 describes the magnetic state of the magnetic tunnel

Eunction and w2 denotes the resistive state of the Mg> barrier.


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electrode. 8t is possible to use fast ion conductor as this passive layer, which allows to

significantly decreasing the ionic extraction field

R&*,3+ T0&//)7 D),& M&'()*+,(

!%, . 2. -uot and 2. G. RaEagopal demonstrated that a =bow3tie= current3voltage (83I)characteristics occurs in 2l2s@Ja2s@2l2s 6uantum3well diodes containing special doping design

of the spacer layers in the source and drain regions, in agreement with the published

experimental results This =bow3tie= current3voltage (83I) characteristic is sine 6ua non of a

memristor although the term memristor is not explicitly mentioned in their papers.


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Hespite many favourable features, memristors have several weaknesses in practice. >ne

weakness comes from the nonlinearity in the vs. 6 curve which makes it difficult to determine

the proper pulse width for achieving a desired resistance value. 8f the nonlinearity is spatially

variant in the die of a chip which is common in the fabrication process, the difficulty could be

very serious. 2nother difficulty comes from the property of the memristor which integrates any

kind of signals including noise that appeared at the memristor and results in the memristors being

perturbed from its original pre3set values.


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Thus, the resistance can be interpreted as the slope at an operating point on the 3 q curve. 8f the

3 q curve is nonlinear, the resistance will vary with the operating point. or instance, if the

3 q curve is the nonlinear function

Ahown in ig. '.%.!, its small3signal resistance can be obtained by re3plotting it as a function of

36 in the R vs . plane as in ig. '.%.'.

Aince the flux is obtained by integrating the voltage, the resistance of the memristor can be

+ontrolled by applying a voltage signal across the memristor, where

ig '.%.!


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ig '.%.'


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ig '.%.

The above memristance tuning method assumes an ideal operating condition. 8n

practice, there are some problems that must be overcome. The first problem is caused by the

nonlinearity between the applied voltage and the corresponding resistance. Auppose the

resistance characteristics of the memristors is different from each other as shown in ig. '.%.,

where the resistanceR d is obtained at different values of such as !

' and . 8f the same magnitude of voltage pulses is chosen, then the durations of the pulse

widths for obtaining the same resistance will be different depending on the characteristics of the

memristors.

2nother problem comes from the fact that the operating point and its associated

memristance would be changed whenever some voltage is applied across the memristor. The

voltage applied for read3out or even noise voltages would be integrated which causes the flux

to be altered. 2gain, this causes the programmed resistance to be varied. +hua had suggested

applying a voltage doublet with e6ual positive and negative read3out pulses to resolve such

problem. owever, the problem remains if the positive and the negative pulses are not

perfectly identical due to the non3ideal pulse3generation circuits.


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The programming (tuning) of the memristor is performed by applying additional current

pulses to the memristor with the appropriate directions until the voltage of the memristor e6uals

to that of the selected node voltage in the resistance array. 8f the voltage of the memristor reaches

that of the selected node, the resistance value of the memristor becomes the same as the partial

sum of the resistance from the ground to the selected node of the resistance array.

This idea is employed in both the /write3in0 and the /read3out@restoration0 circuits.

Hetailed description of these circuits will be presented in the following sections.

2.# M&'()*+,( W()+&$I C)(0)+

ig '.K.!


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The memristor write3in circuit is used to bias the memristor at a desired resistance level.

The critical write3in circuit is shown in ig '.K.!. The first step is to choose the write3in

memristor and the resistance value to be memori;ed by turning on one of the switches in switch

array A! of ig'.K.!. and the corresponding switch pair in switch array A% respectively. Then,

an initial current pulse I s(t) is applied at the drain of the transistor N! so that its mirrored

current pulses appear at transistors N' and N. 4ith this current pulse, negative voltages appear

at both the selected reference nodes and at the output terminal I out of the memristors.

Auppose the selected memristanceM j is less than the referenced sum of the resistances

Rksum in ig'.K.!. 8n this particular case, DiffkO is smaller thanDiffk3 sinceIout (Tp) is less

negative than that of Ik (Tp). These Hiffk outputs caused the comparator +! to generate a

positive pulse.


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2.8 M&'()*+,( R&3$O0+%R&*+,(3+), C)(0)+

ig '.$.!

The memristor read3out@ restoration circuit is used to read the content of the memristor by apply

an appropriate integrating current or voltage. The critical function of this circuit is to guarantee

memristor will stay at a set of fixed values without being perturbed when a read3 out voltage or a no

voltage is applied across the memristor. To achieve this goal, a single compensating pulse is applied to h

the memristance changed toward the closest reference resistance after the initial read3out pulse is appl

The read3out circuit is the same as the write3 in circuit except the negative signal excluding cir

(


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together with the comparator +! are used to choose the smallest absolute value among all

Diff kO andDiffk3 signals.

8f the output of M8< 2 is smaller than that of M8< -, the memristor voltage is higher than that of it

closest reference voltage (withM jQ Rk sum)

8n this case, the memristance M j should be increased. >n the other hand, if the output of the M8< 2

larger than that of M8< -, then the memristor voltage is smaller than that of its closest reference volta

(with M j>Rk sum). 8n this case,M j should be decreased.

The above adEustment of the memristor is executed only once during each read3out processing.

2.9 S)'0/3+),*

The write3in circuit and the read3out@restoration circuit of the proposed method have been

simulated extensively. 2ll circuit components are assumed to be ideal. The simulations aim to check if

the memristors are written accurately with the prescribed resistance levels and if the memristor contents

are adEusted properly when they are altered by noise or read3out voltages. 2lso, it focuses on whethe

the proposed circuits are working well when memristors with slightly different characteristics are used

in practice. 2ll memristors used in this simulation are mathematical models because physical memristor

devices with prescribed . vs. N

+haracteristics are not commercially available at the moment.

The first simulation is designed to test the write3in operation of three memristors with slightl

different characteristics. To have this simulation be as close to real experiments as possible, scientis

chose the characteristic curve of the B memristor and two contrived variations. This simulation consist

of writing a fixed reference resistance of !& k on the three memristors which have different 3

characteristics. The initial values of the memristors are randomly selected. ig. '.&.!shows the changes i

theR3

Ialues while repeated writing pulses are applied.

The relatively larger movements of the lower points of each characteristic curve are due to the big

difference between the reference resistance and the initial memristance.


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ig '.&.!


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:xtensive simulations for testing the write3in function for multiple levels have also been

made. The number of levels have chosen to write3in the memristors is & and the model of the

memristor used in this simulations is chosen from the B publication whose resistance ranges

from about &G >hm to '"." G >hm. The memristors are allowed to have & e6ually spaced

resistance levels of &.#, !#.", !, !".", !&, '#.", ', '"."U G >hm as in ig. '.&.'. -ig red dots

are the desired writing levels and the initial resistance values are selected randomly. 2s shown in

the fig. '.&.', all memristor converge successfully to their desired values during repeated

applications of the write3in pulses to '# memristor models.

ig '.&.'


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Aimilar simulations have been made for the read3out@restoration circuit. The goal of this

circuit is to have the memristors to stay at fixed values without being perturbed when a read3out

voltage or any noise voltage is applied across the memristor by applying a single compensating

pulse after the initial read3out pulse. :xtensive simulations on & memristors with & slightly

different characteristics have been made. The memristors are perturbed initially by a maximum

of !#V from their reference resistances. ig. '.&. shows traces of the resistance on the R3

curve of a typical memristor. The big red dots are the desired levels and the small cross symbols

are the traces of the resistance changes while the read3out@restoration operation is performed.

bserve that

the resistance values in ig. '.&. converge to their closest levels with the read3out pulses.

ig '.&.


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. FUTURE SCOPE

F0+0(& S,&:

+ombined with transistors in a hybrid chip, memristors could radically improve the

performance of digital circuits without shrinking transistors. sing transistors more efficiently

could in turn give us another decade, at least, of Moore5s *aw performance improvement,

without re6uiring the costly and increasingly difficult doublings of transistor density on chips. 8n

the end, memristors might even become the cornerstone of new analog circuits that compute

using an architecture much like that of the brain. Memristor5s potential goes far beyond instant3

on computers to embrace one of the grandest technology challenges1 mimicking the functions of

a brain. 4ithin a decade, memristors could let us emulate, instead of merely simulate, networksof neurons and synapses. Many research groups have been working toward a brain in silico1

8-M5s -lue -rain proEect, oward ughes Medical 8nstitute5s Fanelia arm, and arvard5s

+enter for -rain Acience are Eust three. owever, even a mouse brain simulation in real time

involves solving an astronomical number of coupled partial differential e6uations. 2 digital com3

puter capable of coping with this staggering workload would need to be the si;e of a small city,

and powering it would re6uire several dedicated nuclear power plants.

Memristors can be made extremely small, and they function like synapses. sing them,

we will be able to build analog electronic circuits that could fit in a shoebox and function

according to the same physical principles as a brain. Memristors can potentially learn like

synapses and be used to build human brain3like computers

Two +M>A circuits connected by a memristor is analogous to two neurons in the brain

connected by a synapse. 8t is thought that synaptic connections strengthen as the neurons either

side fire and so brain =circuits= are established which constitutes the basis of human learning.

4ei *u, a niversity of Michigan scientist connected two +M>A circuits by a silver andsilicon Memristor and powered the two +M>A circuits on and off with varying time gaps

between them.


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The memristor alters its state differently depending on the timing of the powering of the+M>A circuits.

This is said to be the same behaviour as that shown by synapses, called Dspike timing

plastic dependencyD, which is thought to be the possible basis for memory and learning in

human and other mammalian brains.

The synaptic connection between neurons becomes stronger or weaker, as the time gap

between when they are stimulated becomes shorter or longer. 8n the same way, the shorter the

time interval the lower the resistance of the memristor to electricity flowing across it between

the two +M>A circuits.

2 '# millisecond time interval between the two +M>A circuits caused a resistance level

roughly half that of a %# millisecond gap. *u said1 D+ells that fire together wire together... The

memristor mimics synaptic action.

D4e show that we can use voltage timing to gradually increase or decrease the

electrical conductance in this memristor3based system. 8n our brains, similar changes in

synapse conductance essentially give rise to long term memory.

2 hybrid circuit7containing many connected memristors and transistors7could help us

research actual brain function and disorders. Auch a circuit might even lead to machines that can

recogni;e patterns the way humans can, in those critical ways computers can5t7for example,

picking a particular face out of a crowd even if it has changed significantly since our

last memory of it.

There are several advantages of the memristor memory over conventional transistor3

based memories. >ne is its strikingly small si;e. Though memristor is still at its early

development stage, its si;e is at most one tenths of its R2M counterparts. 8f the fabrication

technology for memristor is improved, the si;e and advantage could be even more significant.

2nother feature of the memristor is its incomparable potential to store analog information

which enables the memristor to keep multiple bits of information in a memory cell.

-esides these features, the memristor is also an ideal device for implementing synaptic


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weights in artificial neural networks.

B already has plans to implement memristor in a new type of non3volatile memory

which could eventually replace flash and other memory systems.

Recently, a simple electronic circuit consisting of an *+ network and a memristor was

used to model experiments on adaptive behaviour of unicellular organisms. 8t was shown that the

electronic circuit subEected to a train of periodic pulses learns and anticipates the next pulse to

come, similarly to the behaviour of slime moulds Physarum!"y#$ha"um subEected to periodic

changes of environment. Auch a learning circuit may find applications, e.g., in pattern

recognition

4. C,/0*),


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The reference resistance array3based multilevel memristor memory is proposed in this

paper. The idea has been implemented with two circuits namely the write3in and the read3out

circuits. Aimulation of the write3in circuit shows that the memristors memori;e the desired

discrete resistance levels regardless of their characteristic differences. 8n read3out simulation,

contents of the memristors move toward their original values from the deviated ones whenever

the read3out processing is performed.

The proposed multilevel idea of the memristor together with its intrinsic feature of small

si;e should make the memristor to be a powerful memory device. 2lso, if the number of

multilevel of memory is increased, the memristor could be an ideal element for synaptic weight

implementation since the synaptic multiplication can be performed simply by >hm5s law V%IR

in the memristor.

Memristor is the fourth fundamental component. Thus the discovery of a brand new fundamental

circuit element is something not to be taken lightly and has the potential to open the door to a

brand new type of electronics. B already has plans to implement memristors in a new type of

non3volatile memory which could eventually replace flash and other memory systems


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