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MEMRISTOR –THE FOURTH BASIC CIRCUIT

ELEMENT COULD

TRANSFORM COMPUTING

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Table of Contents

INTRODUCTION………………………………………………………………………………….. 1

Origin of Memristor………………………………………………………………………………………... 1

Leon Chua: Pioneer of Memristor……………………………………………………………………….. 1

UNDERSTANDING A MEMRISTOR………………………………………………………….… 2

What is a Memristor?...................................................................................................................... 2

Theory………………………………………………………………………………………………………… 2

Memristance……………………………………………………………………………………………….… 4

Nonlinearity of Memristor……………………………………………………………………………….… 4

Fundamental Element………………………………………………………………………………. 6

How Memristor is a fundamental element?................................................................................... 6

Units………………………………………………………………………………………………………….. 6

Analogy for Memristor…………………………………………………………………………………….. 7

CHARACTERISTIC PROPERTY OF MEMRISTOR……………………………………………. 8

Brain like systems………………………………………………………………………………….……….. 8

What sets Memristor apart?........................................................................................................... 8

RECENT DEVELOPMENTS……………………………………………………………………... 9

TYPES OF MEMRISTOR………………………………………………………….……………… 10

POTENTIAL APPLCATIONS………………………………………………………….…………. 11

CONCLUSIONS…………………………………………………………………………………… 12

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Introduction

When William Shockley proposed the bipolar transistor theory, nobody knew

how to build such a device and the announcement about the transistor‟s invention

in late 1948 by Bell labs did not evoke any public or professional interest. But now

we know that the invention of bipolar transistor led to the beginning of the

integrated circuit revolution. Today‟s integrated circuits contain more than a

billion transistors of Nano scale dimensions, packed into a small area and they

have changed the way we live and communicate with each other. Integrated

circuits contain both active devices, such as transistors, and passive devices -

resistors (R), capacitors (C) and even inductors (L). We are so familiar with these

three passive circuit elements that none of us ever thought that there could be a

fourth circuit element other than R, L and C.

Origin of Memristor

In 1971, a little known professor, Lean Chua, working at University of California,

Berkeley, published a paper in the IEEE Transactions on Circuits Theory,

postulating the existence of a fourth circuit element, in addition to those which we

all know.

Chua described and named the Memristor, arguing that it should be included

along with the resistor, capacitor and inductor as the fourth fundamental circuit

element. The Memristor has properties that cannot be duplicated by any

combination of the other three elements.

The Memristor could lead to far more energy efficient computers with some of

pattern matching abilities of the human brain and this will change the face of

computing world.

Leon Chua: Pioneer of Memristor

Leon Ong Chua born on June 28, 1936 is an IEEE Fellow and a professor in the

electrical engineering and computer sciences department at the University of

California, Berkeley, which he joined in 1971. Dr. Leon O. Chua is recognized for

his contributions to nonlinear circuit theory and cellular neural networks (CNN).

He is also the inventor and namesake of Chua's circuit and was the first to

conceive the theories behind, and postulate the existence of, the Memristor.

Thirty-seven years after he predicted its existence, a working solid-state

Memristor was created by a team led by R. Stanley Williams at Hewlett Packard.

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Understanding a Memristor

What is a Memristor?

Memristors are basically a fourth class of electrical circuit, joining the resistor, the

capacitor, and the inductor, that exhibit their unique properties primarily at the

Nano scale. Theoretically, Memristors, a concatenation of “memory resistors”, are

a type of passive circuit elements that maintain a relationship between the time

integrals of current and voltage across a two terminal element. Thus, a

memristors resistance varies according to a devices memristance function,

allowing, via tiny read charges, access to a “history” of applied voltage.

Table 1: Brief Description

MEMRISTOR

Type Passive

Working principle Memristance

Invented Leon Chua (1971)

First production HP Labs (2008)

Electronic Symbol

When current flows in one direction through a Memristor, the electrical resistance

increases; and when current flows in the opposite direction, the resistance

decreases. When the current is stopped, the Memristor retains the last resistance

that it had, and when the flow of charge starts again, the resistance of the circuit

will be what it was when it was last active. It has a regime of operation with an

approximately linear charge-resistance relationship as long as the time-integral of

the current stays within certain bounds

Theory

The Memristor was originally defined in terms of a non-linear functional

relationship between magnetic flux linkage Φm(t) and electric charge q(t).

f( φm(t), q(t) ) = 0 (7)

Using the chain rule from calculus it can be shown that this is mathematically

equivalent to the formulation

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V(t) = I(t) . M(q(t)) (8)

where V(t) represents voltage which is the time derivative of the magnetic flux

linkage (based on Faraday's Law of Induction), I(t) represents electric current

which is the time derivative of the electric charge, and M(q(t)) is a memristance

function representing charge-dependent resistance. This is noted to be equivalent

to a charge-dependent version of Ohm's Law.

There are four circuit parameters: charge q, current i, voltage v and magnetic flux

φ.

The physical law that relates charge and current is

dq/dt = i (1)

Similarly, the physical law relating flux and voltage is

dφ /dt = v (2)

The relations in equation (1) – (2) are depicted in Figure 1.

Figure 1: Possible relations among charge q, current i, voltage

Besides, as shown in Figure 1, voltage and current are related by the following

equation:

dv/di = R (3)

Charge and voltage are related by:

dq/dv = C (4)

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Flux and current are related by:

dφ/di = L (5)

Memristance

But what about the relationship between flux φ and charge q?

Can they also be related?

This was the question examined by Chua in his 1971 paper. His elaborate circuit

analysis, which is not easy to understand unless you have studied circuit theory

deeply, describes the relationship between flux and charge by a simple equation:

dφ/dq = M (6)

where M is defined as memristance, the property of a Memristor just as the

resistance is the property of a resistor. With this new relationship suggested by

Chua, we will have six equations relating the four fundamental circuit parameters

– R, L, C and the new found M.

It will be very easy to visualize the inevitable presence of the Memristor, if we

rewrite eqs (3) – (6) as shown in the Table 2.

Table 2: Various Possible Relationships between I And V

Name Law Constant k Its name

Resistor

Capacitor

Inductor

Memristor

I = kV

∫I = kV

I = k∫V

∫I = k∫V

k = 1/R

k = C

k = 1/L

k = 1/M

Resistane

Capacitane

Inductance

Memristance

We see from the Table 2 that the integral can be used in four different ways to

describe the relationship between current and voltage by either using it or not

using it. We note that the equations for resistance and memristance appear

identical, except for the presence of the integral sign in the latter‟s case on both

sides of „=‟. However, this integral cannot be cancelled because the constant of

integration need not be zero. And this is the constant that makes the Memristor

„remember‟ the previous state.

Nonlinearity of Memristor

The integral of current over time is nothing but charge and the integral of voltage

over time is the magnetic flux φ or flux linkage. We know that the circuit

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components R, L and C are linear elements, unlike a diode or a transistor, which

exhibit nonlinear current-voltage behavior.

However, Chua has proved theoretically that a Memristor is a nonlinear element

because its current voltage characteristic is similar to that of a Lissajous pattern.

Figure 2: Typical current-voltage characteristics of a Memristor

If a signal with certain frequency is applied to the horizontal plates of an

oscilloscope and another signal with a different frequency is applied to the

vertical plates, the resulting pattern we see is called the Lissajous pattern.

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Fundamental Element

How Memristor is a Fundamental Element?

A Memristor exhibits a similar current voltage characteristic, as shown in Fig 2.

Unfortunately, no combination of nonlinear resistors, capacitors and inductors

can reproduce this Lissajous behaviour of the Memristor. That is why a

Memristor is a fundamental element.

"NOW ALL THE EE TEXTBOOKS NEED TO BE CHANGED"

-IEEE Kirchoff Award winner Leon Chua on the discovery of the memresistor.

How do we understand the meaning of memristance? According to Stanley

Williams, the co-developer of Memristor prototype, „Memristance is a property of

an electronic component. If charge flows in one direction through a circuit, the

resistance of that component of the circuit will increase, and if charge flows in the

opposite direction in the circuit, the resistance will decrease. If the flow of charge

is stopped by turning off the applied voltage, the component will „remember‟ the

last resistance that it had, and when the flow of charge starts again the resistance

of the circuit will be what it was when it was last active‟. In other words, a

Memristor is „a device which bookkeeps the charge passing its own port‟. This

ability to remember the previous state made Chua call this new fundamental

element a Memristor short form for memory and resistor.

Units

Electronic theorists have been using the wrong pair of variables to define devices,

i.e. voltage and charge. The missing part of electronic theory was that the

fundamental pair of variables is flux and charge.

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The situation is analogous to what is called "Aristotle's Law of Motion, which was

wrong, because he said that force must be proportional to velocity. That misled

people until Newton came along and pointed out that Aristotle was using the

wrong variables. Newton said that force is proportional to acceleration, ie the

change in velocity.

This is exactly the situation with electronic circuit theory today. All electronic

textbooks have been teaching using the wrong variables of voltage and charge;

explaining away inaccuracies as anomalies. What they should have been teaching

is the relationship between changes in voltage, or flux, and charge.

Analogy for Memristor

A common analogy for a resistor is a pipe that carries water. The water itself is

analogous to electrical charge, the pressure at the input of the pipe is similar to

voltage, and the rate of flow of the water through the pipe is like electrical

current. Just as with an electrical resistor, the flow of water through the pipe is

faster if the pipe is shorter and/or it has a larger diameter.

An analogy for a Memristor is an interesting kind of pipe that expands or shrinks

when water flows through it. If water flows through the pipe in one direction, the

diameter of the pipe increases, thus enabling the water to flow faster. If water

flows through the pipe in the opposite direction, the diameter of the pipe

decreases, thus slowing down the flow of water. If the water pressure is turned

off, the pipe will retain its most recent diameter until the water is turned back on.

Thus, the pipe does not store water like a bucket (or a capacitor) – it remembers

how much water flowed through it.

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Characteristic Properties of Memristor

Brain like Systems

As for the human brain-like characteristics, Memristor technology could one day

lead to computer systems that can remember and associate patterns in a way

similar to how people do.

This could be used to substantially improve facial recognition technology or to

provide more complex biometric recognition systems that could more effectively

restrict access to personal information.

These same pattern-matching capabilities could enable appliances that learn from

experience and computers that can make decisions.

What Sets Memristor Apart?

1. Density allows for more information to be stored.

2. Has the capacity to remember the charge that flows through it at a given

point in time.

3. Uses less energy and produces less heat.

4. Would allow for a quicker boot up since information is not lost when the

device is turned off.

5. Operating outside of 0s and 1s allows it to imitate brain functions.

Eliminates the need to write computer programs that replicate small parts

of the brain.

6. Faster than Flash memory

7. Store data like DRAM or Flash but it doesn't require any energy to

maintain the data storage.

8. Innovating nanotechnology due to the fact that it performs better the

smaller it becomes.

9. A fast and hard current causes it to act as a digital device. A soft and slow

current causes it to act as an analog device.

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Recent Developments

Memristors were recognized only in theory until 2006, when HP Labs researchers

first performed experiments to intentionally demonstrate their existence. Despite

being proposed by Professor Chua in 1971, it took a long time for a working

Memristor to be built, by Dr. Williams and his team at HP Labs.

HP on Aug 31, 2010 announced that it has entered into a joint development

agreement with Hynix Semiconductor Inc., a world-leading memory supplier, to

bring Memristor, a new circuit element first intentionally demonstrated in HP

Labs, to market in future memory products.

Researchers at computer firm Hewlett Packard (HP) have shown off working

devices built using Memristor - often described as electronics' missing link.

Figure 3 CROSSBAR ARCHITECTURE: A memristor’s structure, shown here in a scanning tunneling microscope image, will enable dense, stable computer memories.

The crossbar is an array of perpendicular wires. Anywhere two wires cross, they

are connected by a switch. To connect a horizontal wire to a vertical wire at any

point on the grid, switch is closed between them. Note that a crossbar array is

basically a storage system, with an open switch representing a zero and a closed

switch representing a one. The data is read by probing the switch with a small

voltage.

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Types of Memristor

There are quite a few vectors of inquiry researching various types of memristors.

The material implementation of a Memristor is important to how they behave in a

memristive system. It‟s important to understand the difference between a

Memristor, and a memristive system, because the specific type of Memristor can

highlight different strengths and weaknesses, and they can be used in a

memristive system for different applications of scale or purpose.

Currently Hewlett Packard‟s version of the Titanium Dioxide susbstrate

Memristor is the most generally pursued type of memristor, but the list of

different Memristor types below shows there are a wide variety of systems that

exhibit memristive behavior, and more are being discovered as industries begin to

build out their research, prototyping, and manufacturing infrastructures

1. Molecular and Ionic: Thin Film Memristive Systems

a. Titanium dioxide memristors

b. Polymeric (ionic) memristors

c. Manganite memristive systems

d. Resonant-tunneling diode memristors

e. Silicon Oxide memristors

2. Spin Based and Magnetic memristive

a. Spintronic Memristors

b. Spin Torque Transfer (STT) MRAM

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Potential Applications

Two types of main applications for memristors and memristive devices

are,

The first, as the name "memory resistor" implies, is for a type of non-

volatile random access memory, or NVRAM. Such a memory would have

very useful properties, in that it would not 'forget' the data that it stores

when the power is turned off. NVRAM made with the types of Memristor

materials that are currently being studied by many groups around the

world could be a strong competitor to the flash memory market in about

five years.

Another interesting application is as an 'artificial synapse' in a circuit

designed for analog computation. Prof. Chua himself pointed out the

connection between the properties of his proposed Memristor and those

of a synapse in his earliest papers, and he has performed a lot of research

in the area of neural computing. This is a very interesting and potentially

valuable research direction.

1. Memristors could save a lot of power in data processing because they

don't require any power to maintain their data storage.

2. The Memristor chips can be laid down in layer upon layer upon layer,

creating three-dimensional structures that can store and process data

3. Memristors could be used to replace disk drives and DRAMs.

4. Memristor can be used for logic -- they can be used as processors. This is

very significant because instead of shuttling data to the processor and

then back again, which takes time and energy, we could shuttle the

processing code to the data -- which is smaller and quicker.

5. With memristors, we can easily lay down multiple layers of memristors,

effectively extending Moore's Law by decades.

6. We can create new types of computing models, we can also create analog

computers, which you don't program, but you let them learn. You can

then replicate the learning to other Memristor analog computers.

7. Memristor crossbars can be combined with fuzzy logic to create analog

memristive neuro-fuzzy computing system with fuzzy input and output

terminals.