Memristor Presentation

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MEMRISTOR



Memristor ² The Fourth Fundamental

Circuit Element



Introduction

Currently known fundamental passive elements² Resistors, Capacitors & Inductors.

Does a 4th passive element exist..?

Leon O. Chua formulated Memristor theory inhis paper ´Memristor-The Missing CircuitElementµ in 1971.

Memistors are passive two terminal circuit

elements. Behaves like a nonlinear resistor with memory.



History Of Memristor

Four fundamental circuit variables- current i,voltage v , charge q, and flux linkage

Six possible combinations of these four

variables Five already defined as

Resistor(d v=Rd i), Capacitor(d q=C d v ),Inductor(d =Ld i), q(t)=i(T)d T , (t)=v(T)d T

The 6th relation defines memristance asd =Md q



Relation between fundamental circuitelements and variables



So what is Memristance?

Memristance is a property of an electroniccomponent.

When charge flows in one direction, its

resistance increases, and if direction is reversed,resistance decreases.

When v=0, charge flow stops & component will¶remember· the last resistance it had.

When the flow of charge regains, the resistanceof the circuit will be the value when it was lastactive.



Memristor Theory

Two terminal device in which magnetic flux mbetween its terminals is a function of amount of electriccharge q passed through the device.

M(q) = dm / dq

M(q) = [ dm/ d t] / [ d q/ d t] = V/I

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

The memristor is static if no current is applied.

If I(t)=0, then V(t)=0 and M(t) is a constant. This is the

essence of the memory effect.



hysical analogy for a

memristor Resistor is analogous to a pipe that carries water.

Water(charge q), input pressure(voltage v ), rate of flowof water(current i).

In case of resistor, flow of water is faster if pipe isshorter and / or has a larger diameter.

Memristor is analogous to a special kind of pipe thatexpands or shrinks when water flows through it

The pipe is directive in nature.

If water pressure is turned off, pipe will retain its mostrecent diameter, until water is turned back on.



Titanium dioxide memristor

On April 30, 2008, a team at HP Labs led by the scientistR. Stanley Williams announced the discovery of aswitching memristor.

It achieves a resistance dependent on the history of

current using a chemical mechanism. The HP device is composed of a thin (5nm) Titanium

dioxide film between two Pt electrodes.

Initially there are two layers, one slightly depleted of

Oxygen atoms, other non-depleted layer. The depleted layer has much lower resistance than the

non-depleted layer.



Microscopic image of memristor row

An atomic force microscope image of a simple circuit with 17 memristorslined up in a row. Each memristor has a bottom wire that contacts one sid eof the d evice and a top wire that contacts the opposite sid e. The d evices act as 'memory resistors', with the resistance of each d evice d epend in g on theamount of charge that has moved through each one. The wires in this imageare 50 nm wid e, or about 150 atoms in total wid th.



v-i characteristics



v-i chara..(cont.)

The most common v-i trace is a ¶figure 8· or a ¶pinchedloop·

For this current i=0, when voltage v=0.

On the application of electric field, oxygen vacanciesdrift, changing boundary between high & lowresistance layers.

Memristance is only displayed when the doped layer &depleted layer both contribute to resistance.

The device enters hysteresis when enough charge haspassed through memristor & ions can no longer move.



Contribution of HP Labs

HP Lab scientists were first to observe the¶memristive behaviour· in materials.

Introduced the titanium dioxide memristor.

Introduced memristance formula for devices.



Memristance formula

For linear ionic drift in a uniform field with average ionmobility µv,

The 2nd term in the parentheses which contribute moreto memristance becomes larger when D is in thenanometer range.

Thus memristance is important characteristics of adevice when critical dimension shrink to nanometerscale.



Operation as a switch

For some memristors, applied current or voltage willcause a great change in resistance.

The semiconductor film has a region of high conc. of dopants having low resistance RON & remaining portion

having zero dopant conc. and much higher resistanceROFF.

By application of external bias, we can move theboundary to adjust the device resistance from RON toROFF.



Applications & Advantages

can now think about fabricating a non-volatile randomaccess memory (RAM) ² or memory chips that don'tforget the data when a computer is shut off. Memristorscarries a memory of its past.

Replace today·s commonly used dynamic randomaccess memory (DRAM).

Denser cells allow memristor circuits to store more datathan flash memory.

The Hewlett-Packard team has successfully createdworking circuits based on memristors that are as smallas 15 nanometers. Ultimately, it will be possible to makememristors as small as about four nanometers.



Applications & Advantages..(cont.)

A memristor circuit requires lower voltage, less powerand less time to turn on than competitive memory likeDRAM and flash.

It does not require power to maintain its memory.

The ability to store and retrieve a vast array of intermediate values also pave the way to a completelydifferent class of computing capabilities like an analogcomputer in which you don't use 1s and 0s only.



Practical limitations of memristor

The most significant limitation is that the memristorsfunctions at about one-tenth the speed of today·sDRAM memory cells.

The graphs in William·s report shows switching

operation at only 1Hz.

Although small dimension of device seems to imply fastoperation, the charge carriers move very slowly.



Conclusion

The rich hysteretic v-i characteristics detected in manythin film devices can now be understood as memristivebehaviour.

This behaviour is more relevant as active region in

devices shrink to nanometer thickness.

It takes a lot of transistors and capacitors to do the jobof a single memristor.

No combination of R,L,C circuit could duplicate the

memristance. So the memristor qualifies as a fundamental circuit

element.

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