Department of Electrical Engineering

NIT Srinagar

SEMINAR REPORT

ON

MEMRISTORS

Report Submitted to :-

Prof. Aijaz Ahmad Zargar

by

Name:- Naveed Bashir Dar

Enrollment no. 38/09

Class Roll no. 06

Semester :- VIIth

CONTENTS

1) Introduction

2) History

3) Speciality of a memristor

4) Memristor

5) Memristance

6) Fabrication by HP Labs

7) Working

8) The ON state and the OFF state

9) Analogous System

10) Advantages of using a memristor

11) Applications

12) Future scope and research

13) Conclusion

14) Bibliography

INTRODUCTION

There are four fundamental circuit variables in circuit theory. They are current, voltage, charge and flux. The three basic two-terminal devices of circuit theory namely the resistor, the capacitor and the inductor are defined in terms of the relation between two of the four fundamental circuit variables. A resistor is defined by the relationship between voltage and current, the capacitor is defined by the relationship between charge and voltage and the inductor is defined by the relationship between flux and current. In addition, the current is defined as the time derivative of the charge and according to Faradays law, the voltage is defined as the time derivative of the flux. These relations are shown in the figure below

Fig.1

In the previous figure, there is a missing link. The relation between the charge and the flux was unknown, and so the device which describes it. This led to the discovery of the fourth fundamental circuit element named Memristor which describes the above missing relation between charge and flux.

HISTORY

Memristor theory was formulated by Prof. Leon Chua in a 1971 paper. Chua strongly believed that a fourth device existed to provide conceptual symmetry with the resistor, inductor, and capacitor. This symmetry follows from the description of basic passive circuit elements as defined by a relation between two of the four fundamental circuit variables. A device linking charge and flux (themselves defined as time integrals of current and voltage respectively), which would be the Memristor, was still hypothetical at the time. However, it would not be until thirty-seven years later, on April 30, 2008, that a team at HP Labs led by the scientist R Stanley Williams announced the first fabricated memristor. Based on a thin film of titanium dioxide, it has been presented as an approximately ideal device.

SPECIALITY OF A MEMRISTOR

The most notable property of a memristor is that it can save its electronic state even when the current is turned off, making it a great candidate to replace today's flash memory. An outstanding feature is its ability to remember a range of electrical states rather than the simplistic "on" and "off" states that today's digital processors recognize. These are the properties that cannot be duplicated by any circuit combination of resistors, capacitors, and inductors which is why memristor qualifies as a fundamental circuit element.

The arrangement of known few fundamental circuit components form the basis of almost all of the electronic devices we use in our everyday life. 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 another era of electronics. HP already has plans to implement memristors in a new type of non-volatile memory which could eventually replace flash and other memory systems.

So is its significance that its innovators say that Memristors are so significant that it would be mandatory to re-write the existing electronics engineering textbooks.

MEMRISTOR

Memristor, the contraction of memory and resistor, is a passive element that provides a functional relation between charge and flux. It is defined as a two-terminal circuit element in which the flux between the two terminals is a function of the amount of electric charge that has passed through the device. Memristor is not an energy storage element (passive element). Fig.2 shows the symbol of a memristor.

Fig.2

Chua defined memristor as a resistor whose resistance level was based on the amount of charge that had passed through it.

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.

A memristor is said to be charge-controlled if the relation between flux and charge is expressed as a function of electric charge and it is said to be flux-controlled if the relation between flux and charge is expressed as a function of the flux linkage.

MEMRISTANCE

Memristance is a property of a memristor to retain its resistance level even after power had been shut down or lets it remember (or recall) the last resistance it had before being shut off. Memristance of a memristor is denoted by since it varies with the amount of charge that has passed through the memristor.

Each memristor is characterized by its memristance function describing the charge-dependent rate of change of flux with charge.The memristor is essentially a two-terminal variable resistor, with resistance dependent upon the amount of charge q that has passed between the terminals. Mathematically

As we know from, Faraday's law of EM induction that magnetic flux is simply the time integral of voltage, and charge is the time integral of current, we may write the more convenient form as

Therefore

It can be inferred from the above equations that memristance is simply charge-dependent resistance. If is a constant, then we obtain Ohm's law .However, the equation is not equivalent because and will vary with time. This equation also reveals that memristance defines a linear relationship between current and voltage, as long as charge does not vary.

Furthermore, the memristor is static if no current is applied i.e. if

then and hence is constant. This is the essence of the memory effect.

The power consumption characteristic recalls that of a resistor i.e.

FABRICATION BY HP LABS

Hewlett Packard used a very thin film of titanium dioxide (TiO2). The thin film is sandwiched between two platinum (Pt) contacts and one side of TiO2 is doped with oxygen vacancies. The oxygen vacancies are positively charged ions. Thus, there is a TiO2 junction where one side is doped and the other side is undoped. The device established by HP is shown in Fig.3 below

Fig.3

In Fig.3 on previous page, D is the device length and w is the length of the doped region. Pure TiO2 is a semiconductor and has high resistivity. The doped oxygen vacancies make the TiO2 material conductive.

WORKING

Pure titanium dioxide (TiO2) which is a semiconductor has high resistance just as in the case of intrinsic silicon, and it can also be doped to make it conducting. If an oxygen atom, which is negatively charged, is removed from its substantial site in TiO2, a positively charged oxygen vacancy is created(V0+) is created , which acts as a donor of electrons. These positively charged oxygen vacancies (V0+) can be made to drift in the direction of applied electric field.

Consider, we have two thin layers of TiO2, one highly conducting layer with lots of oxygen vacancies(V0+ ) and the other layer undoped, which is highly resistive. Suppose that good ohmic contacts are formed using platinum electrodes on either side of sandwich of TiO2, the electronic barrier between the undoped TiO2 and the metal looks broader.

Case #1

When a negative potential V is applied to electrode A in Fig.4, because the positively charged oxygen vacancies(V0+) are attracted towards electrode A, the length of undoped region increases. Under these conditions the electronic barrier at the undoped TiO2 and the metal is still too wide and it will be difficult for the electrons to cross over the barrier as shown in Fig.4 below

Fig.4

Case #2

When a positive potential V is applied at electrode A in Fig.4, the positively charged oxygen vacancies are repelled and moved into the undoped TiO2. This ionic movement towards electrode B reduces the length of undoped region. When more positively charged oxygen vacancies(V0+) reach the TiO2 metal interface, the potential barrier for the electrons becomes very narrow, as shown, making tunneling through the barrier a real possibility. This leads to a large current flow, making the device turn ON. In this case, the positively charged oxygen vacancies (V0+) are present across the length of device. When the polarity of the applied voltage is reversed, the oxygen vacancies can be pushed back into their original place on the doped side, restoring the broader electronic barrier at TiO2 metal interface. This forces the device to turn OFF due to an increase in the resistance of the device and reduce possibility for carrier tunneling .

Case #3

When the applied bias is removed, the positively charged Ti ions (which are actually the oxygen deficient sites) do not move anymore, making the boundary between the doped and undoped layers TiO2 immobile. When we next apply