Memristor

Department of Electrical Engineering NIT Srinagar

SEMINAR REPORT ON

Prof. Aijaz Ahmad Zargar by Naveed Bashir Dar 38/09

. 06

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 Faraday’s 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 𝑀(𝑞) 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 𝑀(𝑞) = 𝑑𝛷/𝑑𝑞 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 𝑀(𝑞) = 𝑑𝛷/𝑑𝑞 = (𝑑𝛷/𝑑𝑡)/(𝑑𝑞/𝑑𝑡) = 𝑉(𝑡)/𝐼(𝑡) Therefore 𝑉(𝑡) = 𝑀(𝑞). 𝐼(𝑡)

It can be inferred from the above equations that memristance is simply charge-dependent resistance. If 𝑀(𝑞) is a constant, then we obtain Ohm's law 𝑅(𝑡) = 𝑉(𝑡)/ 𝐼(𝑡).However, the equation is not equivalent because 𝑞(𝑡) and 𝑀(𝑞) 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 𝐼(𝑡) = 0 then 𝑉(𝑡) = 0 and hence 𝑀(𝑡) is constant. This is the essence of the memory effect. The power consumption characteristic recalls that of a resistor i.e. 𝑃(𝑡) = 𝑉(𝑡). 𝐼(𝑡) = 𝐼(𝑡)2. 𝑀(𝑞)

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 a bias (positive or neagtive ) to the device , it starts from where it was left. This is how it remembers its last resistance.

The ‘ON’ state and the ‘OFF’ state

Fig.5

Expression for memresistance in terms of ROFF and RON M(q) = ROFF {1 – (µv RON/D2).q(t)} where M(q) = Memristance of a device as a function of charge ROFF = High resistance state RON = Low resistance state µv

= Mobility of charge

q(t) = Charge flowing through device at any time t D

= Thickness of semiconductor film sandwiched between two

metal contacts

ANALOGOUS SYSTEM As shown in Fig.6 on next page, 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 it 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.

Fig.6

ADVANTAGES OF USING A MEMRISTOR  Uses less energy and produces less heat.  Memory devices built using memristors have greater data density.

 Combines the jobs of working memory and hard drives into one tiny device.  Faster and less expensive than present day devices.  Would allow for a quicker boot up since information is not lost when the device is turned off.  The information is not lost when the device is turned off.  Eliminates the need to write computer programs that replicate small parts of the brain.  Operating outside of 0s and 1s allows it to imitate brain functions.  It provides greater resiliency and reliability when power is interrupted in data centres.  A very important advantage of memristors is that when used in a device, it can hold any value between 0 and 1. However present day digital devices can hold only 1 or 0. This makes devices implemented using memristors capable of handling more data.  Memristor memory can handle up to 1,000,000 read/write cycles before degradation, compared to flash at 100,000 cycles.  The memristor based crossbar latch memory prototyped by HP can fit 100 gigabits within a square centimetre.

APPLICATIONS REPLACEMENT OF FLASH MEMORY The important potential use of memristor is as a powerful replacement for flash memory- the kind used in applications that require quick writing and rewriting capabilities, such as in cameras

and USB memory sticks. Like flash memory, memristive memory can only be written 10,000 times or so before the constant atomic movements within the device cause it to break down. It is possible to improve the durability of memristors. REPLACEMENT FOR DRAM Computers using conventional D-RAM lack the ability to retain information once they are turned off. When power is restored to a D-RAM-based computer, a slow, energy-consuming "boot-up" process is necessary to retrieve data stored on a magnetic disk required to run the system. the reason computers have to be rebooted every time they are turned on is that their logic circuits are incapable of holding their bits after the power is shut off. But because a memristor can remember voltages, a memristor-driven computer would arguably never need a reboot. “You could leave all your Word files and spreadsheets open, turn off your computer, and go get a cup of coffee or go on vacation for two weeks.” REMOTE SENSING In combination with meminductors and memcapacitors, the complementary circuits to the memristor which allow for the storage of charge, memristors can possibly allow for nano-scale low power memory and distributed state storage. COMPLEX MATHEMATICAL CALCULATIONS Apart from the basic arithmetic calculations, that a memristor circuit can perform, it can be used with operational amplifiers in circuits like that of integrator, differentiator and many others to perform different tasks and calculations.

FUTURE SCOPE AND RESEARCH Recently, researchers have defined two new memdevices namely memcapacitor and meminductor, thus generalizing the concept of memory devices to capacitors and inductors. These are shown in Fig.7 and Fig.8 respectively below

Fig.7 Memcapacitor

Fig.8 Meminductor

The memcapacitor and meminductor are the memdevices in which the capacitance and inductance respectively depends on the state and history of the system.

CONCLUSION Nanotechnology is fast emerging, and nanoscale devices automatically bring in memristive functions. Thus, memristors might revolutionize the 21st century as radically as the transistor in the 20th century. Memristor memories have already been developed and the researchers at HP believe that they can offer a product with a storage density of about 20 gigabytes per square centimetre by 2013. As Prof. Leon Chua rightly said ―”It

is time to rewrite all the Electrical and Electronics Engineering books.” BIBLIOGRAPHY http://www.memristor.org http://en.wikipedia.org/wiki/Memristor http://www.hpl.hp.com/news/2011/apr-jun/memristors.html http://spectrum.ieee.org/semiconductors/design/the-mysteriousmemristor http://www.howstuffworks.com

THE END