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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