1.
PROBLEM STATEMENT
Typically electronics has been defined in terms of three fundamental
elements such as resistors, capacitors and inductors. These three elements are used
to define the four fundamental circuit variables which are electric current, voltage,
charge and magnetic flux.
Resistors are used to relate current to voltage, capacitors to relate voltage to
charge, and inductors to relate current to magnetic flux, but there was no element
which could relate charge to magnetic flux.
To overcome this missing link, scientists came up with a new element called
Memristor. These Memristor has the properties of both a memory element and a
resistor (hence wisely named as Memristor).
Memristor is being called as the fourth fundamental component, hence
increasing the importance of its innovation. Its innovators say, memrisrors are so
significant that it would be mandatory to re-write the existing electronics
engineering textbooks.
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2. INTRODUCTION
Generally when most people think about electronics, they may initially think
of products such as cell phones, radios, laptop computers, etc. others, having some
engineering background, may think of resistors, capacitors, etc. which are the basic
components necessary for electronics to function. Such basic components are fairly
limited in number and each having their own characteristic function.
Memristor theory was formulated and named by 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), 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 would announce the discovery of a switching Memristor. Based
on a thin film of titanium dioxide, it has been presented as an approximately ideal
device.
The reason that the Memristor is radically different from the other
fundamental circuit elements is that, unlike them, it carries a memory of its
past.When you turn off the voltage to the circuit, the Memristor still remembers
how much was applied before and for how long.
That's an effect that can't be duplicated by any circuit combination of
resistors, capacitors, and inductors, which is why the Memristor qualifies as a
fundamental circuit element.
The arrangement of these 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 a brand new type 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 .
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3. FUNDAMENTAL ELEMENTS OF ELECTRONICS
There are basically 3 fundamental elements in electronics:
1) Resistor
2) Capacitor
3) Inductor
Fig.1
Above given fig.1 shows relationship between various electrical parameters
and the elements that are guided or runned by the relation between corresponding
parameters.
4. THE MISSING ELEMENT
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
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Fig.2
not an energy storage element (passive element). Fig. shows the symbol of a
memristor.
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 …..(from fig.1)
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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) …..(1)
Therefore, 𝑉(𝑡) = 𝑀(𝑞). 𝐼(𝑡) …..(2)
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) = 0then 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) …..(3)
5. BASIC CONCEPT
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.
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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.3
6. WORKING
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 TiO 2 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. below
D is the device length and w is the length of the doped region. Pure TiO 2 is a
semiconductor and has high resistivity. The doped oxygen vacancies make the
TiO2 material conductive.
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Fig.4
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
undopedTiO2and 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.5 below
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 TiO 2. 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
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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
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7. ADVANTAGES
1. Uses less energy and produces less heat.
2. Memory devices built using memristors have greater data density.
3. Combines the jobs of working memory and hard drives into one tiny device.
4. Faster and less expensive than present day devices.
5. Would allow for a quicker boot up since information is not lost when the
device is turned off.
6. The information is not lost when the device is turned off.
7. Eliminates the need to write computer programs that replicate small parts of
the brain
8. Operating outside of 0s and 1s allows it to imitate brain functions.
9. It provides greater resiliency and reliability when power is interrupted in
data centres.
10.A very important advantage of memristor 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 are
capable of handling more data.
11.Memristor memory can handle up to 1,000,000 read/write cycles before
degradation, compared to flash at 100,000 cycles.
12.The memristor based crossbar latch memory prototyped by HP can fit 100
gigabits within a square centimetre.
8. DISADVANTAGES
1. Not currently commercially available Current versions
2. only at 1/10th the speed of DRAM
3. Has the ability to learn but can also learn the wrong patterns in the beginning
Since all data on the computer becomes non-volatile, rebooting will not
solve any issues as it often times can with DRAM
4. Suspected by some that the performance and speed will never match DRAM
and transistors
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9. APPLICATIONS
REPLACEMENT FOR 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.
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10.CONCLUSION
By redesigning certain types of circuits to include Memristors, it is possible
to obtain the same function with fewer components, making the circuit itself less
expensive and significantly decreasing its power consumption.
In fact, it can be hoped to combine Memristors with traditional circuit-
design elements to produce a device that does computation. The Hewlett-Packard
(HP) group is looking at developing a Memristor-based nonvolatile memory that
could be 1000 times faster than magnetic disks and use much less power.
As rightly said by Leon Chua and R.Stanley Williams (originators of
Memristor), “Memrisrors are so significant that it would be mandatory to re-
write the existing Electronics Engineering textbooks”.
11.BIBLIOGRAPHY
1) http://www.memristor.org
2) http://en.wikipedia.org/wiki/Memristor
3) http://www.hpl.hp.com/news/2011/apr-jun/memristors.html
4) http://spectrum.ieee.org/semiconductors/design/the-mysterious-memristor
5) http://www.howstuffworks.com
6) L.O Chua and S.M kang 1976, “memristive devices and systems”, Proc.IEEE
64(2), 209-23.
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