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Currently known fundamental passive elements –
Resistors, Capacitors & Inductors.
Does a 4th passive element exist..?
Leon O. Chua formulated Memristor theory in his
paper “Memristor-The Missing Circuit Element” in
1971.
Memistors are passive two terminal circuit elements.
Behaves like a nonlinear resistor with memory.
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Four fundamental circuit variables- current i, voltage
v, charge q, and flux linkage φ
Six possible combinations of these four variables
Five already defined as
Resistor(dv=Rdi), Capacitor(dq=Cdv),
Inductor(dφ=Ldi), q(t)=∫i(T)dT, φ(t)=∫v(T)dT
The 6th relation defines memristance as dφ=Mdq
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Memristance is a property of an electronic
component.
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 resistance of the
circuit will be the value when it was last active.
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Two terminal device in which magnetic flux Φm between its
terminals is a function of amount of electric charge q passed
through the device.
M(q) = dΦm/dq
M(q) = [dΦm/dt] / [dq/dt] = 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.
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Resistor is analogous to a pipe that carries water.
Water(charge q), input pressure(voltage v), rate of flow of
water(current i).
In case of resistor, flow of water is faster if pipe is shorter
and/or has a larger diameter.
Memristor is analogous to a special kind of pipe that expands
or shrinks when water flows through it
The pipe is directive in nature.
If water pressure is turned off, pipe will retain its most recent
diameter, until water is turned back on.
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On April 30, 2008, a team at HP Labs led by the scientist R.
Stanley Williams announced the discovery of a switching
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 nondepleted layer.
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An atomic force microscope image of a simple circuit with 17 memristors
lined up in a row. Each memristor has a bottom wire that contacts one side
of the device and a top wire that contacts the opposite side. The devices act
as 'memory resistors', with the resistance of each device depending on the
amount of charge that has moved through each one. The wires in this image
are 50 nm wide, or about 150 atoms in total width.
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The most common v-i trace is a ‘figure 8’ or a ‘pinched loop’
For this current i=0, when voltage v=0.
On the application of electric field, oxygen vacancies drift,
changing boundary between high & low resistance layers.
Memristance is only displayed when the doped layer &
depleted layer both contribute to resistance.
The device enters hysteresis when enough charge has passed
through memristor & ions can no longer move.
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HP Lab scientists were first to observe the ‘memristive
behaviour’ in materials.
Introduced the titanium dioxide memristor.
Introduced memristance formula for devices.
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For linear ionic drift in a uniform field with average ion
mobility µv,
The 2nd term in the parentheses which contribute more to
memristance becomes larger when D is in the nanometer
range.
Thus memristance is important characteristics of a device
when critical dimension shrink to nanometer scale.
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For some memristors, applied current or voltage will cause 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 resistance ROFF.
By application of external bias, we can move the boundary to
adjust the device resistance from RON to ROFF.
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can now think about fabricating a non-volatile random access
memory (RAM) – or memory chips that don't forget the data
when a computer is shut off. Memristors carries a memory of
its past.
Replace today’s commonly used dynamic random access
memory (DRAM).
Denser cells allow memristor circuits to store more data than
flash memory.
The Hewlett-Packard team has successfully created working
circuits based on memristors that are as small as 15
nanometers. Ultimately, it will be possible to make memristors
as small as about four nanometers.
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A memristor circuit requires lower voltage, less power and less
time to turn on than competitive memory like DRAM 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 completely different class of
computing capabilities like an analog computer in which you
don't use 1s and 0s only.
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The most significant limitation is that the memristors functions
at about one-tenth the speed of today’s DRAM memory cells.
The graphs in William’s report shows switching operation at
only 1Hz.
Although small dimension of device seems to imply fast
operation, the charge carriers move very slowly.
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The rich hysteretic v-i characteristics detected in many thin film
devices can now be understood as memristive behaviour.
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 job of a
single memristor.
No combination of R,L,C circuit could duplicate the
memristance.
So the memristor qualifies as a fundamental circuit element.