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Memristor – The Fourth Fundamental
Circuit Element
Introduction
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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.
History Of Memristor
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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Relation between fundamental circuit
elements and variables
So what is Memristance?
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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Memristor Theory
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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.
Physical analogy for a
memristor
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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.
Titanium dioxide memristor
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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
non-depleted layer.
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Microscopic image of memristor row
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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.
v-i characteristics
v-i chara..(cont.)
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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Contribution of HP Labs
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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Memristance formula
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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.
Operation as a switch
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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Applications & Advantages
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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.
Applications & Advantages..(cont.)
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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.
Practical limitations of memristor
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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.
Conclusion
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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.