Memristor

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Memristor The Fourth Fundamental Circuit
Element
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Introduction

• 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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History Of Memristor

• Four fundamental circuit variables- current i,
  voltage v, charge q, and flux linkage f
• Six possible combinations of these four variables
• Five already defined as
• Resistor(dvRdi), Capacitor(dqCdv),
  Inductor(dfLdi), q(t)?i(T)dT, f(t)?v(T)dT
• The 6th relation defines memristance as dfMdq

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Relation between fundamental circuit elements and
variables
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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 v0, 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

• Two terminal device in which magnetic flux Fm
  between its terminals is a function of amount of
  electric charge q passed through the device.
• M(q) dFm/dq
• M(q) dFm/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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Physical analogy for a memristor

• 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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Titanium dioxide memristor

• 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

• 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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v-i characteristics
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v-i chara..(cont.)

• The most common v-i trace is a figure 8 or a
  pinched loop
• For this current i0, when voltage v0.
• 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

• 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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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

• 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 todays 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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Applications Advantages..(cont.)

• 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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Practical limitations of memristor

• The most significant limitation is that the
  memristors functions at about one-tenth the speed
  of todays DRAM memory cells.
• The graphs in Williams 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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Conclusion

• 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.