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Memristors
By,
Saransh Singh
Contents
• Introduction
• Basic Memristor Model
• V-I Characteristics
• Formula for Memristance
• Types for Memristors
• Working of Memristors
• Merits and Demerits
• Possible Applications
• Conclusion
Introduction
• Currently known fundamental passive elements – Resistors,
Capacitors & Inductors.
• Leon O. Chua formulated Memristor theory in his paper
“Memristor-The Missing Circuit Element” in 1971.
• Later Memristor was named the 4th Fundamental element
• It is a 2 terminal passive device, relates charge to flux
• Behaves like a nonlinear resistor with memory.
• The memristor is currently under development by a team at
Hewlett Packard (HP).
Combination of the 4 Variables
•
Integral of current is charge dq/dt = I (amperes)
•
Integral of voltage is flux dΦ/dt = V (volts)
•
Resistor dv = R di , dv/di = R(ohms)
•
Capacitor dq = C dv , dq/dv = C(farad)
•
Inductor dΦ = L di , dΦ/di = L (henry)
•
dΦ/dq = ?
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.
• 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
Basic Memristor Model
Doped: region of low resistance
 Undoped: region of high resistance
 R off : Resistance when w/d=0
 R on: Resistance when w/d=1

V-I Characteristics
• In ordinary resistors there is a linear relationship between
current and voltage
• However, for memristors a similar graph is a little more
complicated
• These two straight line curves may be
interpreted as two distinct resistance
states with the remainder of the curve
as transition regions between these
two states.
Formula for Memristance
• The Basic Fromula is
• 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
Types of Memristors
• Spintronic Memristor
• Spin Torque Transfer Magneto resistance
• Titanium dioxide memristor
• Polymeric memristor
• Spin memristive systems
• Magnetite memristive systems
• Resonant tunneling diode memristor
Working of Memristors
• Spintronic Memristor
▫ Spin of electrons
▫ Magnetism
▫ Magneto resistance principal
▫ Electrons flow alters the magnetization state
• Titanium Memristors
o Two thin layer sandwich, 1st layer is oxygen deficient
o The oxygen vacancies act as charge carriers and this implies
that the depleted layer has a much lower resistance than the
non-depleted layer
o When an electric field is applied, the oxygen vacancies drift,
changing the boundary between the high-resistance and low-
resistance layers
Titanium Memristor
Memristors as a Storage element
• Nonvolatile
• Energy required during switching
• Memristor as switches in crossbar architecture
• Crossbar Architecture
• Connected mesh of perpendicular wires
• Crossing wires connected by switch
• Switch closed applying positive voltage
• Switch opened by reversed voltage
Merits and Demerits
Merits:
• Eliminates delay
• Speed inversely proportional to size
• Large density 1terabit/cm2
• Analog data storage possible
Demerits:
• Dissipates heat
• No design standards
• Needs defect engineering
Possible Applications
• Cheaper Memristor made chips: They are nanoscale devices
with unique properties: a variable resistance and the ability to
remember the resistance even when the power is off
• A single memristor can perform the same logic functions as
multiple transistors, making them a promising way to increase
computer power
• Memristors could also prove to be a faster, smaller, more
energy-efficient alternative to flash storage
• Memristor as Digital and Analog: A memristive device can
function in both digital and analog forms
• In digital mode, it could substitute conventional solid-state
memories (Flash) with high-speed and less steeply priced
nonvolatile random access memory (NVRAM)
• No Rebooting: The memristor's memory has consequences
• 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 memristordriven computer would arguably never need a reboot
Conclusion
• Latest technology, High speed memory devices, Low power
requirements
• 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
• Memristors made to replace flash memory will likely appear
first; HP's goal is to offer them by 2012
• Beyond that, memristors will likely replace both DRAM and
hard disks in the 2014-to-2016 time frame
• As for memristor-based analog computers, that step may take
20-plus years