1. Memristors
By, Saransh Singh

2. Contents Introduction Basic Memristor Model V-I Characteristics
Formula for Memristance
Types for Memristors
Working of Memristors
Merits and Demerits
Possible Applications
Conclusion

3. 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

4. Behaves like a nonlinear resistor with memory.
The memristor is currently under development by a team at Hewlett Packard (HP).

5. 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 = ?

6. 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.

7. 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

9. 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

10. 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. 

11. 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

12. 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

13. Working of Memristors Spintronic Memristor Spin of electrons Magnetism
Magneto resistance principal
Electrons flow alters the magnetization state

14. Titanium Memristors
Two thin layer sandwich, 1st layer is oxygen deficient
The oxygen vacancies act as charge carriers and this implies that the depleted layer has a much lower resistance than the non-depleted layer
When an electric field is applied, the oxygen vacancies drift, changing the boundary between the high-resistance and low- resistance layers

15. Titanium Memristor

16. 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

18. 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

19. 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

20. 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)

21. 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 memristor- driven computer would arguably never need a reboot

22. 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

23. 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