1. Memristors

2. Introduction
Theoretically, Memristors, a concatenation of “memory resistors”, are a type of passive circuit elements that maintain a relationship between the time integrals of current and voltage across a two terminal element. Electronic symbol

3. Simplified Definition
It is the consolidation of two words namely, MEMORY and RESISTOR.
As the name suggests its resistance (dV/dI) depends on the charge that HAD flowed through the circuit.
When current flows in one direction the resistance increases, in contrast when the current flows in opposite direction the resistance decreases.
However resistance cannot go below zero.
When the current is stopped the resistance remains in the value that it had earlier.
It means MEMRISTOR “REMEMBERS” the current that had last flowed through it.

4. History
Professor Leon Chua
Theory was developed in 1971 by Professor Leon Chua at University of California, Berkeley.
In 2008, a team at HP Labs under R.Stanley Williams claimed to have found Chua's missing memristor based on an analysis of a thin film of titanium dioxide.
In March 2012, a team of researchers from HRL Laboratories and the University of Michigan announced the first functioning memristor array built on a CMOS chip.
R. Stanley Williams

5. Analogy
Memristors behaves like a pipe whose diameter varies according to
the amount and direction of the current passing through it
If the current is turned OFF, the pipes diameter stays same until it is switched ON again
It Remembers what current has flowed through it

6. Fundamental Passive Linear Elements

7. Background
Leon Chua extrapolated a conceptual symmetry between the nonlinear resistor (voltage vs. current), nonlinear capacitor (voltage vs. charge) and nonlinear inductor (magnetic flux linkage vs. current).
He then inferred the possibility of a memristor as another fundamental nonlinear circuit element linking magnetic flux linkage and charge.

8. Theory
The memristor was originally defined in terms of a non-linear functional relationship between magnetic flux linkage Φm(t) and the amount of electric charge that has flowed, q(t)
f(Φm (t),q(t)) = 0
The variable Φm ("magnetic flux linkage") is generalized from the circuit characteristic of an inductor.
It does not represent a magnetic field here.
The symbol Φm may be regarded as the integral of voltage over time.

9. M(q(t)) = Φm/𝒅𝒕 𝒅𝒒/𝒅𝒕 = V(t) I(t)
Memristance
In the relationship between Φm and q, the derivative of one with respect to the other depends on the value of one or the other
So each memristor is characterized by its memristance function describing the charge-dependent rate of change of flux with charge.
M(q) = dΦm dq
Substituting the flux as the time integral of the voltage, and charge as the time integral of current
M(q(t)) = Φm/𝒅𝒕 𝒅𝒒/𝒅𝒕 = V(t) I(t)

10. Device Characteristic property (units) Differential equation
Resistor Resistance (V per A, or Ohm, Ω) R = dV / dI
Capacitor Capacitance (C per V, or Farads) C = dq / dV
Inductor Inductance (Wb per A, or Henrys) L = dΦm / dI
Memristor Memristance (Wb per C, or Ohm) M = dΦm / dq
The above table covers all meaningful ratios of differentials of I, Q, Φm, and V.
No device can relate dI to dq, or dΦm to dV, because I is the derivative of Q and Φm is the integral of V.

11. Current-voltage characteristics for the resistor, capacitor, inductor and memristor.

12. It can be inferred from this that memristance is charge-dependent resistance.
If M(q(t)) is a constant, then we obtain Ohm's Law R(t) = V(t)/ I(t).
If M(q(t)) is nontrivial, however, the equation is not equivalent because q(t) and M(q(t)) can vary with time.
Solving for voltage as a function of time produces
V(t)= M(q(t)) I(t)
This equation reveals that memristance defines a linear relationship between current and voltage, as long as M does not vary with charge.

13. Memory Effect V(t)= M(q(t)) I(t)
The memristor is static if no current is applied.
V(t)= M(q(t)) I(t)
If I(t) = 0, we find V(t) = 0 and M(t) is constant.
This is the essence of the memory effect.

14. P(t) = V(t) I(t) = I2(t) M(q(t))
Power Equation
The power consumption characteristic recalls that of a resistor, I2R.
P(t) = V(t) I(t) = I2(t) M(q(t))
As long as M(q(t)) varies little, such as under alternating current, the memristor will appear as a constant resistor.
If M(q(t)) increases rapidly, however, current and power consumption will quickly stop.

15. Contribution of HP LabsPT
TiO(2-x)
TiO2
3 nm
2 nm
Oxidized
Reduced
(-)ve
(+)ve
TiO2-x region doped with oxygen vacancies
In the TiO2-x region, the ratio between titanium atoms and oxygen atoms has been altered such that there is less oxygen than in a regular TiO2 sample
The resistance of the device when w = D will be designated RON and when w = 0 the resistance will be designated as ROFF .

16. Resistance Naming Convention
Effective Electrical Structure of the HP Memristor
The effective IV behaviour of the structure can be represented as equation

17. Contribution of HP Labs
Further Calculations leads to:
For RON<< ROFF the memristance function was determined to be
M(q(t)) = ROFF . (1- μv RON D2 q(t))
where ROFF represents the high resistance state
RON represents the low resistance state
μv represents the mobility of dopants in the thin film
D represents the film thickness.

18. An array of 17 purpose-built oxygen-depleted titanium dioxide memristors built at HP Labs, imaged by an atomic force microscope.
The wires are about 50 nm, or 150 atoms, wide.

19. Applications of a Memristor
Non-volatile memory applications
Memristors can retain memory states, and data, in power-off modes.
Non-volatile random access memory, or NVRAM is the first application that comes to mind when we hear about memristors.
There are already 3nm Memristors in fabrication now.

20. Low-power and remote sensing applications.
Coupled with memcapacitors and meminductors, the complementary circuits to the memristor which allow for the storage of charge.
Memristors can possibly allow for nano-scale low power memory and distributed state storage, as a further extension of NVRAM capabilities.
These are currently all hypothetical in terms of time to market.

21. Programmable Resistances
While the Memristor can be used at its extreme resistance values in order to provide digital memory, it can also be made to behave in an analog manner.
One potential application of this behaviour is that of a dynamically adjustable electric load .
Thus, existing electronic circuit topologies with characteristics that depend on a resistance can be made with Memristors that behave as variable, programmable resistances.

22. Memristor patents include applications in
Programmable Logic
Signal Processing
Neural Networks
Control Systems
Reconfigurable Computing
Brain-computer Interfaces
RFID.

23. Advantages of Memristors
Has properties which can not be duplicated by the other circuit elements (resistors, capacitors, and inductors
Capable of replacing both DRAM and hard drives
Smaller than transistors while generating less heat
Works better as it gets smaller which is the opposite of transistors
Devices storing 100 gigabytes in a square centimeter have been created using memristors
Quicker boot-ups
Requires less voltage (and thus less overall power required)

24. Disadvantages of Memristors
Not currently commercially available
Current versions only at 1/10th the speed of DRAM
Has the ability to learn but can also learn the wrong patterns in the beginning.
Since all data on the computer becomes non-volatile, rebooting will not solve any issues as it often times can with DRAM.
Suspected by some that the performance and speed will never match DRAM and transistors.

25. References http://en.wikipedia.org/wiki/Memristor
missing-memristor
element.html

26. Thank You