This document is a seminar report on memristors submitted for a bachelor's degree. It provides background on the history of memristor theory, which was first proposed by Leon Chua in 1971. However, an actual physical memristor device was not discovered until 2008 by researchers at HP Labs led by R. Stanley Williams. The memristor is described as a new fundamental circuit element that links the relationship between charge and magnetic flux, completing the set of basic circuit variables. The discovery of the physical memristor validates Chua's theoretical predictions from decades earlier and could open up new applications in electronics and computing.

1. SEMINAR REPORT
ON
MEMRISTOR
Submitted for the partial fulfillment of award
of
Degree of Bachelors of Technology
(Electronics and Communication Engineering)
BY: - ANKUR VERMA
(ROLL NO: - 1113231046)
Department of Electronics and Communication
G.N.I.O.T. GREATER NOIDA
Session 2013-2014

2. CERTIFICATE
This is to certify that ANKUR VERMA (1113231046) of E.C. Third
Year have submitted their seminar report on Memristor under the
guidance of Electronics Engineering Department. This seminar
report is partial fulfillment of their B.Tech course from Uttar Pradesh
Technical University, Lucknow.
Mr. MANISH GUPTA Head of the department
(SEMINAR GUIDE) Brig. M.K.DEWAN

3. ACKNOWLEDGEMENT
We would like to express our immense gratitude to all those who have
directly or indirectly helped us in completing our seminar on
“Memristor”. I would like to thank them for their effective guidance
& kind cooperation without which we would not have been able to
introduce a good presentation and complete this seminar report.
We would like to thank the faculty members of Department of
Electronics & Communication Engineering for their permission
grant, constant reminders and much needed motivation, which helped
us to extract maximum knowledge from the available sources.
Lastly, my sincere thanks to all our friends for their coordination in
completion of this seminar report.
AKASH GARG
Roll No. : - 1113231016
(E.C. 3RD
Year)

4. ABSTRACT
Typically electronics has been define three fundamental circuit components-
resistors, inductors and capacitors are used to define four fundamental circuit
variables which are electric current, voltage, charge and magnetic flux.
Resistors are used to relate current to voltage, capacitors to relate voltage to
charge and inductors to relate current to magnetic flux. But there was no
element which could relate charge to magnetic flux. This lead to the idea and
development of memristors.
In 1971, Leon Chua reasoned on the grounds of symmetry that there
should be a fourth Fundamental circuit element which gives the relationship
between flux and charge. He named this circuit element the memristor, which is
short for memory resistor. In May 2008, Researchers at HP Labs published a
paper announcing a model for the physical realization of the memristor.
Memristor is a concatenation of ―memory resistors‖. The most notable
property of a memristor is that it can save its electronic state even when the
current is turned off, making it a great candidate to replace today's flash
memory. An outstanding feature is its ability to remember a range of electrical
states rather than the simplistic "on" and "off" states that today's digital
processors recognize. Memristor-based computers could be capable of far more
complex tasks.
It is proposed that memory storage devices that has very high data
density and computers that require no time for boot up can be developed using
memristor based hardware. A new physical quantity which is also introduced
associated with memristor. It also solves some unexplained voltage current
characteristics observed in certain materials at atomic levels.
HP has already started produced an oxygen depleted titanium memristor.
i

5. TABLE OF CONTENT
CHAPTER NO. TITLE PAGE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
LIST OF FIGURE
INTRODUCTION…………………
HISTORY………………………….
ADVENT OF HP LABS…………..
MEMRISTOR THEORY…………
MEMRISTOR AND RESISTOR…
MEMRISTOR VS TRANSISTOR..
APPEARANCE OF MEMRISTOR
MEMRISTOR OPERATION……..
PIPE AND CURRENT ANALOGY
APPLICATION…………………….
BENEFITS OF MEMRISTOR……
FUTURE…………………………….
CONCLUSION……………………..
BIBLIOGRAPHY…………………..
iii
1
3
5
7
12
13
15
16
18
20
23
24
25
26
ii

6. LIST OF FIGURE
FIGURE
NO.
FIGURE NAME PAGE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
ABOUT FOUR BASIC CIRCUIT ELEMENTS
ABOUT THE THREE FUNDAMENTAL CIRCUIT
ELEMENTS
SYMBOL OF THE MEMRISTOR
ABOUT V-I CHARACTERISTICS OF A MEMRISTOR
HYSTERESIS MODEL OF RESISTANCE VS. VOLTAGE
CURRENT VOLTAGE CHARACTERISTIC OF RESISTOR
AND MEMRISTOR
CROSSBAR ARRAY STRUCTURE
MOVEMENT OF OXYGEN DEFICIENCY
DIAGRAM OF PIPE AND CURRENT EXAMPLE
NEURAL NETWORKS
FLEXIBLE MEMORY
3
7
8
11
11
12
15
16
18
21
24
iii

7. Generally when most people think about electronics, they may initially think of
products such as cell phones, radios, laptop computers, etc. others, having some
engineering background, may think of resistors, capacitors, etc. which are the
basic components necessary for electronics to function. Such basic components
are fairly limited in number and each having their own characteristic function.
Memristor theory was formulated and named by Leon Chua in a 1971
paper. Chua strongly believed that a fourth device existed to provide conceptual
symmetry with the resistor, inductor, and capacitor. This symmetry follows
from the description of basic passive circuit elements as defined by a relation
between two of the four fundamental circuit variables. A device linking charge
and flux (they defined as time integrals of current and voltage), which would be
the Memristor, was still hypothetical at the time. However, it would not be until
thirty-seven years later, on April 30, 2008, that a team at HP Labs led by the
scientist R. Stanley Williams would announce the discovery of a switching
Memristor. Based on a thin film of titanium dioxide, it has been presented as an
approximately ideal device.
The reason that the Memristor is radically different from the other fundamental
circuit elements is that, unlike them, it carries a memory of its past. When you
turn off the voltage to the circuit, the Memristor still remembers how much was
applied before and for how long. 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.
1 INTRODUCTION
1

8. The arrangement of these few fundamental circuit components form the
basis of almost all of the electronic devices we use in our everyday life. Thus
the discovery of a brand new fundamental circuit element is something not to be
taken lightly and has the potential to open the door to a brand new type of
electronics. HP already has plans to implement Memristors in a new type of
non-volatile memory which could eventually replace flash and other memory
systems.
2

9. The story of the memristor is truly one for the history books. When Leon Chua,
now an IEEE Fellow, wrote his seminal paper predicting the memristor, he was
a newly minted and rapidly rising professor at UC Berkeley. Chua had been
fighting for years against what he considered the arbitrary restriction of
electronic circuit theory to linear systems. He was convinced that nonlinear
electronics had much more potential than the linear circuits that dominate
electronics technology to this day.
Memristance was first predicted by Professor Leon Chua in his paper
Memristor. The missing circuit element published in the IEEE Transactions on
Circuits Theory (1971). In that paper, Prof. Chua proved a number of theorems
to show that there was a 'missing' two terminal circuit element from the family
of "fundamental" passive devices: resistors (which provide static resistance to
the flow of electrical charge), capacitors (which store charges), and inductors
(which resist changes to the flow of charge)—, or elements that do not add
energy to a circuit. He showed that no combination of resistors, capacitors, and
inductors could duplicate the properties of a memristor. This inability to
duplicate the properties of a memristor with the other passive circuit elements is
what makes the memristor fundamental. However, this original paper requires a
considerable effort for a non-expert to follow. In a later paper, Prof. Chua
introduced his 'periodic table' of circuit elements.
Fig 1: Diagram describing the relation between charge, current, voltage and magnetic
flux to one another
2 HISTORY
3

10. The pair wise mathematical equations that relate the four circuit quantities-
charge, current, voltage, and magnetic flux to one another. These can be related
in six ways. Two are connected through the basic physical laws of electricity
and magnetism, and three are related by the known circuit elements: resistors
connect voltage and current, inductors connect flux and current, and capacitors
connect voltage and charge. But one equation is missing from this group: the
relationship between charge moving through a circuit and the magnetic flux
surrounded by that circuit. That is what memristor, connecting charge and flux.
Even before Chua had his eureka moment, however, many researchers
were reporting what they called anomalous current-voltage behavior in the
micrometer-scale devices they had built out of unconventional materials, like
polymers and metal oxides. But the idiosyncrasies were usually ascribed to
some mystery electrochemical reaction, electrical breakdown, or other spurious
phenomenon attributed to the high voltages that researchers were applying to
their devices.
Leon’s discovery is similar to that of the Russian chemist Dmitri
Mendeleev who created and used a periodic table in 1869 to find many
unknown properties and missing elements.
4

11. Even though Memristance was first predicted by Professor Leon Chua,
Unfortunately, neither he nor the rest of the engineering community could come
up with a physical manifestation that matched his mathematical expression.
Thirty-seven years later, a group of scientists from HP Labs has finally
built real working memristors, thus adding a fourth basic circuit element to
electrical circuit theory, one that will join the three better-known ones: the
capacitor, resistor and the inductor.
Interest in the memristor revived in 2008 when an experimental solid
state version was reported by R. Stanley Williams of Hewlett Packard. HP
researchers built their memristor when they were trying to develop molecule-
sized switches in Teramac (tera-operation-persecond multiarchitecture
computer). Teramac architecture was the crossbar, which has since become the
de facto standard for nanoscale circuits because of its simplicity, adaptability,
and redundancy.
A solid-state device could not be constructed until the unusual behavior
of nanoscale materials was better understood. The device neither uses magnetic
flux as the theoretical memristor suggested, nor do stores charge as a capacitor
does, but instead achieves a resistance dependent on the history of current using
a chemical mechanism.
The HP team’s memristor design consisted of two sets of 21 parallel 40-
nm-wide wires crossing over each other to form a crossbar array, fabricated
using nano imprint lithography. A 20-nm-thick layer of the semiconductor
titanium dioxide (TiO2) was sandwiched between the horizontal and vertical
nanowires, forming a memristor at the intersection of each wire pair. An array
of field effect transistors surrounded the memristor crossbar array, and the
memristors and transistors were connected to each other through metal traces.
The crossbar is an array of perpendicular wires. Anywhere two wires
cross, they are connected by a switch. To connect a horizontal wire to a vertical
wire at any point on the grid, you must close the switch between them. Note that
a crossbar array is basically a storage system, with an open switch representing
a zero and a closed switch representing a one. You read the data by probing the
switch with a small voltage. Because of their simplicity, crossbar arrays have a
3 ADVENT OF HP LABS
5

12. much higher density of switches than a comparable integrated circuit based on
transistors.
Stanley Williams found an ideal memristor in titanium dioxide the stuff
of white paint and sunscreen. In TiO2, the dopants don't stay stationary in a high
electric field; they tend to drift in the direction of the current. Titanium dioxide
oxygen atoms are negatively charged ions and its electrical field is huge. This
lets oxygen ions move and change the material’s conductivity, a necessity for
memristors.
The researchers then sandwiched two thin titanium dioxide layers between
two 5 nm thick electrodes. Applying a small electrical current causes the atoms
to move around and quickly switch the material from conductive to resistive,
which enables memristor functionality.
When an electric field is applied, the oxygen vacancies drift changing the
boundary between the high-resistance and low-resistance layers. Thus the
resistance of the film as a whole is dependent on how much charge has been
passed through it in a particular direction, which is reversible by changing the
direction of current. Since the HP device displays fast ion conduction at
nanoscale, it is considered a nanoionic device In the process, the device uses
little energy and generates only small amounts of heat. Also, when the device
shuts down, the oxygen atoms stay put, retaining their state and the data they
represent.
On April 30, 2008, the Hewlett-Packard research team proudly announced
their realization of a memristor prototype.
6

13. Origin of the Memristor :-
There are four fundamental circuit variables in circuit theory. They are
current, voltage, charge and flux. There are six possible combinations of the
four fundamental circuit variables. We have a good understanding of five of
the possible six combinations. The three basic two-terminal devices of
circuit theory namely, the resistor, the capacitor and the inductor are defined
in terms of the relation between two of the four fundamental circuit
variables. A resistor is defined by the relationship between voltage and
current, the capacitor is defined by the relationship between charge and
voltage and the inductor is defined by the relationship between flux and
current. In addition, the current is defined as the time derivative of the
charge and according to Faraday’s law the voltage is defined as the time
derivative of the flux. These relations are shown in Fig. 2
Fig.2: The three circuit elements defined as a relation between four circuit variables
4 MEMRISTOR THEORY
7

14. Definition of a Memristor :-
Memristor, the contraction of memory resistor, is a passive device that
provides a functional relation between charge and flux. It is defined as a
two-terminal circuit element in which the flux between the two terminals is
a function of the amount of electric charge that has passed through the
device. Memristor is not an energy storage element. Fig. 3 shows the
symbol for a memristor.
Fig.3: Symbol of the memristor
A memristor is said to be charge-controlled if the relation between flux and
charge is expressed as a function of electric charge and it is said to be flux-
controlled if the relation between flux and charge is expressed as a function
of the flux linkage.
What is Memristance?
Memristance is a property of the memristor. When charge flows in a
direction through a circuit, the resistance of the memristor increases. When
it flows in the opposite direction, the resistance of the memristor decreases.
If the applied voltage is turned off, thus stopping the flow of charge, the
memristor remembers the last resistance that it had. When the flow of
charge is started again, the resistance of the circuit will be what it was
when it was last active.
8

15. The memristor is essentially a two-terminal variable resistor, with
resistance dependent upon the amount of charge q that has passed between
the terminals.
To relate the memristor to the resistor, capacitor, and inductor, it is helpful
to isolate the term M(q), which characterizes the device, and write it as a
differential equation:
Where Q is defined by and ϕ is defined by
The variable Φ ("magnetic flux linkage") is generalized from the circuit
characteristic of an inductor. The symbol Φ may simply be regarded as the
integral of voltage over time.
Thus, the memristor is formally defined as a two-terminal element in which
the flux linkage (or integral of voltage) Φ between the terminals is a
function of the amount of electric charge Q that has passed through the
device. Each memristor is characterized by its memristance function
describing the charge-dependent rate of change of flux with charge.
Substituting that the flux is simply the time integral of the voltage, and
charge is the time integral of current, we may write the more convenient
form
It can be inferred from this that memristance is simply charge-dependent
resistance. If M(q(t)) is a constant, then we obtain Ohm's law
R(t) = V(t)/ I(t).However, the equation is not equivalent because q(t) and
M(q(t)) will vary with time.
9

16. Solving for voltage as a function of time we obtain
This equation reveals that memristance defines a linear relationship
between current and voltage, as long as M does not vary with charge.
Furthermore, the memristor is static if no current is applied. If I(t) = 0, we
find V(t) = 0 and M(t) is constant. This is the essence of the memory
effect.
The power consumption characteristic recalls that of a resistor, I2
R
As long as M(q(t)) varies little, such as under alternating current, the
memristor will appear as a constant resistor.
Properties of a Memristor
 Current–Voltage Curve of a Memristor
An important fingerprint of a memristor is the pinched hysteresis
loop current voltage characteristic. For a memristor excited by a
periodic signal, when the voltage v(t) is zero, the current i(t) is also
zero and vice versa. Thus, both voltage v(t) and current i(t) have
identical zero-crossing. Another signature of the memristor is that
the ―pinched hysteresis loop‖ shrinks with the increase in the
excitation frequency. Figure 4 shows the pinched hysteresis loop‖
and an example of the loop shrinking with the increase in
frequency. In fact, when the excitation frequency increases towards
infinity, the memristor behaves as a normal resistor.
10

17. Fig. 4: The pinched hysteresis loop and the loop shrinking with the increase in
frequency
 HYSTERESIS MODEL
Hysteresis model illustrates an idealized resistance behavior
demonstrated in accordance with above current-voltage
characteristic wherein the linear regions correspond to a relatively
high resistance (RH) and low resistance (RL) and the transition
regions are represented by straight lines.
Fig 5: Idealized hysteresis model of resistance vs. voltage for memristance switch.
Thus for voltages within a threshold region (-VL2<V<VL1 in Fig.
5) either a high or low resistance exists for the Memristor. For a
voltage above threshold VL1 the resistance switches from a high to
a low level and for a voltage of opposite polarity above threshold
VL2 the resistance switches back to a high resistance.
11

18. This new circuit element shares many of the properties of resistors and shares
the same unit of measurement (ohms). However, in contrast to ordinary
resistors, in which the resistance is permanently fixed, memristance may be
programmed or switched to different resistance states based on the history of the
voltage applied to the memristance material. This phenomena can be understood
graphically in terms of the relationship between the current flowing through a
memristor and the voltage applied across the memristor. In ordinary resistors
there is a linear relationship between current and voltage so that a graph
comparing current and voltage results in a straight line. However, for
memristors a similar graph is a little more complicated.
Fig 6: Current voltage characteristic of resistor and memristor
5 MEMRISTOR AND RESISTOR
12

19. The first transistor was a couple of inches across which was developed about 60
years ago. Today, a typical laptop computer uses a processor chip that contains
over a billion transistors, each one with electrodes separated by less than 50 nm
of silicon. This is more than a 1000 times smaller than the diameter of a human
hair. These billions of transistors are made by top down methods that involve
depositing thin layers of materials, patterning nano-scale stencils and effectively
carving away the unwanted bits. This approach has become overly successful.
The end result is billions of individual components on a single chip, essentially
all working perfectly and continuously for years on end. No other manufactured
technology comes close in reliability or cost.
Still, miniaturization cannot go on forever, because of the basic properties
of matter. We are already beginning to run into the problem that the silicon
semiconductor, copper wiring and oxide insulating layers in these devices are
all made out of atoms. Each atom is about 0.3 nm across.
The entire body of the transistor is being doped less consistently
throughout as its sizes are reduced below the nanometers which make the
transistor more unpredictable in nature. It will be more difficult and costly to
press forward additional research and equipment involving these unpredictable
behaviors as they occur. Therefore the electronic designs will have to replace
their transistors to the memristors which are not steadily infinitesimal, but
increasingly capable.
The memristor is very likely to follow the similar steps of how the
transistor was implemented in our electronic systems. They may argue that the
transistor took approximately sixty years to reach the extent of today’s research
and capabilities. Therefore, the memristors may take approximately just as long
to actually create some of its promising potentials such as artificial intelligence.
This new advancement means more jobs for research and development and
more potential for inventions and designs. Also, the dependency on getting the
transistors to work efficiently in atom sized is lessened.
6 MEMRISTOR VS TRANSISTOR
13

20. Transistor Memristor
3-terminal switching device with
an input electrode (e.g. source),
an output electrode (e.g. drain),
and a control electrode (e.g. gate).
Requires a power source to retain
a data state.
Stores data by electron charge.
Scalable by reducing the lateral
length and width dimensions
between the input and output
electrodes.
Capable of performing analog or
digital electronic functions
depending on applied bias
voltages.
Fabrication requires optical
lithography.
2-terminal device with one of the
electrodes acting either as a
control electrode or a source
electrode depending on the
voltage magnitude.
Does not require a power source
to retain a data state.
Stores data by resistance state.
Scalable by reducing the
thickness of the memristor
materials.
Capable of performing analog or
digital electronic functions
depending on particular material
used for memristor.
Fabrication by optical lithography
but alternative (potentially
cheaper) mass production
techniques such as nano imprint
lithography and self assembly
have also been implemented
Another reason for incorporating memristors is the materials used to make each
element. Transistors are usually made of silicon, a non-metal. While this has
proven to be a very reliable source, it returns to the problem of transistors
needing to become smaller. Because they are made of a non-metal it is much
harder to make them much smaller. Memristors, on the other hand, are made of
titanium oxide. Titanium is a metal which is much easier to make into smaller
size. Since memristors have twelve times the power of transistors, however,
products can be made smaller and more powerful without reducing the size of
the product that powers them.
14

21. HP Labs' memristor has Crossbar type memristive circuits contain a lattice of
40-50nm wide by 2-3nm thick platinum wires that are laid on top of one another
perpendicular top to bottom and parallel of one another side to side. The top and
bottom layer are separated by a switching element approximately 3-30nm in
thickness. The switching element consists of two equal parts of titanium dioxide
(TiO2). The layer connected to the bottom platinum wire is initially perfect
TiO2 and the other half is an oxygen deficient layer of TiO2 represented by
TiO2-x where x represents the amount of oxygen deficiencies or vacancies. The
entire circuit and mechanism cannot be seen by the naked eye and must be
viewed under a scanning tunneling microscope, as seen in Figure 6, in order to
visualize the physical set up of the crossbar design of the memristive circuit
described in this section.
Fig 7: figure showing crossbar architecture and magnified memristive switch having
platinum electrodes and 2 layers of TiO2
7 APPEARANCE OF MEMRISTOR
15

22. The memristor’s operation as a switch can be explained in three steps. These
first of these steps is the application of power or more importantly current to the
memristor. The second step consists of the amount of time that the current flows
across the crossbar gap and how the titanium cube converts from a semi-
conductor to a conductor. The final step is the actual memory of the cube that
can be read as data.
STEP 1:-
As explained above, each gap that connects two platinum wires contains a
mixture of two titanium oxide layers. The initial state of the mixture is halfway
between conductance and semi-conductance. Two wires are selected to apply
power to in either a positive or negative direction. A positive direction will
attempt to close the switch and a negative direction will attempt to open the
switch. The application of this power will be able to completely open the circuit
between the wires but it will not be able to completely close the circuit since the
material is still a semi-conductor by nature. Power can be selectively placed on
certain wires to open and close the switches in the memristor.
Fig 8: TiO2-x layer having oxygen deficiencies over insulating TiO2 layer. (b) Positive
voltage applied to top layer repels oxygen deficiencies in to the insulating TiO2 layer
below. (c) Negative voltage on the switch attracts the positively charged oxygen bubbles
pulling them out of the TiO2.
8 MEMRISTOR OPERATION
16

23. STEP 2:-
The second step involves a process that takes place at the atom level and is not
visible by any means. It involves the atomic process that the gap material, made
from titanium dioxide, goes through that opens and closes the switch. The initial
state of the gap is neutral meaning that it consists of one half of pure titanium
dioxide TiO2 and one half of oxygen starved titanium dioxide TiO2-x where x
in the initial state is 0.05. As positive current is applied, the positively charged
oxygen vacancies push their way into the pure TiO2 causing the resistance in
the gap material to drop, becoming more conductive, and the current to rise.
Inversely, as a negative current is applied the oxygen vacancies withdraw from
the pure TiO2 and condense in the TiO2-x half of the gap material causing the
pure and more resistive TiO2 to have a greater ratio slowing the current in the
circuit. When the current is raised the switch is considered open (HI) and for
data purposes a binary 1. As current is reversed and the current is dropped the
switch is considered closed (LOW) or a binary 0 for data purposes.
STEP 3:-
Step three explains the final step of memristance and is the actual step that
makes the circuit memristive in nature. As explained previously, the concept of
memristance is a resistor that can remember what current passed through it.
When power is no longer applied to the circuit switches, the oxygen vacancies
remain in the position that they were last before the power was shut down. This
means that the value of the resistance of the material gap will remain until
indefinitely until power is applied again. This is the true meaning of
memristance. With an insignificant test voltage, one that won’t affect the
movement of molecules in the material gap will allow the state of the switches
to be read as data. This means that the memristor circuits are in fact storing data
physically.
If we want a positive voltage to turn the memristor off, then we want the
titanium oxide layer with vacancies on the top layer. But if you want a positive
voltage to turn the memristor on, then you need the layers reversed. In its initial
state, a crossbar memory has only open switches, and no information is stored.
But once you start closing switches, you can store vast amounts of information
compactly and efficiently.
17

24. A common analogy to describe a memristor is similar to that of a resistor. Think
of a resistor as a pipe through which water flows. The water is electric charge.
The resistor’s obstruction of the flow of charge is comparable to the diameter of
the pipe: the narrower the pipe, the greater the resistance. For the history of
circuit design, resistors have had a fixed pipe diameter. But a memristor is a
pipe that changes diameter with the amount and direction of water that flows
through it. If water flows through this pipe in one direction, it expands
(becoming less resistive). But send the water in the opposite direction and the
pipe shrinks (becoming more resistive). Further, the memristor remembers its
diameter when water last went through. Turn off the flow and the diameter of
the pipe freezes until the water is turned back on. , the pipe will retain it most
recent diameter until the water is turned back on. Thus, the pipe does not store
water like a bucket (or a capacitor) – it remembers how much water flowed
through it.
Fig 9 .Schematic diagram of pipe and current example
The reason that the memristor is radically different from the other fundamental
circuit elements is that, unlike them, it carries a memory of its past. When you
turn off the voltage to the circuit, the memristor still remembers how much was
applied before and for how long. That's an effect that can't be duplicated by any
9 PIPE AND CURRENT ANALOGY
18

25. circuit combination of resistors, capacitors, and inductors, which is why the
memristor qualifies as a fundamental circuit element. Technically such a
mechanism can be replicated using transistors and capacitors, but, it takes a lot
of transistors and capacitors to do the job of a single memristor.
Memristance is measured by the electrical component memristor. The way
a resistor measures resistance, a conductor measures conduction, and an
inductor measures inductance, a memristor measures memristance. An ideal
memristor is a passive two-terminal electronic device that expresses only
memristance. However it is difficult to build a pure memristor, since every real
device contains a small amount of another property.
Two properties of the memristor attracted much attention. Firstly, its
memory characteristic, and, secondly, its nanometer dimensions. The memory
property and latching capability enable us to think about new methods for nano-
computing. With the nanometer scale device provides a very high density and is
less power hungry. In addition, the fabrication process of nano-devices is
simpler and cheaper than the conventional CMOS fabrication, at the cost of
extra device defects.
At the architectural level, a crossbar-based architecture appears to be the
most promising nanotechnology architecture. Inherent defect-tolerance
capability, simplicity, flexibility, scalability, and providing maximum density
are the major advantages of this architecture by using a memristor at each cross
point.
Memristors are passive elements, meaning they cannot introduce energy
into a circuit. In order to function, memristors need to be integrated into circuits
that contain active elements, such as transistors, which can amplify or switch
electronic signals. A circuit containing both memristors and transistors could
have the advantage of providing enhanced functionality with fewer components,
in turn minimizing chip area and power consumption.
19

26.  NON-VOLATILE MEMORY : -
Non-volatile memory is the dominant area being pursued for memristor
technology. Of course most of the companies listed (with the exception
of Hewlett Packard) do not refer to their memory in terms of the
memristor and rather use a variety of acronyms (i.e. RRAM, CBRAM,
PRAM, etc.) to distinguish their particular memory design. While these
acronyms do represent real distinctions in terms of the materials used or
the mechanism of resistance switching employed, the materials are still
all memristors because they all share the same characteristic voltage-
induced resistance switching behavior covered by the mathematical
memristor model of Chua. Flash memory currently dominates the
semiconductor memory market. However, each memory cell of flash
requires at least one transistor meaning that flash design is highly
susceptible to an end to Moore’s law. On the other hand, memristor
memory design is often based on a crossbar architecture which does not
require transistors in the memory cells. Although transistors are still
necessary for the read/write circuitry, the total number of transistors for a
million memory cells can be on the order of thousands instead of
millions and the potential for addressing trillions of memory cells exists
using only millions (instead of trillions) of transistors. Another
fundamental limitation to conventional memory architectures is Von
Neumann’s bottleneck which makes it more difficult to locate
information as memory density increases. Memristors offer a way to
overcome this hurdle since they can integrate memory and processing
functions in a common circuit architecture providing a de-segregation
between processing circuitry and data storage circuitry.
 LOGIC/COMPUTATION : -
The uses of memristor technology for logic and computational electronics
is less well developed than for memory architectures but the seeds of
innovation in this area are currently being sown. Memristors appear
particularly important to the areas of reconfigurable computing
architectures such as FPGAs in which the arrangement between arrays of
basic logic gates can be altered by reprogramming the wiring
interconnections. Memristors may be ideal to improve the integration
density and reconfigurability of such systems. In addition, since some
10 APPLICATIONS
20

27. memristor materials are capable of tunablity in their resistance state they
can provide new types of analog computational systems which may find
uses in modeling probabilistic systems (e.g. weather, stock market, bio
systems) more efficiently than purely binary logic-based processors.
 NEUROMORPHIC ELECTRONICS: -
Neuromorphics has been defined in terms of electronic analog circuits
that mimic neurobiological architectures. Since the early papers of Leon
Chua it was noted that the equations of the memristor were closely related
to behavior of neural cells. Since memristors integrate aspects of both
memory storage and signal processing in a similar manner to neural
synapses they may be ideal to create a synthetic electronic system similar
to the human brain capable of handling applications such as pattern
recognition and adaptive control of robotics better than what is achievable
with modern computer architectures.
Fig 10: neural networks
21

28.  MEMRISTOR MEMORY : -
Memristors can be used as non-volatile memory, allowing greater data
density than hard drives. The memristor based crossbar latch memory
prototyped by HP can fit 100 gigabits within a square centimeter. HP also
claims that memristor memory can handle up to 1,000,000 read/write
cycles before degradation, compared to flash at 100,000 cycles. In
addition, memristors also consume less power.
In memristor memories, the reading operation is performed by
applying a voltage lesser than the threshold value. The memristor will
conduct even at this voltage if it is on. If it is off then it will not conduct.
To write one of the logic levels (0 or 1) a voltage greater than the
threshold value is applied. To write the other logic level, a voltage of
opposite polarity whose magnitude is greater than the threshold voltage is
applied. This turns the memristor off.
Memristors can remember even when the power is turned off. Thus, the
computers developed using memristors will have no boot up time. The
computer can be turned on, like turning on a light switch and it will
instantly display all information that was there on it when it was turned
off.
22

29.  Provides greater resiliency and reliability when power is interrupted in
data centers.
 Have great data density.
 Combines the jobs of working memory and hard drives into one tiny
device.
 Faster and less expensive than MRAM.
 Uses less energy and produces less heat.
 Would allow for a quicker boot up since information is not lost when
the device is turned off.
 Operating outside of 0s and 1s allows it to imitate brain functions.
 Does not lose information when turned off.
 Has the capacity to remember the charge that flows through it at a given
point in time.
 Conventional devices use only 0 and 1; Memristor can use anything
between 0 and 1(0.3, 0.8, 0.5, etc.)
 Faster than Flash memory.
 By changing the speed and strength of the current, it is possible to
change the behavior of the device.
 A fast and hard current causes it to act as a digital device.
 A soft and slow current causes it to act as an analog device.
 100 GBs of memory made from memristors on same area of 16 GBs of
flash memory.
 High Defect Tolerance allows high defects to still produce high yields
as opposed to one bad transistor which can kill a CPU.
 Compatible with current CMOS interfaces.
 As non-volatile memory, memristors do not consume power when idle.
 3 Memristors to make a NAND gate, 27 NAND gates to make a
Memristor!!!
 More magnetic than magnetic disks.
11 BENEFITS OF MEMRISTOR
23

30. Memristor bridges the capability gaps that electronics will face in the near
future according to Moore’s Law and will replace the transistor as the main
component on integrated circuit (IC) chips.
The possibilities are endless since the memristor provides the gap to
miniaturizing functional computer memory past the physical limit currently
being approached upon by transistor technology.
When is it coming? Researchers say that no real barrier prevents
implementing the memristor in circuitry immediately. But it's up to the business
side to push products through to commercial reality. Memristors made to
replace flash memory (at lower cost and lower power consumption) 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.
Fig 11: Flexible memory
12 FUTURE
24

31. Thus the discovery of a brand new fundamental circuit element is something not
to be taken lightly and has the potential to open the door to a brand new type of
electronics. Memristor will change circuit design in the 21st century as radically
as the transistor changed it in the 20th. Note that the transistor was lounging
around as a mainly academic curiosity for a decade until 1956, when a
revolutionary app the hearing aid brought it into the marketplace.
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. In fact, it
can be hoped to combine Memristors with traditional circuit-design elements to
produce a device that does computation. The Hewlett-Packard (HP) group is
looking at developing a memristor-based nonvolatile memory that could be
1000 times faster than magnetic disks and use much less power.
Memristor open door to a wide area of research in the field of computer
hardware and memory storage devices that has much higher data density. As
rightly said by the originators of memristor, Leon Chua and R . Stanley
Williams, ―Memristors are so significant that it would be mandatory to re-
write the existing electronic engineering textbooks.‖
13 CONCLUSION
25

32. 1. Memristor resistance modulation for analog applications Tsung Wen Lee
and Janice H Nickel IEEE,electron device letters, vol 33,oct ,2012
2. Memristor applications for programmable analog ICs, Sangho Shin and
Kyungmin Kim,IEEE Transactions on nanotechnology, vol 10,2011
3. Compact models for memristors based on charge flux constitutive
relationships, IEEE,2010 IEEE Spectrum: The Mysterious Memristor By
Sally Adee http://www.spectrum.ieee.org/may08/6207
4. Memristors Ready For Prime Time R. Colin Johnson
URL:http://www.eetimes.com/showArticle.jhtml?articleID=208803176
5. Flexible memristor: Memory with a twist Vol. 453, May 1, 2008.
PHYSorg.com
6. L. O. Chua, Memristor The missing circuit element, IEEE Trans. Circuit
Theory, vol. CT-18, pp. 507–519, 1971.
7. Memristor - Wikipedia, the free encyclopedia
8. http://www.hpl.hp.com/
9. How We Found the Missing Memristor‖ By R. Stanley Williams,
December 2008 · IEEE Spectrum, www.spectrum.ieee.org
10. http://avsonline.blogspot.com/
11. http://memristor.pbworks.com/
12. http://4engr.com/
13. http://knol.google.com/
14. http://newsvote.bbc.co.uk/mpapps/pagetools/email/news.bbc.co.uk/2/
hi/technology/7377 063.stm
15. http://hubpages.com/topics/technology/5338
16. http://totallyexplained.com/
14 BIBLIOGRAPHY
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