RVR Institute of Engineering & Technology 1. INTRODUCTION 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 (themselves 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. EEE Department 1
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RVR Institute of Engineering & Technology
1. INTRODUCTION
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 (themselves 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.
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.
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2. HISTORY
The transistor was invented in 1925 but lay dormant until finding a corporate
champion in BellLabs during the 1950s. Now another groundbreaking electronic circuit
may be poised for the same kind of success after laying dormant as an academic curiosity
for more than three decades. Hewlett-Packard Labs is trying to bring the memristor, the
fourth passive circuit element after the resistor, and the capacitor the inductor into the
electronics mainstream. Postulated in 1971, the “memory resistor” represents a potential
revolution in electronic circuit theory similar to the invention of transistor.
The history of the memristor can be traced back to nearly four decades ago when
in 1971, Leon Chua, a University of California, Berkeley, engineer predicted that there
should be a fourth passive circuit element in addition to the other three known passive
elements namely the resistor, the capacitor and the inductor. He called this fourth element
a “memory resistor” or a memristor. Examining the relationship between charge, current,
voltage and flux in resistors, capacitors, and inductors in a 1971 paper, Chua postulated
the existence of memristor. Such a device, he figured, would provide a similar
relationship between magnetic flux and charge that a resistor gives between voltage and
current. In practice, that would mean it acted like a resistor whose value could vary
according to the current passing through it and which would remember that
value even after the current disappeared.
Fig1. The Simplest Chua’s Circuit. Fig2. Realization of Four Element Chua’s Circuit, NR
is Chua Diode. Fig3. Showing Memristor as Fourth Basic Element. But the hypothetical
device was mostly written off as a mathematical dalliance. However, it took more than
three decades for the memristor to be discovered and come to life. Thirty years after
Chua’s Proposal of this mysterious device, HP senior fellow Stanley Williams and his
group were working on molecular electronics when they started to notice strange
behavior in their devices. One of his HP collaborators, Greg Snider, then rediscovered
Chua's work from 1971. Williams spent several years reading and rereading Chua's
papers. It was then that Williams realized that their molecular devices were really
memristors.
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Fig2.1. The Simplest Chua’s Circuit
Fig2.2 Realization of Four Element Fig2.3 Showing Memristor as Fourth
Chua’s Circuit Basic Element
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3.NEED FOR MEMRISTOR
A memristor is one of four basic electrical circuit components, joining the
resistor, capacitor, and inductor. The memristor, short for “memory resistor” was first
theorized by student Leon Chua in the early 1970s. He developed mathematical equations
to represent the memristor, which Chua believed would balance the functions of the other
three types of circuit elements.
The known three fundamental circuit elements as resistor, capacitor and
inductor relates four fundamental circuit variables as electric current, voltage, charge and
magnetic flux. In that we were missing one to relate charge to magnetic flux. That is
where the need for the fourth fundamental element comes in. This element has been
named as memristor.
Memristance (Memory + Resistance) is a property of an Electrical Component
that describes the variation in Resistance of a component with the flow of charge. Any
two terminal electrical component that exhibits Memristance is known as a Memristor.
Memristance is becoming more relevant and necessary as we approach smaller circuits,
and at some point when we scale into nano electronics, we would have to take
memristance into account in our circuit models to simulate and design electronic circuits
properly. An ideal memristor is a passive two-terminal electronic device that is built to
express only the property of memristance (just as a resistor expresses resistance and an
inductor expresses inductance). However, in practice it may be difficult to build a 'pure
memristor,' since a real device may also have a small amount of some other property,
such as capacitance (just as any real inductor also has resistance).A common analogy for
a resistor is a pipe that carries water. The water itself is analogous to electrical charge, the
pressure at the input of the pipe is similar to voltage, and the rate of flow of the water
through the pipe is like electrical current. Just as with an electrical resistor, the flow of
water through the pipe is faster if the pipe is shorter and/or it has a larger diameter. An
analogy for a memristor is an interesting kind of pipe that expands or shrinks when water
flows through it. If water flows through the pipe in one direction, the diameter of the pipe
increases, thus enabling the water to flow faster. If water flows through the pipe in the
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opposite direction, the diameter of the pipe decreases, thus slowing down the flow of
water. If the water pressure is turned off, 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.
Possible applications of a Memristor include Nonvolatile Random Access
Memory (NVRAM), a device that can retain memory information even after being
switched off, unlike conventional DRAM which erases itself when it is switched off.
Another interesting application is analog computation where a memristor will be able to
deal with analog values of data and not just binary 1s and 0s.
Figure 3.1 Fundamental circuit Elements and Variables.
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4. TYPES OF MEMRISTOR
• Titanium dioxide memristor
• Polymeric memristor
• Spin memristive systems
• Magnetite memristive systems
• Resonant tunneling diode memristor
4.1 Titnium Doxide memristor:-
Interest in the memristor revived in 2008 when an experimental solid state version
was reported by R. Stanley Williams of Hewlett Packard. 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 stores
charge as a capacitor does, but instead achieves a resistance dependent on the history of
current using a chemical mechanism.
The HP device is composed of a thin (5 nm) titanium dioxide film between two
electrodes. Initially, there are two layers to the film, one of which has a slight depletion
of oxygen atoms. The oxygen vacancies act as charge carriers, meaning that the depleted
layer has a much lower resistance than the non-depleted layer. When an electric field is
applied, the oxygen vacancies drift (see Fast ion conductor), 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.
Memristance is displayed only when both the doped layer and depleted layer contribute
to resistance. When enough charge has passed through the memristor that the ions can no
longer move, the device enters hysteresis. It ceases to integrate q=∫Idt but rather keeps q
at an upper bound and M fixed, thus acting as a resistor until current is reversed.
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Memory applications of thin-film oxides had been an area of active investigation
for some time. IBM published an article in 2000 regarding structures similar to that
described by Williams.Samsung has a pending U.S. patent application for several oxide-
layer based switches similar to that described by Williams. Williams also has a pending
U.S. patent application related to the memristor construction.
Although the HP memristor is a major discovery for electrical engineering theory,
it has yet to be demonstrated in operation at practical speeds and densities. Graphs in
Williams' original report show switching operation at only ~1 Hz. Although the small
dimensions of the device seem to imply fast operation, the charge carriers move very
slowly. In comparison, the highest known drift ionic mobilities occur in advanced
superionic conductors, such as rubidium silver iodide with about 2×10−4 cm²/(V·s)
conducting silver ions at room temperature. Electrons and holes in silicon have a mobility
~1000 cm²/(V·s), a figure which is essential to the performance of transistors. However, a
relatively low bias of 1 volt was used, and the plots appear to be generated by a
mathematical model rather than a laboratory experiment.
4.2 Polymeric memristor:-
In July 2008, Victor Erokhin and Marco P. Fontana, in Electrochemically
controlled polymeric device: a memristor (and more) found two years ago,claim to have
developed a polymeric memristor before the titanium dioxide memristor more recently
announced.
4.3 Spin memristive systems:-
A fundamentally different mechanism for memristive behavior has been proposed
by Yuriy V. Pershin and Massimiliano Di Ventra in their paper "Spin memristive
systems". The authors show that certain types of semiconductor spintronic structures
belong to a broad class of memristive systems as defined by Chua and Kang. The
mechanism of memristive behavior in such structures is based entirely on the electron
spin degree of freedom which allows for a more convenient control than the ionic
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transport in nanostructures. When an external control parameter (such as voltage) is
changed, the adjustment of electron spin polarization is delayed because of the diffusion
and relaxation processes causing a hysteresis-type behavior.
This result was anticipated in the study of spin extraction at semiconductor/ferromagnet
interfaces,but was not described in terms of memristive behavior. On a short time scale,
these structures behave almost as an ideal memristor this result broadens the possible
range of applications of semiconductor spintronics and makes a step forward in future
practical application of the concept of memristive systems.
4.4 Manganite memristive systems:-
Although not described using the word "memristor", a study was done of bilayer
oxide films based on manganite for non-volatile memory by researchers at the University
of Houston in 2001. Some of the graphs indicate a tunable resistance based on the
number of applied voltage pulses similar to the effects found in the titanium dioxide
memristor materials described in the Nature paper "The missing memristor found".
4.5 Resonant Tunneling Diode Memristor:-
In 1994, F. A. Buot and A. K. Rajagopal of the U.S. Naval Research Laboratory
demonstrated that a ‘bow-tie’ current-voltage (I-V) characteristics occurs in
AlAs/GaAs/AlAs quantum-well diodes containing special doping design of the spacer
layers in the source and drain regions, in agreement with the published experimental
results. This ‘bow-tie’ current-voltage (I-V) characteristic is sine qua non of a memristor
although the term memristor is not explicitly mentioned in their papers. No magnetic
interaction is involved in the analysis of the ‘bow-tie’ I-V characteristics.
.
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5. MEMRISTOR THEORY AND ITS PROPERTIES
5.1 Definition of Memristor:-
“The memristor is formally defined as a two-terminal element in which the
magnetic flux Φm between the terminals is a function of the amount of electric charge q
that has passed through the device.”
Figure 5.1. Symbol of Memristor.
Chua defined the element as a resistor whose resistance level was based on the
amount of charge that had passed through the memristor
5.2 Memristance:-
Memristance is a property of an electronic component to retain its resistance
level even after power had been shut down or lets it remember (or recall) the last
resistance it had before being shut off.
5.3 Theory:-
Each memristor is characterized by its memristance function describing the
charge-dependent rate of change of flux with charge.
……………………………….5.3.1
Noting from Faraday's law of induction that magnetic flux is simply the
time integral of voltage, and charge is the time integral of current, we may write the more