1 CHAPTER 1 INTRODUCTION 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. 1.1. 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.
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CHAPTER 1
INTRODUCTION
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.
1.1. 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.
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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.
1.2. HISTORY
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 domi-
nate 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
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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.1.1 : Describing the relation between charge,
current, voltage and magnetic flux to one another
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.
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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.
1.2.1. HP’s first step:
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-per-second
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 nanoimprint 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,