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Published on Apr 02, 2024


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.

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.

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

Titanium Dioxide Memristor It is a solid state device that uses nano scale thin-ilms to produce a Memristor. The device consists of a thin titanium dioxide film (50nm) in between two electrodes (5nm) one Titanium and the other latinum. Initially, there are two layers to the titanium dioxide film, one of which has a slight depletion of oxygen atoms. The oxygen vacancies act as charge carriers and this implies that the depleted layer has a much lower resistance than the no depleted layer. 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.


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. 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


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.


Each memristor is characterized by its memristance function describing the charge-dependent rate of change of flux with charge. 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 convenient form It can be inferred from this that memristance is simply charge-dependent resistance. . i.e. ,

V(t) = M(q(t))*I(t)

This equation reveals that memristance defines a linear relationship between current and voltage, as long as charge does not vary. Of course, nonzero current implies instantaneously varying charge. Alternating current, however, may reveal the linear dependence in circuit operation by inducing a measurable voltage without net charge movement as long as the maximum change in q does not cause much change in M.

Current vs. Voltage characteristics

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 as shown in Fig. 3 illustrates the current vs. voltage behavior of memristance.

In contrast to the straight line expected from most resistors the behavior of a memristor appear closer to that found in hysteresis curves associated with magnetic materials. It is notable from Fig. 3 that two straight line segments are formed within the curve. 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.

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