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In electrical circuit theory, the memristor is a passive circuit element. It has been described as the fourth basic type of passive circuit element, alongside the well-known capacitor, resistor, and inductor.^[1] The name is a portmanteau of memory resistor. Since news of the creation of a working memristor in April 2008, the memristor is popularly being referred to, accurately, as a flux capacitor due to memristance being a relation between charge and magnetic flux; this is a humorous reference to the flux capacitor from the Back to the Future trilogy. ^{[citation needed]}

Although the memristor was predicted and described in 1971 by Leon Chua of UC Berkeley, in a paper in IEEE Transactions on Circuit Theory,^[2] it was a hypothetical device for 37 years, with no known physical examples. In April 2008, a working memristor was announced by a team of researchers at HP Labs.^[3]^[4]^[5]

The era of nanoscale electronics will be enabled by the memristor. This is not just an invention, it is a basic scientific discovery.
— Leon Chua, April 2008, EETimes^[6]

The new circuit element will enable the development of new class of high-density digital memory. Performance of memristors improves as they are scaled down, and they generate less heat than transistors. The memristor also has unique analog properties that may lead to the invention of other devices.^[6]

Definition

The memristor is an element in which the magnetic flux $\Phi _{m}$ is a function of the accumulated electric charge q in the device. The rate of change of flux with charge

M(q)={\frac {\mathrm {d} \Phi _{m}}{\mathrm {d} q}}

is known as memristance. This is comparable to the other three fundamental circuit elements:

Resistance: $R(I)={\frac {\mathrm {d} V}{\mathrm {d} I}}$
Inductance: $L(I)={\frac {\mathrm {d} \Phi _{m}}{\mathrm {d} I}}$
Capacitance: ${\frac {1}{C(q)}}={\frac {\mathrm {d} V}{\mathrm {d} q}}$

Here $q$ is electrical charge, $I$ is electrical current, $V$ is electrical potential and $\Phi _{m}$ is magnetic flux. The differential forms of these equations are used because we are comparing non-linear circuit elements; a linear memristor would be uninteresting, as explained below.

Applying Faraday's Law of Induction and the chain rule to the equation defining the memristance, one obtains that the voltage V across a memristor is related to the current I by the instantaneous value of the memristance:

V(t)=M(q(t))I(t)\,

Thus at any given instant, a memristor behaves like an ordinary resistor. However, its "resistance" M(q) is a value which depends on the charge accumulated in the device. This differs from ordinary resistors where the resistance is determined by fixed physical properties and transistors where the resistance is controlled by either the voltage at or current through a gate electrode. A linear memristor (one for which M is constant) would thus be indistinguishable from an ordinary linear resistor (one for which R is constant), with M = R. Memristance can be said to depend on the history of the current that has flowed through the device the same way the voltage of capacitors does.

The memristor is capable of "remembering" how much electrical current most recently passed through it in one direction versus another. Thus, it can "remember" the state it was last in. This feat will allow future computers to potentially instantly boot up, for RAM to match the most previous state of the computer when it was last turned off will no longer need to be recreated through a long load up process.

Fabrication

Interest in the memristor revived in 2007 when an experimental solid-state version was reported^[7]^[8] by Stanley Williams^[9] of Hewlett Packard. A solid-state device could not be constructed until the unusual behavior of nanoscale materials made it possible. The device does not use magnetic flux as the theoretical memristor suggested, nor stores charge as a capacitor does, but instead achieves a resistance dependent on the current history using a chemical mechanism.

The HP device is composed of a thin (5nm) 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, 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 current has been passed through it.^[3]

Samsung has a pending U.S. patent application for a memristor similar to that described by Williams. Thus it is questionable whether Williams's group is the originator of this structure.^[10]

Potential applications

Williams's solid-state memristors can be combined into transistors, though much smaller.^{[dubious – discuss]} They can also be fashioned into non-volatile solid-state memory, which would allow greater data density than hard drives with access times potentially similar to DRAM, replacing both components.^[11] HP prototyped a crossbar latch memory using the devices that can fit 100 gigabit in a square centimeter.^[6] The highest-density Flash memories store 16 gigabit in the same area, for comparison. HP has reported that its version of the memristor is about one tenth the speed of DRAM.^[12]

The devices' resistance would be read with alternating current so that they do not affect the stored value.^[13]

Some patents related to memristors appear to include applications in programmable logic,^[14] signal processing,^[15] neural networks,^[16] and control systems.^[17]

Other types

Apart from the solid-state memristor, various devices can be characterized as having memristive behavior.

Electrochemical cell

The memristor was used for characterizing the behavior of electrochemical cells.^[18]

References

^ Tour, James M; He, Tao (2008), "Electronics: The fourth element", Nature, 453: 42–43, doi:10.1038/453042a
^ Chua, Leon O (Sep 1971), "Memristor—The Missing Circuit Element", IEEE Transactions on Circuit Theory, CT-18 (5): 507–519{{citation}}: CS1 maint: date and year (link)
^ ^a ^b Strukov, Dmitri B; Snider, Gregory S; Stewart, Duncan R; Williams, Stanley R (2008), "The missing memristor found", Nature, 453: 80–83, doi:10.1038/nature06932
^ Marks, Paul (2008-04-30). "Engineers find 'missing link' of electronics". New Scientist. Retrieved 2008-04-30. {{cite web}}: Check date values in: |date= (help)
^ "Researchers Prove Existence of New Basic Element for Electronic Circuits -- Memristor'". Physorg.com. 2008-04-30. Retrieved 2008-04-30. {{cite web}}: Check date values in: |date= (help)
^ ^a ^b ^c "'Missing link' memristor created". EETimes. 2008-04-30. Retrieved 2008-04-30. {{cite web}}: Check date values in: |date= (help); Cite has empty unknown parameter: |1= (help)
^ Fildes, Jonathan (2007-11-13). "Getting More from Moore's Law". BBC. Retrieved 2008-04-30. {{cite web}}: Check date values in: |date= (help)
^ "Bulletin for Electrical and Electronic Engineers of Oregon" (PDF). Institute of Electrical and Electronics Engineers. Sept 2007. Retrieved 2008-04-30. {{cite web}}: Check date values in: |date= (help)
^ R. Stanley Williams, HP biography
^ US Patent Application 11/655,193
^ Kanellos, Michael (2008-04-30). "HP makes memory from a once theoretical circuit". CNET News.com. Retrieved 2008-04-30. {{cite web}}: Check date values in: |date= (help)
^ Markoff, John (2008-05-01). "H.P. Reports Big Advance in Memory Chip Design". NY Times. Retrieved 2008-05-01. {{cite web}}: Check date values in: |date= (help)
^ http://arstechnica.com/news.ars/post/20080501-maintaining-moores-law-with-new-memristor-circuits.html
^ U.S. Patent 7,203,789
^ U.S. Patent 7,302,513
^ U.S. Patent 7,359,888
^ U.S. Patent Application 11/976,927
^ Chen W-K (ed.), The Circuits and Filters Handbook, 2nd ed, CRC Press 2003, ISBN 0849309123. Chapter 12, "Circuit Elements, Modeling, and Equation Formulation"

External Links

HP Reveals Memristor, The Fourth Passive Circuit Element April 30, 2008
BBC News - Electronics' 'missing link' found 01 May 2008
Nature News - Found: the missing circuit element 30 Apr 2008
Wired.com - Scientists Create First Memristor: Missing Fourth Electronic Circuit Element 30 Apr 2008
EE Times - 'Missing link' memristor created: Rewrite the textbooks? 30 April 2008

This electronics-related article is a stub. You can help Wikipedia by expanding it.

[1] Tour, James M; He, Tao (2008), "Electronics: The fourth element", Nature, 453: 42–43, doi:10.1038/453042a

[2] Chua, Leon O (Sep 1971), "Memristor—The Missing Circuit Element", IEEE Transactions on Circuit Theory, CT-18 (5): 507–519{{citation}}: CS1 maint: date and year (link)

[Williams08-3] Strukov, Dmitri B; Snider, Gregory S; Stewart, Duncan R; Williams, Stanley R (2008), "The missing memristor found", Nature, 453: 80–83, doi:10.1038/nature06932

[4] Marks, Paul (2008-04-30). "Engineers find 'missing link' of electronics". New Scientist. Retrieved 2008-04-30. {{cite web}}: Check date values in: |date= (help)

[5] "Researchers Prove Existence of New Basic Element for Electronic Circuits -- Memristor'". Physorg.com. 2008-04-30. Retrieved 2008-04-30. {{cite web}}: Check date values in: |date= (help)

[EETimes-6] "'Missing link' memristor created". EETimes. 2008-04-30. Retrieved 2008-04-30. {{cite web}}: Check date values in: |date= (help); Cite has empty unknown parameter: |1= (help)

[7] Fildes, Jonathan (2007-11-13). "Getting More from Moore's Law". BBC. Retrieved 2008-04-30. {{cite web}}: Check date values in: |date= (help)

[8] "Bulletin for Electrical and Electronic Engineers of Oregon" (PDF). Institute of Electrical and Electronics Engineers. Sept 2007. Retrieved 2008-04-30. {{cite web}}: Check date values in: |date= (help)

[9] R. Stanley Williams, HP biography

[10] US Patent Application 11/655,193

[11] Kanellos, Michael (2008-04-30). "HP makes memory from a once theoretical circuit". CNET News.com. Retrieved 2008-04-30. {{cite web}}: Check date values in: |date= (help)

[12] Markoff, John (2008-05-01). "H.P. Reports Big Advance in Memory Chip Design". NY Times. Retrieved 2008-05-01. {{cite web}}: Check date values in: |date= (help)

[13] ttp://arstechnica.com/news.ars/post/20080501-maintaining-moores-law-with-new-memristor-circuits.html

[14] U.S. Patent 7,203,789

[15] U.S. Patent 7,302,513

[16] U.S. Patent 7,359,888

[17] U.S. Patent Application 11/976,927

[18] Chen W-K (ed.), The Circuits and Filters Handbook, 2nd ed, CRC Press 2003, ISBN 0849309123. Chapter 12, "Circuit Elements, Modeling, and Equation Formulation"

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@@ Line 60: / Line 60: @@
 is known as ''memristance''. This is comparable to the other three fundamental circuit elements:
-* [[Electrical resistance|Resistance]]: <math>R(I)=\frac{\mathrm V}{\mathrm I}</math>
+* [[Electrical resistance|Resistance]]: <math>R(I)=\frac{\mathrm dV}{\mathrm dI}</math>
 * [[Inductance]]: <math>L(I) = \frac{\mathrm d\Phi_m}{\mathrm dI}</math>
 * [[Capacitance]]: <math>\frac{1}{C(q)}=\frac{\mathrm dV}{\mathrm dq}</math>
-Here <math>q</math> is [[electrical charge]], <math>I</math> is [[electrical current]], <math>V</math> is [[electrical potential]] and <math>\Phi_m</math> is [[magnetic flux]].
+Here <math>q</math> is [[electrical charge]], <math>I</math> is [[electrical current]], <math>V</math> is [[electrical potential]] and <math>\Phi_m</math> is [[magnetic flux]]. The differential forms of these equations are used because we are comparing non-linear circuit elements; a linear memristor would be uninteresting, as explained below.
 Applying [[Faraday's Law of Induction]] and the [[chain rule]] to the equation defining the memristance, one obtains that the voltage ''V'' across a memristor is related to the current ''I''  by the instantaneous value of the memristance:
@@ Line 70: / Line 70: @@
 : <math>V(t) = M(q(t)) I(t) \,</math>
-Thus at any given instant, a memristor behaves like an ordinary resistor. However, its "resistance" ''M(q)'' is a value which depends on the charge accumulated in the device. This differs from ordinary resistors where the resistance is determined by fixed physical properties and transistors where the resistance is controlled by either the voltage at or current through a gate electrode. A linear memristor (one for which ''M'' is constant) would thus be indistinguishable from a linear resistor (one for which ''R'' is constant), with ''M = R''. Memristance can be said to depend on the history of the current that has flowed through the device the same way the voltage of capacitors does.
+Thus at any given instant, a memristor behaves like an ordinary resistor. However, its "resistance" ''M(q)'' is a value which depends on the charge accumulated in the device. This differs from ordinary resistors where the resistance is determined by fixed physical properties and transistors where the resistance is controlled by either the voltage at or current through a gate electrode. A linear memristor (one for which ''M'' is constant) would thus be indistinguishable from an ordinary linear resistor (one for which ''R'' is constant), with ''M = R''. Memristance can be said to depend on the history of the current that has flowed through the device the same way the voltage of capacitors does.
 The memristor is capable of "remembering" how much electrical current most recently passed through it in one direction versus another. Thus, it can "remember" the state it was last in. This feat will allow future computers to potentially instantly boot up, for RAM to match the most previous state of the computer when it was last turned off will no longer need to be recreated through a long load up process.