Memristor

A memristor - the name is a suitcase word from English memory (memory) and resistor (electrical resistance) - is a hypothetical passive electrical component that has an electrical resistance between its two connections that increases or decreases as the charge flows through it, depending on the direction . Without current, the voltage is zero and the resistance is retained. The memristor was seen as the fourth fundamental passive component , along with the resistor , capacitor and coil . However, it has been shown that there can only be three fundamental passive components and that the memristor is an active component.

Various components under development that behave approximately as postulated are also referred to as memristors. Integrated circuits with many such elements are intended to combine data processing and storage and be suitable for neural networks .

history

Leon Chua , from the University of California, Berkeley , described the memristor and its properties as early as 1971, which at that time did not exist as a passive component. The first physical realization of a thin-film composite with such properties was announced in 2007. In April 2008, researchers from Hewlett-Packard presented a relatively simply structured layer composite made of titanium dioxide with platinum electrodes as memristors. At the end of August 2010 it was shown in work by Jun Yao from Rice University that even simple silicon dioxide works as a layer material.

In July 2012 criticism was voiced that the description of the physical concept for so-called “memristive systems” could contradict the Landauer principle , a fundamental principle of information processing. This criticism regarding the fundamental problems of the memorial concept was confirmed in 2013 by Di Ventra and Pershin. However, the authors do not question the possible applications of the similarly behaving components.

construction

Memristor made of doped titanium dioxide. Above: low electrical conductivity; below: high electrical conductivity

In 2007, a static version of the memrister was produced for the first time under Richard Stanley Williams . This memristor stores its state in chemical form through the incorporation of doping atoms in a semiconductor .

The memristor manufactured by Hewlett-Packard consists of a titanium dioxide layer a few nanometers thick between two platinum electrodes. The right part of the titanium dioxide layer colored in the picture is doped with oxygen vacancies (p-doping) and has a high electrical conductivity. The left part of the titanium dioxide layer is an insulator. When an electric field is applied, the oxygen vacancies drift, shifting the space charge zone. This reduces the thickness of the insulation layer. As the thickness of the insulation layer becomes smaller, the conductivity of the memristor increases, with the tunnel effect ( field emission ) playing an essential role.

Experimentally, such a memristor is characterized in a u / i diagram by a hysteresis curve that runs almost through the coordinate zero point (pinched hysteresis loop), see adjacent sketch. The state of the memristor is characterized by the location of the dividing line between the differently doped areas.

The Rice University memristor from 2010 is characterized by an even simpler structure. It consists of a 5 to 20 nanometer thick silicon dioxide layer between conductively doped silicon layers. An additional layer of graphene originally intended to be active turned out to be superfluous. The component then only needs two connections like a resistor (as opposed to three in a flash memory cell) and can be implemented extremely inexpensively on an area of ​​approx. 10 nanometers edge length and due to the simple structure. The function is that in the oxide layer when the programming voltage is applied, paths made of pure silicon nanocrystals (without the oxygen, crystals each approx. 5 nanometers long) arrange themselves to form a conductive structure that can be repeatedly and reproducibly destroyed by another voltage.

Function equations

Hysteresis curve for the memristor as a function of the angular frequency ω with ω ₁  <  ω ₂

Classification of the memristor in the basic electrical parameters

A memristor is defined as a component in which the flux and the electrical charge q are coupled via a time-independent, generally non-linear function . This memristance function is defined by the rate of change of the flow with the charge: ${\displaystyle \textstyle \Phi =\Phi _{0}+\int _{0}^{t}U(t)\mathrm {d} t}$ ${\displaystyle \Phi =f(q)}$

${\displaystyle M(q)={\frac {\mathrm {d} \Phi }{\mathrm {d} q}}}$

The quantity is called (incremental) memristance or memristivity and has the unit ohm (Ω). The magnetic flux is defined by the time integral of the terminal voltage applied to the memristor (see voltage time area ) and has the SI unit Weber (Wb). In fact, when an electrical voltage is applied, no magnetic field is actually created on the memristor, ideally considered. In contrast to the electrical coil, an electrical field is also formed inside the memristor that corresponds to the voltage applied from outside. The circulating voltage (induced voltage) in the circuit is therefore zero, so that no induction takes place. ${\displaystyle M}$ ${\displaystyle \Phi }$ ${\displaystyle U(t)}$

The behavior of the memristor thus complements the three other fundamental components

	electric charge	electrical current
Electric voltage	(reciprocal) capacity ${\displaystyle {\frac {1}{C}}={\frac {\mathrm {d} U}{\mathrm {d} q}}={\frac {\mathrm {d} {\dot {\Phi }}}{\mathrm {d} q}}}$	Resistivity ${\displaystyle R={\frac {\mathrm {d} U}{\mathrm {d} I}}={\frac {\mathrm {d} {\dot {\Phi }}}{\mathrm {d} {\dot {q}}}}}$
Magnetic river	Memristivity ${\displaystyle M={\frac {\mathrm {d} \Phi }{\mathrm {d} q}}}$	Inductance ${\displaystyle L={\frac {\mathrm {d} \Phi }{\mathrm {d} I}}={\frac {\mathrm {d} \Phi }{\mathrm {d} {\dot {q}}}}}$

Here is the electrical charge, the electrical current, the electrical voltage and the (magnetic) flux. ${\displaystyle q}$ ${\displaystyle I}$ ${\displaystyle U}$ ${\displaystyle \Phi }$

As shown, the relationships apply

${\displaystyle I(t)={\frac {\mathrm {d} q}{\mathrm {d} t}}}$

and

${\displaystyle U(t)={\frac {\mathrm {d} \Phi }{\mathrm {d} t}}}$

The voltage U at a memristor depends directly on the memristance via the current I :

${\displaystyle U(t)=M(q(t))\cdot I(t)}$

For every moment a memristor behaves like a normal resistor, but its "resistance" M ( q ) depends on the past of the current. A linear memristor (with constant M ) can not be distinguished from an electrical resistance with M  =  R.

The reverse applies to the current I :

${\displaystyle I(t)=W(\Phi (t))\cdot U(t)}$

With

${\displaystyle W(\Phi (t))=M(q(t))^{-1}={\frac {\mathrm {d} q}{\mathrm {d} \Phi }}}$

The quantity W is called incremental conductance and has the unit Siemens (S) .

The charge stored in the memristor is the integral of the electric current over time

${\displaystyle q(t)=\int \limits _{-\infty }^{t}I(t)\ \mathrm {d} t=q(t_{0})+\int \limits _{t_{0}}^{t}I(t)\ \mathrm {d} t}$,

while the flux present in the memristor is given by the integral of the electrical voltage over time.

${\displaystyle \Phi (t)=\int \limits _{-\infty }^{t}U(t)\ \mathrm {d} t=\Phi (t_{0})+\int \limits _{t_{0}}^{t}U(t)\ \mathrm {d} t}$

In practical implementation, this integration is neither unlimited nor linear due to the limited number of charge carriers, but it does have a monotonous profile.

The electrical power P converted in the memristor is given by

${\displaystyle P(t)=U(t)\cdot I(t)=M(q(t))\cdot I(t)^{2}={\frac {U(t)^{2}}{M(q(t))}}}$

As this is the memristor is a passive device that applies for also . ${\displaystyle M(q(t))\geq 0}$ ${\displaystyle P(t)\geq 0}$

Hypothetical application

Temporary symbol of a memrister proposed by Chua, not standardized

The first prototypes and samples of memristors were produced in 2007 and circuit combinations such as memristors were developed in the following years . As of 2013, practical applications are not foreseeable. However, it is conceivable that memristors could replace transistors in areas where amplification is not required . However, there is no practical proof of this replacement in the form of memristors available on the market.

In May 2008, the scientists at Hewlett-Packard had advanced into the 15 nanometer range.

Patents on memristors include applications in the fields of programmable logic , electronic signal processing , artificial neural networks, and control systems .

Neuristors

In the form of neuristors , memristors should be able to function like biological synapses and allegedly predestine them for applications in the field of artificial intelligence .

Storage

The power consumption of memories with memristors as the storage element is far lower than the power consumption of conventional DRAM chips. However, the non-volatile memristors currently only achieve around a tenth of the speed of the latter. Another advantage is the high packing density . The “crossbar” storage system presented by HP has a packing density of 100  Gibit / cm², while the storage units available during the same period have a density of 16 Gibit / cm². Memristors can be manufactured using the same processes as semiconductor structures and can therefore be integrated into microelectronic circuits.

In addition to the much lower power consumption, computers that are equipped with memristors, u. a. also offer the advantage of being ready for operation immediately after switching on without booting . The memristor retains its memory content when it is read out using alternating current.

literature

• Dmitri B. Strukov, Gregory S. Snider, Duncan R. Stewart, R. Stanley Williams: The missing memristor found . In: Nature . tape 453 , no. 7191 , April 1, 2008, p. 80-83 , doi : 10.1038 / nature06932 .
• R. Stanley Williams: How we found the missing memristor . In: IEEE spectrum . tape 45 , no. 12 , 2008, p. 28-35 ( spectrum.ieee.org ).
• Yogesh N. Joglekar, Stephen J. Wolf: The elusive memristor: properties of basic electrical circuits . arxiv : 0807.3994 .
• Frank Y. Wang: Memristor for introductory physics . arxiv : 0808.0286 .

Web links

Wiktionary: Memristor  - explanations of meanings, word origins, synonyms, translations

Commons : Memristors  - collection of images, videos and audio files

• Interactive database of scientific articles on memristor .
• Helmut Martin-Jung: The nano super storage . sueddeutsche.de, July 8, 2010
• Jamie Beckett: Demystifying the memristor: Proof of fourth basic circuit element could transform computing . HP Labs, April 2008, quote: "As for the human brain-like characteristics, memristor technology could one day lead to computer systems that can remember and associate patterns in a way similar to how people do."
• Video: HP's Stan Williams explains the memristor . IEEE Spectrum. Retrieved August 7, 2010.
• Video: Animation of the current-voltage characteristic of a memristor for different frequencies . Wolfram Demonstration Project.

Individual evidence

1. ↑ Sascha Vongehr, Xiangkang Meng: The Missing memristor has been Not Found. Scientific Reports 5, 2015, doi: 10.1038 / srep11657 (free full text).
2. ↑ Isaac Abraham: The case for rejecting the memristor as a fundamental circuit element . In: Scientific Reports . 2018, doi : 10.1038 / s41598-018-29394-7 . (free full text).
3. ↑ Satyajeet Sahoo, SRS Prabaharan: Nano-Ionic Solid State Resistive Memories (Re-RAM): A Review . In: Journal of Nanoscience and Nanotechnology , 17, 2017, doi: 10.1166 / jnn.2017.12805 ; researchgate.net (PDF).
4. ↑ Olga Krestinskaya, Alex Pappachen James, Leon O. Chua: Neuro-memristive Circuits for Edge Computing: A review. arXiv: 1807.00962 , 2018.
5. ^ Leon O. Chua: Memristor — The Missing Circuit Element. In: IEEE Transactions on Circuit Theory. 1971 ( ieeeghn.org (PDF) accessed May 16, 2010).
6. ↑ Q. Wang, DS Shang, ZH Wu, LD Chen, XM Li: “Positive” and “negative” electric-pulse-induced reversible resistance switching effect in Pr0.7Ca0.3MnO3 films. In: Appl. Phys. A , 86, 2007, pp. 357-360.
7. ↑ HP Labs: Memristor found: HP Labs proves fourth integrated circuit element
8. ↑ Jun Yao et al .: Resistive Switches and Memories from Silicon Oxide. Nano Lett. 10, 2010, doi: 10.1021 / nl102255r .
9. ↑ Christof Windeck: Memristor made of silicon oxide nanowires. Heise-Newsticker, Sept. 2, 2010.
10. ^ P. Meuffels, R. Soni: Fundamental Issues and Problems in the Realization of Memristors " . Arxiv : 1207.7319v1 ([cond-mat.mes-hall]).
11. ↑ Massimiliano Di Ventra, Pershin, Yuriy V .: On the physical properties of memristive, memcapacitive and meminductive systems . In: Nanotechnology . 24, No. 25, 2013. arxiv : 1302.7063 . bibcode : 2013Nanot..24y5201D . doi : 10.1088 / 0957-4484 / 24/25/255201 .
12. ↑ Massimiliano Di Ventra, Yuriy V. Pershin: Memcomputing: a computing paradigm to store and process information on the same physical platform. Nature Physics 9, 2013, doi: , arXiv: 1211.4487 .
13. ↑ Jonathan Fildes: Getting More from Moore's Law . BBC, September 2007.
14. ↑ Bulletin for Electrical and Electronic Engineers of Oregon (PDF) September 2007
15. ↑ Dmitri B. Strukov, Gregory S. Snider, Duncan R. Stewart, Stanley R. Williams: The missing memristor found. In: Nature. 453, 2008, pp. 80-83.
16. ↑ Chris Mellor: HP 100TB Memristor drives by 2018 - if you're lucky, admits tech titan . The Register, Nov. 2013.
17. ↑ Patent US7203789 . ‌
18. ↑ Patent US7302513 . ‌
19. ↑ Patent US7359888 . ‌
20. ↑ Patent US7609086 : Crossbar control circuit. Published October 27, 2009 , Inventor: Blaise Laurent Mouttet. ‌
21. ^ John Markoff: HP Reports Big Advance in Memory Chip Design . New York Times , May 1, 2008.
22. ↑ HP invents electrical resistance with memory . heise online, May 1, 2008
23. ^ Ethan Gutmann, Maintaining Moore's law with new memristor circuits . Ars Technica, May 2008