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| {{Infobox electronic component
| | When yoս havе by no means regarded diet in your diet, you might feel intіmidated in tҺe beginning. It can overpowеr all of them with thе quantity of vitamins and minerals a body dеmands. The following pοѕt gives some useful guіdance for arranging the appropriate substance and ɦaving on the path to very good nutrition.<br><br> |
| | component = Memristor
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| | type = [[Passivity (engineering)|Passive]]
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| | working_principle = Memristance
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| | invented = [[Leon Chua]] (1971)
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| | first_produced = [[HP Labs]] (2008)
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| | symbol = [[File:Memristor-Symbol.svg]]
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| }}
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| {{Memory types}}
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| The '''memristor''' ({{IPAc-en|ˈ|m|ɛ|m|r|ɨ|s|t|ər}}; a portmanteau of "memory resistor") was originally envisioned in 1971 by circuit theorist [[Leon Chua]] as a missing non-linear [[passivity (engineering)|passive]] [[terminal (electronics)|two-terminal]] [[electronic component|electrical component]] relating electric charge and magnetic flux linkage.<ref name="chua71">{{citation |last=Chua |first=L. O. |year=1971 |title=Memristor—The Missing Circuit Element |journal=[[IEEE Transactions on Circuit Theory]] |volume=CT-18 |issue=5 |pages=507–519 |doi=10.1109/TCT.1971.1083337 }}</ref> According to the governing mathematical relations, the memristor’s [[electrical resistance]] (memristance) is not constant but depends on the history of current that had previously flowed through the device, ''i.e.'', its current resistance depends on how much electric charge has flowed in what direction through it in the past. The device remembers its history, that is, when the electric power supply is turned off, the memristor remembers its most recent resistance until it is turned on again.<ref name="Williams08">{{citation |last=Strukov |first=D. B. |last2=Snider |first2=G. S. |last3=Stewart|first3=D. R. |last4=Williams|first4=S. R. |year=2008 |title=The missing memristor found |journal=[[Nature (journal)|Nature]] |volume=453 |issue=7191 |pages=80–83 |doi=10.1038/nature06932 |pmid=18451858 |bibcode = 2008Natur.453...80S }}</ref><ref>{{cite web |title=Memristor FAQ |url=http://www.hpl.hp.com/news/2008/apr-jun/memristor_faq.html |publisher=[[Hewlett-Packard]] |accessdate=2010-09-03 }}</ref> Thermodynamic considerations, however, show that such a memristor component cannot exist as a solid state device in physical reality because its behavior would be inconsistent with fundamental laws of [[non-equilibrium thermodynamics]].<ref name="Meuffels_2012" /><ref name="DiVentra_2013" />
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| Leon Chua has more recently argued that the definition could be generalized to cover all forms of 2-terminal non-volatile memory devices based on resistance switching effects<ref name="chua11">{{citation |last=Chua |first=L. O. |year=2011 |title=Resistance switching memories are memristors |journal=Applied Physics A |volume=102 |issue=4 |pages=765–783 |doi=10.1007/s00339-011-6264-9|bibcode = 2011ApPhA.102..765C }}</ref> although some experimental evidence contradicts this claim, since a non-passive [[nanobatteries|nanobattery]] effect is observable in resistance switching memory.<ref name=memristor_nanobattery>{{Cite doi|10.1038/ncomms2784|edit}}</ref> Chua also argued that the memristor is the oldest known circuit element with its effects predating the [[resistor]], [[capacitor]] and [[inductor]].<ref name="Memristor200yearsold">{{Citation |last=Clarke |first=Peter |date=23 May 2012 |title=Memristor is 200 years old, say academics |url=http://www.eetimes.com/electronics-news/4373652/Academics-Memristor-is-200-years-old |work=[[EE Times]] |accessdate=2012-05-25 }}</ref> The memristor is currently under development by various teams including [[Hewlett-Packard]], [[SK Hynix]] and [[HRL Laboratories]].
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| In 2008, a team at [[HP Labs]] claimed to have found Chua's missing memristor based on an analysis of a [[thin film]] of [[titanium dioxide]].<ref name="EETimes">{{Citation |last=Johnson |first=R. C. |date=30 April 2008 |title='Missing link' memristor created |url=http://www.eetimes.com/electronics-news/4076910/-Missing-link-memristor-created-Rewrite-the-textbooks- |work=[[EE Times]] |accessdate=2008-04-30 }}</ref> However, some skepticism has been expressed regarding this analysis.<ref name="Meuffels_2012" /> These devices are intended for applications in [[nanoelectronic]] memories, computer logic and [[neuromorphic]] computer architectures.<ref>{{Citation |last=Marks |first=P. |date=30 April 2008 |title=Engineers find 'missing link' of electronics |url=http://www.newscientist.com/article/dn13812 |work=[[New Scientist]] |accessdate=2008-04-30 }}</ref> In October 2011, the team announced the commercial availability of memristor technology within 18 months, as a replacement for [[Flash memory|Flash]], [[Solid-state drive|SSD]], [[Dynamic random-access memory|DRAM]] and [[Static random-access memory|SRAM]].<ref name="IEF2011">{{Citation |date=7 October 2011|title=HP to replace flash and SSD in 2013|url=http://www.electronicsweekly.com/Articles/06/10/2011/51988/ief2011-hp-to-replace-flash-and-ssd-in-2013.htm}}</ref> Commercial availability was more recently estimated as 2018.<ref name="memristor2018">{{Citation |date=1 November 2013|title=HP 100TB Memristor drives by 2018 – if you're lucky, admits tech titan|url=http://www.theregister.co.uk/2013/11/01/hp_memristor_2018/}}</ref> In March 2012, a team of researchers from [[HRL Laboratories]] and the [[University of Michigan]] announced the first functioning memristor array built on a [[CMOS]] chip.<ref name="HRLmemristor">{{cite press release |url=http://www.hrl.com/hrlDocs/pressreleases/2012/prsRls_120323.html|title=Artificial synapses could lead to advanced computer memory and machines that mimic biological brains |publisher=HRL Laboratories |date=March 23, 2012 |accessdate=March 30, 2012}}</ref>
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| [[Image:Memristor.jpg|thumb|right|225px|An array of 17 purpose-built [[oxygen]]-depleted [[titanium dioxide]] memristors built at [[HP Labs]], imaged by an [[atomic force microscope]]. The wires are about 50 nm, or 150 atoms, wide.<ref>{{cite web |last=Bush |first=S. |date=2 May 2008 |title=HP nano device implements memristor |url=http://www.electronicsweekly.com/Articles/2008/05/02/43658/hp-nano-device-implements-memristor.htm |work=[[Electronics Weekly]] }}</ref> [[Electric current]] through the memristors shifts the oxygen vacancies, causing a gradual and persistent change in [[electrical resistance]].<ref>{{cite web |last= Kanellos |first=M. |url=http://news.cnet.com/8301-10784_3-9932054-7.html |title=HP makes memory from a once-theoretical circuit |date=30 April 2008 }}</ref>]]
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| ==Background==
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| [[File:Two-terminal non-linear circuit elements.svg|thumb|right|Conceptual symmetry between the resistor, capacitor, inductor, and the memristor.]]
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| In his 1971 paper, Chua extrapolated a conceptual symmetry between the nonlinear resistor (voltage vs. current), nonlinear capacitor (voltage vs. charge) and nonlinear inductor (magnetic flux linkage vs. current). He then inferred the possibility of a memristor as another fundamental nonlinear circuit element linking magnetic flux linkage and charge. In contrast to a linear (or nonlinear) resistor the memristor has a dynamic relationship between current and voltage including a memory of past voltages or currents. Other scientists had proposed dynamic memory resistors such as the [[memistor]] of Bernard Widrow, but Chua attempted to introduce mathematical generality.
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| Memristor resistance depends on the integral of the input applied to the terminals (rather than on the instantaneous value of the input as in a varistor).<ref name="Williams08">{{citation |last=Strukov |first=D. B. |last2=Snider |first2=G. S. |last3=Stewart|first3=D. R. |last4=Williams|first4=S. R. |year=2008 |title=The missing memristor found |journal=[[Nature (journal)|Nature]] |volume=453 |issue=7191 |pages=80–83 |doi=10.1038/nature06932 |pmid=18451858 |bibcode = 2008Natur.453...80S }}</ref> Since the element "remembers" the amount of current that last passed through, it was tagged by Chua with the name "memristor". Another way of describing a memristor is as any passive two-terminal circuit element that maintains a [[function (mathematics)|functional relationship]] between the [[time integral]] of [[electric current|current]] (called charge) and the time integral of [[voltage]] (often called flux, as it is related to [[magnetic flux]]). The slope of this function is called the '''memristance''' ''M'' and is similar to variable resistance. However, purely current- or voltage-controlled memristors cannot exist in physical reality because they would then operate in conflict with fundamental laws of [[non-equilibrium thermodynamics]].<ref name="Meuffels_2012" /><ref name="DiVentra_2013" />
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| The memristor definition is based solely on the fundamental circuit variables of current and voltage and their time-integrals, just like the [[resistor]], [[capacitor]] and [[inductor]]. Unlike those three elements however, which are allowed in linear time-invariant or [[LTI system theory]], memristors of interest have a dynamic function with memory and may be described as some function of net charge. There is no such thing as a standard memristor. Instead, each device implements a particular [[function (mathematics)|function]], wherein the integral of voltage determines the integral of current, and vice versa. A linear time-invariant memristor, with a constant value for ''M'', is simply a conventional resistor.<ref name="chua71"/> Like other two-terminal components, real-world devices are never purely memristors ("ideal memristor"), but also exhibit some amount of capacitance, resistance and inductance.
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| ==Memristor definition and criticism==
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| According to the original 1971 definition, the memristor was the fourth fundamental circuit element, forming a non-linear relationship between electric charge and magnetic flux linkage. In 2011 [[Leon Chua|Chua]] argued for a broader definition that included all 2-terminal non-volatile memory devices based on resistance switching.<ref name="chua11" /> Williams argued that [[MRAM]], [[phase change memory]] and [[RRAM]] were memristor technologies.<ref name="Mellor2011">{{Citation |last=Mellor |first=Chris |date=10 October 2011|title=HP and Hynix to produce the memristor goods by 2013|url=http://www.theregister.co.uk/2011/10/10/memristor_in_18_months/ |work=The Register |accessdate=2012-03-07}}</ref> Some researchers argued that biological structures such as blood<ref name="Courtland2011">{{Citation |last=Courtland |first=Rachel |date=1 April 2011|title=Memristors...Made of Blood?|url=http://spectrum.ieee.org/tech-talk/semiconductors/materials/blood-memristor |work=[[IEEE Spectrum]] |accessdate=2012-03-07}}</ref> and skin<ref name="McAlpine2011">{{Citation |last=McAlpine |first=Kate |date=2 March 2011 |title=Sweat ducts make skin a memristor|url=http://www.newscientist.com/article/mg20928024.500-sweat-ducts-make-skin-a-memristor.html |work=[[New Scientist]] |accessdate=2012-03-07}}</ref> fit the definition. Others argued that the memory device under development by [[HP Labs]] and other forms of [[RRAM]] were memristive systems but part of a broader class of variable resistance systems <ref name="Clarke2012">{{Citation |last=Clarke |first=Peter |date=16 January 2012 |title=Memristor brouhaha bubbles under |url=http://www.eetimes.com/electronics-news/4234678/Memristor-brouhaha-bubbles-under |work=[[EETimes]] |accessdate=2012-03-02 }}</ref> and that a broader definition of memristor is a scientifically unjustifiable land grab that favored HP's memristor patents.<ref name="PaulMarks2012">{{Citation |last=Marks |first=Paul |date=23 February 2012 |title=Online spat over who joins memristor club|url=http://www.newscientist.com/article/mg21328535.200-online-spat-over-who-joins-memristor-club.html |work=[[New Scientist]] |accessdate=2012-03-19 }}</ref>
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| Meuffels and Schroeder noted that one of the early memristor papers included a mistaken assumption regarding ionic conduction.<ref name="Meuffels_2011">
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| {{citation
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| |last=Meuffels |first=P.
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| |last2=Schroeder |first2=H.
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| |year=2011
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| |journal=[[Applied Physics A]]
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| |title=Comment on "Exponential ionic drift: fast switching and low volatility of thin-film memristors" by D.B. Strukov and R.S. Williams in Appl. Phys. A (2009) 94: 515-519
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| |url=http://www.springerlink.com/content/0x5426p281610331/
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| |accessdate=2012-08-09
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| |doi=10.1007/s00339-011-6578-7
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| |volume=105
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| |pages=65 |bibcode = 2011ApPhA.105...65M }}</ref> Meuffels and Soni discussed issues and problems in the realization of memristors.<ref name="Meuffels_2012">
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| {{citation
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| |last=Meuffels |first=P.
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| |last2=Soni |first2=R.
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| |year=2012
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| |journal=[[arXiv]]
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| |title=Fundamental Issues and Problems in the Realization of Memristors
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| |arxiv=1207.7319 |bibcode = 2012arXiv1207.7319M }}</ref> They claimed that the physics behind the HP memristor model conflicts with fundamentals of solid state electrochemistry as the coupling of electronic/ionic diffusion currents was not considered. Additionally, they pointed to issues concerning fundamentals of [[non-equilibrium thermodynamics]]: the dynamic state equations formulated for memristors like the HP memristor imply the possibility of violating [[Landauer's principle]] of the minimum amount of energy required to change "information" states in a system.<ref name="Meuffels_2012" /> This critique was endorsed by [[Di Ventra]] and Pershin.<ref name="DiVentra_2013">{{cite journal|last=Di Ventra|first=Massimiliano|coauthors=Pershin, Yuriy V.|title=On the physical properties of memristive, memcapacitive and meminductive systems|journal=Nanotechnology|year=2013|volume=24|issue=25|doi=10.1088/0957-4484/24/25/255201|url=http://iopscience.iop.org/0957-4484/24/25/255201/|arxiv = 1302.7063 |bibcode = 2013Nanot..24y5201D }}</ref>
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| Nonvolatile information storage requires the existence of energy barriers that separate distinct memory states from each other.<ref name="Meuffels_2012" /><ref name="DiVentra_2013" /> Memristors whose resistance (memory) states depend only on the current (like the HP memristor) or voltage history would be unable to protect their memory states against unavoidable fluctuations and thus permanently suffer information loss: the proposed hypothetical concept provides no physical mechanism enabling such systems to retain memory states after the applied current or voltage stress is removed. Such elements can therefore not exist, as they would always be susceptible to a so-called “stochastic catastrophe”.<ref name="DiVentra_2013" />
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| Other researchers noted that memristor models based on the assumption of linear ionic drift do not account for asymmetry between set time (high-to-low resistance switching) and reset time (low-to-high resistance switching) and do not provide ionic mobility values consistent with experimental data. Non-linear ionic drift models have been proposed to compensate for this deficiency.<ref name="Mitre_2012">
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| {{citation
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| |last=Hashem |first=N.
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| |last2=Das |first2=S.
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| |year=2012
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| |journal=[[Applied Physics Letters]]
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| |title=Switching-time analysis of binary-oxide memristors via a non-linear model
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| |url=http://www.mitre.org/work/tech_papers/2012/11_3987/11_3987.pdf
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| |accessdate=2012-08-09
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| |doi=10.1063/1.4726421
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| |volume=100
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| |issue=26
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| |pages=262106 |bibcode = 2012ApPhL.100z2106H }}</ref>
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| Martin Reynolds, an electrical engineering analyst with research outfit [[Gartner]], commented that while HP was being sloppy in calling their device a memristor, critics were being pedantic in saying it was not a memristor.<ref name="Martin Reynolds">{{Citation |last=Garling |first=Caleb |date=25 July 2012 |title=Wonks question HP's claim to computer-memory missing link|url=http://www.wired.com/wiredenterprise/2012/07/memristors/ |work=Wired.com |accessdate=2012-09-23 }}</ref>
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| ==Experimental tests for memristors==
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| [[Leon Chua|Chua]] suggested experimental tests to determine if a device may properly be categorized as a memristor:<ref>{{cite journal|last=Chua|first=L.O.|coauthors=Sung Mo Kang,|title=Memristive devices and systems|journal=Proceedings of the IEEE|date=1976|volume=64|issue=2|pages=209–223|doi=10.1109/PROC.1976.10092}}</ref>
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| *The [[Lissajous curve]] in the voltage-current plane is a pinched [[hysteresis]] loop when driven by any bipolar periodic voltage or current without respect to initial conditions.
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| *The area of each lobe of the pinched hysteresis loop shrinks as the frequency of the forcing signal increases.
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| * As the frequency tends to infinity, the hysteresis loop degenerates to a straight line through the origin, whose slope depends on the amplitude and shape of the forcing signal.
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| According to Chua<ref name="MemristorExperimentalTests">{{Citation |last=Chua |first=Leon |date=13 June 2012 |title=Memristors: Past, Present and future |url=http://sti.epfl.ch/files/content/sites/sti/files/shared/sel/pdf/Abstract_Prof_Chua.pdf |accessdate=2013-01-12 }}</ref> all resistive switching memories including [[ReRAM]], [[MRAM]] and [[phase change memory]] meet these criteria and are memristors. However, the lack of data for the Lissajous curves over a range of initial conditions or over a range of frequencies, complicates assessments of this claim.
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| Experimental evidence shows that redox-based resistance memory ([[ReRAM]]) includes a nanobattery effect that is contrary to Chua's memristor model. This indicates that the memristor theory needs to be extended or corrected to enable accurate ReRAM modeling.<ref name="memristor_nanobattery"/>
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| ==Theory==
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| The memristor was originally defined in terms of a non-linear functional relationship between magnetic flux linkage ''Φ''<sub>m</sub>(t) and the amount of electric charge that has flowed, ''q(t)'':<ref name="chua71" />
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| :<math>f(\mathrm \Phi_\mathrm m(t),q(t))=0</math>
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| The variable ''Φ''<sub>m</sub> ("magnetic [[flux linkage]]") is generalized from the circuit characteristic of an inductor. It ''does not'' represent a magnetic field here. Its physical meaning is discussed below. The symbol ''Φ''<sub>m</sub> may be regarded as the integral of voltage over time.<ref>{{Citation|first=Heinz |last=Knoepfel|title=Pulsed high magnetic fields|location=New York|publisher= North-Holland|year=1970|pages=37, Eq. (2.80)}}</ref>
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| In the relationship between ''Φ''<sub>m</sub> and q, the derivative of one with respect to the other depends on the value of one or the other, and so each memristor is characterized by its memristance function describing the charge-dependent rate of change of flux with charge.
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| : <math>M(q)=\frac{\mathrm d\Phi_m}{\mathrm dq} </math>
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| Substituting the flux as the time integral of the voltage, and charge as the time integral of current, the more convenient form is
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| : <math>M(q(t))=\cfrac{\mathrm d\Phi_m/\mathrm dt}{\mathrm dq/\mathrm dt}=\frac{V(t)}{I(t)}</math>
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| To relate the memristor to the resistor, capacitor, and inductor, it is helpful to isolate the term ''M''(''q''), which characterizes the device, and write it as a differential equation.
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| {| class="wikitable"
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| ! Device !! Characteristic property (units) !! Differential equation
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| | [[Resistor]] || Resistance ([[Volt|V]] per [[Ampere|A]], or [[Ohm]], Ω) || R = dV / dI
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| | [[Capacitor]] || Capacitance ([[Coulomb|C]] per V, or [[Farad]]s) || C = dq / dV
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| | [[Inductor]] || Inductance ([[Weber (unit)|Wb]] per A, or [[Henry (unit)|Henry]]s) || L = dΦ<sub>m</sub> / dI
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| |-
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| | Memristor || Memristance (Wb per C, or Ohm) || M = dΦ<sub>m</sub> / dq
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| |}
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| The above table covers all meaningful ratios of differentials of ''I'', ''Q'', ''Φ''<sub>m</sub>, and ''V''. No device can relate ''dI'' to ''dq'', or ''dΦ''<sub>m</sub> to ''dV'', because ''I'' is the derivative of ''Q'' and ''Φ''<sub>m</sub> is the integral of ''V''.
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| It can be inferred from this that memristance is charge-dependent [[electrical resistance|resistance]]. If ''M''(''q(t)'') is a constant, then we obtain [[Ohm's Law]] ''R(t)'' = ''V(t)''/'' I(t)''. If ''M''(''q(t)'') is nontrivial, however, the equation is not equivalent because ''q(t)'' and ''M''(''q(t)'') can vary with time. Solving for voltage as a function of time produces
| |
| | |
| :<math>V(t) =\ M(q(t)) I(t)</math>
| |
| | |
| This equation reveals that memristance defines a linear relationship between current and voltage, as long as ''M'' does not vary with charge. Nonzero current implies time 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 [[small signal model|much]] change in ''M''.
| |
| | |
| Furthermore, the memristor is static if no current is applied. If ''I''(''t'') = 0, we find ''V''(''t'') = 0 and ''M''(''t'') is constant. This is the essence of the memory effect.
| |
| | |
| The [[power consumption]] characteristic recalls that of a resistor, ''I''<sup>2</sup>''R''.
| |
| | |
| :<math>P(t) =\ I(t)V(t) =\ I^2(t) M(q(t))</math>
| |
| | |
| As long as ''M''(''q''(''t'')) varies little, such as under alternating current, the memristor will appear as a constant resistor. If ''M''(''q''(''t'')) increases rapidly, however, current and power consumption will quickly stop.
| |
| | |
| ''M''(''q'') is physically restricted to be positive for all values of ''q'' (assuming the device is passive and does not become [[superconductive]] at some ''q''). A negative value would mean that it would perpetually supply energy when operated with alternating current.
| |
| | |
| In 2008 researchers from [[HP Labs]] introduced a model for a memristance function based on thin films of [[titanium dioxide]].<ref name="Williams08" /> For R<sub>ON</sub><<R<sub>OFF</sub> the memristance function was determined to be
| |
| :<math>M(q(t)) = R_\mathrm{OFF} \cdot \left(1-\frac{\mu_{v}R_\mathrm{ON}}{D^2} q(t)\right)</math>
| |
| where R<sub>OFF</sub> represents the high resistance state, R<sub>ON</sub> represents the low resistance state, μ<sub>v</sub> represents the mobility of dopants in the thin film, and D represents the film thickness. The HP Labs group noted that "window functions" were necessary to compensate for differences between experimental measurements and their memristor model due to nonlinear ionic drift and boundary effects.
| |
| | |
| ===Operation as a switch===
| |
| For some memristors, applied current or voltage causes substantial change in resistance. Such devices may be characterized as switches by investigating the time and energy that must be spent to achieve a desired change in resistance. This assumes that the applied voltage remains constant. Solving for energy dissipation during a single switching event reveals that for a memristor to switch from ''R''<sub>on</sub> to ''R''<sub>off</sub> in time ''T''<sub>on</sub> to ''T''<sub>off</sub>, the charge must change by ΔQ = ''Q''<sub>on</sub>−''Q''<sub>off</sub>.
| |
| | |
| :<math>E_{\mathrm{switch}}
| |
| =\ V^2\int_{T_\mathrm{off}}^{T_\mathrm{on}} \frac{\mathrm dt}{M(q(t))}
| |
| =\ V^2\int_{Q_\mathrm{off}}^{Q_\mathrm{on}}\frac{\mathrm dq}{I(q)M(q)}
| |
| =\ V^2\int_{Q_\mathrm{off}}^{Q_\mathrm{on}}\frac{\mathrm dq}{V(q)} =\ V\Delta Q </math>
| |
| | |
| Substituting ''V''=''I''(''q'')''M''(''q''), and then ∫d''q''/''V'' = ∆''Q''/''V'' for constant ''V''To produces the final expression. This power characteristic differs fundamentally from that of a [[metal oxide semiconductor]] [[transistor]], which is capacitor-based. Unlike the transistor, the final state of the memristor in terms of charge does not depend on bias voltage.
| |
| | |
| The type of memristor described by Williams ceases to be ideal after switching over its entire resistance range, creating [[hysteresis]], also called the "hard-switching regime".<ref name="Williams08"/> Another kind of switch would have a cyclic ''M''(''q'') so that each ''off''-''on'' event would be followed by an ''on''-''off'' event under constant bias. Such a device would act as a memristor under all conditions, but would be less practical.
| |
| | |
| ===Memristive systems===
| |
| The memristor was generalized to memristive systems in Chua's 1976 paper.<ref name="chua76">{{cite journal|last=Chua|first=L.O.|first2=Sung Mo|last2=Kang|title=Memristive devices and systems|journal=Proceedings of the IEEE|date=1 January 1976|volume=64|issue=2|pages=209–223|doi=10.1109/PROC.1976.10092}}</ref> Whereas a memristor has mathematically [[scalar (mathematics)|scalar]] state, a system has [[tuple|vector]] state. The number of state variables is independent of the number of terminals.
| |
| | |
| Chua applied this model to empirically-observed phenomena, including the [[Hodgkin-Huxley model]] of the [[axon]] and a [[thermistor]] at constant ambient temperature. He also described memristive systems in terms of energy storage and easily-observed electrical characteristics. These characteristics might match [[resistive random-access memory]] relating the theory to active areas of research.
| |
| | |
| In the more general concept of an ''n''-th order memristive system the defining equations are
| |
| | |
| :<math>y(t)=g(\textbf{x},u,t)u(t),</math>
| |
| :<math>\dot{\textbf{x}}=f(\textbf{x},u,t) </math>
| |
| | |
| where ''u(t)'' is an input signal, ''y(t)'' is an output signal, the vector '''x''' represents a set of ''n'' state variables describing the device, and ''g'' and ''f'' are [[continuous functions]]. For a current-controlled memristive system the signal ''u(t)'' represents the current signal, ''i(t)'' and the signal ''y(t)'' represents the voltage signal ''v(t)''. For a voltage-controlled memristive system the signal ''u(t)'' represents the voltage signal ''v(t)'' and the signal ''y(t)'' represents the current signal ''i(t)''.
| |
| | |
| The ''pure'' memristor is a particular case of these equations, namely when ''x'' depends only on charge ('''x'''=''q'') and since the charge is related to the current via the time derivative d''q''/d''t''=''i(t)''. Thus for ''pure'' memristors ''f'' (i.e. the rate of change of the state) must be equal or proportional to the current ''i(t)'' .
| |
| | |
| ===Pinched hysteresis===
| |
| [[File:Pinched crossing hysteresis.png|thumb|right|Example of pinched hysteresis curve, V versus I]]
| |
| One of the resulting properties of memristors and memristive systems is the existence of a pinched [[hysteresis]] effect.
| |
| <ref name="DiVentraPershin2011">
| |
| {{citation
| |
| |last=Pershin |first=Y.V.
| |
| |last2=DiVentra |first2=M.
| |
| |year=2011
| |
| |journal=[[ArXiv]]
| |
| |title=Memory effects in complex materials and nanoscale systems
| |
| |doi=10.1080/00018732.2010.544961
| |
| |bibcode = 2011AdPhy..60..145P |arxiv = 1011.3053
| |
| |volume=60
| |
| |issue=2
| |
| |pages=145 }}</ref> For a current-controlled memristive system, the input ''u(t)'' is the current ''i(t)'', the output ''y(t)'' is the voltage ''v(t)'', and the slope of the curve represents the electrical resistance. The change in slope of the pinched hysteresis curves demonstrates switching between different resistance states which is a phenomenon central to [[ReRAM]] and other forms of two-terminal resistance memory. At high frequencies, memristive theory predicts the pinched hysteresis effect will degenerate, resulting in a straight line representative of a linear resistor. It has been proven that some types of non-crossing pinched hysteresis curves (denoted Type-II) cannot be described by memristors.<ref name="Biolek2011">
| |
| {{citation
| |
| |last=Biolek |first=D.
| |
| |last2=Biolek |first2=Z.
| |
| |last3=Biolkova |first3=V.
| |
| |year=2011
| |
| |journal=[[Electronics Letters]]
| |
| |title=Pinched hysteresis loops of ideal memristors, memcapacitors and meminductors must be 'self-crossing'
| |
| |volume=47
| |
| |issue=25 |pages=1385–1387
| |
| |doi=10.1049/el.2011.2913
| |
| }}</ref>
| |
| | |
| ===Extended memristive systems===
| |
| | |
| Some researchers have raised the question of the scientific legitimacy of HP's memristor models in explaining the behavior of ReRAM.<ref name="Clarke2012" /><ref name="PaulMarks2012" /> and have suggested extended memristive models to remedy perceived deficiencies.<ref name="memristor_nanobattery"/>
| |
| | |
| One example<ref name="memresistor">
| |
| {{citation
| |
| |last=Mouttet |first=Blaise
| |
| |year=2012
| |
| |journal=[[ArXiv]]
| |
| |title=Memresistors and non-memristive zero-crossing hysteresis curves
| |
| |arxiv=1201.2626
| |
| |bibcode = 2012arXiv1201.2626M }}</ref> attempts to extend the memristive systems framework by including dynamic systems incorporating higher-order derivatives of the input signal ''u(t)'' as a series expansion
| |
| | |
| :<math>y(t)=g_0(\textbf{x},u)u(t)+ g_1(\textbf{x},u){\operatorname{d}^2u\over\operatorname{d}t^2}+ g_2(\textbf{x},u){\operatorname{d}^4u\over\operatorname{d}t^4}+ ... + g_m(\textbf{x},u){\operatorname{d}^{2m}u\over\operatorname{d}t^{2m}},</math>
| |
| :<math>\dot{\textbf{x}}=f(\textbf{x},u) </math>
| |
| | |
| where ''m'' is a positive integer, ''u(t)'' is an input signal, ''y(t)'' is an output signal, the vector '''x''' represents a set of ''n'' state variables describing the device, and the functions ''g'' and ''f'' are [[continuous function]]s. This equation produces the same zero-crossing hysteresis curves as memristive systems but with a different [[frequency response]] than that predicted by memristive systems.
| |
| | |
| Another example suggests including an offset value ''a'' to account for an observed nanobattery effect which violates the predicted zero-crossing pinched hysteresis effect.<ref name="memristor_nanobattery"/>
| |
| | |
| :<math>y(t)=g_0(\textbf{x},u)(u(t)-a),</math>
| |
| :<math>\dot{\textbf{x}}=f(\textbf{x},u) </math>
| |
| | |
| ==Implementations==
| |
| | |
| ===Titanium dioxide memristor===
| |
| Interest in the memristor revived when an experimental solid state version was reported by [[R. Stanley Williams]] of [[Hewlett Packard]].<ref>
| |
| {{Citation
| |
| |last=Fildes |first=J.
| |
| |date=13 November 2007
| |
| |title=Getting More from Moore's Law
| |
| |url=http://news.bbc.co.uk/2/hi/technology/7080772.stm
| |
| |publisher=BBC News
| |
| |accessdate=2008-04-30
| |
| }}</ref><ref>
| |
| {{Citation
| |
| |last=Taylor |first=A. G.
| |
| |year=2007
| |
| |title=Nanotechnology in the Northwest
| |
| |url=http://www.ieee-or.org/beeep/2007/sep/beeep_sep07.pdf
| |
| |journal=[[Bulletin for Electrical and Electronic Engineers of Oregon]]
| |
| |volume=51
| |
| |issue=1 |page=1
| |
| }}</ref><ref>
| |
| {{Citation
| |
| |title=Stanley Williams
| |
| |url=http://www.hpl.hp.com/people/stan_williams/
| |
| |publisher=[[Hewlett-Packard|HP Labs]]
| |
| |accessdate=2011-03-20
| |
| }}</ref> The article was the first to demonstrate that a solid-state device could have the characteristics of a memristor based on the behavior of [[nanoscale]] thin films. 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.
| |
| | |
| Although not cited in HP's initial reports on their [[TiO2|TiO<sub>2</sub>]] memristor, the resistance switching characteristics of titanium dioxide were originally described in the 1960s.<ref name="Argall1968">
| |
| {{Citation
| |
| | last = Argall | first = F.
| |
| | year = 1968
| |
| | title = Switching Phenomena in Titanium Oxide Thin Films
| |
| | url = http://www.sciencedirect.com/science/article/pii/0038110168900920
| |
| | journal = [[Solid-State Electronics]]
| |
| | volume = 11
| |
| | issue = 5 | pages = 535–541
| |
| | doi = 10.1016/0038-1101(68)90092-0
| |
| |bibcode = 1968SSEle..11..535A }}</ref>
| |
| | |
| The HP device is composed of a thin (50 [[nanometer|nm]]) [[titanium dioxide]] film between two 5 nm thick [[electrode]]s, one [[titanium]], the other [[platinum]]. 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 carrier]]s, 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.<ref name="Williams08"/> Since the HP device displays fast ion conduction at nanoscale, it is considered a [[nanoionic device]].<ref name=Terabe2007>
| |
| {{citation
| |
| | last1 = Terabe | first1 = K.
| |
| | last2 = Hasegawa | first2 = T.
| |
| | last3 = Liang | first3 = C.
| |
| | last4 = Aono | first4 = M.
| |
| | year = 2007
| |
| | title = Control of local ion transport to create unique functional nanodevices based on ionic conductors
| |
| | journal = [[Science and Technology of Advanced Materials]]
| |
| | volume = 8 | issue = 6 | pages = 536–542
| |
| | doi = 10.1016/j.stam.2007.08.002
| |
| |bibcode = 2007STAdM...8..536T }}</ref>
| |
| | |
| 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''=∫''I''d''t'', but rather keeps ''q'' at an upper bound and ''M'' fixed, thus acting as a constant resistor until current is reversed.
| |
| | |
| 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.<ref name=Beck2000>
| |
| {{citation
| |
| | last1 = Beck | first1 = A.
| |
| | coauthors = ''et al.''
| |
| | year = 2000
| |
| | title = Reproducible switching effect in thin oxide films for memory applications
| |
| | journal = [[Applied Physics Letters]]
| |
| | volume = 77 | page = 139
| |
| | doi = 10.1063/1.126902
| |
| |bibcode = 2000ApPhL..77..139B }}</ref> [[Samsung]] has a U.S. patent for oxide-vacancy based switches similar to that described by Williams.<ref>
| |
| {{Citation
| |
| |title=US Patent 7,417,271
| |
| |url=http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO1&Sect2=HITOFF&d=PALL&p=1&u=%2Fnetahtml%2FPTO%2Fsrchnum.htm&r=1&f=G&l=50&s1=7417271.PN.&OS=PN/7417271&RS=PN/7417271
| |
| }}</ref> Williams also has a U.S. patent application related to the memristor construction.<ref>
| |
| {{Citation
| |
| |title=US Patent Application 11/542,986
| |
| |url=http://appft1.uspto.gov/netacgi/nph-Parser?Sect1=PTO2&Sect2=HITOFF&u=%2Fnetahtml%2FPTO%2Fsearch-adv.html&r=1&p=1&f=G&l=50&d=PG01&S1=20080090337.PGNR.&OS=dn/20080090337&RS=DN/20080090337
| |
| }}</ref>
| |
| | |
| In April 2010, HP labs announced that they had practical memristors working at 1 [[Nanosecond|ns]] (~1 GHz) switching times and 3 nm by 3 nm sizes,<ref>
| |
| {{Citation
| |
| |title=Finding the Missing Memristor - R. Stanley Williams
| |
| |url=http://www.youtube.com/watch?v=bKGhvKyjgLY
| |
| }}</ref> which bodes well for the future of the technology.<ref>
| |
| {{Citation
| |
| |last=Markoff |first=J.
| |
| |date=7 April 2010
| |
| |title=H.P. Sees a Revolution in Memory Chip
| |
| |url=http://www.nytimes.com/2010/04/08/science/08chips.html?hpw
| |
| |work=[[New York Times]]
| |
| }}</ref> At these densities it could easily rival the current sub-25 nm [[flash memory]] technology.
| |
| | |
| ===Polymeric memristor===
| |
| In 2004, Krieger and Spitzer described dynamic doping of polymer and inorganic dielectric-like materials that improved the switching characteristics and retention required to create functioning nonvolatile memory cells.<ref>
| |
| {{Citation
| |
| |last=Krieger |first=J. H.
| |
| |last2=Spitzer |first2=S. M.
| |
| |year=2004
| |
| |chapter=Non-traditional, Non-volatile Memory Based on Switching and Retention Phenomena in Polymeric Thin Films
| |
| |title=Proceedings of the 2004 Non-Volatile Memory Technology Symposium
| |
| |page=121
| |
| |publisher=[[IEEE]]
| |
| |doi=10.1109/NVMT.2004.1380823
| |
| |isbn=0-7803-8726-0
| |
| }}</ref> They used a passive layer between electrode and active thin films, which enhanced the extraction of ions from the electrode. It is possible to use [[fast ion conductor]] as this passive layer, which allows a significant reduction of the ionic extraction field.
| |
| | |
| In July 2008, Erokhin and Fontana claimed to have developed a polymeric memristor before the more recently announced titanium dioxide memristor.<ref name=Erokhin2008>
| |
| {{cite arXiv
| |
| | last1 = Erokhin | first1 = V.
| |
| | last2 = Fontana | first2 = M.P.
| |
| | year = 2008
| |
| | title = Electrochemically controlled polymeric device: A memristor (and more) found two years ago
| |
| | class=cond-mat.soft
| |
| | eprint = 0807.0333
| |
| }}</ref>
| |
| | |
| In 2012, Crupi, Pradhan and Tozer described a proof of concept design to create neural synaptic memory circuits using organic ion-based memristors.<ref>
| |
| {{Citation
| |
| |last=Crupi |first=M.
| |
| |last2=Pradhan |first2=L.
| |
| |last3=Tozer |first3=S.
| |
| |title=Modelling Neural Plasticity with Memristors
| |
| |journal=IEEE Canadian Review
| |
| |url=http://www.ieee.ca/canrev/cr68/IEEECanadianReview_no68.pdf
| |
| |issue=68
| |
| |pages=10–14
| |
| |date=July 2012
| |
| |year=2012
| |
| |publisher=[[Canadian Publications]]
| |
| |issn=1481-2002
| |
| }}</ref> The synapse circuit demonstrated [[long-term potentiation]] for learning as well as inactivity based forgetting. Using a grid of circuits, a pattern of light was stored and later recalled. This mimics the behavior of the V1 neurons in the [[primary visual cortex]] that act as spatiotemporal filters that process visual signals such as edges and moving lines.
| |
| | |
| ===Ferroelectric memristor===
| |
| | |
| The [[ferroelectric]] memristor<ref>
| |
| {{citation
| |
| |last=Chanthbouala |first=A.
| |
| |year=2012
| |
| |title=A ferroelectric memristor
| |
| |journal=[[Nature Materials]]
| |
| |volume=11
| |
| |pages = 860–864
| |
| |doi=10.1038/nmat3415
| |
| |url = http://www.nature.com/nmat/journal/v11/n10/full/nmat3415.html
| |
| |last2=Garcia
| |
| |first2=Vincent
| |
| |last3=Cherifi
| |
| |first3=Ryan O.
| |
| |last4=Bouzehouane
| |
| |first4=Karim
| |
| |last5=Fusil
| |
| |first5=Stéphane
| |
| |last6=Moya
| |
| |first6=Xavier
| |
| |last7=Xavier
| |
| |first7=Stéphane
| |
| |last8=Yamada
| |
| |first8=Hiroyuki
| |
| |last9=Deranlot
| |
| |first9=Cyrile
| |
| |issue=10
| |
| |arxiv = 1206.3397 |bibcode = 2012NatMa..11..860C }}</ref> is based on a thin ferroelectric barrier sandwiched between two metallic electrodes. Switching the polarization of the [[ferroelectric]] material by applying a positive or negative voltage across the junction can lead to a two order of magnitude resistance variation: R<sub>OFF</sub> >> R<sub>ON</sub> (an effect called Tunnel Electro-Resistance). In general, the polarization does not switch abruptly. The reversal occurs gradually through the nucleation and growth of ferroelectric domains with opposite polarization. During this process, the resistance is neither R<sub>ON</sub> or R<sub>OFF</sub>, but in between. When the voltage is cycled, the ferroelectric domain configuration evolves, allowing a fine tuning of the resistance value. The ferroelectric memristor's main advantages are that ferroelectric domain dynamics can be tuned, offering a way to engineer the memristor response, and that the resistance variations are due to purely electronic phenomena, aiding device reliability, as no deep change to the material structure is involved.
| |
| | |
| ===Spin memristive systems===
| |
| | |
| ====Spintronic memristor====
| |
| Chen and Wang, researchers at disk-drive manufacturer [[Seagate Technology]] described three examples of possible magnetic memristors.<ref name=Xiaobin2009>
| |
| {{citation
| |
| | last1 = Wang | first1 = X.
| |
| | last2 = Chen | first2 = Y.
| |
| | last3 = Xi | first3 = H.
| |
| | last4 = Dimitrov | first4 = D.
| |
| | last5 = Dimitrov
| |
| | year = 2009
| |
| | first5 = D.
| |
| | title = Spintronic Memristor through Spin Torque Induced Magnetization Motion
| |
| | journal = [[IEEE Electron Device Letters]]
| |
| | volume = 30 | issue = 3 | pages = 294–297
| |
| | doi = 10.1109/LED.2008.2012270
| |
| |bibcode = 2009IEDL...30..294W }}</ref> In one device resistance occurs when the spin of electrons in one section of the device points in a different direction from those in another section, creating a "domain wall", a boundary between the two sections. Electrons flowing into the device have a certain spin, which alters the device's magnetization state. Changing the magnetization, in turn, moves the domain wall and changes the resistance. The work's significance led to an interview by [[IEEE Spectrum]].<ref name=Neil2009>
| |
| {{citation
| |
| | last1 = Savage | first1 = N.
| |
| | year = 2009
| |
| | title = Spintronic Memristor
| |
| | url = http://www.spectrum.ieee.org/semiconductors/devices/spintronic-memristors
| |
| | work = [[IEEE Spectrum]]
| |
| | accessdate = 2011-03-20
| |
| }}</ref> A first experimental proof of the [[spintronic]] memristor based on domain wall motion by spin currents in a magnetic tunnel junction was given in 2011.<ref name=Chanthbouala2011>
| |
| {{citation
| |
| | last1 = Chanthbouala | first1 = A.
| |
| | year = 2011
| |
| | title = Vertical-current-induced domain-wall motion in MgO-based magnetic tunnel junctions with low current densities
| |
| | journal = [[Nature Physics]]
| |
| | volume = 7 | pages = 626–630
| |
| | doi = 10.1038/nphys1968
| |
| | url = http://www.nature.com/nphys/journal/v7/n8/full/nphys1968.html
| |
| | last2 = Matsumoto
| |
| | first2 = R.
| |
| | last3 = Grollier
| |
| | first3 = J.
| |
| | last4 = Cros
| |
| | first4 = V.
| |
| | last5 = Anane
| |
| | first5 = A.
| |
| | last6 = Fert
| |
| | first6 = A.
| |
| | last7 = Khvalkovskiy
| |
| | first7 = A. V.
| |
| | last8 = Zvezdin
| |
| | first8 = K. A.
| |
| | last9 = Nishimura
| |
| | first9 = K.
| |
| | issue = 8
| |
| |arxiv = 1102.2106 |bibcode = 2011NatPh...7..626C }}</ref>
| |
| | |
| ====Spin-transfer torque magnetoresistance====
| |
| [[Spin-transfer torque]] [[MRAM]] is a well-known device that exhibits memristive behavior. The resistance is dependent on the magnetic state of a [[magnetic tunnel junction]], i.e., on the relative magnetization alignment of the two electrodes. This can be controlled by spin torque induced by current flowing through the junction. However, the length of time the current flows through the junction determines the amount of current needed, i.e., charge is the key variable.<ref>
| |
| {{citation
| |
| |last=Huai |first=Y.
| |
| |year=2008
| |
| |title=Spin-Transfer Torque MRAM (STT-MRAM): Challenges and Prospects
| |
| |journal=[[AAPPS Bulletin]]
| |
| |volume=18 |issue=6 |page=33
| |
| |doi=
| |
| }}</ref>
| |
| | |
| Additionally, Krzysteczko et al.,<ref name="krzysteczko2009apl">
| |
| {{citation
| |
| |last=Krzysteczko |first=P.
| |
| |last2=Günter |first2=R.
| |
| |last3=Thomas |first3=A.
| |
| |year=2009
| |
| |journal=[[Applied Physics Letters]]
| |
| |title=Memristive switching of MgO based magnetic tunnel junctions
| |
| |volume=95
| |
| |issue=11 |page=112508
| |
| |doi=10.1063/1.3224193
| |
| |bibcode = 2009ApPhL..95k2508K |arxiv = 0907.3684 }}</ref> reported that [[MgO]]-based magnetic tunnel junction s show memristive behavior based on the drift of oxygen vacancies within the insulating MgO layer ([[Resistive random-access memory|resistive switching]]). Therefore, the combination of spin-transfer torque and resistive switching leads naturally to a second-order memristive system described by the state vector '''x'''=(''x<sub>1</sub>'',''x<sub>2</sub>''), where ''x<sub>1</sub>'' describes the magnetic state of the electrodes and ''x<sub>2</sub>'' denotes the resistive state of the MgO barrier. In this case the change of ''x<sub>1</sub>'' is current-controlled (spin torque is due to a high current density) whereas the change of ''x<sub>2</sub>'' is voltage-controlled (the drift of oxygen vacancies is due to high electric fields). The presence of both effects in a memristive magnetic tunnel junction led to the idea of a nanoscopic synapse-neuron system.<ref name="krzysteczko2012advmat">
| |
| {{citation
| |
| |last=Krzysteczko |first=P. |last2=Münchenberger |first2=J. |last3=Schäfers |first3=M. |last4=Reiss |first4= G. |last5=Thomas |first5=A.
| |
| |year=2012
| |
| |journal=[[Advanced Materials]]
| |
| |title=The Memristive Magnetic Tunnel Junction as a Nanoscopic Synapse-Neuron System
| |
| |volume=24
| |
| |issue=6 |page=762
| |
| |doi=10.1002/adma.201103723}}</ref>
| |
| | |
| ====Spin memristive system====
| |
| A fundamentally different mechanism for memristive behavior has been proposed by Pershin<ref>[http://www.physics.sc.edu/~pershin/ Yuriy V. Pershin]</ref> and [[Di Ventra]].<ref>[http://physics.ucsd.edu/~diventra/ Massimiliano Di Ventra]</ref><ref name=Pershin2008>
| |
| {{citation
| |
| | last1 = Pershin | first1 = Y. V.
| |
| | last2 = Di Ventra | first2 = M.
| |
| | year=2008
| |
| | title = Spin memristive systems: Spin memory effects in semiconductor spintronics
| |
| | journal = [[Physical Review B]]
| |
| | volume=78
| |
| | issue = 11 | page=113309
| |
| | doi=10.1103/PhysRevB.78.113309
| |
| |bibcode = 2008PhRvB..78k3309P |arxiv = 0806.2151 }}</ref> The authors show that certain types of semiconductor spintronic structures belong to a broad class of memristive systems as defined by Chua and Kang.<ref name="chua76"/> 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 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 hysteresis. This result was anticipated in the study of spin extraction at semiconductor/ferromagnet interfaces,<ref>
| |
| {{citation
| |
| |last=Pershin |first=Y. V.
| |
| |last2=Di Ventra |first2=M.
| |
| |year=2008
| |
| |title=Current-voltage characteristics of semiconductor/ferromagnet junctions in the spin-blockade regime
| |
| |journal=[[Physical Review B]]
| |
| |volume=77
| |
| |issue=7 |page=073301
| |
| |doi=10.1103/PhysRevB.77.073301
| |
| |bibcode = 2008PhRvB..77g3301P |arxiv = 0707.4475 }}</ref> but was not described in terms of memristive behavior. On a short time scale, these structures behave almost as an ideal memristor.<ref name="chua71"/> This result broadens the possible range of applications of semiconductor spintronics and makes a step forward in future practical applications.
| |
| | |
| ==Applications==
| |
| Williams' solid-state memristors can be combined into devices called [[crossbar latch]]es, which could replace transistors in future computers, given their much higher circuit density.
| |
| | |
| They can potentially be fashioned into [[non-volatile memory|non-volatile]] solid-state memory, which would allow greater data density than hard drives with access times similar to [[Dynamic random access memory|DRAM]], replacing both components.<ref>
| |
| {{Citation
| |
| |last=Kanellos |first=M.
| |
| |date=30 April 2008
| |
| |title=HP makes memory from a once theoretical circuit
| |
| |url=http://news.cnet.com/8301-10784_3-9932054-7.html
| |
| |work=[[CNET|CNET News]]
| |
| |accessdate=2008-04-30
| |
| }}</ref> HP prototyped a crossbar latch memory that can fit 100 [[gigabit]]s in a square centimeter,<ref name="EETimes"/> and proposed a scalable 3D design (consisting of up to 1000 layers or 1 [[petabit]] per cm<sup>3</sup>).<ref>
| |
| {{Cite media
| |
| |url=http://www.youtube.com/watch?v=bKGhvKyjgLY&t=37m45s
| |
| |title=Finding the Missing Memristor - R. Stanley Williams
| |
| }}</ref> In May 2008 HP reported that its device reaches currently about one-tenth the speed of DRAM.<ref>
| |
| {{Citation
| |
| |last=Markoff |first=J.
| |
| |date=1 May 2008
| |
| |title=H.P. Reports Big Advance in Memory Chip Design
| |
| |url=http://www.nytimes.com/2008/05/01/technology/01chip.html
| |
| |publisher=New York Times
| |
| |accessdate=2008-05-01
| |
| }}</ref> The devices' resistance would be read with [[alternating current]] so that the stored value would not be affected.<ref>
| |
| {{Citation
| |
| |last=Gutmann |first=E.
| |
| |date=1 May 2008
| |
| |title=Maintaining Moore's law with new memristor circuits
| |
| |url=http://arstechnica.com/old/content/2008/05/maintaining-moores-law-with-new-memristor-circuits.ars
| |
| |work=[[Ars Technica]]
| |
| |accessdate=2008-05-01
| |
| }}</ref> In May 2012 it was reported that access time had been improved to 90 nanoseconds if not faster, approximately one hundred times faster than contemporaneous flash memory, while using one percent as much energy.<ref>{{Citation
| |
| |last=Palmer |first=Jason
| |
| |date=18 May 2012
| |
| |title=Memristors in silicon promising for dense, fast memory
| |
| |url=http://www.bbc.co.uk/news/science-environment-18103772
| |
| |publisher=BBC News
| |
| |accessdate=2012-05-18
| |
| }}</ref>
| |
| | |
| Memristor patents include applications in [[Programmable logic device|programmable logic]],<ref>{{US patent|7203789}}</ref> [[signal processing]],<ref>{{US Patent|7302513}}</ref> [[neural networks]],<ref>{{US patent|7359888}}</ref> [[control theory|control systems]],<ref>{{US Patent|7609086}}</ref> [[reconfigurable computing]],<ref>{{US Patent|7902857}}</ref> [[brain-computer interfaces]]<ref>{{US Patent|7902867}}</ref> and [[RFID]].<ref>{{US Patent|8113437}}</ref> Memristive devices are potentially used for stateful logic implication, allowing a replacement for CMOS-based logic computation. Several early works in this direction are reported.<ref>
| |
| {{Citation
| |
| |last= Lehtonen |first=E.
| |
| |year=2010
| |
| |title=Two memristors suffice to compute all Boolean functions
| |
| |url=http://www.mendeley.com/research/two-memristors-suffice-compute-boolean-functions/
| |
| |work=[[Electronics Letters]]
| |
| |accessdate=2011-10-12
| |
| }}</ref>
| |
| <ref>
| |
| {{Citation
| |
| |last= Chattopadhyay |first=A.
| |
| |year=2011
| |
| |title=2011 IEEE/IFIP 19th International Conference on VLSI and System-on-Chip
| |
| |url=http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6081665
| |
| |work=[[VLSI-SoC]]
| |
| |accessdate=2011-10-12
| |
| |doi= 10.1109/VLSISoC.2011.6081665
| |
| |chapter= Combinational logic synthesis for material implication
| |
| |last2= Rakosi
| |
| |first2= Zoltan
| |
| |isbn= 978-1-4577-0170-2
| |
| |pages= 200
| |
| }}</ref>
| |
| | |
| In 2009, a simple electronic circuit<ref>
| |
| {{citation
| |
| | last1 = Pershin | first1 = Y. V.
| |
| | last2 = La Fontaine | first2 = S.
| |
| | last3 = Di Ventra | first3 = M.
| |
| | year = 2009
| |
| | title = Memristive model of amoeba learning
| |
| | journal = [[Physical Review E]]
| |
| | volume = 80
| |
| | issue = 2 | page = 021926
| |
| | doi= 10.1103/PhysRevE.80.021926
| |
| |bibcode = 2009PhRvE..80b1926P |arxiv = 0810.4179 }}</ref> consisting of an LC network and a memristor was used to model experiments on adaptive behavior of unicellular organisms.<ref name="amoebaexp">
| |
| {{citation
| |
| |last=Saigusa |first=T.
| |
| |last2=Tero |first2=A.
| |
| |last3=Nakagaki |first3=T.
| |
| |last4=Kuramoto |first4=Y.
| |
| |year=2008
| |
| |title=Amoebae Anticipate Periodic Events
| |
| |journal=[[Physical Review Letters]]
| |
| |volume=100 |issue=1 |page=018101
| |
| |doi=10.1103/PhysRevLett.100.018101
| |
| |pmid=18232821 |bibcode=2008PhRvL.100a8101S
| |
| }}</ref> It was shown that subjected to a train of periodic pulses, the circuit learns and anticipates the next pulse similar to the behavior of slime molds ''[[Physarum polycephalum]]'' where the viscosity of channels in the cytoplasm responds to periodic environment changes.<ref name="amoebaexp"/> Applications of such circuits may include, e.g., [[pattern recognition]]. The [[DARPA]] [[SyNAPSE]] project funded HP Labs, in collaboration with the [[Boston University]] Neuromorphics Lab, to develop neuromorphic architectures which may be based on memristive systems. In 2010, [[Massimiliano Versace|Versace]] and Chandler described the MoNETA (Modular Neural Exploring Traveling Agent) model.<ref>
| |
| {{Citation
| |
| | last=Versace | first=M.
| |
| | last2=Chandler | first2=B.
| |
| | year = 2010
| |
| | title = MoNETA: A Mind Made from Memristors
| |
| | url = http://spectrum.ieee.org/robotics/artificial-intelligence/moneta-a-mind-made-from-memristors/0
| |
| | journal = [[IEEE Spectrum]]
| |
| | volume = 12 | pages = 30–37
| |
| | doi=10.1109/MSPEC.2010.5644776
| |
| | issue=12
| |
| }}</ref> MoNETA is the first large-scale neural network model to implement whole-brain circuits to power a virtual and robotic agent using memristive hardware.<ref>{{Citation
| |
| | last=Snider |first=G.
| |
| | coauthors=''et al.''
| |
| | year = 2011
| |
| | title = From Synapses to Circuitry: Using Memristive Memory to Explore the Electronic Brain
| |
| | journal = [[IEEE Computer]]
| |
| | volume = 44
| |
| | issue=2 | pages = 21–28
| |
| | doi = 10.1109/MC.2011.48
| |
| }}</ref> Application of the memristor crossbar structure in the construction of an analog soft computing system was demonstrated by Merrikh-Bayat<ref>[http://ee.sharif.edu/~f_merrikhbayat/ Farnood Merrikh-Bayat]</ref> and Shouraki.<ref>[http://ee.sharif.edu/~bagheri-s/ Saeed Bagheri Shouraki]</ref><ref>
| |
| {{Citation
| |
| | last=Merrikh-Bayat | first=F.
| |
| | last2=Bagheri-Shouraki | first2=S.
| |
| | year = 2011
| |
| | title = Memristor crossbar-based hardware implementation of IDS method
| |
| | journal = [[IEEE Transactions on Fuzzy Systems]]
| |
| | doi = 10.1109/TFUZZ.2011.2160024
| |
| | last3=Rohani
| |
| | first3=Ali
| |
| | volume=19
| |
| | issue=6
| |
| | pages=1083
| |
| }}</ref> In 2011 they showed <ref>
| |
| {{Citation
| |
| | last=Merrikh-Bayat | first=F.
| |
| | last2=Bagheri-Shouraki | first2=S.
| |
| | year = 2011
| |
| | title = Efficient neuro-fuzzy system and its Memristor Crossbar-based Hardware Implementation
| |
| | arxiv =1103.1156
| |
| |bibcode = 2011arXiv1103.1156M }}</ref> how memristor crossbars can be combined with [[fuzzy logic]] to create an analog memristive [[neuro-fuzzy]] computing system with fuzzy input and output terminals. Learning is based on the creation of fuzzy relations inspired from [[Hebbian theory|Hebbian learning rule]].
| |
| | |
| In 2013 Leon Chua published a tutorial underlining the broad span of complex phenomena and applications that memristors span and how they can be used as non-volatile analog memories and can mimic classic habituation and learning phenomena.<ref>[http://iopscience.iop.org/0957-4484/24/38/383001 Chua, Leon. "Memristor, Hodgkin–Huxley, and Edge of Chaos." ''Nanotechnology'' 24 383001]</ref>
| |
| | |
| ==Memcapacitors and meminductors==
| |
| In 2009, [[Massimiliano Di Ventra|Di Ventra]], Pershin and Chua extended<ref>
| |
| {{citation
| |
| | last1 = Di Ventra | first1 = Massimiliano
| |
| | last2 = Pershin | first2 = Yuriy V
| |
| | last3 = Chua | first3 = Leon
| |
| | title = Circuit elements with memory: memristors, memcapacitors and meminductors
| |
| | journal=Proceedings of the IEEE
| |
| | volume=97
| |
| | issue = 10
| |
| | page=1717
| |
| | year=2009
| |
| | doi= 10.1109/JPROC.2009.2021077
| |
| }}</ref> the notion of memristive systems to capacitive and inductive elements in the form of memcapacitors and meminductors, whose properties depend on the state and history of the system, further extended in 2013 by Di Ventra and Pershin.<ref name="DiVentra_2013" />
| |
| | |
| ==Timeline==
| |
| | |
| ===1808===
| |
| [[Sir Humphry Davy]] is claimed by [[Leon Chua]] to have performed the first experiments showing the effects of a memristor.<ref name="Memristor200yearsold" /><ref>{{cite journal|last=Prodromakis|first=Themistoklis|last2=Toumazou|first2=Christofer|last3=Chua|first3=Leon|title=Two centuries of memristors|journal=Nature Materials|volume=11|issue=6|pages=478–481|doi=10.1038/nmat3338|date=June 2012|bibcode = 2012NatMa..11..478P }}</ref>
| |
| | |
| ===1960===
| |
| [[Bernard Widrow]] coins the term [[memistor]] (i.e. memory resistor) to describe components of an early artificial neural network called [[ADALINE]].
| |
| | |
| ===1968===
| |
| Argall publishes an article showing the resistance switching effects of TiO2 which was later claimed in 2008 to be evidence of a memristor by researchers from Hewlett Packard.<ref name="Argall1968"/>
| |
| | |
| ===1971===
| |
| [[Leon Chua]] postulated a new two-terminal circuit element characterized by a relationship between charge and flux linkage as a fourth fundamental circuit element.<ref name="chua71"/>
| |
| | |
| ===1976===
| |
| Chua and his student Sung Mo Kang generalized the theory of memristors and memristive systems including a property of zero crossing in the [[Lissajous curve]] characterizing current vs. voltage behavior.<ref name="chua76"/>
| |
| | |
| ===2007===
| |
| On April 10 {{US patent|7203789}} was issued. It described implementations of 2-terminal resistance switches similar to memristors in reconfigurable computing architectures.
| |
| | |
| On November 27 {{US Patent|7302513}} was issued. it described implementations of 2-terminal resistance switches similar to memristors in [[signal processing]] and [[pattern recognition]].
| |
| | |
| ===2008===
| |
| On April 15 {{US patent|7,359,888 }} was issued, including basic claims to a nanoscale 2-terminal resistance switch crossbar array formed as a [[neural network]].
| |
| | |
| On May 1 Strukov, Snider, Stewart and Williams published an article in Nature identifying a link between the 2-terminal resistance switching behavior found in nanoscale systems and memristors.<ref>
| |
| {{citation
| |
| | url=http://www.nature.com/nature/journal/v453/n7191/full/nature06932.html | volume=453 | issue=7191 | doi=10.1038/nature06932 | pmid=18451858
| |
| |bibcode = 2008Natur.453...80S
| |
| | title=The missing memristor found
| |
| | year=2008
| |
| | last1=Strukov
| |
| | first1=Dmitri B.
| |
| | last2=Snider
| |
| | first2=Gregory S.
| |
| | last3=Stewart
| |
| | first3=Duncan R.
| |
| | last4=Williams
| |
| | first4=R. Stanley
| |
| | journal=Nature
| |
| | pages=80–3 }}</ref>
| |
| | |
| On August 26 {{US patent|7417271}} was issued, including claims covering the device described in the Nature article by Strukov et al.
| |
| | |
| On October 28 {{US patent|7443711}} was issued, including basic claims to a tunable nanoscale 2-terminal resistance switch.
| |
| | |
| ===2009===
| |
| On January 23 [[Di Ventra]], Pershin and Chua extended the notion of memristive systems to capacitive and inductive elements, namely [[capacitor]]s and [[inductor]]s whose properties depend on the state and history of the system.<ref>
| |
| {{Citation
| |
| |author=Massimiliano Di Ventra
| |
| |author2=Pershin
| |
| |author3=Chua
| |
| |doi=10.1109/JPROC.2009.2021077
| |
| |journal=Proceedings of the IEEE 97 (2009)
| |
| |volume=97
| |
| |title=Circuit elements with memory: memristors, memcapacitors and meminductors
| |
| |issue=10
| |
| |pages=1717–1724
| |
| |year=2009
| |
| |arxiv=0901.3682
| |
| |postscript=.
| |
| }}</ref>
| |
| | |
| On May 1 Kim, et al. described a newly discovered memristor material based on magnetite nanoparticles and proposed an extended memristor model including both time-dependent resistance and time-dependent capacitance.<ref>{{doi|10.1021/nl900030n}}</ref>
| |
| | |
| On July 13 Mouttet described a memristor-based pattern recognition circuit performing an analog variation of the [[exclusive nor]] function. The circuit architecture was proposed as a way to circumvent [[Von Neumann bottleneck|Von Neumann architecture#Von Neumann bottleneck]] for processors used in robotic control systems.<ref name="IMETI09">
| |
| {{citation
| |
| | last = Mouttet
| |
| | first = Blaise L
| |
| | title = Memristor Pattern Recognition Circuit Architecture for Robotics
| |
| | journal = Proceedings of the 2nd International Multi-Conference on Engineering and Technological Innovation
| |
| | volume = II
| |
| | pages = 65–70
| |
| | year = 2009
| |
| | url = http://www.iiis2009.org/imeti/program/HTML/program-20.htm
| |
| }}</ref>
| |
| | |
| On August 4 Choi e. al. described the physical realization of an electrically modifiable array of memristive neural synapses.<ref name="Gwangju2009">
| |
| {{citation
| |
| | last1 = Choi | first1 = H
| |
| | coauthors = ''et al.''
| |
| | title = An electrically modifiable synapse array of resistive switching memory
| |
| | year = 2009
| |
| | journal = Nanotechnology
| |
| | volume = 20 | issue = 34 | page = 345201
| |
| | doi = 10.1088/0957-4484/20/34/345201
| |
| | pmid = 19652272
| |
| |bibcode = 2009Nanot..20H5201C }}</ref>
| |
| | |
| ===2010===
| |
| | |
| On April 8 Borghetti, et al. described an array of memristors demonstrated the ability to perform logical operations.<ref name="Nature2010">
| |
| {{citation
| |
| | last1 = Borghetti | first1 = Julien
| |
| | author2 = Snider, Gregory S.
| |
| | author3 = Kuekes, Philip J.
| |
| | author4 = Yang, J. Joshua
| |
| | author5 = Stewart, Duncan R.
| |
| | author6 = Williams, R. Stanley
| |
| | title = 'Memristive' switches enable 'stateful' logic operations via material implication
| |
| | year = 2010
| |
| | issue = 7290
| |
| | volume = 464
| |
| | journal = Nature
| |
| | url = http://www.nature.com/nature/journal/v464/n7290/full/nature08940.html
| |
| | pmid = 20376145
| |
| | doi = 10.1038/nature08940
| |
| | bibcode = 2010Natur.464..873B
| |
| | pages = 873–6
| |
| }}</ref>
| |
| | |
| On April 20 Memristor-based content addressable memory (MCAM) was introduced.<ref name="Kavehei2010b">
| |
| {{citation
| |
| | last1 = Eshraghian | first1 = K.
| |
| | last2 = Rok Cho | first2 = K.R.
| |
| | last3 = Kavehei | first3 = O.
| |
| | last4 = Kang | first4 = S.K.
| |
| | last5 = Abbott | first5 = D.
| |
| | last6 = Kang | first6 = S.M.
| |
| | title = Memristor MOS Content Addressable Memory (MCAM): Hybrid Architecture for Future High Performance Search Engines
| |
| | year = 2010
| |
| | page = 3687
| |
| | volume = 1005
| |
| | journal = IEEE Transactions on Very Large Scale Integration (VLSI) Systems
| |
| | arxiv = 1005.3687
| |
| | bibcode = 2010arXiv1005.3687E
| |
| }}</ref>
| |
| | |
| On June 1 Mouttet argued that the interpretation of the memristor as a fourth fundamental was incorrect and that the HP Labs device was part of a broader class of memristive systems.<ref name="MythicalMemristor">
| |
| {{citation
| |
| | last1 = Mouttet | first1 = Blaise
| |
| | title = The mythology of the memristor
| |
| | year = 2010
| |
| | series = ISCAS
| |
| | place = Paris, France
| |
| | url = http://www.slideshare.net/blaisemouttet/mythical-memristor
| |
| }}</ref>
| |
| | |
| On August 31 HP announced they had teamed up with [[Hynix]] to produce a commercial product dubbed "ReRam".<ref>
| |
| {{cite news
| |
| | title = HP and Hynix to popularize new kind of chip circuit dubbed "memristor"
| |
| | date = September 1, 2010
| |
| | work = Reuters
| |
| | url = http://www.reuters.com/article/idUS254583059320100901
| |
| }}</ref>
| |
| | |
| On December 7 So and Koo developed a [[hydrogel]] form of memristor that was speculated to be useful to construct a [[brain-computer interface]].<ref>
| |
| {{cite news
| |
| | url = http://spectrum.ieee.org/semiconductors/materials/chemists-construct-squishy-memristors-and-diodes
| |
| | title = Chemists Construct Squishy Memristors and Diodes
| |
| | date = December 7, 2010
| |
| | work = IEEE Spectrum
| |
| }}</ref>
| |
| | |
| ===2011===
| |
| In October Tse demonstrated printed memristive counters based on solution processing, with potential applications as low-cost packaging components (no battery needed; powered by energy scavenging mechanism).<ref>
| |
| {{cite news
| |
| | url = http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=5991940
| |
| | title = Solution-Processed Memristive Junctions Used in a Threshold Indicator
| |
| | date = Oct 2011
| |
| | doi = 10.1109/TED.2011.2162334
| |
| | work = IEEE Transactions on Electronic Devices
| |
| }}</ref>
| |
| | |
| ===2012===
| |
| On March 23 [[HRL Laboratories]] and the [[University of Michigan]] announced the first functioning memristor array built on a CMOS chip for applications in [[neuromorphic]] computer architectures.<ref name="HRLmemristor" />
| |
| | |
| On July 31 Meuffels criticized the generalized memristor concept.<ref name="Meuffels_2012" />
| |
| | |
| ===2013===
| |
| | |
| On February 27 Thomas et al., constructed a memristor capable of learning. The approach utilizes memristors as key components in a blueprint for an artificial brain.<ref>
| |
| {{cite news
| |
| | url = http://www.rdmag.com/news/2013/02/memristor-%E2%80%9Clearns%E2%80%9D-provides-blueprint-artificial-brain
| |
| | title = Memristor that "learns" provides blueprint for artificial brain
| |
| | date = Feb 2012
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| | work = R&D magazine
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| }}</ref>
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| On April 23 Valov, et al., argued that the current memristive theory must be extended to a whole new theory to properly describe redox-based resistively switching elements (ReRAM). The main reason is the existence of nanobatteries in redox-based resistive switches which violates the memristor theory's requirement for a pinched hysteresis.<ref name="memristor_nanobattery"/>
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| ==See also==
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| {{Portal|Electronics}}
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| *[[Memistor]]
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| *[[Electrical element]]
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| *[[List of emerging technologies]]
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| *[[Physical neural network]]
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| *[[RRAM]]
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| ==External links==
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| * [http://www.youtube.com/watch?v=n3XzuBt54ig Video: Finding the missing memristor | Stanford University (2012)]
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| * [http://memlinks.eu Interactive database of memristor papers (2013)]
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| ==References==
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| {{reflist|colwidth=30em}}
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| {{Commons category|Memristors}}
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| {{Emerging technologies}}
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| {{Electronic components}}
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| [[Category:Electrical components]]
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| [[Category:Emerging technologies]]
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| [[Category:American inventions]]
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