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忆阻器

C的发展历史
• 2008年（距蔡教授提出忆阻器已经37年过去了）
才出现了转机，另一个由 Stanley Williams 领军的 HP 团队在研究二氧化钛的时候，意外地发现了二氧化钛在某些情况的电子特性比较奇特。最终由此制出了第四电子元件。
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忆阻器构成及原理
一块极薄的二氧化钛被夹在两个电极中间，这些二氧化钛又被分成两个部份，一半是正常的（图二中undoped 部分）二氧化钛，另一半进行了“掺杂”（图二中doped部分），少了几个氧原子。当“掺杂”的那一半带正电，因此电流通过时电阻比较小，而且当电流从“掺杂”的一边通向正常的一边时，在电场的影响之下缺氧的 “掺杂物”会逐渐往正常的一侧游移，使得以整块材料来言，“掺杂”的部份会占比较高的比重，整体的电阻也就会降低。反之，当电流从正常的一侧流向“掺杂”的一侧时，电场会把缺氧的“掺杂物”从回推，电阻就 5 会跟着增加。
companylogo忆阻器最简单的应用就是作为非易失性阻抗存储器rram今天的动态随机存储器所面临的最大问题是当你关闭pc电源时动态随机存储器就忘记了那里曾有过什么所以下次打开计算机电源你就必须坐在那儿等到所有需要运行计算机的东西都从硬盘装入到动态随机存储器
1.发展历史介绍 2.原理介绍 3.特性 4.应用
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忆阻器的特性
• 忆阻器是一种有记忆功能的非线性电阻。通过控制
电流的变化可改变其阻值，如果把高阻值定义为 “1”，低阻值定义为“0”，则这种电阻就可以实现存储数据的功能。 • 忆阻器器件的特征是它可以记忆流经它的电荷数量。忆阻器的电阻取决于多少电荷经过了这个器件。即使断电它的电阻也会保持不变，记住断电那一刻的状态。 • 由于忆阻器的电阻值是随流过的电流来决定，所以它也能定义除1和0以外的其他状态。

忆阻器桥式突触结构神经网络的学习PPT

Memristor Bridge Synapse-Based Neural Network and Its Learning· Act as nonvolatile analog memories,they are programmable, and scalableto nano dimensions简要介绍&基础铺垫2016/9/18 Sunday神经网络的硬件实现问题· 神经网络中用到的的BP算法成功应用于语音/手写/脸部识别以及机器人控制等· 神经网络的硬件实现的成功与否，取决于accuracy,chip area, processing speed三者的权衡。

· 优点：比起软件实现的神经网络1.更快的processing speed2.对chip area的更有效利用· 缺点：1.limited accuracy due to spatial nonuniformity(空间的不均匀性) and nonideal responses2.nonvolatile weight storage(非易失性存储)硬件实现主要的两个困难1.材料上的困难：In analog hardware implementations, the weights are usually stored inresistors, capacitors, and floating gate transistors(浮栅晶体管)Floating gate transistors has been used successfully as synapses(突触) in conjunction with analog multipliers, but it suffers from high nonlinearity(非线性) in synaptic weightings.2.学习算法上的困难：与BP算法的software实现相比，BP算法的hardware实现较为困难，并且这些困难会因电子元件的imperfections and mismatch而加剧。

第四种电子元件——忆阻器

长沙学院CHANGSHA UNIVERSITY 《信息科学与技术导论》课程论文论文题目:第四种基本电路元件--忆阻器系部：电子与通信工程系专业：电子信息工程学生姓名：班级：学号长沙学院教务处二○一一年二月制摘要5年前《自然》杂志的一篇论文，让“忆阻器”三个字广为人知。

这一被美国加州大学伯克利分校教授蔡少棠于1971年预言存在的第四种基本电路元件，在经历晶体管时代漫长的“下落不明”后，被惠普实验室首先“找到”，轰动了全球电子学界。

忆阻器是一类具有电阻记忆行为的非线性电路元件，被认为是除电阻、电容、电感外的第四个基本电路元件。

本文回顾了忆阻器的概念和数学定义，重点介绍了惠普实验室的P t / T iO 2 / P t 三明治结构的忆阻器薄膜器件模型和忆阻器元件某些值得关注的特性，如滞回曲线特性。

阐述了忆阻器在D-RAM的替代品、类脑系统、生物记忆行为仿真、基础电路和器件设计方面的应用前景。

关键词：忆阻器，理想元件，忆阻应用ABSTRACT5 years ago "Nature" magazine of a paper，so that "memristor" words known. This is the University of California，Berkeley professor Leon Chua predicted the existence of a fourth basic circuit element in 1971，after the transistor era long "missing" after being the first "found" HP Labs，the global electronic academic sensation. Memristor is a class of nonlinear circuit element having a resistance memory behavior is considered in addition to resistors，capacitors，inductors outside the fourth basic circuit element. This paper reviews the memristor concept and mathematical definition，focusing on the HP Labs P t / T iO 2 / P t memristor film memristor device model and some of the sandwich structure components noteworthy features，such as hysteresis curve characteristics. Memristor elaborated in alternative D-RAM, the class brain systems, biological memory behavioral simulation, basic circuits and devices prospect design.Keywords：memristor，ideal components，memristive applications目录摘要................................................................................................................... I I ABSTRACT .......................................................................................................... I I 一引言.. 0二忆阻器的概念和定义 0三忆阻器应用领域及研究方向展望 (2)（一）D-RAM的替代品——非易失性阻抗存储器( RRAM) (2)（二）类脑系统——模拟大脑的功能 (3)四中国忆阻器现状 (4)（一）有望续写摩尔定律 (4)（二）国内外鲜明对比 (5)（三）鸿沟待跨越 (6)结束语 (6)参考文献 (7)一引言很多人知道电阻器（抵抗电流）、电容器（存储电荷）和电感器（抵抗电流的变化），但很少有人知道第四类可记忆二端元件：忆阻器、忆容器和忆感器。

TiO2-忆阻器

HP实验室的研究模型
由一排横向和一排纵向的电线组成的网格，在每一个交叉点上，要放一个开关连接一条横向和纵向的电线。让这两条电线控制这个开关的状态，那网格上的每一个交叉点都能储存一个位的数据。这种材料必须要能有“开”、“关”两个状态，这两个状态必须要能控制，在不改变状态的前提下，发挥其开关的效果，允许或阻止电流的流过。
开关机制取决于： 1、氧化物材料(掺杂氧空位的浓度、氧化物的最佳生长窗口、正常氧化物的电阻率不可过高也不可过低、适当退火温度的电学性质最优） 2、电极材料 3、偏压幅度大小和脉冲时间（频繁正负偏压之间的激励） 4、环境条件（器件需洁净，小的水分子或金属纳米粒子可能导致器件短路）
1、用扫描隧道显微镜去探测双极性开关中导电细丝的形成与减退 2、用X射线衍射分析掺杂薄膜的结晶相 3、用X射线光电子谱分析金属的氧化态 4、测其I-V特性
具有忆阻现象的十字交叉矩阵示意图
二、TiO2薄膜器件—忆阻器模型
两个电极为Pt材料，薄膜夹层左边区域为TiO2具有很高的忆阻值Roff, 右边区域为TiO2-x(掺杂氧缺位)具有低的忆阻值Ron，当掺杂的那一半带正电，电流通过时电阻较小，而且当电流从掺杂的一边通向正常的一边时，在电场的影响之下缺氧的掺杂物会逐渐往正常的一侧游移，使得以整块材料来言，掺杂的部分会占比较高的比重，杂质均匀的分布在金属氧化半导体中，整体的电阻也会降低。反之，当电流从正常的一侧流向掺杂的一侧时，电场会把缺氧的掺杂物往回推，被推到某一端,导致杂质的分布极端不均，电阻就会跟着增加。因此，整个器件就相当于一个滑动变阻器。
三、忆阻器的研究进展及应用前景
1、忆阻器的研究进展
2、应用前景
1）忆阻器在人工神经网络中的应用

忆阻器及忆阻混沌电路ppt课件

上述四个电路变量两两之间→_可→以建立六个数学关系式，其中五对关系式已经为大家所熟知——分别来自R、C、L、Q 的定义和法拉第电磁感应定律（如图1所示），但φ、Q 间的关系却一直没被揭示。
1 引言
根据图1中基本变量组合完备性原理，，美国加州大学伯克利分校华裔科学家蔡少棠于1971年从理论上预测了描述电荷和磁通关系元件的存在性，并且定义这类元件为记忆电阻器（简称忆阻器，英文名称为Memristor）.
忆阻器与忆阻混沌电路
学号：姓名：
目录
1 2 3
忆引基阻于言器三的次等模型效型忆电阻路器模的型混沌电路 4
LOGO
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1 引言
由电路基本理论可知，电路和元件特性是有四个基本变量来描述的，分别为四个电路变量电压（V）、电流（I）、磁通量（φ）和电荷量（Q） a.电压和电流关系→电阻器R b.电压和电荷关系→电容器C c.电流和磁通关系→电感器L
图3 HP TiO2 忆阻的基本模型
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➢ HP TiO2忆阻线性杂质漂移模型和非线性窗函数模型可以统一表示为:
式中：i为输入电流； v 为输出电压； RON.ROFF和k 为系统参数； x为状态变量； M(x)代表忆阻模型的忆阻器； Fn(x)(n=1,2,3,4,5)分别代表HP线性窗函数和4种非线性窗函数
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2 忆阻器模型
2.1 忆阻器的定义 2.2 物理器件模型 2.3 数学理论模型
2.3.1 分段线性模型 2.3.2 三次型非线性模型 2.3.3 二次型非线性模型
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2 忆阻器模型
2.1 忆阻器的定义
➢ 忆阻器是一个基本的无源二端元件，它的磁通量φ 与累积的电荷q 之间的关系可以用φ -q 或q- φ平面上的一条曲线f(φ ，q) = 0 来确定，忆阻器分为荷控忆阻器和磁控忆阻器两种，如图2所示

忆阻器的发展与应用

未来研究方向和前景展望
新型材料与技术
探索新型材料和技术，提高忆阻器的性能、稳定性和可靠性
，降低成本。
神经形态计算
利用忆阻器模拟神经元和突触的功能，构建神经形态计算系统，实现更高效、智能的计算。
物联网与边缘计算
将忆阻器应用于物联网和边缘计算领域，实现数据的就近存储和处理，提高响应速度和能效比。
化学气相沉积
通过化学反应在基底上生成忆阻材料薄膜。
微纳加工技术
光刻技术
利用光刻胶和光刻机对忆阻材料进行微细加工。
刻蚀技术
采用干法刻蚀或湿法刻蚀技术，对忆阻材料进行高精度刻蚀。
纳米压印技术
利用纳米压印模板在忆阻材料上压印出纳米级图案。
性能测试与表征方法
电学性能测试
测试忆阻器的电阻、电容、电感等电学性能。
应用
MRAM具有非易失性、高速、低功耗等优点，被广泛应用于嵌入式系统、移动设备、航空航天等领域。同时，MRAM还有望成为未来神经形态计算和量子计算的重要硬件基础。
各类存储器性能比较
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02
03
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速度
RRAM和PCRAM的读写速度较快，而MRAM的读写速度
相对较慢。
功耗
RRAM和PCRAM的功耗较低，而MRAM的功耗相对较高
神经形态计算挑战
神经形态计算在硬件实现、算法设计、系统集成等方面面临诸多挑战，如神经元和突触的复杂动态特性、硬件资源的有限性等。
基于忆阻器的突触仿生器件
忆阻器作为突触仿生器件
忆阻器具有非易失性、连续可调电阻等特性，可模拟生物突触的权重调节和信息传递功能。
突触仿生器件应用
基于忆阻器的突触仿生器件在图像识别、语音识别、自然语言处理等任务中展现出良好性能。

忆阻器应用

Received February3,2013,accepted April14,2013,published May10,2013.Digital Object Identifier10.1109/ACCESS.2013.2259891Memristor-Based Nonvolatile Random Access Memory:Hybrid Architecture for Low Power Compact Memory DesignSYED SHAKIB SARWAR,SYED AN NAZMUS SAQUEB,FARHAN QUAIYUM(Student Member,IEEE),ANDA.B.M.HARUN-UR RASHID(Senior Member,IEEE)Department of Electrical and Electronic Engineering,Bangladesh University of Engineering and Technology,Dhaka1000,Bangladesh.Corresponding author:S.S.Sarwar(syed.shakib@)This work was supported by the Ministry of Science and Technology,Government of Bangladesh,under the Science and Technology Special Research Grant for2012–2013.ABSTRACT In this paper,a new approach toward the design of a memristor based nonvolatile static random-access memory(SRAM)cell using a combination of memristor and metal-oxide semiconductor devices is proposed.Memristor and MOSFETs of the Taiwan Semiconductor Manufacturing Company’s180-nm technology are used to form a single cell.The predicted area of this cell is signiﬁcantly less and the average read–write power is∼25times less than a conventional6-T SRAM cell of the same complementary metal-oxide semiconductor technology.Read time is much less than the6-T SRAM cell.However,write time is a bit higher,and can be improved by increasing the mobility of the memristor.The nonvolatile characteristic of the cell makes it attractive for nonvolatile random access memory design.INDEX TERMS CMOS,memory element,memristor(M),NVRAM,SPICE model.I.INTRODUCTIONChua[1]hypothesized the existence of a fourth passive two-terminal circuit element called the memristor in1971 (the other three elements being the resistor,capacitor and inductor).In2008,researchers at Hewlett Packard(HP)Labs reported that the memristor was realized physically using two-terminal titanium-di-oxide(TiO2)nanoscale device[2]. HP Labs described theﬁrst experimental demonstration of a physical memristor,ﬁnally conﬁrming Chua’s the-ory and sparking much excitement in the electronics and business circles[3].Basically the memristor is a resis-tance with memory;when a voltage is applied to this ele-ment,its resistance changes and remains on that particu-lar value when the source is removed.The main differ-ence between the memristor(M)and the three traditional circuit elements(R,L,C)is its nonlinear input-output characteristics.The HP memristor exploits certain nanoscale properties of a titanium-di-oxide TiO2thinﬁlm.Other physical embodi-ments of memristors may also be possible and it has been recently proposed that coupling of currentﬂow and spin transport at nanoscale dimensions can be used to realize memristance[4],[5].Analog circuit applications incorpo-rating the memristor are rapidly emerging in the literature. Witrisal considered Memristors in an ultra-wideband receiver to reduce signal processing power[6].Memristors are also used as programmable resistive loads in a differential ampli-ﬁer[7].Varghese and Gandi used memristor as a source degeneration element in a complementary metal-oxide semi-conductor(CMOS)differential pair[8].Reference[9]shows a variety of programmable analog functional blocks based on analog memristor memory including an Op-Amp based variable gain ampliﬁer(VGA).Pulse-programming methods for memristive analog memory in a differential pair ampliﬁer are considered in[10].Memristors have been studied intensively among many researchers because of their possibilities,especially as a strong candidate for future memories[11].Non-volatile prop-erty and high packing density in a crossbar array particularly excites the researchers.The main feature of our proposed circuit is its non-volatility.The data is stored in the memory even when the power is turned off for an indeﬁnite time. Another feature is its reduced size compared to the conven-tional6T-SRAM.As only three transistors are used in eachS.S.Sarwar et al.:Memristor-Based Nonvolatile Random Access Memorycell of the proposed circuit,its area can be much less than the conventional SRAM cells.The power consumed by the proposed structure is signiﬁcantly less than the conventional SRAM structure.All these features are discussed further later on in this paper.The paper starts off with the introduction of memristors and its characteristics.After that some related works were discussed.Then it goes straight into the structure of our proposed circuit,its working principle and its functionality, then it discusses the perspectives,draws some comparisons, andﬁnally it concludes with the possible future prospects of the circuit.II.MEMRISTOR AS A MEMORY ELEMENTStrukov et al.[2]presented a physical model of the memristor. They have shown that the memristor can be characterized by an equivalent time-dependent resistor whose value at a time t is linearly proportional to the quantity of charge q that has passed through it.They realized a proof-of-concept memris-tor,which consists of a thin nanolayer(2nm)of TiO2and a second oxygen deﬁcient nanolayer of TiO2−x(8nm)sand-wiched between two Pt nanowires.Oxygen(O2−)vacancies are+2mobile carriers and are positively charged.A change in distribution of O2−within the TiO2nanolayer changes the resistance.By applying a positive voltage,to the top platinum nanowire,oxygen vacancies drift from the TiO2−x layer to the TiO2undoped layer,thus changing the boundary between the TiO2−x and TiO2layers.As a consequence,the overall resistance of the layer is reduced corresponding to an‘‘ON’’state.When enough charge passes through the memristor that ions can no longer move,the device enters a hysteresis region and keeps q at an upper bound withﬁxed memristance, M(memristor resistance).By reversing the process,the(a)(b)FIGURE1.(a)Characterizing the memristor and(b)change of resistance when a3.6V p–p square wave is applied.oxygen defects diffuse back into the TiO2−x nanolayer. The resistance returns to its original state,which corre-sponds to an‘‘OFF’’state.The signiﬁcant aspect to be noted here is that only ionic charges,namely oxygen vacan-cies(O2−)through the cell,change memristance.The resistance change is non-volatile hence the cell acts as a memory element.Fig.1(a)shows the doped and undoped region of a memristor.If a voltage is applied across the memristorv(t)=M(t)i(t)[2](1)M(t)=R ONw(t)D+R OFF1−w(t)D(2) where R ON is the resistance of completely doped memristor and R OFF is the resistance of completely undoped memristor, w(t)is given bydw(t)dt=µvR ONDi(t)(3)µv is the average dopant mobility and D is the length of the memrsitor.To consider the nonlinearity produced from the edge of the thinﬁlm,a window function[2],[12],[13] should be multiplied to the right side of(3).fw(t)D=1−2w(t)D−12p.(4)The spice model[13]which makes use of non-linear dopant drift in modelling is used for simulation.Change of resistance of a memristor applying3.6V p–p square wave across it is shown in Fig.1(b).Following parameters were used for simulation:R ON=100 ,R OFF=20k ,p=10, D=3nm andµv=350×10−9m2/s/V.Resistance of the memristor changes from20k to100 in positive cycle.This change occurs in reverse direction when the square pulse reverses its direction.III.RELATED WORKSSRAM is a form of semiconductor memory widely used in electronics,microprocessor and general computing applica-tions.This form of semiconductor memory gains its name from the fact that data is held in there in a static fashion, and does not need to be dynamically updated as in the case of DRAM memory.While the data in the SRAM memory does not need to be refreshed dynamically,it is still volatile, meaning that when the power is removed from the memory device,the data is not held,and will disappear.The opera-tion of the SRAM memory cell is relatively straightforward. When the cell is selected,the value to be written is stored in the cross-coupledﬂip-ﬂops.The cells are arranged in a matrix,with each cell individually addressable.Most SRAM memories select an entire row of cells at a time,and read out the contents of all the cells in the row along the column lines.Access to the SRAM memory cell is enabled by the Word Line.This controls the two access control transistors which control whether the cell should be connected to the bit lines.These two lines are used to transfer data for both readS.S.Sarwar et al.:Memristor-Based Nonvolatile Random AccessMemoryand write operations.The most commonly used SRAM type is the6T SRAM which offers better electrical performances from all aspects(speed,noise immunity,standby current).The smallest6T-SRAM cell that has been fabricated till today has an area of0.08µm2and it was fabricated in the22nm pro-cess using immersion and EUV lithography[15].The main disadvantages of the6T SRAM structure are its large size and high power consumption.To overcome these limitations, memristive-RAMs are being developed recently.According to HP,resistive random access memory(ReRAMs),which are memristor-based versions of both DRAM and SRAM,ought to speed up computers immensely.Along with HP,Samsung and many other companies are working on memristor tech-nology.There are several researches on memristor based memories. In[16],a complementary resistive switch was introduced.It consists of two anti-serial memristive elements which vali-dates the construction of large passive crossbar arrays witha drastic reduction in power consumption.Junsangsri et al.[17]presented a novel memory cell consisting of a mem-ristor and ambipolar transistors.Macroscopic models were utilized to characterize the operations of that memory cell. In[18],Kamran Eshraghian et al.provided a new approach towards the design and modeling of memristor based con-tent addressable memory(MCAM)using a combination of memristor and MOS devices to form the core of a mem-ory/compare logic cell.This cell forms the building block of the CAM architecture.The non-volatile characteristic and the minuteness together with compatibility of the memristor with CMOS processing technology increases the packing density, provides new approach towards power management through disabling CAM blocks without loss of stored data,which reduces power dissipation.This inspired us to design a SRAM cell using Memristor-MOS hybrid architecture exploiting the non-volatile characteristic and the nanoscale geometry of a memristor.IV.PROPOSED SRAM CELLElectrical scheme of the proposed SRAM cell is shown in Fig.2(a).Two memristors are used as memory element.The arrangement is in such a way that during write cycle,they are connected in parallel but in opposite polarity[Fig.2(b)] and during read cycle,they are connected in series[Fig.2(c)]. These connections are established by two NMOS pass tran-sistors T1and T2.A third transistor T3is used to isolate a cell from other cells of the memory array during read and write operations.The gate input of T3is the Comb signal which is the OR of RD and WR signals.If a bit is to be written,RD is taken to the LOW state and WR and Comb are taken to the HIGH state.As a result,circuit of Fig.2(b)is formed.The voltage across the memristors is(V D−VDD/4). Depending on the data,it can be positive(if D=1i.e. V D=VDD)or negative(if D=0i.e.V D=0V).As polarities of the memristors are opposite,change of mem-ristances(or resistances)will also take place in the opposite direction.Now if the data is to be read,RD and Combare(a)(b)(c)FIGURE2.(a)Three transistor–two memristor SRAM cell(b)circuit when RD=0,WR=1,and Comb=1.(c)Circuit when RD=1,WR=0,and Comb=1.taken to the HIGH state and this forms the circuit shown in Fig.2(c).V oltage at D is now:V D=VDD2−V DD4×R2(R1+R2)+V DD4(5) where,R1and R2are the resistances of M1and M2respec-tively.If‘‘1’’was written during write cycle,R2becomes sig-niﬁcantly greater than R1and then V D is greater than VDD/4. If‘‘0’’was written,R1becomes signiﬁcantly greater than R2 which makes V D to be as close as VDD/4.A comparator can be used as a sense ampliﬁer to interpret these voltages as HIGH or LOW correctly.V.SIMULATIONS AND ANALYSISIn Fig.3,a16×16array is formed for the veriﬁcation of array structure of our proposed NVRAM cell.Data is fed through wordlines/bitlines.Switching between i/p and o/p is done with the help of CMOS transmission gate controlled by Vdt and Vdtb signals which are complement of each other. In practical circuits,this purpose is served through encoders. Several simulations were done to test the validity of our proposed SRAM structure and compare it with the traditional SRAM structures.In the simulations data was written and read to calculate several important parameters such as write time,read time,power consumption etc.A comparator can be used as a sense ampliﬁer to interpret these voltages as HIGH or LOW correctly.The reference of the comparator should be tied to0.26V.Simulations of the circuits are based on the following parameters:R ON=100 ,R OFF=20k ,p= 10,D=3nm andµv=350×10−9m2/s/V.The NVRAM cell has been implemented using TSMC180nm technology.S.S.Sarwar et al.:Memristor-Based Nonvolatile Random AccessMemory FIGURE3.16×16array structure.(a)(b)FIGURE4.(a)Timing diagram of input pulses during write operation. (b)Change of resistance of the two memristors of cell20during write operation.A.WRITE OPERATIONIn theﬁrst write cycle,‘‘1’’was written to cell2.Vwr2, Vrow0and Vdt0were set to HIGH state to select this cell. Timing diagram in Fig.4(a)shows Vwr2,Vdt0pulses and also shows the data in d0which is Vwd0.This write cycle starts from40ns and during this cycle,Vwr2=1,Vdt0=1FIGURE5.Timing diagram of read operation.and Vwd0=1.In the next cycle,a‘‘0’’was written to cell18 (from50ns)and to do this,Vwr2,Vrow1,Vdt1were set to HIGH state and Vwd1was set to LOW state.Finally a‘‘1’’was written to cell20(from60ns).For this,Vwr4,Vrow1, Vdt1and Vwd1,all were set to HIGH state.In Fig.4(b), plot of the resistance of two memristors in cell20shows the alteration of resistance while writing‘‘1’’into it.B.READ OPERATIONAfter writing‘‘1’’in cell2,the stored data was read(from 48ns).For this,Vrd2was set to HIGH state and data at dn0 is checked.In Fig.5,timing diagram of read cycles is shown.S.S.Sarwar et al.:Memristor-Based Nonvolatile Random AccessMemory FIGURE6.Evidence of non-volatility of the memristor SRAM cell.Afterwriting‘‘1’’in cell18,all the power sources are turned off during the time interval50–69ns.A read operation is done after turning on the powersources and found‘‘1’’in cell18.During read operation at cell2,dn0was found HIGH.Then after two write cycles,cell20was read(from68ns)and found HIGH at dn1.Finally,cell18was read(from69ns)and found LOW at dn1.So after reading a cell,data was found to be exactly the same as it was written previously in that cell.Thus, the array structure shows proper functionality both in read and write operations.VI.PERSPECTIVESOur proposed memristor based memory cell is non-volatile in nature.After writing‘‘1’’in cell18,all the power sources were turned off during the time interval50–69ns(Fig.6).A read operation is done after turning on the power sources and found‘‘1’’in cell18.This proves the non-volatile nature of the cell.The write and read times were measured and compared in Table1:TABLE1.Write/read time comparison.Operation Proposed SRAM Cell(ns)6-T Cell[19](ns)Write 5.90.85Read0.2 1.23The proposed NVRAM cell requires a bit more time for the write cycle than the conventional SRAM cells.By further increasing the mobility of the memristors,the write cycle time can be considerably reduced.Fig.7shows the inverse relation between mobility of the memristor and the write cycle time.The read cycle time depends on the sensitivity and responsiveness of the sense ampliﬁer.From simulation the power dissipation curve was found and integration was done to get the energy dissipated for sep-arate operations(writing and reading‘‘1’’&‘‘0’’).And then the energy values were divided by respective operation cycle times to get the corresponding power dissipations(Table2). The obtained values were then averaged to get the total power dissipation.This was compared with the value of the conventional SRAM cell in Table3.FIGURE7.Inverse relation between mobility of the memristor and the write cycle time.TABLE2.Power dissipation during different operations.Operation Wr0Wr1Rd0Rd1Energy(fJ/cycle)191.01803.4961.3668 Power(µW)32.37136.18306.85340Peak power(mW)0.935 2.5 5.8 5.9 TABLE3.Power comparison.OperationProposed SRAM Cell(mW)6-T Cell[19](mW)Power0.40710.373Power consumption is much less than6-T cell which can be reduced more by designing a faster comparator which would reduce the read time.The area of the proposed memory cell can be predicted to be much less than the area of conventional6-T SRAM cell, as only three transistors are used along with two memristors. As memristors can be as small as3nm,the area can be further reduced if we can switch to more recent fabrication technologies such as22nm technology.VII.CONCLUSIONIn this paper,we proposed a new idea of NVRAM cell using memristor.The read time is much faster compared to a conventional SRAM and the power consumption is also much smaller.However the writing speed is not satisfactory compared to existing SRAM cells due to the low mobility of the memristor in the SPICE model we used.Recent researches suggest that the write time can be signiﬁcantly reduced[14], [20]using state-of-the-art fabrication techniques.The com-parator used to read the data can be replaced by a more com-pact and efﬁcient sense ampliﬁer which in turn would further decrease the read time.There are further scopes to work onS.S.Sarwar et al.:Memristor-Based Nonvolatile Random Access Memorypower consumption as well.Overall,it can be said that our proposed NVRAM is a combination of new technology and innovative design which can open a new door in theﬁeld of memory design.REFERENCES[1]L.Chua,‘‘Memristor-the missing circuit element,’’IEEE Trans.CircuitTheory,vol.18,no.5,pp.507–519,Sep.1971.[2] D.Struckov,G.Snider,D.Stewart,and R.Williams,‘‘The missing mem-ristor found,’’Nature,vol.453,no.7191,pp.80–83,2008.[3]G.Chen,‘‘Leon Chua’s memristor,’’IEEE Circuits Syst.Mag.,vol.8,no.2,pp.55–56,Apr.2008.[4]Y.V.Pershin and M.DiVentra,‘‘Spin memristive systems:Spin mem-ory effects in semiconductor spintronics,’’Phys.Rev.B,vol.78,no.11, pp.113309-1–113309-4,2008.[5]X.Wang,Y.Chen,H.Xi,H.Li,and D.Dimitrov,‘‘Spintronic memris-tor through spin-torque-induced magnetization motion,’’IEEE Electron Device Lett.,vol.30,no.3,pp.294–297,Mar.2009.[6]K.Witrisal,‘‘Memristor based stored reference receiver-the UWB solu-tion,’’Electron.Lett.,vol.45,no.14,pp.713–714,2009.[7]S.Shin,K.Kim,and S.M.Kang,‘‘Memristor basedﬁne resolutionprogrammable resistance and its applications,’’in Proc.IEEE Int.Conf.Commun.,Circuits,Syst.,Jul.2009,pp.948–951.[8] D.Varghese and G.Gandi,‘‘Memristor based highline arrange differentialpair,’’in Proc.IEEE mun.,Circuits Syst.,Jul.2009,pp.935–938.[9]Y.V.Pershin and M.DiVentra,‘‘Practical approach to programmableanalog circuits with memristors,’’IEEE Trans.Circuits Syst.I,Reg.Paper, vol.57,no.8,pp.1857–1864,Jan.2010.[10]S.Shin,K.Kim,and S.M.Kang,‘‘Memristor applications for pro-grammable analog ICs,’’IEEE Trans.Nanotechnol.,vol.10,no.2, pp.266–274,Mar.2011.[11] D.Batas and H.Fiedler,‘‘A memristor SPICE implementation and a newapproach for magneticﬂux controlled memristor modeling,’’IEEE Trans.Nanotechnol.,vol.10,no.2,pp.250–255,Mar.2011.[12] D.B.Strukov and S.Williams,‘‘Exponential ionic drift:Fast switching andlow volatility of thin-ﬁlm memristors,’’Appl.Phys.A,Mater.Sci.Process., vol.94,no.3,pp.515–519,2009.[13]Z.Biolek,D.Biolek,and V.Biolkov,‘‘A SPICE model of memristor withnonlinear dopant drift,’’Radio Eng.J.,vol.18,no.2,p.211,2009. [14]N.Y.Joglekar and S.J.Wolf,‘‘The elusive memristor:Properties of basicelectrical circuits,’’Eur.J.Phys.,vol.30,no.4,p.661,2009.[15]O.Wood,C.Koay,K.Petrillo,H.Mizuno,S.Raghunathan,J.Arnold,D.Horak,M.Burkhardt,G.McIntyre,Y.Deng, Fontaine,U.Oko-roanyanwu,A.Tchikoulaeva,T.Wallow,H.-C.James,M.Colburn,S.S.C.Fan,Bala S.Haran,and Y.Yin,‘‘Integration of EUV lithography in the fabrication of22-nm node devices,’’Proc.SPIE vol.7271,pp.727104-1–727104-2,2009.[16] E.Linn,R.Rosezin,C.Kügeler,and R.Waser,‘‘Complementary resis-tive switches for passive nanocrossbar memories,’’Nature Mater.,vol.9, pp.403–406,Apr.2010.[17]P.Junsangsri and F.Lombardi,‘‘A memristor-based memory cell usingambipolar operation,’’in Proc.IEEE29th put.Design,Oct.2011,pp.148–153.[18]K.Eshraghian,K.-R.Cho,O.Kavehei,S.KuKang,D.Abbott,andS.M.Steve Kang,‘‘Memristor MOS content addressable memory (MCAM):Hybrid architecture for future high performance search engines,’’IEEE Trans.Very Large scale Integr.(VLSI)Syst.,vol.19,no.8, pp.1407–1417,Aug.2011.[19]G.M.Sreerama Reddy and P.C.Reddy,‘‘Design and implementation of8K-bits low power SRAM in180nm technology,’’in Proc.Int.Multi Conf.put.Sci.,vol.2.Mar.2009,pp.1–8.[20]J.Borghetti,G.S.Snider,P.J.Kuekes,J.J.Yang, D.R.Stewart,R.S.Williams,‘‘‘Memristive’switches enable’stateful’logic operations via material implication,’’Nature,vol.464,pp.873–876,Apr.2010.SYED SHAKIB SARWAR(S’11)was born inDhaka,Bangladesh,in1989.He received the B.Sc.degree in electrical and electronic engineeringfrom the Bangladesh University of Engineeringand Technology(BUET),Dhaka,Bangladesh,in2012.He is currently pursuing the M.Sc.degreein electrical and communication Engineering fromthe Department of Electrical and Electronic Engi-neering,BUET.Since2012,he has been a Faculty Member of Electrical and Electronic Engineering Department,BRAC University,Dhaka. His current research interests include high frequency,low power analog and mixed-signal integrated circuits,FPGA based digital circuit prototyping, artiﬁcial neural systems,and image processing.Mr.Sarwar has been with the IEEE Solid State Circuits Society since2012. He represented the BUET team in the IFEC-2011Workshop during the IEEE Applied Power Electronics Conference in Dallas,TX,USA.SYED AN NAZMUS SAQUEB(S’11)was bornin Natore,Bangladesh,in1988.He received theB.Sc.degree in electrical and electronic engineer-ing from the Bangladesh University of Engineeringand Technology(BUET),Dhaka,Bangladesh,in2012.Since2012,he has been a Faculty Member of theElectrical and Electronic Engineering Department,University of Asia Paciﬁc,Dhaka.He is pursuingthe M.Sc.degree in electrical and communication engineering from the Department of EEE,BUET.His current research inter-ests include analog and mixed-signal circuit design,neuromorphic circuits, biomedical VLSI systems,and circuit design with novel devices.Mr.Saqueb has been with the IEEE Solid State Circuits Society since2012.FARHAN QUAIYUM(S’11)was born in Dhaka,Bangladesh,in1989.He received the B.Sc.degreein electrical and electronic engineering from theBangladesh University of Engineering and Tech-nology,Dhaka,Bangladesh,in2012.He has been an ASIC Design Engineer withFastrack Anontex Ltd.,since June2012.He ispursuing the M.Sc.degree in electrical and com-munication engineering from the Department ofEEE,BUET.His current research interests include high speed digital circuit design,ultra-low-power/low voltage circuits,and embeddedsystems.A.B.M.HARUN-UR RASHID(M’89–SM’02)received the B.Sc.degree in electrical and elec-tronic engineering from the Bangladesh Universityof Engineering and Technology(BUET)Dhaka,Bangladesh,in1984,the M.Sc.degree in elec-tronic engineering from Oita University,Japan,in1988,and the Ph.D.degree in electronic engineer-ing from the University of Tokyo,Tokyo,Japan,in1996.He has been as a Faculty Member with the Department of Electrical and Electronic Engineering,BUET,where he is a Professor since2006.He served as a Design Engineer with Texas Instruments Japan Ltd.,from1988to1993,where he worked on the research and devel-opment of1.2µm Bi-CMOS process for mixed signal VLSI circuits.He was a Research Fellow with the Research Center for Nanodevices and Systems, Hiroshima University,Tokyo,Japan,from2001to2003,where he worked in the design and demonstration of on-chip wireless interconnect.His current research interests include high speed and low power circuit design using novel nanodevices,very high frequency analog integrated circuit design,and on-chip wireless interconnect design.。

什么是忆阻器

什么是忆阻器？忆阻器忆阻器的英文 Memristor 来自「Memory（记忆）」和「Resistor（电阻）」两个字的合并，从这两个字可以大致推敲出它的功用来。

最早提出忆阻器概念的人，是华裔的科学家蔡少棠，当时任教于美国的柏克莱大学。

时间是 1971 年，在研究电荷、电流、电压和磁通量之间的关系时，蔡教授推断在电阻、电容和电感器之外，应该还有一种组件，代表着电荷与磁通量之间的关系。

这种组件的效果，就是它的电阻会随着通过的电流量而改变，而且就算电流停止了，它的电阻仍然会停留在之前的值，直到接受到反向的电流它才会被推回去。

用常见的水管来比喻，电流是通过的水量，而电阻是水管的粗细时，当水从一个方向流过去，水管会随着水流量而越来越粗，这时如果把水流关掉的话，水管的粗细会维持不变；反之当水从相反方向流动时，水管就会越来越细。

因为这样的组件会「记住」之前的电流量，因此被称为忆阻器。

忆阻器有什么用？在发现的当时...没有。

蔡教授之所以提出忆阻器，只是因为在数学模型上它应该是存在的。

为了证明可行性，他用一堆电阻、电容、电感和放大器做出了一个模拟忆阻器效果的电路，但当时并没有找到什么材料本身就有明显的忆阻器的效果，而且更重要的，也没有人在找 -- 那是个连集成电路都还刚起步不久的阶段，离家用电脑开始普及都还有至少 15 年的时间呢！于是这时候 HP 就登场了。

事实上 HP 也没有在找忆阻器，当时是一个由 HP 的 Phillip J Kuekes 领军的团队，正在进行的一种称为Crossbar Latch 的技术的研究。

Crossbar Latch 的原理是由一排横向和一排纵向的电线组成的网格，在每一个交叉点上，要放一个「开关」连结一条横向和纵向的电线。

如果能让这两条电线控制这个开关的状态的话，那网格上的每一个交叉点都能储存一个位的数据。

这种系统下数据密度和存取速度都是前所未闻的，问题是，什么样的材料能当这个开关？这种材料必需要能有「开」、「关」两个状态，这两个状态必需要能操纵，更重要的，还有能在不改变状态的前提下，发挥其开关的效果，允许或阻止电流的通过。

忆阻器

忆阻器(Memristor)忆阻器被证实存在按照我们目前的知识，基本的无源电子元件只有3大类，即电阻器、电容器和电感器。

而事实上，无源电路中有4大基本变量，即电流、电压、电荷和磁通量。

早在1971年加州大学伯克利分校的蔡少棠(Leon Chua)教授就提出一种预测：应该有第四个元件的存在。

他在其论文《忆阻器：下落不明的电路元件》提出了一类新型无源元件—记忆电阻器(简称忆阻器)的原始理论架构，推测电路有天然的记忆能力。

忆阻器是一种有记忆功能的非线性电阻。

通过控制电流的变化可改变其阻值，如果把高阻值定义为“1”，低阻值定义为“0”，则这种电阻就可以实现存储数据的功能。

2008年，美国惠普实验室下属的信息和量子系统实验室的研究人员在英国《自然》杂志上发表论文宣称，他们已经证实了电路世界中的第四种基本元件———忆阻器(Memristor)的存在，并成功设计出一个能工作的忆阻器实物模型。

在该系统中，固态电子和离子运输在一个外加偏置电压下是耦合在一起的。

这一发现可帮助解释过去50年来在电子装置中所观察到的明显异常的回滞电流—电压行为的很多例子。

忆阻器器件的最有趣的特征是它可以记忆流经它的电荷数量。

其电阻取决于多少电荷经过了这个器件，即让电荷以一个方向流过，电阻会增加；如果让电荷以反向流动，电阻就会减小。

简单地说，这种器件在任一时刻的电阻是时间的函数———多少电荷向前或向后经目前已经可以通过一些技术途径实现忆阻器，但制约这类新硬件发展的主要问题是电路中的设计。

目前还没有忆阻器的设计模型使其用于电路当中。

有人预测，这种产品5年后才可能投入商业应用。

忆阻器将有可能用来制造非易失性存储设备、即开型PC（个人电脑）、更高能效的计算机和类似人类大脑方式处理与联系信息的模拟式计算机等，甚至可能会通过大大提高晶体管所能达到的功能密度，这将对电子科学的发展历程产生重大影响。

忆阻器基础电子学教科书列出三个基本的被动电路元件：电阻器、电容器和电感器；电路的四大基本变量则是电流、电压、电荷和磁通量。

电路分析路基础忆阻元件

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2.换路定则
换路定则(circuit changing rule)：在电容电流和电感电压为有界值的情况下，电容电压不能跃变，电感电流不能跃变。 u ( 0 ) u ( 0 ) C C i ( 0 ) i ( 0 ) L L
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3.初始值的确定
§5-3 忆阻元件
北京邮电大学电子工程学院
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开始
忆阻元件
三种无源元件——电阻R、电容C和电感L与电路的基本变量之间的联系。
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电路基本变量之间的关系结构图 1971年加州大学伯克利分校的华裔科学家蔡少棠提出在和q之间存在类似R、L、C的第四类基本电路元件 ——忆阻器。
§5-4 换路定则及初始值的确定
内容提要
基本概念
换路定则
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1.基本概念
换路(circuit changing)：由于某种原因(例如电源或某部分电路的接通或断开、电路元件参数的改变等)使电路的工作状态发生变化，使其由一种工作状态变化到另外一种工作状态，将这种工作状态的改变称为换路。过渡过程(transition)：换路过程中电路的电量随时间变化的过程称为过渡过程或瞬态(transient)。电路的瞬态分析：对电路过渡过程的分析。初始值(initial value)：电量在换路后瞬间的值。 u(0 ) i ( 0 ) t 0 换路前时刻：换路时刻： t0 换路后时刻： t 0 u(0 ) i (0 )
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例题3 如图所示电路中，已知 uC (0 ) 5V, iL (0 ) 0。
解பைடு நூலகம் 画出 0 等效电路

精选忆阻器及忆阻混沌电路.ppt

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2 忆阻器模型
2.1 忆阻器的定义 2.2 物理器件模型 2.3 数学理论模型
2.3.1 分段线性模型 2.3.2 三次型非线性模型 2.3.3 二次型非线性模型
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2 忆阻器模型
2.1 忆阻器的定义
➢ 忆阻器是一个基本的无源二端元件，它的磁通量φ 与累积的电荷q 之间的关系可以用φ -q 或q- φ平面上的一条曲线f(φ ，q) = 0 来确定，忆阻器分为荷控忆阻器和磁控忆阻器两种，如图2所示
上述四个电路变量两两之间→_可→以建立六个数学关系式，其中五对关系式已经为大家所熟知——分别来自R、C、L、Q 的定义和法拉第电磁感应定律（如图1所示），但φ、Q 间的关系却一直没被揭示。
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1 引言
根据图1中基本变量组合完备性原理，，美国加州大学伯克利分校华裔科学家蔡少棠于1971年从理论上预测了描述电荷和磁通关系元件的存在性，并且定义这类元件为记忆电阻器（简称忆阻器，英文名称为Memristor）.
忆阻器的出现，将不仅使得集成电路元件变得更小，计算机可以即开机关，而且拥有可以模拟复杂的人脑神经功能的超级能力。
因此，忆阻器的记忆特性将→_对→计算机科学，生物工程学，神经网络，电子工程，通信工程等产生极其深远的影响，同时，忆阻电路的存在，使基础元件由电阻，电容和电感增加到四个，忆阻器为电路设计及其忆阻电路应用提供了全新的发展空间。
忆阻器与忆阻混沌电路
学号：姓名：
忆阻器的等效电路模型
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基于三次型忆阻器的混沌电路
LOGO
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1 引言
由电路基本理论可知，电路和元件特性是有四个基本变量来描述的，分别为四个电路变量电压（V）、电流（I）、磁通量（φ）和电荷量（Q） a.电压和电流关系→电阻器R b.电压和电荷关系→电容器C c.电流和磁通关系→电感器L

忆阻器桥式突触结构神经网络的学习PPT

精选忆阻器及忆阻混沌电路.ppt

图1 电路的四个基本变量与四个基本元件
.新.
1 引言
忆阻器具有其他三种基本元件任意组合都不能复制的特性，是一种有记忆功能的非线性电阻，可以记忆流经它的电荷数量，通过控制电流的变化可改变其阻值。
2008年5月，惠普公司实验室研究人员Strukov等在 Nature上首次报道了忆阻器的实现性，其研究成果震惊了国际电工电子技术世界，极大的唤起了人们开展忆阻器的全方位研究的兴趣。
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图（2）反相加法电路
(3)同相比例电路
➢ 图下所示电路是一个同相放大器。根据理想运算放大器的二个特点可以知道，
u+=u-=ui,i1=i2 由图可以列出
i1
ui R1
,
i2
u uo R3ຫໍສະໝຸດ ui uo R3可得 uo
1
R3 R1
ui
当电阻R1=∞（断开）或者
R3=0时，式可以写成
式中，a,b>0,sgn(.)为符号函数。因此，可得到它相应的忆导
W () dq() a b d
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2.3.3 二次型非线性模型
图 6 有源磁控忆阻器特性曲线及其忆导关系曲线
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2.3.3 二次型非线性模型
➢ 由于有源磁控忆阻器的忆导在一定范围内可以变成负值，因此其
即时功率p(t) W ( (t))u(t)2 0
W () d 0.5(c d)[sgn( 1) sgn( 1)]
或 q() d 0.5(c d)( 1 1)
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相应的忆阻和忆导分别为
M (q) b 0.5(a b)[sgn(q 1) sgn(q 1)]
W () d 0.5(c d)[sgn( 1) sgn( 1)]

Memristor忆阻器的发展及应用

可以做电子开关
5
模拟忆阻器特性
P型忆阻器
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模拟忆阻器特性
输入i(t)：一个0.0001A，1KHz的正弦信号输出电压：滞前的周期性变化的类正弦波波形伏安特性
看出：在线性阶段，忆阻器表现出普通电阻的性质
，而非线性阶段则表现出忆阻特性，即前一时刻的
输入回应向后一时刻的输出
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在存储中的应用
传统：6个CMOS一个存储单元信息传输方式：不同电平表示不同数据状态
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在存储中的应用
交叉杆结构存储阵列是由一排横向和一排纵向的纳米线组成的网格，在每一个交叉点上就是类似上文的存储单元，以其高阻态代表逻辑‘１’，低阻态代表逻辑‘０ ’来实现存储．
存储阵列
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在存储中的应用
三维堆叠
２００５年，惠普实验室就设计了交叉杆的一种３维堆叠结构。在衬底上对称堆叠几层忆阻器交叉杆存储阵列，两层阵列之间通过绝缘层隔离．这样可以提高忆阻器的空间密度，还能实现多层次的并行读写．
2. 美光
美光早在2007年就提出了这种技术，此后几乎每年都会透露一些进展，但就
是距离量产遥遥无期，这次也没有给出具体时间表。技术指标优势不明显
13
THANKS
FOR LISTENING
不断的推迟，预期遥遥无期
2010—合作投产
2011—承诺2013夏推出替代闪存存储方案；2012——延期通告推至2014
惠普CTO Martin Fink表示该公司将开始生产100TB忆阻器存储驱动器，具体时间为2018年并于2016年同DIMM相结合，并计划在本个十年末登陆全新设备：The Machine
现在：一个忆阻器构成一个存储单元信息传输方式：不同阻态表示不在存储中的应用

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对（5）式求积分
x (t ) v
RON q (t ) 2 D
（7）
令

D2
V
v(t ) [ X (t ) ROFF dx (1 X (t ))] RON dt
由（2）（3）（5）得
（8）
假设施加电压的时刻为
t t
t0
vdt , r
ROFF RON
t0
v( s )d ( s ) ( X ( s )
忆阻器的仿真与特性分析
忆阻器的研究背景
忆阻器理论与原理
忆阻器simulink仿真
忆阻器的提出
忆阻器是由加州大学伯克利分校蔡少棠教授 1971 年提出。顾名思义，忆阻器的得名来源于其阻值对所通过的电荷量的依赖性。简单的说，忆阻器的电阻值取决于多少电荷经过了这个器件。也就是说，让电荷以一个方向流过，电阻会增加；如果让电荷以相反的方向流过，电阻就会减小。
f ( x) 1 (2 x 1)2 p
（6）
其中p是一个正整数，是函数的控制参数。这个函数的缺点是存在边界效应，即当到达边界点（ x =0或者x =1）后就永远保持那个状态，再施加反向电流也无法改变忆阻器的阻值了。
1 In1 Scope2
100 Constant1 Product Add1
这里存在一个明显的问题：就是缺少了一种能够将电荷与磁通量关联起来的电路元件。而这种元件可由电荷和磁通量之间的关系来定义。忆阻器代表了磁通与电荷之间的关系，因而它被认为是电阻、电容、电感之外的第四种基本无源电路元件。
美国惠普实验室研究人员于2008年成功研制了首个能工作的忆阻器
由17条二氧化钛纳米结构（约50nm宽）所制成的忆阻器，中间以导线连接
忆阻器的数学模型
蔡少棠教授给出的忆阻器数学模型如下

M (q) d (q) / dq
v(t ) M [q(t )]i(t )
（1）

（2）
在上图所示的模型中，掺杂层的厚度w会在电场作用下改变，并依赖于流过忆阻器的电荷数。根据忆阻器内部离子漂移的情况不同，可将忆阻器分为理想忆阻器和实际忆阻器模型。理想忆阻器模型也称为线性离子漂移模型，其阻值为

x(t )
dx(t ) dt
(t ) c)
r 1
v(t )
（11）

r 2 2(r 1)(
v(t )
(t ) c)
（12）

i(t )
Ron r 2 2(r 1)(
(t ) c)
（13）
忆阻器的阻值是随着的增大而减小的，磁通量是电压对时间的积分。因此，当施加单向正电压的时候，忆阻器的阻值会单调递减；施加单向负电压的时候，阻值则会单调递增。由于仿真电路使用的窗函数，所以当阻值达到饱和值的时候，再施加反向电压则不会起作用。

RMEM ( X ) RON X ROFF (1 X )
(3)
其中， x 表示如下
W X D
（4）
掺杂层与非掺杂层边界的移动速度，即w的移动速度依赖于掺杂层的薄膜厚度、电阻和流经电流等表达式如下
v RON dx ki (t ), k dt D2
V 1014 m2 s1v1
忆阻器的记忆机理
图中的就是一种半导体，具有高阻抗，但可以对它掺杂来降低阻抗。如果一个具有负电荷的氧原子在 Ti 中被移走，占位后固定在氧原子位置上不会再继续移动，这使得的掺杂层和非掺杂层的界限固定。当再次施加电压时，它将从上次停止位置继续移动，这个特性使得其具备了记忆流过电荷的能力。
1)阶跃信号下的输出阶跃信号的初值为 0，终值是 1，跳变时间是 1 秒。
2）阶跃信号的初值为 1，终值是-1，跳变时间是 0.2 秒，
3）阶跃信号的初值为 1，终值是-1，跳变时间是 1 秒，
正弦信号下的输出输出：幅值为2，周期为1秒时。输出如图
忆阻器的潜在应用价值之一是创建计算机系统，通过忆阻器创建的计算机系统可以拥有类似人类的记忆和联想模式。这可以改进模糊识别技术，或者建立更加复杂的生物识别系统，如提升人脸识别技术的准确性，这是传统器件无可比拟的特性。这种模式匹配功能能够应用到机器学习和决策领域，从而进一步提高电气设备的智能化水平。
Divide1 1 Out1 XY Graph
1 Constant2 Add Product1 Scope 16000 Constant 0.3 1 Constant3 u(1)^u(2) Add2 Fcn Add3 1 Constant8 >= 1 Switch 100 2 Gain 10^(-14) 10 Constant4 2 Gain1 Constant5 Switch1 >= 0 Constant9 0 10*10^(-9) Constant7 u^2 Fcn1 Constant6 Divide Constant10 Scope1 Product2 1 xo s Integrator
忆阻器的特点
忆阻器输入输出关系是非线性的。忆阻器的输入和输出都是连续的, 因而其存储的精度理论上是无限的。由于忆阻器是基本无源电路元器件，可以方便的将其应用在电路中，形成混合型电路。由于在电荷流经的时候，忆阻器的内部结构产生变化并能在新的状态下长时间保持。因而具有非易失性的特点。以上特点都使得忆阻器具备了传统存储器材无可比拟的优势，它的高存储量、小体积、易集成、非易失性使得它成为下一代存储元件的理想选择。
忆阻器的物理模型
它是由两层二氧化钛薄膜夹在两个铂片电极之间构成的。这两种半导体材料分别是经过掺杂的未经过掺杂的。
设D为忆阻器的二氧化钛薄膜的厚度，w表示元件的参杂层的厚度，掺杂宽度w 能够随外电场改变。当u > 0 时，正向电荷通过忆阻器，w会增大，从而总阻值变小；当u < 0 时，反向电流通过忆阻器，因而w减小，总阻值变大。总的来说，宏观上看忆阻器就像是一个滑动变阻器，而其滑片是由流经该忆阻的电荷自动控制的。
忆阻器的发展前景
在目前的工艺水平下，基于忆阻器的内存芯片存储密度要比目前基于晶体管的芯片高出至少一个数量级，而且该数值会随着忆阻器技术的更加成熟而进一步提高。此外，该存储芯片的运行速度也非常快，将信息存储在忆阻器内存上的速度比存储在快闪内存上的速度高出 3 个数量级。
忆阻器内存的另一关键性优势是其非易失性，目前广泛使用的 DRAM 上存储的内容会随着时间而丢失，因此必须不断地刷新，在存储器数量庞大的时候会消耗巨大的能量。而忆阻器内存因内部构造的原因，一旦写入可以长期保存，不需要被反复刷新。
t0
ROFF dx( s) (1 X (s))) ds RON ds
（9）
(t ) (
其中
1 r 2 x (t ) rx(t ) c) 2
（10）
c

r 1 2 x (t0 ) rx(t0 ), (t0 ) 0 2
r r 2 2(r 1)(
（5）
是平均离子漂移率。
由此可知，在理想忆阻器模型中，离子漂移呈线性特征。然而，实际的忆阻器由于尺寸微小，在电压作用下易受到电场的影响。这将导致离子漂移产生非线性。这种非线性在忆阻器的边界会更加明显。为了对真实情况进行模拟，需在式右侧乘一个窗函数，可写作

dx ki (t ) f ( x) dt

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