Memristor: the Missing Link Discovered

MEMRISTOR: THE MISSING LINK DISCOVERED

SUBMITTED TO: SUBMITTED BY:

SHAILENDRA (1208/06)

NIT KURUKSHETRA PANKAJ (1212/06)

ACKNOWLEDGEMENT

We would like to express our gratitude towards Mr. NAVDEEP MITTAL, Lecturer Department of Electronics & Communication for providing us the opportunity to give a seminar on this topic of technical interest. We are thankful to him for all the support and motivation. We would also like to thank my friends and classmates who have provided us with their invaluable advice and help.

CONTENTS

1. INTRODUCTION 2. MEMRISTOR FUNDAMENTALS 3. MEMRISTOR SWITCHING MECHANISM 4. RECENT ADVANCEMENTS IN MEMRISTOR TECHNOLOGY 5. POTENTIAL MEMRISTOR APPLICATIONS 6. SUMMARY ABSTRACT

This paper analyzes the fourth fundamental circuit element named ‘Memristor’ which had been proposed by a University of California, Berkeley engineer, Leon Chua in 1971, and has recently been developed by a group of researchers at Hewlett–Packard led by Stanley Williams. The paper studies the implications of the discovery of this new element and highlights its potential applications in the circuit design and computer technology. INTRODUCTION

In the last few decades, the age old dream of building an artificial brain, i.e. using biological cognitive systems as a benchmark and inspiration to fabricate complex material assemblies which can learn, make decisions, analyze information in a highly parallel way: in other words, highly efficient bio-inspired information processors, has acquired the concreteness of real life research. Many programs and projects in materials science, nanotechnologies, ICT, biosciences use the relevant biological systems and processes as the basic paradigm for the research. However the enormous complexity of even the simplest brains still puts a barrier to the realization of such ambitions. Hence most of the current research (apart from theoretical modelling and simulations) deals with the fabrication and characterization of specific components which are expected to mimic in their functional behaviour neurons, synapses, or use biological molecules to build innovative sensing or electronic components. Recently a non-linear inorganic thin film two electrode device has been reported which the authors claim to be the very first memristor, i.e. a resistor with memory or which can learn.

When studying circuit theory we learn that there are three fundamental circuit elements the resistor, the capacitor and the inductor. The first element determines the relation between current and voltage, the second between charge and voltage, and the third between current and magnetic flux (or the time integral of the voltage). These passive two-terminal devices are basic building blocks of modern electronics and are therefore ubiquitous in circuits. However, we are also taught that they do not store information. Even if the state of one of the above elements changes, the information about the new state will be lost once we turn off the power source and wait some time. This point may seem irrelevant but it is instead fundamentally crucial: storing information without the need of a power source would represent a paradigm change in electronics. For instance, we would need many less active elements (like transistors) to perform any type of computation or processing.

HISTORY The transistor was invented in 1925 but lay dormant until finding a corporate champion in Bell Labs during the 1950s. Now another groundbreaking electronic circuit may be poised for the same kind of success after laying dormant as an academic curiosity for more than three decades. Hewlett-Packard Labs is trying to bring the memristor, the fourth passive circuit element after the resistor, and the capacitor the inductor into the electronics mainstream. Postulated in 1971, the “memory resistor” represents a potential revolution in electronic circuit theory similar to the invention of transistor. The history of the memristor can be traced back to nearly four decades ago when in 1971, Leon Chua, a University of California, Berkeley, engineer predicted that there should be a fourth passive circuit element in addition to the other three known passive elements namely the resistor, the capacitor and the inductor. He called this fourth element a “memory resistor” or a memristor. Examining the relationship between charge, current, voltage and flux in resistors, capacitors, and inductors in a 1971 paper, Chua postulated the existence of memristor. Such a device, he figured, would provide a similar relationship between magnetic flux and charge that a resistor gives between voltage and current. In practice, that would mean it acted like a resistor whose value could vary according to the current passing through it and which would remember that value even after the current disappeared.

Fig. The Simplest Chua’s Circuit. Fig. Realization of Four Element Chua’s Circuit, NR is Chua Diode.

Fig. Showing Memristor as Fourth Basic Element. But the hypothetical device was mostly written off as a mathematical dalliance. However, it took more than three decades for the memristor to be discovered and come to life. Thirty years after Chua’s Proposal of this mysterious device, HP senior fellow Stanley Williams and his group were working on molecular electronics when they started to notice strange behavior in their devices. One of his HP collaborators, Greg Snider, then rediscovered Chua's work from 1971. Williams spent several years reading and rereading Chua's papers. It was then that Williams realized that their molecular devices were really memristors.

MEMRISTOR FUNDAMENTALS Chua noted that there are six different mathematical relations connecting pairs of the four fundamental circuit variables: electric current i, voltage v, charge q and magnetic flux ɸ. One of these relations ,the charge is the time integral of the current, is determined from the definitions of two of the variables, and another, the flux is the time integral of the electromotive force, or voltage, is determined from Faraday’s law of induction. Thus, there should be four basic circuit elements described by the remaining relations between the variables. The three known circuit elements are described by the following equations dv/di = r incremental resistance dɸ/di = L inductance dv/dq = 1/C inverse capacitance The ‘missing’ element—the memristor, with memristance M, provides a functional relation between charge and flux as given under dɸ/dq = M(q) memristance

The above equation can also be written in the following form

(dɸ/dt)/(dq/dt) = M(q(t)), or

v(t)/i(t) = M(q(t)) (1)

Thus, it can be clearly seen from equation (1) that memristor is basically a charge dependent resistor. The expression for voltage is given as

v(t) = M(q(t)) i(t) (2)

This equation reveals that memristance defines a linear relationship between current and voltage, as long as charge does not vary. Of course, nonzero current implies time varying charge. Furthermore, the memristor is static if no current is applied. If i(t) = 0, we find v(t) = 0 and M(q(t)) is constant. This is the essence of the memory effect. The power consumption characteristics are comparable to resistor and the power consumed is given by i2r. This is expressed in the relations that follow where power depends on the memristance.

p(t) = i(t) v(t)

p(t) = i2(t) M(q(t)) (3)

As long as M(q(t)) varies little, such as under alternating current, the memristor will appear as a resistor. If M(q(t)) increases rapidly, however, current and power consumption will quickly stop. The graphs [3] below show the memristor i-v characteristics as predicted by Chua and as determined by Stanley Williams experimentally. The loops map the switching behavior of the device. It begins with a high resistance, and as the voltage increases, the current slowly increases. As charge flows through the device, the resistance drops, and the current increases more rapidly with increasing voltage until the maximum is reached. Then, as the voltage decreases, the current decreases but more slowly, because charge is flowing through the device and the resistance is still dropping. The result is an on-switching loop. When the voltage turns negative, the resistance of the device increases, resulting in an off-switching loop. Figure 1: Graph of the memristive behaviour proposed by Chua Figure 2: Experimental graph of memristive behavior

In the general framework of circuit theory, Chua had predicted the necessity of the existence of the fourth passive two-electrode electrical element establishing the connection between the magnetic flux and charge10. The element, called “memristor”, should act according to the following relationship: dϕ = Mdq where dϕ and dq are variations of the magnetic flux and charge, respectively, while M is the memristance. Of particular interest are the non-linear characteristics of the element, for instance when M is not a constant but it is a function of the charge flow and elapsed time. In this case, the element properties may be influenced its functioning history: i.e. it will have memory. Apart from the obvious value of such device taken singly, here we wish to emphasize its potential as a key element of networks with adaptive properties, capable of learning, information analysis and decision making. In other words, its behaviour could mimic the features of synapses in the nervous system. Variation of the element properties (resistance, in particular) according to the previous experience or to external stimuli (e.g. appropriate electrical pulses) will play the same role as the variation of the synaptic weight functions in nervous system, leading to learning and memory mechanisms described by the Hebbian rule11. MEMRISTOR SWITCHING MECHANISM

HP Labs’ memristor is a two terminal, two layer semiconductor built from layers of titanium dioxide sandwiched between two metal electrodes in a crossbar architecture. One layer of TiO2 is doped with oxygen vacancies, making it a semiconductor, while the adjacent layer is undoped, leaving it in its natural state as an insulator. The crossbar architecture is a fully connected mesh of perpendicular wires. Any two crossing wires are connected by a switch[6]. To close the switch, a positive voltage is applied across the two wires to be connected. To open the switch, the voltage is reversed.

THE SWITCH A switch is a 40-nanometer cube of titanium dioxide (TiO2) in two layers: The lower TiO2 layer has a perfect 2:1 oxygen-to-titanium ratio, making it an insulator. By contrast, the upper TiO2 layer is missing 0.5 percent of its oxygen (TiO2-x), so x is about 0.05. The vacancies make the TiO2-x material metallic and conductive. The oxygen deficiencies in the TiO2-x manifest as “bubbles” of oxygen vacancies scattered throughout the upper layer. A positive voltage on the switch repels the (positive) oxygen deficiencies in the metallic upper TiO2-x layer, sending them into the insulating TiO2 layer below. That causes the boundary between the two materials to move down, increasing the percentage of conducting TiO2-x and thus the conductivity of the entire switch. The more positive voltage is applied, the more conductive the cube becomes. A negative voltage on the switch attracts the positively charged oxygen bubbles, pulling them out of the TiO2. The amount of insulating or resistive TiO2 increases, thereby making the switch resistive as a whole. The more negative voltage is applied, the less conductive the cube becomes.

Figure 3: Memristor switch with oxygen vacancies

Figure 4: Positive voltage applied to memristor switch

This memristive switch is special because when the voltage is turned off, positive or negative, the oxygen bubbles do not migrate. They stay where they are, which means that the boundary between the two titanium dioxide layers is frozen. That is how the memristor “remembers” how much voltage was last applied. MEMORISTERS ELEMENT The recently reported memristor has exhibited some variation of the element properties (resistance, in particular) according to the history of the voltage application. The reported results are rather interesting as they allow to describe some phenomena, previously observed in nanostructures, from the new view point. However, there are two limits to consider the element as a fundamental finding from basic and applied points of view. Firstly, it seems not completely correct to call the reported element as “memristor”. As mentioned by the Authors, there is not a direct relationship between the variation of the magnetic flux and charge. Moreover, such direct relationship cannot be found in two-electrode devices, at least if based on the suggested physical principles. In fact, the element functioning was based on the longitudinal displacement of the doping impurities in the applied electric field, while the current variation was measured in the same direction. Instead, in order to obtain the connection between charge and magnetic flux, motion of charges in two perpendicular directions is required. Secondly, the reported experimental characteristics can be attributed also to a bistable electrical device rather then to an element which is purported to be used as a synaptic analogue, which must vary its resistance gradually according to its previous history.

In this respect, even if it was not specifically considered as “memristor”, an electrochemically controlled hybrid ionic-conducting polymeric device7, besides already having the memory and learning characteristics proposed for the TiO2 device, has much more potential for application to bio-inspired information processing and in particular to the fabrication of complex adaptive networks, in which it would be the “synaptic” node. The working principle of the element is based on the dramatic variation of the electronic conductivity in a thin (50nm) conducting polymer (polyaniline, PANI) multilayer in oxidized and reduced states17. Such variation is induced and regulated by ionic flux into (and out of) the PANI multilayer at the junction with a film of a solid electrolyte (Li-doped Polyethylene oxide, PEO). The scheme of the element is shown in Fig. 1. Although when connected in the circuit, the element would have two working electrodes only, the functioning of the single element is best described by considering a third “reference” (i.e. kept at ground potential) electrode. Thus there are two currents flows (electronic and ionic) which can be measured. The position of the second ammeter is also shown in Fig. 1 by a dashed line. Fig. 1. Scheme of the electrochemical element and its symbol (upper panel) for electric circuits. Active layer was formed from the conducting polymer (PANI) with attached two metal electrodes. A stripe of solid electrolyte (lithium perchloride doped polyethylene oxide (PEO)) was formed in the central part of the PANI layer in order to provide a suitable medium for redox reactions. The area of PANI layer under the electrolyte is the active zone. The reference potential was provided by a silver wire inserted into the electrolyte. The wire was connected to the one of two metal electrodes as shown in the figure.

The mechanisms of resistance variation occurring within the element are illustrated in Fig. 2. Fig. 2. Mechanisms of conductivity variation in the electrochemical polymeric element. Green areas correspond to the PANI in its oxidized conducting state, while blue areas represents PANI in reduced insulating form. The orange dots represent the Li ions, the arrows the prevalent direction of motion. (a) Positive potential is applied to the initially insulating (blue area) device. Electrical potential profile along the PANI layer is shown in the central part. Only some part of the active zone is at the potential higher than the oxidizing potential. Transformation of the PANI into the conducting state will take place only in this restricted zone. However, the transformation will result in the redistribution of the potential profile and new zones (shifted into left direction) will arrive to the oxidizing potential and will have the possibility to be transferred into the conducting state. Therefore, in this case we will have gradual displacement of the conducting zone boundary, that determines much slower kinetics of the conductivity variation (bottom part) for the positive voltage. (b) Negative voltage is applied to the initially conducting element. Electrical potential

profile along the PANI layer is shown in the central part. All active zone is under the reduction potential. Therefore, reduction and transformation of PANI into the insulating state takes place simultaneously in the whole active area providing rather fast kinetics of the transformation (bottom part). The element is characterized by two charge flows in perpendicular directions. Thus, this electrochemical device is more similar to the hypothetical memristor, suggested 40 years ago by Chua10. Ionic flow is determined by the actual potential of the active area with respect to the reference value (ground potential in this case) and provides incoming-outgoing Li+ ions to the PANI layer, thereby varying its conductivity18. The actual resistance of the active zone is determined by the time integral of the ionic current (transferred charge). It is important that the value of the ionic current is more then one order of magnitude less than the current in PANI layer. Therefore, the actual measured current of the element in the conducting state, i.e. the sum of the electron and ionic currents, is mainly determined by the first contribution. This configuration allows the element to memorize the information on its previous experience in signal transmitting. Let us consider the current temporal behaviour for the positive bias (Fig. 2a bottom panel). It exhibits a rather slow increase of the conductivity. This establishes the basis for unsupervised learning and synaptic-like behaviour. In fact, if we consider a network constructed from many such elements, connected in a complex way in order to provide numerous different pathways for the signal between any input-output pairs, there will be an increase of the conductivity of the those elements which are involved into the most frequently used pathways. Thus, similar stimuli (signals configuration on input electrodes), repeated in the future, will have an increased probability to result in similar conclusions (output signals). This is very similar to synaptic function (learning) in real biological systems, summarized in the Hebbian rule. The behaviour of the element at negative bias is also interesting. It can be used to avoid network saturation: periodic short-time application of negative signals between all input-output pairs will prevent reaching the highest conducting level for all elements of the network, which would preclude further learning. In addition, this characteristic allows in principle supervised learning for networks of such elements. Application of negative bias between selected input-output pairs will destroy a priori wrong but statistically preferential signal pathways, established occasionally during unsupervised learning. At the level of simple circuits and networks, we have already demonstrated the validity of the above considerations. A circuit based on one electrochemical element only, has demonstrated unsupervised learning. A simple network of 8 interconnected electrochemical elements, has shown supervised learning, i.e. a variation of the output signal according to the external training procedure at the input electrodes. Another, unexpected, interesting feature of the element was observed when the material of the reference electrode was changed20. Simple substitution of the silver wire with a graphite stripe resulted in the appearance of current auto-oscillations at constant applied voltage in a simple twoelectrode element! A typical curve is shown in Fig. 3. The observed phenomenon is connected to charge accumulation by the material of the reference electrode (graphite). Thus, the reference potential is not fixed anymore. Several processes must be considered to explain such oscillating behaviour of the current: redox reactions in the active area of PANI layer according to its actual potential with respect to reference point; redistribution of the applied voltage profile along the PANI layer length according to the conductivity state of its different parts; accumulation and release of the charges in the material of the reference electrode resulting in the variation of its potential. A heuristic model, based on the consideration of all possible electrical phenomena in the element, has resulted in qualitative explanation of the observed characteristics, allowing the connection between electrical behaviour and materials properties, such as ionic diffusion and redox potentials. However, on a more fundamental level, it is possible to see several similarities of the observed phenomenon with well-known Belousov-Zhabotinsky (BZ) reaction. In both cases we deal with reduction and oxidation processes, while accumulation and release of the charge at the reference point together with cyclic redistribution of the applied voltage profile in our device can be considered as analogues of the processes responsible for the production and inhibition of the catalyser in BZ reactions. If so, this would be the first demonstration of the appearance of rhythmic oscillations of electrical signals, instead of optical or viscoelastic properties variation cycles, usually observed in such reactions. This feature is very important as similar non-equilibrium processes occur in biological systems. More specifically, the behaviour of our oscillating device seems to mimic that of a specific neuron in that part of the Limnea Stagnalis brain devoted to feeding behavior Fig. 3. Temporal dependence of the current of the electrochemical device at constant applied voltage of +2.0 V with a graphite reference electrode which allows the charge accumulation. In conclusion, here we have shown that a “memristor” was already found more than two years ago, and that its characteristics make it much more promising as a basic building block of simple or complex adaptive electrical circuits, with all the advantages of the “bottom up” structured assembly fabrication procedures of molecular systems. The memory and learning properties of the device alone have already been demonstrated, and the outlook for application to more complex functional networks (deterministic or self-assembled) seems very promising. Statistically formed hybrid networks of conducting-ionic polymer fibers have also shown similar features to deterministic elements, indicating that the bottom-up statistical self-assembly approach to the fabrication of complex adaptive networks is a viable alternative to standard fabrication.

Furthermore, although most of our work was performed on macroscopic systems (apart from the nanoscale of the active conducting polymer film thickness), our preliminary results show that there is in principle no obstacle to miniaturization to the micron or the submicron scale, yielding organic signal processors with high parallelism and a density of active components comparable to that of standard inorganic microelectronics.

Finally, such systems, being, as they are, based on basic cognitive processes of biological systems, have the full potential of serving as synthetic testing grounds for learning theories and algorithms.

RECENT ADVANCEMENTS IN MEMRISTOR TECHNOLOGY

The resistance of the memristor changes as the current flows through the device. Due to this property, HP has made the

Figure 5: Negative voltage applied to memristor switch

memristor the key element in the overall program to build an entirely new kind of memory using crossbar switches. By using a technique called nanoimprint lithography, HP has already perfected a method of fabricating crossing arrays of ultra dense perpendicular metal lines – the crossbar. By picking one line from the top array and one line from the bottom array, any bit can be directly addressed to the point where two lines cross, enabling crossbar arrays that pack 100 Gbits/cm2 [4] in comparison to flash memory that can currently store 32Gbits/cm2..With memristors composed of inorganic TiO2, HP believes it has the edge over flash and other alternative memory technologies such as phase change RAM (PRAM).HP has already demonstrated that it can control its memristor material by sending current through it to change the resistance at a crossbar point. By merely measuring its resistance on any element of an array, HP claims it can determine the state of the non-volatile bits as “on” or “off”’. HP also promises to speed up the development of a prototype chip for its RRAM.

HP researchers say that the memristor material works by the thinning of the Schottky barrier— the electronic barrier at the interface between the metals and semiconductors—rather than by changing the bulk characteristics of TiO2. The next milestone will be fabricating a crossbar memory array on a conventional silicon chip, with the read/write and addressing circuitry in silicon and the memory embedded into the metallization layers on top.

POTENTIAL MEMRISTOR APPLICATIONS

The memristor has turned out to be an electronic component that offers both memory and logic functions in one simple package. It has the potential to transform the semiconductor industry, enabling smaller, faster, cheaper chips and computers. Moore's law, which predicts that technology will double the number of transistors that fit on an integrated circuit every two years, has held true since the mid 1960s. The more transistors on a chip, the faster the chip can operate. But this is getting more and more difficult to achieve. This transistor scaling now faces several practical and fundamental challenges including increased power dissipation as transistors shrink, difficulties in laying out all the necessary interconnects, and the high cost to minimize device variations. Memristors have a simpler structure and are attractive for applications such as memories because it is much easier to pack a large number of them on a single chip to achieve the highest possible density. The density of a memristor-based memory chip could be at least an order of magnitude a factor of 10 which is much higher than current transistor-based chips. Such high density circuits can also be very fast. It will be possible to save the data to a memristor memory three times faster than saving to today's flash memory.

Another benefit of memristor memory is that it's not volatile, as today's DRAM memory is. DRAM, which stands for dynamic random access memory, is part of the computer's quick-access memory that helps the machine run faster. DRAM is overwritten multiple times a second because it fades with time. Memristor memory would not have to be overwritten. It is more stable. Also, the reason computers have to be rebooted every time they are turned on is that their logic circuits are incapable of holding their bits after the power is shut off. But because a memristor can remember voltages, a memristor-driven computer would arguably never need a reboot.

One of the far –term and perhaps the most important application of memristors could be in the development of devices that can emulate neural responses. Memristance can explain Spike- Time-Dependent-Plasticity in Neural Synapses [5]. Spike-Time-Dependent-Plasticity (STDP) is a mechanism which describes a neuronal synaptic learning mechanism. STDP was originally postulated as a computer learning algorithm, and is being used by the machine intelligence and computational neuroscience community. At the same time its biological and physiological foundations have been reasonably well established during the past decade. If memristance and STDP can be related, then (a) recent discoveries in nanophysics and nanoelectronic principles may shed new lights into understanding the intricate molecular and physiological mechanisms behind STDP in neuroscience, and (b) new neuromorphic-like computers built out of nanotechnology memristive devices could incorporate the biological STDP mechanisms yielding a new generation of self-adaptive ultrahigh- dense intelligent machines. Scientists are working to understand how neural and memristance parameters modulate STDP, which might bring new insights to neurophysiologists in searching for the ultimate physiological mechanisms responsible for STDP in biological synapses. The study also intends to incorporate STDP learning mechanisms into a new generation of nanotechnology computers employing memristors. Figure 6: STDP function measured experimentally on biological synapses

Figure 7: STDP predicted using memristance model

The fact that STDP is closely related to memristance is also supported by figure (7) and figure(8), which clearly show that STDP function as determined experimentally matches closely to that predicted using the memristance model. SUMMARY

The impact that the memristor can have on the existing technology is colossal. The other applications that the memristor can be put to are still to be discovered. Work has to be done to explore the dimensions and fields that this new element can affect. This new element has certainly showed a lot of promise and also has the potential to be another milestone in the path of evolution of technology for the better. REFERENCES

[1] Sally Adee, ‘The Mysterious Memristor’. Available at http://www.pdf-search- engine.com/memristor-pdf.html ebook_pdf.

[2] Available at http://en.wikipedia.org/wiki/Memristor .

[3] ‘IEEE Spectrum_The Mysterious Memristor’, Page-12/14. Available at http://www.pdf- search-engine.com/memristor-pdf.html ebook_pdf.

[4] ‘Will memristors prove irresistible?’ Page- 5/5 EE TIMES-Issue 1538, Monday, August 18, 2008. Available at http://www.eetimes.com/TechSearch/Search.jhtml;jsessionid=MZ2MHQVNHGLWKQSNDLR SKHSCJUNN2JVN? site_id=EE+Times&Site+ID=EE+Times&queryText=memristor&Search.x=0&Search.y=0&Sea rch=Search

[5] Bernabé Linares-Barranco and Teresa Serrano-Gotarredona, ‘Memristance can explain Spike-Time-Dependent-Plasticity in neural synapses’. Available at http://www.pdf-search- engine.com/memristor-pdf.html ebook_pdf..