Resistive Switching Memories

Introduction

The ever-growing demand for improved computing performance has driven the search for new computing technologies, Technologies which are smaller, faster and less power consuming. There is a necessary condition in implementing any new technology that must be scalable and capable. Memristor or memristive nanodevices are expected to be this new technology. Memristive devices are electrical resistance switches that can retain a state of internal resistance based on the history of applied voltage and current. These devices can store and process information and offer several key performance characteristics that exceed conventional integrated circuit technology[1]. Here we have tried to provide a brief introduction about these resistive switching memories, their mechanisms, applications, and future prospects.

Discussion

What is Memristor?

It is general knowledge that there are three basic passive circuit elements namely, the resistor, the capacitor, and the inductor. However, Leon Chua in 1971 from symmetry arguments proposed that there must be one another fundamental element, which he called the memristor. Chua noted that there must be six different mathematical relations taking two at a time from four fundamental circuit variables: electric current , voltage charge and magnetic flux . The two of these equations are from the fundamental definition of charge and current i.e. and the second is from the Faraday’s law i.e. . The remaining three equations define resistance , capacitance and inductance . Since there is no term defining the relation between the magnetic flux and the charge, Chua hypothesized the presence of a missing element, namely, memristance M, which gives a functional relationship between the magnetic flux and charge.

In the case of linear elements, the constant memristance behaves the same as the resistance but when the memristance is a function of charge and time then it has very interesting applications. Such a non-linear relationship between and for a sinusoidal input results into Lissajous figures. And it has been observed that no nonlinear combination of the inductor, capacitor or the resistor produces the same results as the memristor, though the same results can be produced using active elements such as amplifiers.

The most basic equations for the current controlled memristor is given as

Where the is the state variable and is the generalized resistance that is dependent on the internal state of the device.

In 1976 Chua and Kang generalized the concept of Memristor to a new class of dynamical systems which is given by following mathematical equations

Where can be a set of state variables and and can in general be explicit functions of time. Here the flux in the memristive system is not uniquely defined by the charge, which makes it different from ordinary memristor.

Figure 1The four fundamental two-terminal circuit elements: resistor, capacitor, inductor, and memristor. Resistors and memristors are subsets of a more general class of dynamical devices, memristive systems.

It has been observed that the resistive switching property for the memristors appears in the nanoscale systems such as thin films. The rich hysteretic characteristics detected in many thin-film,two-terminal devices can now be understood as memristive behavior defined by coupled equations of motion: some for (ionized) atomic degrees of freedom that define the internal state of the device, and others for the electronic transport. This behavior is increasingly relevant as the active region in many electronic devices continues to shrink to a width of only a few nanometers, so even a low applied voltage corresponds to a large electric field that can cause charged species to move. Such dopant or impurity motion through the active region can produce dramatic changes in the device resistance. Including memristors and memristive systems in integrated circuits has the potential to significantly extend circuit functionality as long as the dynamical nature of such devices is understood and properly used. Important applications include ultra-dense, semi-non-volatile memories and learning networks that require a synapse-like function[2].

Working

There are several proposed mechanisms for defining how actually the switching is happening, but as of now there has been no specific mechanism that defines all, in fact, there are different mechanisms for specific materials, some of which are briefly introduced below, but, before that it should be known that there are two schemes of switching with respect to the electrical polarity- Unipolar & Bipolar.

1. Unipolar: When the switching doesn’t depend on the polarity of the voltage or current signal. The system is switched on when a particular voltage is applied. The state changes from high resistance to low resistance. There is also a control circuit that limits the current. The system is switched off by applying a voltage of value lower than the set value.
2. Bipolar: When the system switches on for one polarity and off for another polarity of the voltage signal.

Fuse Anti-Fuse Type

This switching is based on thermal effect which is unipolar in characteristics. The ON condition is initiated by voltage induced partial dielectric breakdown which modifies the material in the discharge filament due to Joule heating. Due to compliance current weak conductive filament with controlled resistance is formed. The high-power density (1012 W cm-3) generated locally, disrupts the filament again, and leads to the OFF state. The value of compliance current is the critical parameter for this unipolar phenomenon. TiO2 shows bipolar switching, but for a particular value of compliance current, it shows unipolar switching. Other examples of fuse- anti-fuse: NiO, Pt/Nio/Pt thin film integrated over CMOS.

Reduction process induced by cation migration

For a particular polarity of voltage cations in the ionic conductor move towards the cathode and get reduced. These reduced metal atoms grow towards the anode. As the bridge gets complete between anode and cathode, the switch gets ON. At the anode, the equal no. of ions dissolve in an ionic conductor, to maintain the number of cations. This process accounts for bipolar switching in MIM. For this, the electrode is made from electrochemically active metal, solid-state electrolyte as ion conducting “I” layer and counter electrode from inert metal. When the polarity changes, the metal atoms dissolve at the edge of filament, the bridge is broken, and the switch turns off. This process does not cause any permanent damage to MIM, and hence can be used for quite a long time. To obtain faster switching we can either Increase the bias voltage or Reduce the size of a metal filament.

Redox process induced by anion migration

When cathode blocks ion exchange oxygen-deficient region starts building up towards anode, during the electroforming process. The deficiency is compensated by metal ions by trapping electrons from the cathode. This reduced valence state of metal cations converts the oxide into a metallically conducting phase. This is called virtual cathode, and it moves towards the anode, forming a conductive path. The oxidation at anode release the oxygen gas. The electroforming conditions vary for different size of MIM crystals. Macroscopic crystals require 100V for several hours, whereas for nanocrystals the switching cycle at 1V is sufficient. After the electroforming process is complete the bipolar switching takes place between the anode and virtual cathode, through local redox reactions in which the contacts are formed and broken at different cycles. Depending upon charge transferred during switching the resistance of the MIM can be varied at intermediate levels. This can serve the purpose of creating multibit storage memory cells. Thin films of oxides like Ta2O5, Nb2O5, VO2, TiO2, Sr2O3.Cr(epitaxial), can be used.

Resistive switching systems involving organic molecules

It aims at using properties like molecular redox, configuration and conformation changes, molecular electron excitation, or molecular spin properties so as to affect the electron transfer coefficient. The “I” layer is represented by organic molecules or polymers that vary from 30nm to 1µm. It is seen in a large variety of MIM systems. But the database is not sufficient to draw any conclusion. In most studies the Aluminum top electrode has been used, that is deposited over the organic layer as an ex-situ deposition step. Recent experiments show that the switching takes place between Al2O3 layer formed between the organic layer and aluminum metal. In some cases, the ‘I’ layer in a MIM system is a monomolecular film or even a single molecule contacted by a metal tip on the nanoscale. Thus, great care needs to exercise while studying the behavior of organic molecules in switching. Although some of them have great electronic properties, they are bounded by the electrode materials and the experimental boundary conditions.

Applications of Resistive Switching

The research activities are primarily driven by the search for the ideal memory device – a ‘universal memory’ which has high speed, low energy and high endurance of static RAM & high density, low cost and non-volatility of flash memories. Hybrid CMOS/Memristor circuits, and especially with the passive crossbar architecture is most likely to provide the results for the universal memory.

The Logic applications of memristors are also being explored which could possibly remove the main inefficiency of FPGA (Field Programmable Gate Arrays) i.e. Large overhead associated with storing the circuit configuration information in local memory, which consumes 50-90% of the chip area[1]. It has been shown that in hybrid FPGA circuits (nanoimprinted 100 nm scale TiO2-x memristor devices integrated with 0.5 µm CMOS technology[1]) nanoscale memristors can be used to improve density by more than 10 or 100 times for the conservative architecture as compared to the conventional architectures. Memristors have also been shown implementing material implication logic where the Boolean logic states are stored as resistance state rather than voltage levels (as in conventional logics).

Another potential application of resistive switching is the Neuromorphic devices. Despite the exponential growth in CMOS performance, the mammalian brains are far more efficient for many computational tasks such as Classification and Pattern Recognition than today's digital computers. In a paper published in 2012 by Alibart F., Gao L.G., Hoskins B.D., and Strukov D.B. hybrid circuits were shown performing analog dot-product computation. The crude estimates have suggested that circuits with ultimately scaled CMOS technology and sub-10-nm scale memristive devices can challenge the complexity and connectivity of the human brain.

Figure 2 gives the proper structure and explanation of possible applications of the resistive switching (memristors)

Figure 2 Prospective applications of memristive circuits. a–c, Digital memories and storage: in memories a resistance state represents one or more bits of information that are read by sensing current flowing through the device at a smaller non-perturbative bias. When combined in circuits, memory cells containing a memristor and a select device are organized in roughly square arrays with multiple cells sharing row (word) and column (bit) lines. The select device, implemented for example, with a transistor in a conventional 1-transistor/1-resistor (1T1R) cell architecture (a) enables unique access (read/write) to a particular row of cells at a time via bit lines by asserting the corresponding select word line. A much denser alternative to the 1T1R architecture without a dedicated transistor is shown in b, c (passive crossbar memory). In passive memory, select functionality is implemented via the diode-like I–V of the cross-point device. If the current is negligible for V < |VTH| then choosing a read voltage such that VTH < VREAD < 2VTH allows suppression of leakage current when sensing a particular cell (b). Strong nonlinearity in switching dynamics helps avoid another problem specific to 0-transistor/1-resistor (0T1R) architectures: disturbance of half-selected devices (c), which are typically biased at half of the write voltage VWRITE/2 applied to switch a particular cell in the array. A number of biasing schemes as well as different approaches for current sensing have been proposed, see, for example, ref. 155 for more details. d, Programmable logic: in the conservative approach memristors serve as the configurable interconnect in FPGA-like circuits. A specific memristor would control whether two wires (for example, the input of some Boolean gates and output of another) are electrically connected. The operation of the FPGA consists of two stages: first, a particular computation task is mapped to the FPGA structure by setting connectivity of the gates via programming appropriate cross-points to the ON state. During the second much longer stage, the connectivity pattern is fixed (that is, memristors do not change their state), and the FPGA runs a specific task with the programmed circuit. e, f, In a more aggressive approach, in addition to serving as a programmable interconnect memristors also implement a part of the logic gate functionality. The I–V nonlinearity of the memristive devices is used to implement diode-resistor logic (f), whereas a CMOS subsystem is used for signal restoration and inversion. g–i, Bio-inspired and mixed-signal information processing: hybrid CMOS/memristor circuits may also enable efficient analog dot-product computation, which is a key operation in artificial neural networks and many other information processing tasks. In the simplest model, artificial neural networks can be represented by a graph (g) with nodes corresponding to neurons and graph edges that correspond to synapses (d). In parallel, each node processes input information from the preceding nodes and then passes it to the next layer of nodes. h, A typical operation of the node would involve summation of input signals, with each scaled by the corresponding edge weights, followed by a specific threshold function of the node (not shown). In hybrid CMOS/memristor circuits memristive devices implement density-critical configurable analog weights, crossbar wires serve as axons and dendrites, and CMOS is used for the summing amplifier to provide gain and signal restoration. As a result, individual voltages applied to memristors can be multiplied by the unique weight (conductance) of the memristor and summed up by a CMOS amplifier, thus implementing dot-product computation in an analog fashion. Here x1, x2, and y are input and output voltages for the considered synapses and neuron, correspondingly, whereas w1 and w2 are conductances of the corresponding memristive devices. [1]

Carbon as a choice for resistive switching material

Carbon appears in many forms ranging from sp2-dominated conducting graphite to sp3-dominated insulating diamond. The one main property of carbon is that one can switch from the low conductive state to the high conductive state and vice versa by applying appropriate current pulses to the carbon element (Figure 3)

Figure 3 The principal operation of carbon memory depends on the starting material (insulating carbon or conductive carbon). Insulating carbon can be switched to conductive sp2-rich carbon by inducing electrical breakdown. Conductive carbon can be switched to sp3-rich carbon, by inducing a quenched state with a short high current pulse of sufficient current density, which is in the order of 1GA/cm2.[7]

Another benefit provided by the carbon is its high resilience which allows for high-temperature operations. Single-elemental nature of carbon helps in the scaling of memory devices to very small dimensions (currently 50nm) i.e. it leads to low power consumption. There are different forms of carbons which can be used for making memristors few of which are briefly described below.

Carbon Nano-tubes

CNT is sp2-type species of carbon which shows a drastic reduction in conductivity with the introduction of only a single sp3-bond in their configuration. The CC bonds on the walls have high curvature which makes them susceptible to breaking due to thermal oscillations of atoms which results in non-hexagonal vacancies that reduce conductance. Also, the CNTs shows self-healing properties when they are subjected to moderate current flow. Usually, the CNTs require high current densities for switching, but, the for a longer CNT the current requirement reduces.

Figure 4 Experimental determination of the critical (switching) current in single-walled CNTs.[7]

Conductive Carbon

Conductive carbon is graphene-like material with high electrical conductivity and is seen as new CMOS compatible material for interconnect applications. But, it can also be used for resistive switching. The structure is shown in figure 5. Using the nanoholes and a few monolayer thick cladding layer of CC will reduce the current requirement and accordingly reduce the effect of carbon cross-section to that of large diameter single-walled CNTs.

Figure 5 Conductive carbon (CC) samples [7]

Insulating Carbon

Insulating Carbon appears in many forms, amorphous and diamond-like carbon are the most promising materials for resistive switching. They can be easily manufactured at low costs using PECVD, these materials show a change in conductance when subjected to unipolar electrical pulses. The high resilience to a variety of external stimuli of amorphous and diamond-like carbon ensures the robustness of the system against heat, friction, wear, and corrosion.

The sp2 chains in amorphous or DLC lead to an electrically conductive state whereas sp3 dominated carbon gives high resistance. The two known mechanisms for switching from high to low resistance in ta-C, are re-hybridizing carbon atoms from sp3 to sp2 and arranging the sp2 hybridized atoms so that they form a conductive pathway [3]. (figure 6)

Figure 6 MD simulation result of filamentary switching in t-aC for low resistance (LRS) and high resistance state (HRS). For the SET and RESET states, sp2 carbon atoms are shown. Each color represents a different cluster of conjugated sp2 atoms.[3]

It has been seen that for reversible switching the sp3 content should not be less than 35%.

Oxygenated Carbon

The oxygenated carbon is nothing but the amorphous carbon doped with oxygen i.e. a-COx. The T gradient makes repeatable reversible switching a key challenge for ta-C but oxygenation of carbon provides an electrochemical component in the switching mechanism which in turn makes repeatable reversible switching possible but, at the cost of bipolar operation. Still, as of now, a-COx is the most promising material for carbon-based resistive switching devices.

The comparison of ta-C and a-COx based memory devices is given in table 1.

Table 1 [3]

Prospects

Before knowing the challenges we must know what are the areas that are needed to be focused on for developing the memristive systems. Figure 7 shows the requirements which are ranked quantitatively for separate applications.

Figure 7 Device performance requirements for representative applications. A number of device requirements are ranked (qualitatively) among four considered applications. A higher position on the axis implies a higher required value of the specific metric. The dashed red line indicates best-reported memristor experimental data (which are reported for different devices and hence might not be necessarily combined in a single device).[1]

The two main challenges are (a) Device Variability and (b) Current-voltage nonlinearity.

References

1. J. Joshua Yang, Dmitri B. Strukov and Duncan R. Stewart. Memristive devices for computing 
2. Dmitri B. Strukov, Gregory S. Snider, Duncan R. Stewart & R. Stanley Williams. The missing memristor found 
3. W. W. Koelmans, T. Bachmann, F. Zipoli, A. K. Ott, C. Ferrari, O. Cojocaru-Mir©din, S. Zhang, C. Scheu, M. Wuttig, V. K. Nagareddy, M. F. Craciun, A. M. Alexeev, C. D. Wright, V. P. Jonnalagadda, A. Curioni, A. Sebastian & E. Eleftheriou. Carbon-based resistive memories.
4. Rainer Waser and Masakazu Aono. Nanoionics-based resistive switching memories
5. Eike Linn, Roland Rosezin, Carsten Kügeler & Rainer Waser. Complementary resistive switches for passive nanocrossbar memories
6. Akihito Sawa. Resistive switching in transition metal oxides
7. Franz Kreupl, Rainer Bruchhaus, Petra Majewski, Jan B. Philipp, Ralf Symanczyk, Thomas Happ, Christian Arndt, Mirko Vogt, Roy Zimmermann, Axel Buerke, Andrew P. Graham & Michael Kund. Carbon-Based Resistive Memory

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