In the OSTI Collections: Memristors
Dr. William N. Watson, Physicist
DOE Office of Scientific and Technical Information
- Experimental characterization of memristors
- Mathematical modeling of memristors
- Other memristor types and uses
- Available through OSTI's SciTech Connect
- Available through DoE PAGES
- Available through DOepatents
- Additional references
All materials known to us as of this writing will, within the range of temperatures we ordinarily experience, resist the flow of electric current by dissipating some of the energy of the electrically charged particles that make up the current. The dissipation occurs as these particles collide with atoms of the material they pass through and lose some of their energy to them.
How resistive most materials are at any moment is affected little if any by the amount of charge that has passed through them earlier, but some materials become significantly more or less resistive to current depending on the flow of charge that they’ve already conducted. Materials that exhibit this latter behavior have long been known. However, interest in the phenomenon has become more widespread in the last several years, largely through two events.
One event, which set the stage for the other, was the 1971 publication of an analysis of passive electric-circuit components.[IEEE] UC Berkeley electrical engineer Leon Chua considered how the three familiar passive components—capacitors, inductors, and resistors—each related two different electrical quantities. A capacitor consists of a pair of conducting plates separated by an insulating gap that can accumulate opposite electrical charges on each plate. The amounts of positive and negative electric charge stored on the plates depend on the plates’ voltage difference. An inductor is basically an electromagnet whose magnetic field, like that of any electromagnet, impedes any change in the current through it. The amount of magnetic flux[Wikipedia] linked through the inductor—whose rate of change with time (or time derivative[Wikipedia]) equals the difference in voltage at opposite ends of the inductor—depends on how rapidly charge flows through the inductor’s coils. And the rate of charge flow through a resistor, which simply resists that flow, depends on the voltage difference between the current’s entry and exit points.
These three components relate different combinations of electrical quantities from two pairs (charge and its rate of flow over time; voltage difference and magnetic flux linkage). What if a fourth circuit component related the other combination? Chua examined what a component that related electric charge to magnetic flux linkage would be like, and how it might be used in electrical circuits. According to his analysis, the component should behave much like a resistor, but one whose resistance depended on the net charge flow that had already passed through it. If power to the circuit were switched off, whatever resistance the component would have at that time would be the resistance it would have once the circuit was switched back on. Since this resistorlike component would thus retain a memory of its last resistance, Chua called it a memristor.
Figure 1. Leon Chua proposed in 1971 the possibility of a fourth passive element of electrical circuits, analogous to the long-used resistor, capacitor, and inductor. An inductor’s inductance is the derivative of magnetic flux linkage φ through its coils with respect to the current i passing through it; a capacitor’s capacitance is the derivative of the size of each plate’s electric charge q with respect to the voltage difference v across its plates; and a resistor’s resistance is the derivative of voltage difference v across it with respect to current i through it. Analogously, the fourth circuit element would be characterized by the derivative of flux linkage φ to charge q. Such a circuit element would act like a resistor whose resistance depended on its current-conducting history—in effect, a resistor with a memory. Chua named such devices memristors.
Voltage difference v and current i are both intrinsically related to flux linkage φ and charge q respectively, in that v and i are the respective derivatives of φ and q with respect to time t.
As noted above, some materials’ electrical resistances were already known to be significantly affected by their charge-conducting history.[Nature Materials] But the connection to Chua’s memristor concept, originally emphasizing a connection between electric charge and magnetic flux linkage, received relatively little notice until 2008, when researchers at HP Labs announced their construction of a nonmagnetic variable resistor that nonetheless exhibited a memory for its last resistance.[Nature] The Hewlett-Packard group described the device’s properties in terms of Chua’s memristor concept, with a mathematical model that related the device’s charge conduction to the time antiderivative[Wikipedia] of the voltage difference across it, though for this device the antiderivative had no relation to a magnetic flux linkage. Announcing their device as the realization of a memristor brought new attention to Chua’s earlier idea. Much of the attention led to a sorting out of how the new device did and did not actually match Chua’s 1971 concept, while other work focused on inventing other devices with similar properties and understanding how they function.
Memristor experiments and analyses have been motivated by their range of known and expected uses, from simplifying the readouts of measuring devices to advancing the information storage and processing capabilities of computers. As one research report[SciTech Connect] states, memristors are among “the strongest candidates” to replace flash memory[Wikipedia], and possibly dynamic[Wikipedia] and static[Wikipedia] random access memory, in the near future, as well as having great potential to enable novel high-performance computing architectures beyond complementary metal-oxide-semiconductor (CMOS) technology[Wikipedia]. The reports discussed below describe recent work in this field sponsored by the U.S. Department of Energy at Sandia National Laboratories and other research centers.
A memristor can be useful if its resistance can be switched between as few as two standard values, one high and one low, so that currents are thus more or less turned “on” and “off”. For reliable operation, the different resistances should remain the same and switch consistently under the same conditions, no matter how many switching cycles the memristor undergoes. Researchers at Sandia observed how consistently memristors made of tantalum oxide behaved when they were cycled through various voltage differences, finding among other things that the memristors’ cycle-to-cycle variation tended to increase when their “off” resistances were set higher, and that thicker memristors were more promising as devices that could be switched among more than two resistance states. These results and others are described in an April 2015 slide presentation “Characterizing Switching Variability in TaOx Memristors”[SciTech Connect], which also mentions one specific reason for the interest in consistency: the potential for memristors as energy- and space-efficient circuit elements in computers whose design imitates certain features of nerve-cell networks.[Wikipedia]
Other work at Sandia was focused on optimizing a particular fabrication process to yield reliable memristors made of a layer of tantalum on a film of tantalum oxide. The poster “Characterization of Memristor Devices Fabricated with Ion Assisted Deposition”[SciTech Connect] describes the process, which involves bombarding a film of material with ions to energize it, thus enabling the film’s own atoms and ions to arrange themselves in ways that they wouldn’t otherwise, while the film is being grown by more and more atoms and ions being deposited onto it. The process yielded dense, stable oxide films by limiting how rapidly metal atoms and oxygen ions were deposited on them, thus better controlling each film’s composition. Memristors prepared using different ion bombardment rates, and having different oxide-layer thicknesses and compositions, were put through millions of switching cycles to find which processes yielded the most reliable devices; after their work, the experimenters recommended future fabrication of tantalum-oxide based memristors to incorporate large oxygen concentrations through high rates of ion bombardment.
A significant obstacle to developing and using memristors has been that the physical mechanisms of their switching behavior are incompletely understood. The current understanding, as far as it goes, is represented by mathematical models of the mechanisms which, to the extent of their accuracy, allow various hard-to-measure memristor parameters to be calculated from other measurable ones.
One set of mathematical models is actually patented together with methods for operating memristive memory devices. U.S. Patent 9,336,870 B1, “Methods for resistive switching of memristors”[DOepatents], notes that the physical mechanisms that govern memristor switching are hard to measure. For instance, standard electron microscopy of the single, filamentous conducting path of one type of memristor typically just provides a single post-mortem snapshot of the path, and almost no experimental data had been gathered when the patent was written about how conducting filaments’ temperatures change. The mathematical models described in the patent all assume steady heat flow in memristors’ conducting filaments, with different models specifying different heat flow distributions in space.
Memristor current conduction can be modeled even more precisely than the heat-flow equations of Patent 9,336,870 B1 suggest. The slide presentation “The Role of Joule Heating and Defect Chemistry in Memristor Modeling”[SciTech Connect] describes simplified mathematical models of three different processes. One of these models how vacant spots, which are defects in the otherwise regular array of a memristor’s atoms, become contiguous as the atoms move around to form a filament of vacancies through which electric charges can flow. Another model describes the heating of the material produced when electrical charges collide with the material’s atoms (“Joule heating”[Wikipedia]). The third model accounts for charge carriers’ quantum-physical wave motion and their reactions with defects in the memristor materials’ atomic lattices. Further work planned when the presentation was made included integrating the second and third models to see how the charges’ wave motion was affected by their heating the memristor material, determining the level of lattice defects, reaction rates, and mobilities, and investigating the Poole-Frenkel effect[Wikipedia] of large electric fields on the motion of electrons through the memristor.
Two slide presentations for scientific conferences[SciTech Connect, SciTech Connect] and a journal article prepared for the latter conference[SciTech Connect] describe an even more detailed model that accounts for the distribution of temperature in a memristor as well as the motion and electric fields of the memristor’s individual charge carriers: electrons, ions, the aforementioned atomic-lattice vacancies, and a different kind of vacancy among possible electron states (“holes”)[Wikipedia]. The presentations also describe what the model implies about the way a tantalum oxide memristor’s resistance is switched to low values, turning current “on”, and to high values, turning current “off”. The model was found to agree qualitatively with experiment, and indicated that in tantalum oxide memristors, electric-field and thermal effects are both important.
A technical report from Sandia National Labs published more than a year later, “Fully-Coupled Thermo-Electrical Modeling and Simulation of Transition Metal Oxide Memristors”[SciTech Connect], gives further, more detailed description of the mathematical model and its implications for memristors made with oxides of various transition metals (notes and links added):
The switching mechanism in TaOx [tantalum oxide] and TiOx [titanium oxide] memristors that alters the state of the device between that of a high-resistance off-state and that of a low-resistance on-state is believed to involve defect chemistry reactions and migration of oxygen anions and neutral and positively charged oxygen vacancies. These processes lead to the formation of Ta- or Ti-rich conducting filaments [67,72]. Voltage sweeps conducted on these and other oxide-based memristors induce changes to the oxygen vacancy concentration profiles in the device. The result is a characteristic I-V [current-voltage] hysteresis[Wikipedia] [history-dependence of state] whereby one of the two paths of the hysteresis curve in the low-voltage bias regime represents a high resistance off-state and the other a low-resistance on-state. [Compare Figure 2 above.] … These changes are governed by the evolving oxide defect chemistry that is controlled by Joule heating and high electric-field processes. Accordingly, these devices require an initial electroforming cycle in order to induce oxygen-vacancy rich filament regions that form a low-resistance channel. When applying higher voltages to the device, outside those of the read window, state changes can be induced. [Pp. 38, 40.]
The simulation tool that Sandia researchers have based on this model, being “successfully validated on the existing experimental data”, is expected to “greatly aid Sandia experimentalists in device optimization for different applications” while it “can be extended to simulate other novel beyond-CMOS technologies such as phase-change devices, and ultra-scaled batteries (e.g., Li-ion)” (p. 71). To assess memristors’ potential to replace CMOS-based devices at “the end of scaling” at smaller device sizes around 5 nanometers, the extensions will likely require describing the motions of electric-charge carriers in greater detail than the current mathematical model incorporates, including quantum-mechanical features of electrons and holes (p. 72).
The memristors whose analysis is described in the aforementioned reports consist of oxides between metal electrodes. That structure and composition also characterize many capacitors. Sandia researchers have analyzed transport processes in both memristors and capacitors with the same mathematical models, as reported in an abstract[SciTech Connect] for a presentation at the March 2016 American Physical Society meeting. The mathematical models took quantum-mechanical features of electrons crossing the metal-oxide interfaces of both types of device into account, as well as the effects of Joule heating and strong electric fields on their oxide-defect chemistry. But despite the similarity of their structures and transport mechanisms, the two types of device have different transport mechanisms. The mathematical model described also includes effects of pulsed ionizing radiation, which was found useful for showing whether a metal-oxide-metal system was in a capacitive or memristive state.
Ionizing radiation might encounter memristors for reasons other than to distinguish them from capacitors. Some electronic devices have functions to perform in high-radiation environments, so they need to be designed to withstand the radiation. Results of mathematically modeling such situations are described in a paper[SciTech Connect] and poster[SciTech Connect] intended for presentation at an IEEE conference on nuclear space and radiation effects. The mathematical model of oxides and semiconducting materials accounts for how radiation affects the materials’ concentrations of different charge, and approximates some of the carriers’ wavelike quantum-mechanical behavior at metal-oxide interfaces. Calculations based on initial assumptions revealed a large discrepancy with experiment—under assumed conditions, the current through an irradiated tantalum oxide memristor was calculated to be only about one ten-millionth as large as actually observed. This led to revisiting some assumptions. Experiments with the model indicate that the increase of current that flows through memristors when irradiated depend significantly on the properties of vacancies in the tantalum oxide where oxygen atoms would otherwise be—properties that haven’t been well known. Assuming somewhat different vacancy properties, the model’s implications about current flow became different enough to remove much of the discrepancy with real memristors.
Much memristor research is also being conducted outside Sandia National Labs.
Some work involves using memristors as internal sensors in devices that can act on or sense other things outside themselves. A collaboration between researchers at Sandia, the University of Texas at El Paso, and the Universidad Autónoma de Ciudad Juárez in Mexico mathematically analyzed a microelectromechanical system (MEMS)[OSTI] design that incorporates a memristor. They found, as reported in “MEMS closed-loop control incorporating a memristor as feedback sensing element”[DoE PAGES], that small-scale parallel-plate capacitors used as actuators or sensors would have a greater range of movement if a memristor was used to provide feedback on the capacitor’s width. The plate separation in a small-scale parallel-plate capacitor, when it’s used as an actuator or sensor, can be changed stably over only 1/3 of the maximum plate gap if the actuator/sensor lacks positional feedback, since a capacitor has a pull-in instability once the oppositely charged plates’ mutual attraction exceeds the opposing force of a spring. 85% of the maximum gap can be used if conventional electric components are used to provide positional feedback. But according to the model described in the paper, using a memristor for positional feedback should allow plate movement through 95% of the interplate gap.
Other research focuses on memristors themselves. A patent[DOepatents] assigned to Los Alamos National Security, LLC, which operates Los Alamos National Laboratory, addresses a nonuniformity in memristor quality that’s inherent in the way conducting filaments appear to be produced in the kind of memristors described above. With respect to the physical mechanism behind their memristive behavior, the patent’s background section states:
The mechanism is believed to involve coupled electron-ion dynamics involving changes in the electronic barrier at an interface under an electric field. These changes are believed to result from oxygen deficient channels in the material. Single-phase binary and ternary metal oxides in their virgin states do not contain these channels, but application of a suitable voltage to the virgin sample has been found to initiate memristive behavior [15, 16]. The application of a voltage or current to the virgin sample suitable for initiating memristive behavior is known in the art as ‘electroforming’. Nanoionic circuit elements that can operate at room temperature have not yet been prepared by any process other than electroforming.
However, there are problems associated with the use of electroforming to provide memristive behavior because electroforming is a destructive process with a random and uncontrollable nature [11, 15, 17]. Samples may be damaged or destroyed by the high voltage or current , and memristors prepared by electroforming may also suffer from problems of non-uniformity and non-reproducibility [11, 17].
Accordingly, the patent describes a less random way to produce memristors of a more consistent quality, by using pulsed laser deposition[Wikipedia] to build a comblike structure of samarium oxide nanocolumns within a matrix of strontium titanium oxide. The vertical interfaces between the nanocolumns and matrix contain built-in oxygen deficiencies, “likely resulting from a structural incompatibility” between the two materials, which don’t have to be generated by a random electroforming process.
It has been widely assumed that oxide memristors gain or lose resistance because of the motion of oxygen ions; indeed, such motion is assumed in the memristor models developed at Sandia Labs. However, studies involving scanning tunneling microscopy have prompted the proposal that metal-ion motion could also contribute to the resistance change of these materials. Researchers at the University of Massachusetts Amherst, Brookhaven National Laboratory, and the Air Force Research Laboratory's Information Directorate produced a memristor consisting of hafnium oxide between tantalum and platinum electrodes, which they (a) switched between not just two resistance levels but 24 levels, (b) found to operate through over a hundred billion cycles with the ability to “remember” its last resistance for what should be much more than 10 years, even at temperatures of 85° Celsius (185° Fahrenheit), and (c) mathematically modeled as working by movement of both oxygen and metal atoms.
As the researchers reported in “Sub-10 nm Ta Channel Responsible for Superior Performance of a HfO2 Memristor”[DoE PAGES], this memristor was found to be reversibly switchable within 5 nanoseconds—and might be switched even faster if shorter pulses could be generated and transmitted to it. These features suggest that such memristors are suitable for nonvolatile memory and data storage. The way their high and low resistances vary oppositely with temperature suggest that changes in conducting channel composition switches their resistance rather than changes in channel size; furthermore, the devices’ retentive “memory” of their last resistance implies that tantalum ions migrate into the hafnium oxide and contribute to conducting-channel formation. Other experiments with electrical pulse trains show that this type of memristor can be continuously tuned in a manner similar to the potentiation and depression of a biological synapse[Wikipedia], making it a “promising candidate as [an] electronic synapse” in computers that work more like a biological nervous system than current machines do.
Figure 6. From p. 22 of “Sub-10 nm Ta Channel Responsible for Superior Performance of a HfO2 Memristor”[DoE PAGES], under the caption “Direct observation of a Ta-rich and O-deficient conduction channel”:Left (a): Image taken with a scanning transmission electron microscope of a conduction channel less than 10 nanometers wide connecting tantalum (Ta) and platinum (Pt) electrodes. “The conduction channel is brighter in the image, which means it contains more atoms with large atomic numbers (Ta in this case).” Middle (b): Comparison of the energies of electron beams passing through different parts of the structure, collected at the pristine hafnium oxide (HfO2) layer, the conduction channel region, and the tantalum (Ta) electrode. The graph “indicates the conduction channel is Ta-rich” because, when an electron from the beam collides with an electron in one the material’s atoms and loses energy to it, the amount of energy lost depends partly on what chemical element the atom represents. Measuring the energy losses can thus show what elements the electron beam has collided with.[Wikipedia] Right (c): electron energy-loss spectra “taken at three areas, which clearly show the conduction channel is also O-deficient.”—P. 22, “Sub-10 nm Ta Channel Responsible for Superior Performance of a HfO2 Memristor”[DoE PAGES].
The significance of memristors as components in advanced computer designs is briefly noted in another paper, by researchers at Spain’s University of the Basque Country, at Ikerbasque (the Basque Foundation for Science), and at the University of California, San Diego. Circuit elements with memory do more than just store information: they can simultaneously process it. This is one respect in which brains function differently from the way almost all computers do, wherein information has to be communicated between separate memory and processing components. But since memristors can accomplish information storage and processing with a single action, they may be useful for making computers with more brainlike capabilities than would be feasible in computers that have separate processing and memory units, even though the new family of computer designs might for a long time be much simpler than the brains of living organisms.
The prospect of quasineural computers is appearing as another trend arrives at a significant point. Computers, and electronic devices generally, have become more capable as people have figured out how to make the circuit components smaller. But as component designs been miniaturized toward atomic size, the components display specifically quantum-mechanical features. Though all physical systems, even large ones, are governed by the laws of quantum physics, the probability amplitudes and related features that characterize quantum physics are generally most clearly evident in smaller-scale systems. Computing systems with salient quantum-mechanical properties can represent information not only as simple bits, either 1s or 0s, but as “qubits”, which can be both 1s and 0s at the same time. This allows new ways to process information and determine things that are impractical or impossible to find with even the most powerful non-qubit computers.[OSTI]
The paper “Quantum memristors”[DoE PAGES] considers a device for neuronlike quantum information processing. It gives a schematic description of an electrical conductor whose input and output ends have their voltage difference continually monitored, with the difference controlling via a feedback mechanism the rate at which the conductor can dissipate energy from the charges it conducts to its environment—meaning that the voltage difference controls the conductor’s resistance, so its resistance depends on the device’s history. Quantum-physical relations among the charge flow, voltage, and energy dissipation rate are accounted for in the paper’s mathematical model. The model implies—correctly, if its accounting is accurate and leaves out nothing important—that the conductor-monitor system would function as a quantum-mechanical memristor. This suggests that it might be possible to build computers that could not only store and process information as brains do, with the same single actions, but perform those actions on qubits, thus processing information with still greater efficiency.
Figure 7. Left (a): Schematic diagram of an LC (inductance-capacitance) circuit, with an inductor on the left and a capacitor in the middle, shunted by a “quantum memristor” on the right—a tunable dissipative environment, represented by a resistor with a knob to choose a resistance between R1 and R2; a “weak measurement” of the voltage difference across the tunable resistor, represented by a voltmeter; and a feedback between the weak voltage measurement and the resistor’s tuning knob. The voltage measurement is “weak” in that it provides very little information as it disturbs the entity it measures very little.[Wikipedia] Right (b): “Feedback model of a memristor and implementation in quantum dynamics via a feedback-controlled open quantum system.”—From p. 2, “Quantum memristors”[DoE PAGES].
CMOS (Complementary metal-oxide-semicondutor technology)
Available through OSTI’s SciTech Connect
“Fully-Coupled Thermo-Electrical Modeling and Simulation of Transition Metal Oxide Memristors” [Metadata]
Sandia National Laboratories
“Characterizing Switching Variability in TaOx Memristors” (slides) [Metadata]
“Characterization of Memristor Devices Fabricated with Ion Assisted Deposition” (poster) [Metadata]
Proposed for presentation at the Student Intern Symposium held July 30, 2015 in Albuquerque, New Mexico.
“The Role of Joule Heating and Defect Chemistry in Memristor Modeling” [Metadata]
“Three-Dimensional Fully-Coupled Electrical and Thermal Transport Model of Oxide Memristors” (slides) [Metadata]
“Three-Dimensional Fully-Coupled Electrical and Thermal Transport Model of Dynamic Switching in Oxide Memristors” (slides) [Metadata]
“Transport Physics in Thin-Film Oxides: From Capacitors to Memristors” (abstract) [Metadata]
“The Effects of Ionizing Radiation on TaOx-based Memristors” (paper) [Metadata]
Proposed for presentation at the Institute of Electrical and Electronics Engineers (IEEE) 2015 Nuclear and Space Radiation Effects Conference (NESREC) held July 13-17, 2015 in Boston, Massachusetts.
“The Effects of Ionizing Radiation on TaOx-based Memristors” (poster) [Metadata]
Proposed for presentation at the Institute of Electrical and Electronics Engineers (IEEE) 2015 Nuclear and Space Radiation Effects Conference (NESREC) held July 13-17, 2015 in Boston, Massachusetts.
Available through DoE PAGES
“Three-dimensional fully-coupled electrical and thermal transport model of dynamic switching in oxide memristors” [Metadata]
“MEMS closed-loop control incorporating a memristor as feedback sensing element” [Metadata]
“Sub-10 nm Ta Channel Responsible for Superior Performance of a HfO2 Memristor” [Metadata]
“Quantum memristors” [Metadata]
Available through DOepatents
“Methods for resistive switching of memristors” [Metadata]
U.S. Patent 9,336,870 B1
Patent File Date: 2015 Feb 03
Assignee: Sandia Corporation
“Memristor comprising film with comb-like structure of nanocolumns of metal oxide embedded in a metal oxide matrix” [Metadata]
U.S. Patent 9,029,985 B2
Patent File Date: 2014 May 20
Assignee: Los Alamos National Security, LLC
“Memristor—The missing circuit element” [Metadata]
Paper in which Leon Chua introduced his memristor concept.
“Two centuries of memristors” [Metadata]
Published online 22 May 2012
Imperial College London (United Kingdom)
Paper discussing materials whose electrical resistances were known to be significantly affected by their charge-conducting history, long before Chua’s memristor proposal or HP Labs researchers’ announcement of a nonmagnetic memristor.
“The missing memristor found” [Metadata]
1 May 2008
“In the OSTI Collections: MEMS”, August 2015