Julien Borghetti

'Memristive' switches enable 'stateful' logic operations via material implication.

The authors of the International Technology Roadmap for Semiconductors—the industry consensus set of goals established for advancing silicon integrated circuit technology—have challenged the computing research community to find new physical state variables (other than charge or voltage), new devices, and new architectures that offer memory and logic functions beyond those available with standard transistors. Recently, ultra-dense resistive memory arrays built from various two-terminal semiconductor or insulator thin film devices have been demonstrated. Among these, bipolar voltage-actuated switches have been identified as physical realizations of ‘memristors’ or memristive devices, combining the electrical properties of a memory element and a resistor. Such devices were first hypothesized by Chua in 1971 (ref. 15), and are characterized by one or more state variables that define the resistance of the switch depending upon its voltage history. Here we show that this family of nonlinear dynamical memory devices can also be used for logic operations: we demonstrate that they can execute material implication (IMP), which is a fundamental Boolean logic operation on two variables p and q such that pIMPq is equivalent to (NOTp)ORq. Incorporated within an appropriate circuit, memristive switches can thus perform ‘stateful’ logic operations for which the same devices serve simultaneously as gates (logic) and latches (memory) that use resistance instead of voltage or charge as the physical state variable.

Switching dynamics in titanium dioxide memristive devices

Memristive devices are promising components for nanoelectronics with applications in nonvolatile memory and storage, defect-tolerant circuitry, and neuromorphic computing. Bipolar resistive switches based on metal oxides such as TiO2 have been identified as memristive devices primarily based on the “pinched hysteresis loop” that is observed in their current-voltage (i-v) characteristics. Here we show that the mathematical definition of a memristive device provides the framework for understanding the physical processes involved in bipolar switching and also yields formulas that can be used to compute and predict important electrical and dynamical properties of the device. We applied an electrical characterization and state-evolution procedure in order to capture the switching dynamics of a device and correlate the response with models for the drift diffusion of ionized dopants (vacancies) in the oxide film. The analysis revealed a notable property of nonlinear memristors: the energy required to switch a me...

Coupled Ionic and Electronic Transport Model of Thin-Film Semiconductor Memristive Behavior

The memristor, the fourth passive circuit element, was predicted theoretically nearly 40 years ago, but we just recently demonstrated both an intentional material system and an analytical model that exhibited the properties of such a device. Here we provide a more physical model based on numerical solutions of coupled drift-diffusion equations for electrons and ions with appropriate boundary conditions. We simulate the dynamics of a two-terminal memristive device based on a semiconductor thin film with mobile dopants that are partially compensated by a small amount of immobile acceptors. We examine the mobile ion distributions, zero-bias potentials, and current-voltage characteristics of the model for both steady-state bias conditions and for dynamical switching to obtain physical insight into the transport processes responsible for memristive behavior in semiconductor films.

A hybrid nanomemristor/transistor logic circuit capable of self-programming

Memristor crossbars were fabricated at 40 nm half-pitch, using nanoimprint lithography on the same substrate with Si metal-oxide-semiconductor field effect transistor (MOS FET) arrays to form fully integrated hybrid memory resistor (memristor)/transistor circuits. The digitally configured memristor crossbars were used to perform logic functions, to serve as a routing fabric for interconnecting the FETs and as the target for storing information. As an illustrative demonstration, the compound Boolean logic operation (A AND B) OR (C AND D) was performed with kilohertz frequency inputs, using resistor-based logic in a memristor crossbar with FET inverter/amplifier outputs. By routing the output signal of a logic operation back onto a target memristor inside the array, the crossbar was conditionally configured by setting the state of a nonvolatile switch. Such conditional programming illuminates the way for a variety of self-programmed logic arrays, and for electronic synaptic computing.

The switching location of a bipolar memristor: chemical, thermal and structural mapping

Memristors are memory resistors promising a rapid integration into future memory technologies. However, progress is still critically limited by a lack of understanding of the physical processes occurring at the nanoscale. Here we correlate device electrical characteristics with local atomic structure, chemistry and temperature. We resolved a single conducting channel that is made up of a reduced phase of the as-deposited titanium oxide. Moreover, we observed sufficient Joule heating to induce a crystallization of the oxide surrounding the channel, with a peculiar pattern that finite element simulations correlated with the existence of a hot spot close to the bottom electrode, thus identifying the switching location. This work reports direct observations in all three dimensions of the internal structure of titanium oxide memristors.

Electrical transport and thermometry of electroformed titanium dioxide memristive switches

We investigated the electrical transport of electroformed titanium dioxide memristive switches from liquid helium to room temperatures in order to better understand their internal states. After electroforming, we observed a continuous transition between two distinct limiting behaviors: a nearly Ohmic “ON”-state and an “OFF”-state characterized by conduction through a barrier. We interpret our data in terms of a model in which the electroforming step creates a conducting channel that does not completely bridge the metal contacts on the titanium dioxide film. The switching then occurs as a result of voltage-induced changes in the oxygen vacancy concentration in the gap between the tip of the channel and the adjacent metal contact. We used the metallic resistivity of the conduction channel as an in situ thermometer to measure the local device temperature, thus revealing an important implicit state variable.

Coexistence of Memristance and Negative Differential Resistance in a Nanoscale Metal‐Oxide‐Metal System

Memristive devices are nonlinear dynamical systems [ 1 ] that exhibit continuous, reversible and nonvolatile resistance changes that depend on the polarity, magnitude and duration of an applied electric fi eld. The memristive properties of metal/ metal oxide/metal (MOM) materials systems were discovered [ 2 , 3 ] in the 1960s and studied extensively for decades without reaching a consensus [ 4–6 ] on the physical switching mechanism. Recent research revealed that memristive switching is caused by electric fi eld-driven motion of charged dopants that defi ne the interface position between conducting and semiconducting regions of the metal oxide fi lm. [ 7–12 ] There have also been multiple reports of current-controlled negative differential resistance (CC-NDR) in electroformed MOM devices since the early 1960s (e.g. oxides of V, [ 13–17 ] Nb, [ 18 , 19 ] Ta, [ 20 ] Ti, [ 20–23 ] and Fe [ 24 ] ), and there have been a variety of proposals for the physical mechanism. Current work presents persuasive evidence that CC-NDR in these materials is due to a Joule-heating induced metal-insulator transition (MIT). [ 25 , 26 ] When the device is locally self-heated past the critical MIT temperature the resistivity drops abruptly, which has an unstable positive feedback effect on the current and results in the formation of a metallic phase conductive fi lament, [ 15 , 16 ] a necessary condition [ 27 ] for bulk CC-NDR. Independent researchers have recently shown [ 28 , 29 ] that the Magnéli phase Ti 4 O 7 [ 30 , 31 ] can be present in electroformed fi lms of memristive TiO 2 and may act as the source and sink for oxygen vacancies during memristive switching. Ti 4 O 7 is also known to exhibit a metal insulator transition at 155 K, [ 32–34 ] which opens the possibility to study nanoscale devices that simultaneously exhibit both CC-NDR and memristance. As shown in Figure 1 a, we have observed that electroformed titanium dioxide MOM devices can simultaneously exhibit both memristance and CC-NDR when immersed in liquid He. Here we derive an analytical model for the coexistence of both phenomena, which can be described by two independent mechanisms: (a) at all temperatures the memristance is due to the fi eld-driven motion of oxygen vacancies, and (b) at low temperatures the CC-NDR is caused by an insulator-to-metal phase transition triggered by Joule heating [ 13 , 14 , 25 , 26 ] of an electroformed conduction channel, probably the Magnéli phase Ti 4 O 7 . [ 28 , 29 ] Additionally, we analyze the electrical oscillations

A memristor-based nonvolatile latch circuit

Memristive devices, which exhibit a dynamical conductance state that depends on the excitation history, can be used as nonvolatile memory elements by storing information as different conductance states. We describe the implementation of a nonvolatile synchronous flip-flop circuit that uses a nanoscale memristive device as the nonvolatile memory element. Controlled testing of the circuit demonstrated successful state storage and restoration, with an error rate of 0.1%, during 1000 power loss events. These results indicate that integration of digital logic devices and memristors could open the way for nonvolatile computation with applications in small platforms that rely on intermittent power sources. This demonstrated feasibility of tight integration of memristors with CMOS (complementary metal-oxide-semiconductor) circuitry challenges the traditional memory hierarchy, in which nonvolatile memory is only available as a large, slow, monolithic block at the bottom of the hierarchy. In contrast, the nonvolatile, memristor-based memory cell can be fast, fine-grained and small, and is compatible with conventional CMOS electronics. This threatens to upset the traditional memory hierarchy, and may open up new architectural possibilities beyond it.

Observation of two resistance switching modes in TiO2 memristive devices electroformed at low current.

We report the observation of two resistance switching modes in certain 50 nm × 50 nm crossbar TiO(2) memristive devices that have been electroformed with a low-current process. The two switching modes showed opposite switching polarities. The intermediate state was shared by both modes (the ON state of the high-resistance mode or the OFF state of the low-resistance mode) and exhibited a relaxation to a more resistive state, including an initial transient decay. The activation energies of such a decay and ON-switching to the intermediate state were determined to be 50-210 meV and 1.1 eV, respectively. Although they are attributed to the coexistence of charge trapping and ionic motion, the ionic motion dominates in both switching modes. Our results indicate that the two switching modes in our system correspond to different switching layers adjacent to the interfaces at the top and bottom electrodes.

Hybrid CMOS/memristor circuits

This is a brief review of recent work on the prospective hybrid CMOS/memristor circuits. Such hybrids combine the flexibility, reliability and high functionality of the CMOS subsystem with very high density of nanoscale thin film resistance switching devices operating on different physical principles. Simulation and initial experimental results demonstrate that performance of CMOS/memristor circuits for several important applications is well beyond scaling limits of conventional VLSI paradigm.