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. An important class of memristive devices are two-terminal resistance switches based on ionic motion, which are built from a simple conductor/insulator/conductor thin-film stack. These devices were originally conceived in the late 1960s and recent progress has led to fast, low-energy, high-endurance devices that can be scaled down to less than 10 nm and stacked in three dimensions. However, the underlying device mechanisms remain unclear, which is a significant barrier to their widespread application. Here, we review recent progress in the development and understanding of memristive devices. We also examine the performance requirements for computing with memristive devices and detail how the outstanding challenges could be met.

Nanoscale metal/oxide/metal switches have the potential to transform the market for nonvolatile memory and could lead to novel forms of computing. However, progress has been delayed by difficulties in understanding and controlling the coupled electronic and ionic phenomena that dominate the behaviour of nanoscale oxide devices. An analytic theory of the 'memristor' (memory-resistor) was first developed from fundamental symmetry arguments in 1971, and we recently showed that memristor behaviour can naturally explain such coupled electron-ion dynamics. Here we provide experimental evidence to support this general model of memristive electrical switching in oxide systems. We have built micro- and nanoscale TiO2 junction devices with platinum electrodes that exhibit fast bipolar nonvolatile switching. We demonstrate that switching involves changes to the electronic barrier at the Pt/TiO2 interface due to the drift of positively charged oxygen vacancies under an applied electric field. Vacancy drift towards the interface creates conducting channels that shunt, or short-circuit, the electronic barrier to switch ON. The drift of vacancies away from the interface annilihilates such channels, recovering the electronic barrier to switch OFF. Using this model we have built TiO2 crosspoints with engineered oxygen vacancy profiles that predictively control the switching polarity and conductance.

The accumulation and extrusion of Ca 2+ in the pre-and postsynaptic compartments play a critical role in initiating plastic changes in biological synapses. To emulate this fundamental process in electronic devices, we developed diffusive Ag-in-oxide memristors with a temporal response during and after stimulation similar to that of the synaptic Ca 2+ dynamics. In situ high-resolution transmission electron microscopy and nanoparticle dynamics simulations both demonstrate that Ag atoms disperse under electrical bias and regroup spontaneously under zero bias because of interfacial energy 2 minimization, closely resembling synaptic influx and extrusion of Ca 2+ , respectively.The diffusive memristor and its dynamics enable a direct emulation of both short-and long-term plasticity of biological synapses and represent a major advancement in hardware implementation of neuromorphic functionalities.CMOS circuits have been employed to mimic synaptic Ca 2+ dynamics, but three-terminal devices bear limited resemblance to bio-counterparts at the mechanism level and require significant numbers and complex circuits to simulate synaptic behavior [1][2][3] . A substantial reduction in footprint, complexity and energy consumption can be achieved by building a two-terminal circuit element, such as a memristor directly incorporating Ca 2+ -like dynamics.Various types of memristors based on ionic drift (drift-type memristor) 4-8 have recently been utilized for this purpose in neuromorphic architectures [9][10][11][12][13][14][15] . Although qualitative synaptic functionality has been demonstrated, the fast switching and non-volatility of drift memristors optimized for memory applications do not faithfully replicate the nature of plasticity. Similar issues also exist in MOS-based memristor emulators [16][17][18] , although they are capable of simulating a variety of synaptic functions including spike-timing-dependent plasticity (STDP). Recently, Lu's group adopted second-order drift memristors to approximate the Ca 2+ dynamics of chemical synapses by utilizing thermal dissipation 19 or mobility decay 20 , which successfully demonstrated STDP with non-overlapping spikes and other synaptic functions, representing a significant step towards bio-realistic synaptic devices. This approach features repeatability and simplicity, but the significant differences of the dynamical response from actual synapses limit the fidelity and variety of desired synaptic functions. A device with similar physical behavior as the biological Ca 2+ dynamics would enable improved emulation of synaptic function and broad applications to neuromorphic computing. Here we report such an emulator, which is a memristor based on metal atom 3 diffusion and spontaneous nanoparticle formation, as determined by in situ high-resolution transmission electron microscopy (HRTEM) and nanoparticle dynamics simulations. The dynamical properties of the diffusive memristors were confirmed to be functionally equivalent to Ca 2+ in bio-synapses, and their operating characteri...

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.

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