Dmitri B. Strukov

The missing memristor found

Anyone who ever took an electronics laboratory class will be familiar with the fundamental passive circuit elements: the resistor, the capacitor and the inductor. However, in 1971 Leon Chua reasoned from symmetry arguments that there should be a fourth fundamental element, which he called a memristor (short for memory resistor). Although he showed that such an element has many interesting and valuable circuit properties, until now no one has presented either a useful physical model or an example of a memristor. Here we show, using a simple analytical example, that memristance arises naturally in nanoscale systems in which solid-state electronic and ionic transport are coupled under an external bias voltage. These results serve as the foundation for understanding a wide range of hysteretic current–voltage behaviour observed in many nanoscale electronic devices that involve the motion of charged atomic or molecular species, in particular certain titanium dioxide cross-point switches.

Memristive devices for computing

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.

Training and operation of an integrated neuromorphic network based on metal-oxide memristors

Despite much progress in semiconductor integrated circuit technology, the extreme complexity of the human cerebral cortex, with its approximately 1014 synapses, makes the hardware implementation of neuromorphic networks with a comparable number of devices exceptionally challenging. To provide comparable complexity while operating much faster and with manageable power dissipation, networks based on circuits combining complementary metal-oxide-semiconductors (CMOSs) and adjustable two-terminal resistive devices (memristors) have been developed. In such circuits, the usual CMOS stack is augmented with one or several crossbar layers, with memristors at each crosspoint. There have recently been notable improvements in the fabrication of such memristive crossbars and their integration with CMOS circuits, including first demonstrations of their vertical integration. Separately, discrete memristors have been used as artificial synapses in neuromorphic networks. Very recently, such experiments have been extended to crossbar arrays of phase-change memristive devices. The adjustment of such devices, however, requires an additional transistor at each crosspoint, and hence these devices are much harder to scale than metal-oxide memristors, whose nonlinear current–voltage curves enable transistor-free operation. Here we report the experimental implementation of transistor-free metal-oxide memristor crossbars, with device variability sufficiently low to allow operation of integrated neural networks, in a simple network: a single-layer perceptron (an algorithm for linear classification). The network can be taught in situ using a coarse-grain variety of the delta rule algorithm to perform the perfect classification of 3 × 3-pixel black/white images into three classes (representing letters). This demonstration is an important step towards much larger and more complex memristive neuromorphic networks.

CMOL FPGA: a reconfigurable architecture for hybrid digital circuits with two-terminal nanodevices

This paper describes a digital logic architecture for ‘CMOL’ hybrid circuits which combine a semiconductor–transistor (CMOS) stack and two levels of parallel nanowires, with molecular-scale nanodevices formed between the nanowires at every crosspoint. This cell-based, field-programmable gate array (FPGA)-like architecture is based on a uniform, reconfigurable CMOL fabric, with four-transistor CMOS cells and two-terminal nanodevices (‘latching switches’). The switches play two roles: they provide diode-like I –V curves for logic circuit operation, and allow circuit mapping on CMOL fabric and its reconfiguration around defective nanodevices. Monte Carlo simulations of two simple circuits (a 32-bit integer adder and a 64-bit full crossbar switch) have shown that the reconfiguration allows one to increase the circuit yield above 99% at the fraction of bad nanodevices above 20%. Estimates have shown that at the same time the circuits may have extremely high density (approximately 500 times higher than that of the usual CMOS FPGAs with the same design rules), while operating at higher speed at acceptable power consumption. (Some figures in this article are in colour only in the electronic version)

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...

Memristor-CMOS hybrid integrated circuits for reconfigurable logic

Hybrid reconfigurable logic circuits were fabricated by integrating memristor-based crossbars onto a foundry-built CMOS (complementary metal-oxide-semiconductor) platform using nanoimprint lithography, as well as materials and processes that were compatible with the CMOS. Titanium dioxide thin-film memristors served as the configuration bits and switches in a data routing network and were connected to gate-level CMOS components that acted as logic elements, in a manner similar to a field programmable gate array. We analyzed the chips using a purpose-built testing system, and demonstrated the ability to configure individual devices, use them to wire up various logic gates and a flip-flop, and then reconfigure devices.

High precision tuning of state for memristive devices by adaptable variation-tolerant algorithm

Using memristive properties common for titanium dioxide thin film devices, we designed a simple write algorithm to tune device conductance at a specific bias point to 1% relative accuracy (which is roughly equivalent to seven-bit precision) within its dynamic range even in the presence of large variations in switching behavior. The high precision state is nonvolatile and the results are likely to be sustained for nanoscale memristive devices because of the inherent filamentary nature of the resistive switching. The proposed functionality of memristive devices is especially attractive for analog computing with low precision data. As one representative example we demonstrate hybrid circuitry consisting of an integrated circuit summing amplifier and two memristive devices to perform the analog multiply-and-add (dot-product) computation, which is a typical bottleneck operation in information processing.

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.

Pattern classification by memristive crossbar circuits using ex situ and in situ training

Memristors are memory resistors that promise the efficient implementation of synaptic weights in artificial neural networks. Whereas demonstrations of the synaptic operation of memristors already exist, the implementation of even simple networks is more challenging and has yet to be reported. Here we demonstrate pattern classification using a single-layer perceptron network implemented with a memrisitive crossbar circuit and trained using the perceptron learning rule by ex situ and in situ methods. In the first case, synaptic weights, which are realized as conductances of titanium dioxide memristors, are calculated on a precursor software-based network and then imported sequentially into the crossbar circuit. In the second case, training is implemented in situ, so the weights are adjusted in parallel. Both methods work satisfactorily despite significant variations in the switching behaviour of the memristors. These results give hope for the anticipated efficient implementation of artificial neuromorphic networks and pave the way for dense, high-performance information processing systems.

Four-dimensional address topology for circuits with stacked multilayer crossbar arrays

We present a topological framework that provides a simple yet powerful electronic circuit architecture for constructing and using multilayer crossbar arrays, allowing a significantly increased integration density of memristive crosspoint devices beyond the scaling limits of lateral feature sizes. The truly remarkable feature of such circuits, which is an extension of the CMOL (Cmos + MOLecular-scale devices) concept for an area-like interface to a three-dimensional system, is that a large-feature-size complimentary metal-oxide-semiconductor (CMOS) substrate can provide high-density interconnects to multiple crossbar layers through a single set of vertical vias. The physical locations of the memristive devices are mapped to a four-dimensional logical address space such that unique access from the CMOS substrate is provided to every device in a stacked array of crossbars. This hybrid architecture is compatible with digital memories, field-programmable gate arrays, and biologically inspired adaptive networks and with state-of-the-art integrated circuit foundries.