With their working mechanisms based on ion migration, the switching dynamics and electrical behaviour of memristive devices resemble those of synapses and neurons, making these devices promising candidates for brain-inspired computing. Built into large-scale crossbar arrays to form neural networks, they perform efficient in-memory computing with massive parallelism by directly using physical laws. The dynamical interactions between artificial synapses and neurons equip the networks with both supervised and unsupervised learning capabilities. Moreover, their ability to interface with analogue signals from sensors without analogue/digital conversions reduces the processing time and energy overhead. Although numerous simulations have indicated the potential of these networks for brain-inspired computing, experimental implementation of large-scale memristive arrays is still in its infancy. This Review looks at the progress, challenges and possible solutions for efficient brain-inspired computation with memristive implementations, both as accelerators for deep learning and as building blocks for spiking neural networks.

Memristive crossbar arrays for brain-inspired computing

Neuromorphic computers comprised of artificial neurons and synapses could provide a more efficient approach to implementing neural network algorithms than traditional hardware. Recently, artificial neurons based on memristors have been developed, but with limited bio-realistic dynamics and no direct interaction with the artificial synapses in an integrated network. Here we show that a diffusive memristor based on silver nanoparticles in a dielectric film can be used to create an artificial neuron with stochastic leaky integrate-and-fire dynamics and tunable integration time, which is determined by silver migration alone or its interaction with circuit capacitance. We integrate these neurons with nonvolatile memristive synapses to build fully memristive artificial neural networks. With these integrated networks, we experimentally demonstrate unsupervised synaptic weight updating and pattern classification.

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Fully memristive neural networks for pattern classification with unsupervised learning

A simple noise model of a microwave MESFET (MODFET, HEMT, etc.) is described and verified at room and cryogenic temperatures. Closed-form expressions for the minimum noise temperature, the optimum generator impedance, the noise conductance, and the generator-impedance-minimizing noise measure are given in terms of the frequency, the elements of a FET equivalent circuit, and the equivalent temperatures of intrinsic gate resistance and drain conductance to be determined from noise measurements. These equivalent temperatures are demonstrated in the case of a Fujitsu FHR01FH MODFET to be independent of frequency in the frequency range in which 1/f noise is negligible. Thus, the model allows prediction of noise parameters for a broad frequency range from a single frequency noise parameter measurement. The relationships between this approach and other relevant studies are established. >

Modeling of noise parameters of MESFETs and MODFETs and their frequency and temperature dependence

The Hamiltonian Heff of an open quantum system consists formally of a first-order interaction term describing the closed (isolated) system with discrete states and a second-order term caused by the interaction of the discrete states via the common continuum of scattering states. Under certain conditions, the last term may be dominant. Due to this term, Heff is non-Hermitian. Using the Feshbach projection operator formalism, the solution ΨEc of the Schrodinger equation in the whole function space (with discrete as well as scattering states, and the Hermitian Hamilton operator H) can be represented in the interior of the localized part of the system in the set of eigenfunctions λ of Heff. Hence, the characteristics of the eigenvalues and eigenfunctions of the non-Hermitian operator Heff are contained in observable quantities. Controlling the characteristics by means of external parameters, quantum systems can be manipulated. This holds, in particular, for small quantum systems coupled to a small number of channels. The paper consists of three parts. In the first part, the eigenvalues and eigenfunctions of non-Hermitian operators are considered. Most important are the true and avoided crossings of the eigenvalue trajectories. In approaching them, the phases of the λ lose their rigidity and the values of observables may be enhanced. Here the second-order term of Heff determines decisively the dynamics of the system. The time evolution operator is related to the non-Hermiticity of Heff. In the second part of the paper, the solution ΨEc and the S matrix are derived by using the Feshbach projection operator formalism. The regime of overlapping resonances is characterized by non-rigid phases of the ΨEc (expressed quantitatively by the phase rigidity ρ). They determine the internal impurity of an open quantum system. Here, level repulsion passes into width bifurcation (resonance trapping): a dynamical phase transition takes place which is caused by the feedback between environment and system. In the third part, the internal impurity of open quantum systems is considered by means of concrete examples. Bound states in the continuum appearing at certain parameter values can be used in order to stabilize open quantum systems. Of special interest are the consequences of the non-rigidity of the phases of λ not only for the problem of dephasing, but also for the dynamical phase transitions and questions related to them such as phase lapses and enhancement of observables.

https://iopscience.iop.org/article/10.1088/1751-8113/42/15/153001/pdf

A non-Hermitian Hamilton operator and the physics of open quantum systems

Transient electron transport and velocity overshoot in wurtzite GaN, InN, and AlN are examined and compared with that which occurs in GaAs. For all materials, we find that electron velocity overshoot only occurs when the electric field is increased to a value above a certain critical field, unique to each material. This critical field is strongly dependent on the material, about 4 kV/cm for the case of GaAs but much higher for the III–nitride semiconductors: 140 kV/cm for GaN, 65 kV/cm for InN, and 450 kV/cm for AlN. We find that InN exhibits the highest peak overshoot velocity and that this velocity overshoot lasts over the longest distances when compared with GaN and AlN. Finally, using a one-dimensional energy–momentum balance approach, a simple model is used to estimate the cutoff frequency performance of nitride based heterojunction field effect transistors (HFETs) and a comparison is made to recently fabricated AlGaN/GaN HFETs.

Transient electron transport in wurtzite GaN, InN, and AlN

A method to determine the small-signal equivalent circuit of FETs is proposed This method consists of a direct determination of both the extrinsic and intrinsic small-signal parameters in a low-frequency band This method is fast and accurate, and the determined equivalent circuit fits the S-parameters well up to 265 GHz >

A new method for determining the FET small-signal equivalent circuit

The authors report on detection of terahertz radiation by high electron mobility nanometer InGaAs∕AlInAs transistors. The photovoltaic type of response was observed at the 1.8–3.1THz frequency range, which is far above the cutoff frequency of the transistors. The experiments were performed in the temperature range from 10to80K. The resonant response was observed and was found to be tunable by the gate voltage. The resonances were interpreted as plasma wave excitations in the gated two-dimensional electron gas. The minimum noise equivalent power was estimated, showing possible application of these transistors in sensing of terahertz radiation.

Resonant and voltage-tunable terahertz detection in InGaAs /InP nanometer transistors

A simple self‐consistent model is described, which takes into account nonstationary electron‐dynamic effects and gate‐edge effects in submicrometer gate FET devices. Analytical formulations are used to describe nonstationary electron dynamics, which are derived by fitting steady‐state results of Monte Carlo calculations. The first results show a significant improvement in the transconductance gm as well as in the cutoff frequency for submicrometer devices. A first attempt to optimize the impurity concentration level is made which shows that a compromise can be found for present‐day feasible submicrometer gate devices.

Modeling of a submicrometer gate field‐effect transistor including effects of nonstationary electron dynamics

Terahertz emission from InGaAs∕InAlAs lattice-matched high electron mobility transistors was observed. The emission appears in a threshold-like manner when the applied drain-to-source voltage UDS is larger than a threshold value UTH. The spectrum of the emitted signal consists of two maxima. The spectral position of the lower-frequency maximum (around 1 THz) is sensitive to UDS and UGS, while that of the higher frequency one (around 5 THz) is not. The lower-frequency maximum is interpreted as resulting from the Dyakonov–Shur instability of the gated two-dimensional electron fluid, while the higher frequency is supposed to result from current-driven plasma instability in the ungated part of the channel. The experimental results are confirmed by and discussed within Monte Carlo calculations of the high-frequency current noise spectra.

Voltage tuneable terahertz emission from a ballistic nanometer InGaAs∕InAlAs transistor

As Moore's law reaches its end, traditional computing technology based on the Von Neumann architecture is facing fundamental limits. Among them is poor energy efficiency. This situation motivates the investigation of different processing information paradigms, such as the use of spiking neural networks (SNNs), which also introduce cognitive characteristics. As applications at very high scale are addressed, the energy dissipation needs to be minimized. This effort starts from the neuron cell. In this context, this paper presents the design of an original artificial neuron, in standard 65 nm CMOS technology with optimized energy efficiency. The neuron circuit response is designed as an approximation of the Morris-Lecar theoretical model. In order to implement the non-linear gating variables, which control the ionic channel currents, transistors operating in deep subthreshold are employed. Two different circuit variants describing the neuron model equations have been developed. The first one features spike characteristics, which correlate well with a biological neuron model. The second one is a simplification of the first, designed to exhibit higher spiking frequencies, targeting large scale bio-inspired information processing applications. The most important feature of the fabricated circuits is the energy efficiency of a few femtojoules per spike, which improves prior state-of-the-art by two to three orders of magnitude. This performance is achieved by minimizing two key parameters: the supply voltage and the related membrane capacitance. Meanwhile, the obtained standby power at a resting output does not exceed tens of picowatts. The two variants were sized to 200 and 35 μm2 with the latter reaching a spiking output frequency of 26 kHz. This performance level could address various contexts, such as highly integrated neuro-processors for robotics, neuroscience or medical applications.

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Alain Cappy

Papers

A new method for determining the FET small-signal equivalent circuit

Resonant and voltage-tunable terahertz detection in InGaAs /InP nanometer transistors

Modeling of a submicrometer gate field‐effect transistor including effects of nonstationary electron dynamics

Voltage tuneable terahertz emission from a ballistic nanometer InGaAs∕InAlAs transistor

A 4-fJ/Spike Artificial Neuron in 65 nm CMOS Technology.