Design and implementation of artificial neuromorphic systems able to provide brain akin computation and/or bio-compatible interfacing ability are crucial for understanding the human brain's complex functionality and unleashing brain-inspired computation's full potential. To this end, the realization of energy-efficient, low-area, and bio-compatible artificial synapses, which sustain the signal transmission between neurons, is of particular interest for any large-scale neuromorphic system. Graphene is a prime candidate material with excellent electronic properties, atomic dimensions, and low-energy envelope perspectives, which was already proven effective for logic gates implementations. Furthermore, distinct from any other materials used in current artificial synapse implementations, graphene is biocompatible, which offers perspectives for neural interfaces. In view of this, we investigate the feasibility of graphene-based synapses to emulate various synaptic plasticity behaviors and look into their potential area and energy consumption for large-scale implementations. In this article, we propose a generic graphene-based synapse structure, which can emulate the fundamental synaptic functionalities, i.e., Spike-Timing-Dependent Plasticity (STDP) and Long-Term Plasticity. Additionally, the graphene synapse is programable by means of back-gate bias voltage and can exhibit both excitatory or inhibitory behavior. We investigate its capability to obtain different potentiation/depression time scale for STDP with identical synaptic weight change amplitude when the input spike duration varies. Our simulation results, for various synaptic plasticities, indicate that a maximum 30% synaptic weight change and potentiation/depression time scale range from [-1.5 ms, 1.1 ms to [-32.2 ms, 24.1 ms] are achievable. We further explore the effect of our proposal at the Spiking Neural Network (SNN) level by performing NEST-based simulations of a small SNN implemented with 5 leaky-integrate-and-fire neurons connected via graphene-based synapses. Our experiments indicate that the number of SNN firing events exhibits a strong connection with the synaptic plasticity type, and monotonously varies with respect to the input spike frequency. Moreover, for graphene-based Hebbian STDP and spike duration of 20ms we obtain an SNN behavior relatively similar with the one provided by the same SNN with biological STDP. The proposed graphene-based synapse requires a small area (max. 30 nm2), operates at low voltage (200 mV), and can emulate various plasticity types, which makes it an outstanding candidate for implementing large-scale brain-inspired computation systems.

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Designing and implementing artificial systems that can be interfaced with the human brain or that can provide computational ability akin to brain's processing information efficient style is crucial for understanding human brain fundamental operating principles and to unleashing the full potential of brain-inspired computing. As basic neural network components, responsible for information transfer between neurons, artificial synapses able to emulate analog biological synaptic behaviour are of particular interest. State of the art CMOS and memristor-based synapses suffer from scalability drawbacks (large energy consumption and area footprint), variability-induced instability, and are not bio-compatible. In this paper, we propose a generic Graphene Nanoribbon (GNR) based synapse structure and demonstrate that by changing GNR geometry and external bias voltages it can emulate different synaptic plasticity behaviours, i.e., Spike Timing Dependent Plasticity and LongTerm Depression and Potentiation, and that both excitatory and inhibitory synaptic behavior can be obtained with the same GNR geometry. To demonstrate biologically plausible operation, we make use of low voltage bias, i.e., 0.1V, 0.2 V, and consider inputs consistent with measured brain synapses data, i.e.,-50 mV to 50 mV pre-and post-synaptic spikes voltage range, and-60ms to 60 ms time range. The simulations indicate that by changing the GNR shape we can enrich the plasticity behaviour (potentially beyond the considered cases) and the plasticity change of 100% provided by natural synapses can be achieved. Our investigation clearly suggests that the proposed GNR synapse structure is a promising candidate for large-scale neuromorphic systems integration, which might potentially bring novel insight on brain neurophysiology, as it requires a small footprint, is energy effective, biocompatible, and versatile from the synaptic behaviour point of view.

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As CMOS scaling is reaching its limits, high power density and leakage, low reliability, and increasing IC production costs are prompting for developing new materials, devices, architectures, and computation paradigms. Additionally, temperature variations have a significant impact on devices and circuits reliability and performance. Graphene's remarkable properties make it a promising post Silicon frontrunner for carbon-based nanoelectronics. While for CMOS gates temperature effects have been largely investigated, for gates implemented with atomic-level Graphene Nanoribbons (GNRs), such effects have not been explored. This paper presents the results of such an analysis performed on a set of GNR-based Boolean gates by varying the operation temperature within the military range, i.e., -55°C to 125°C, and evaluating by means of SPICE simulations gate output signal integrity, propagation delay, and power consumption. Our simulation results reveal that GNR-based gates are robust with respect to temperature variation, e.g., 5.2% and 5.3% maximum variations of NAND output logic '1' (VOH) and logic '0' ($V$OL) voltage levels, respectively. Moreover, even in the worst condition GNR-based gates outperform CMOS FinFET 7nm counterparts, e.g., 1.6× smaller delay and 185× less power consumption for the INV case, which is strengthening their great potential as basic building blocks for future reliable, low-power, nanoscale carbon-based electronics.

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Designing and implementing artificial neuromorphic systems, which can provide biocompatible interfacing, or the human brain akin ability to efficiently process information, is paramount to the understanding of the human brain complex functionality. Energy-efficient, low-area, and biocompatible artificial neurons are key ubiquitous components of any large scale neural systems. Previous CMOS-based neurons implementations suffer from scalability drawbacks and cannot naturally mimic the analog behavior. Memristor and phase-changed neurons have variability-induced instability drawbacks, and usually rely on additional CMOS circuitry. However, graphene, despite its ballistic transport, inherently analog nature, and biocompatibility, which provide natural support for biologically plausible neuron implementations has only been considered for Boolean logic implementations. In this paper, we propose an ultra-compact, all graphene-based nonlinear Leaky Integrate-and-Fire spiking neuron. By means of SPICE simulations, we validate its basic functionality and investigate the output spikes response under stochastic noisy input spike trains with a variable firing rate, from 20 to 200 spikes per second. Simulation results indicate neuron robustness to noisy scenarios, and neuronal output firing regularity. The small area and the low energy consumption, due to 200mV supply voltage operation, can benefit the implementation of large scale neural networks, and the biologically plausible operating conditions (e.g., 2ms and 100mV spike duration and amplitude), can promote the interfacebility of graphene-based artificial neurons with biological counterparts. @en

To fully unleash the potential of graphene-based devices for neuromorphic computing, we propose a graphene synapse and a graphene neuron that form together a basic Spiking Neural Network (SNN) unit, which can potentially be utilized to implement complex SNNs. Specifically, the proposed synapse enables two fundamental synaptic functionalities, i.e., Spike-Timing-Dependent Plasticity (STDP) and Long-Term Plasticity, and both Long-Term Potentiation (LTP) and Long-Term Depression (LTD) can be emulated with the same structure by properly adjusting its bias. The proposed neuron captures the essential Leaky Integrate and Fire spiking neuron behavior with post firing refractory interval. We demonstrate the proper operation of the graphene SNN unit by relying on a mixed simulation approach that embeds the high accuracy of atomistic level simulation of graphene structures conductance within the SPICE framework. Subsequently, we analyze the way graphene synaptic plasticity affects the behavior of a 2-layer SNN example consisting of 6 neurons and demonstrate that LTP significantly increases the number of firing events while LTD is diminishing them, as expected. To assess the plausibility of the graphene SNN reaction to input stimuli we simulate its behavior by means of both SPICE and NEST, a well established SNN simulation framework, and demonstrate that the obtained reactions, characterized in terms of total number of firing events and mean Inter-Spike Interval (ISI) length, are in close agreement, which clearly suggests that the proposed design exhibits a proper behavior. Further, we prove the unsupervised learning capabilities of the proposed design by considering a 2-layer SNN consisting of 30 neurons meant to recognize the characters 'A,' 'E,' 'I,' 'O,' and 'U,' represented with a 5 by 5 black and white pixel matrix. The SPICE simulation results indicate that the graphene SNN is able to perform unsupervised character recognition associated learning and that its recognition ability is robust to input character variations. Finally, we note that our proposal results in a small real-estate footprint (max. 30 nm^2 are required by one graphene-based device) and operates at 200 mV supply voltage, which suggest its suitability for the design of large-scale energy-efficient computing systems.

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As CMOS feature size is reaching atomic dimensions, unjustifiable static power, reliability, and economic implications are exacerbating, thus prompting for research on new materials, devices, and/or computation paradigms. Within this context, Graphene Nanoribbons (GNRs), owing to graphene’s excellent electronic properties, may serve as basic structures for carbon-based nanoelectronics. However, the graphene intrinsic energy bandgap absence hinders GNR-based devices and circuits implementation. As a result, en route to graphene-based logic circuits, finding a way to open a sizable energy bandgap, externally control GNR’s conduction, and construct reliable high-performance graphene-based gates are the main desideratum. To this end, first, we propose a GNR-based structure (building block) by extending it with additional top gates and back gate while considering five GNR shapes with zigzag edges in order to open a sizeable bandgap, and further investigate GNR geometry and contact topology influence on its conductance and current characteristics. Second, we present a methodology of encoding the desired Boolean logic transfer function into the GNR electrical characteristics, i.e., conduction maps, and then evaluate the effect of VDD variation on GNR conductance. Moreover, we find a proper external electric mean (e.g., top gates and back gates) to control the GNR behavior. Third, we develop a parameterized Verilog-A SPICEcompatible GNR model based on Non-Equilibrium Green’s Function (NEGF)-Landauer formalism that builds upon an accurate physics formalization, which enables to symbiotically exploit accurate physics results from Matlab Simulink and optimized SPICE circuit solvers (e.g., Spectre, HSPICE). Subsequently, we construct graphene-based Boolean gates by means of two complementary GNRs, and design a GNR-based 1-bit Full Adder and a SRAM cell. Finally, we extend the NEGF-Landauer simulation framework with the self-consistent Born approximation while taking into account the temperature-induced phenomena in GNR electron transport, i.e., electron-phonon interactions for both optical and acoustic phonons, and further explore the graphene-based gates performance robustness under temperature variations.@en

Hysteretic behavior has been experimentally observed in graphene-based structures and has a major influence on graphene surface potential and gate field modulation ability. Thus, a graphene electronic transport modelling methodology, which incorporates hysteresis effects is crucial in order to properly assess gated-controlled graphene structures response and performance. To this end, we propose an atomistic-level electronic transport model, which is non restricted to rectangular graphene geometries and captures hysteretic effects caused by near-interfacial traps, provided that interface traps trapping/detrapping time constant and density are known. We apply the model on a rectangular graphene shape and validate our results against experimentally measured drain current vs. top gate voltage hysteresis curves. Moreover, to demonstrate model's versatility we consider two non-rectangular Graphene NanoRibbons (GNRs) and investigate their hysteresis behaviour. Our experiments indicate good agreement between simulated and measured results, which qualifies the model appropriate for traps-aware exploration of the conduction behaviour of graphene-based devices and circuits.

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Graphene, due to its wealth of remarkable electronic properties, emerged as a potent post-Si forerunner for nanoelectronics. To enable the exploration and evaluation of potential graphene-based circuit designs, we propose a fast and accurate Verilog-A physics-based model of a 5-terminal trapezoidal Quantum Point Contact (QPC) Graphene Nano-Ribbon (GNR) structure with parametrizable geometry. The proposed model computes the GNR conductance based on the Non-Equilibrium Green's Function (NEGF)-Landauer formalism, via a Simulink model called from within the Verilog-A model. Furthermore, model accuracy and versatility are demonstrated by means of Simulink assisted Cadence Spectre simulation of a simple test case GNR-based circuit and a GNR-based 2-input XOR gate.

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As CMOS feature size is reaching atomic dimensions, unjustifiable static power, reliability, and economic implications are exacerbating, thereby prompting for conducting research on new materials, devices, and/or computation paradigms. Within this context, graphene nanoribbons (GNRs), owing to graphene's excellent electronic properties, may serve as basic structures for carbon-based nanoelectronics. In this paper, we make use of the fact that GNR behavior can be modulated via top/back gate contacts to mimic a given functionality and combine complementary GNRs for constructing Boolean gates. We first introduce a generic gate structure composed of a pull-up GNR performing the gate Boolean function and a pull-down GNR performing its complement. Then, we seek GNR dimensions and gate topologies required for the design of 1-, 2-, and 3-input graphene-based Boolean gates, validate the proposed gates by means of SPICE simulation, which makes use of a non-equilibrium Green's function Landauer formalism based Verilog-A model to calculate GNR conductance, and evaluate their performance with respect to propagation delay, power consumption, and active area footprint. Simulation results indicate that, when compared with 7 nm FinFET CMOS counterparts, the proposed gates exhibit 6 × to 2 orders of magnitude smaller propagation delay, 2 to 3 orders of magnitude lower power consumption, and necessitate 2 orders of magnitude smaller active area footprint. We further present full adder (FA) and SRAM cell GNR designs, as they are currently fundamental components for the construction of any computation system. For an effective FA implementation, we introduce a 3-input MAJORITY gate, which apart of being able to directly compute FA's carry-out is an essential element in the implementation of error correcting codes codecs, which outperforms the CMOS equivalent carry-out calculation circuit by 2 and 3 orders of magnitude in terms of delay and power consumption, respectively, while requiring 2 orders of magnitude less area. The proposed FA exhibits 6.2 × smaller delay, 3 orders of magnitude less power consumption, while requiring 2 orders of magnitude less area, when compared with the 7 nm FinFET CMOS counterpart. However, because of the effective carry-out circuitry, a GNR-based n-bit ripple carry adder, whose performance is linear in the carry-out path, will be 108 × faster than an equivalent CMOS implementation. The GNR-based SRAM cell provides a slightly better resilience to dc-noise characteristics, while performance-wise has a 3.6 × smaller delay, consumes 2 orders of magnitude less power, and requires 1 order of magnitude less area than the CMOS equivalent. These results clearly indicate that the proposed GNR-based approach is opening a promising avenue toward future competitive carbon-based nanoelectronics.

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In this paper, we augment a trapezoidal Quantum Point Contact topology with top gates to form a butterfly Graphene Nanoribbon (GNR) structure and demonstrate that by adjusting its topology, its conductance map can mirror basic Boolean functions, thus one can use such structures instead of transistors to build carbon-based gates and circuits. We first identify by means of Design Space Exploration specific GNR topologies for 2- and 3-input {AND, NAND, OR, NOR, XOR, XNOR} and demonstrate by means of the Non-Equilibrium Green Function - Landauer based simulations that butterfly GNR-based structures operating at V _DD = 0.2 V outperform 7 nm @ V _DD = 0.7 V CMOS counterparts by 2 to 3, 1 to 2, and 3 to 4, orders of magnitude in terms of delay, power consumption, and power-delay product, respectively, while requiring 2 orders of magnitude less active area. Subsequently, we investigate the effect of V _DD variations and the V _DD value lower bound. We demonstrate that the NOR butterfly GNR structures are quite robust as their conductance and delay are changing by no more than 2% and 6%, respectively, and that AND and NOR GNR geometries can operate even at 10 mV. Finally, we consider the aspects related to the practical realization of the proposed structures and conclude that even if there are still hurdles on the road ahead the latest graphene fabrication technology developments, e.g., surface-assisted synthesis, our proposal opens an alternative towards effective carbon-based nanoelectronic circuits and applications.

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With CMOS feature size heading towards atomic dimensions, unjustifiable static power, reliability, and economic implications are exacerbating, prompting for research on new materials, devices, and/or computation paradigms. Within this context, Graphene Nanorib-bons (GNRs), owing to graphene’s excellent electronic properties, may serve as basic blocks for carbon-based nanoelectronics. In this paper we build upon the fact that GNR behaviour can be controlled according to some desired functionality via top/back gate contacts and propose to combine GNRs with complementary functionalities to construct Boolean gates. To this end, we introduce a generic GNR-based Boolean gate structure, composed of two GNRs, i.e., a pull-up GNR performing the gate Boolean function and a pull-down GNR performing the inverted Boolean function. Subsequently, by properly adjusting GNRs’ dimensions and topology, we design 2-input AND, NAND, and XOR graphene-based Boolean gates, as well as 1-input gates, i.e., inverter and buffer. Our SPICE simulations indicate that the proposed gates exhibit a smaller propagation delay, from 23% for the XOR gate to 6× for the AND gate, and 2 orders of magnitude smaller power consumption, when compared with 7 nm CMOS based counterparts, while requiring a 1 to 2 orders of magnitude smaller active area footprint. These results clearly indicate that GNR-based gates have great potential as basic building blocks for future beyond CMOS energy effective nanoscale circuits.

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As CMOS feature size approaches atomic dimensions, unjustifiable static power, reliability, and economic implications are exacerbating, prompting for research and development on new materials, devices, and/or computation paradigms. Within this context, Graphene Nanoribbons (GNRs), owing to graphene's excellent electronic properties, may serve as basic blocks for carbon-based nanoelectronics. En route to GNR-based logic circuits, the ability to externally control GNRs' conduction to map a basic Boolean logic function onto its electrical characteristics, with a high 1ON/1OFF ratio, and uncompromised carriers mobility, is the main desideratum. To this end, we augment a trapezoidal GNR with top gates as controlling inputs, and investigate its conductance G by means of the NEGF-Landauer formalism. Further, we demonstrate that the butterfly GNR can exhibit conduction maps (high G for logic “1”, and low G for logic “0”) capturing the functionality of 2 and 3-input Boolean gates, by properly adjusting its topology and dimensions. Our simulations prove butterfly GNR structure capability to capture basic Boolean logic transfer functions, while potentially providing 30× and 3000× smaller propagation delay and gate active area, respectively, when compared to 15 nm CMOS equivalent counterparts, establishing GNR's potential as basic building block for future graphene-based logic gates.@en