An extended Hückel theory based atomistic model for graphene nanoelectronics

An atomistic model based on the spin-restricted extended Hückel theory (EHT) is presented for simulating electronic structure and I–V characteristics of graphene devices. The model is applied to zigzag and armchair graphene nano-ribbons (GNR) with and without hydrogen passivation, as well as for bilayer graphene. Further calculations are presented for electric fields in the nano-ribbon width direction and in the bilayer direction to show electronic structure modification. Finally, the EHT Hamiltonian and NEGF (Nonequilibrium Green’s function) formalism are used for a paramagnetic zigzag GNR to show 2e ²/h quantum conductance.     

Computational study of double-gate graphene nano-ribbon transistors

The ballistic performance of graphene nanoribbon (GNR) MOSFETs with different width of armchair GNRs is examined using a real-space quantum simulator based on the Non-equilibrium Green’s Function (NEGF) approach, self-consistently coupled to a 3D Poisson’s equation for electrostatics. GNR MOSFETs show promising device performance, in terms of low subthreshold swing and small drain-induced-barrier-lowing due to their excellent electrostatics and gate control (single monolayer). However, the quantum tunneling effects play an import role in the GNR device performance degradation for wider width GNR MOSFETs due to their reduced bandgap. At 2.2 nm width, the OFF current performance is completely dominated by tunneling currents, making the OFF-state of the device difficult to control.     

First-principles versus semi-empirical modeling of global and local electronic transport properties of graphene nanopore-based sensors for DNA sequencing

Using first-principles quantum transport simulations, based on the nonequilibrium Green function formalism combined with density functional theory (NEGF+DFT), we examine changes in the total and local electronic currents within the plane of graphene nanoribbon with zigzag edges (ZGNR) hosting a nanopore which are induced by inserting a DNA nucleobase into the pore. We find a sizable change of the zero-bias conductance of two-terminal ZGNR + nanopore device after the nucleobase is placed into the most probable position (according to molecular dynamics trajectories) inside the nanopore of a small diameter \(D=1.2\) nm. Although such effect decreases as the nanopore size is increased to \(D=1.7\) nm, the contrast between currents in ZGNR + nanopore and ZGNR + nanopore + nucleobase systems can be enhanced by applying a small bias voltage \(V_b \lesssim 0.1\) V. This is explained microscopically as being due to DNA nucleobase-induced modification of spatial profile of local current density around the edges of ZGNR. We repeat the same analysis using NEGF combined with self-consistent charge density functional tight-binding (NEGF+SCC-DFTB) or self-consistent extended Hückel (NEGF+SC-EH) semi-empirical methodologies. The large discrepancy we find between the results obtained from NEGF+DFT vs. those obtained from NEGF+SCC-DFTB or NEGF+SC-EH approaches could be of great importance when selecting proper computational algorithms for in silico design of optimal nanoelectronic sensors for rapid DNA sequencing.     

Carrier scattering and impact ionization in bilayer graphene

Transport properties of carriers in bilayer graphene (BLG) were studied. Several analytical models were developed for drift velocity, scattering rate and ionization coefficient of BLG for the first time. Then, the joint effect of temperature and potential difference of layers were addressed on the modeled parameters. The accuracy of the proposed models for drift velocity and scattering rate was verified by the simulation results of published works. In addition, the analytical results of ionization coefficient of BLG were compared with those of silicon.     

Reduced thickness interconnect model using GNR to avoid crosstalk effects

In this research article, we propose a reduced thickness multilayer graphene nanoribbon (MLGNR) interconnect model to reduce crosstalk effects. The \(10\times \) higher current capability of MLGNR than copper (Cu) makes it an attractive choice to alleviate electromigration problem. The lower resistance of MLGNR is also an important factor to reduce interconnect delay. We have shown that a reduced thickness interconnect structure using MLGNR can reduce the crosstalk effects significantly without compromising the other benefits. The analysis is performed for side-contact GNR (SC-GNR) and top-contact GNR (TC-GNR) structure. Our analysis shows that the reduced thickness side-contact GNR interconnects can achieve \(\sim \)1.02 to \(2.36\times \) reduction in crosstalk induced delay as compared with Cu. Our analysis also shows that the top-contact GNR structure with few layers can also achieve \(\sim \)1.58 to \(1.95\times \) reduction in crosstalk induced delay as compared with Cu. We have performed crosstalk noise and overshoot/undershoot analysis using our proposed model. It is shown that the near-end and far-end crosstalk noise and overshoot/undershoot for SC-GNR and TC-GNR structures are significantly smaller than that of Cu.     

Atomistic non-equilibrium Green’s function simulations of Graphene nano-ribbons in the quantum hall regime

The quantum Hall effect in Graphene nano-ribbons (GNR) is investigated with the non-equilibrium Green’s function (NEGF) based quantum transport model in the ballistic regime. The nearest neighbor tight-binding model based on p _z orbital constructs the device Hamiltonian. GNRs of different edge geometries (Zigzag and Armchair) are considered. The magnetic field is included in both the channels and contact through Peierls substitution. Efficient algorithms for calculating the surface Green function are used to reduce computation time to enable simulating realistically large dimensions comparable to those used in experiments. Hall resistance calculations exactly reproduce the quantum Hall plateaus observed in the experiments. Use of large dimensions in the simulation is crucial in order to capture the quantum Hall effect within experimentally magnetic fields relevant 10–20 T. R. Golizadeh-Mojarad and A.N.M. Zainuddin contributed equally to this work.     

Negative differential resistance in graphene-nanoribbon–carbon-nanotube crossbars: a first-principles multiterminal quantum transport study

We simulate quantum transport between a graphene nanoribbon (GNR) and a single-walled carbon nanotube (CNT) where electrons traverse vacuum gap between them. The GNR covers CNT over a nanoscale region while their relative rotation is 90^°, thereby forming a four-terminal crossbar where the bias voltage is applied between CNT and GNR terminals. The CNT and GNR are chosen as either semiconducting (s) or metallic (m) based on whether their two-terminal conductance exhibits a gap as a function of the Fermi energy or not, respectively. We find nonlinear current-voltage (I–V) characteristics in all three investigated devices—mGNR-sCNT, sGNR-sCNT and mGNR-mCNT crossbars—which are asymmetric with respect to changing the bias voltage from positive to negative. Furthermore, the I–V characteristics of mGNR-sCNT crossbar exhibits negative differential resistance (NDR) with low onset voltage V _NDR?0.25 V and peak-to-valley current ratio ?2.0. The overlap region of the crossbars contains only ?460 carbon and hydrogen atoms which paves the way for nanoelectronic devices ultrascaled well below the smallest horizontal length scale envisioned by the international technology roadmap for semiconductors. Our analysis is based on the nonequilibrium Green function formalism combined with density functional theory (NEGF-DFT), where we also provide an overview of recent extensions of NEGF-DFT framework (originally developed for two-terminal devices) to multiterminal devices.     

The influence of the zigzag and armchair leads on quantum transport through the graphene based quantum rings

The conductivity of a graphene ring with two semi-infinite, armchair and zigzag leads has been investigated. We have performed numerical calculations based on the nearest neighbor tight-binding Hamiltonian and Dirac point approximation. A Non-Equilibrium Green’s Function (NEGF) approach has been employed to calculate the electric current under an applied bias voltage, in this two terminal mesoscopic system. We have studied the effect of the external magnetic field on transport characteristics of this graphene-based quantum ring. Coherent transport features of the system have been studied. It was shown that there is significant distinction between the I–V characteristics (and also the Aharonov-Bohm effect) of the graphene rings depending on the edge structure of the leads.     

Random phonon model of dissipative electron transport in nanowire MOSFETs

A method for quantum transport simulations of nanowire (NW) field-effect transistors (FETs) with inelastic electron–phonon scattering processes incorporated is presented in this paper. The microscopic device Hamiltonian with realistic phonon spectrum and electron–phonon interaction is transformed into an equivalent low-dimensional transport model with discrete random phonon modes. The electron–phonon coupling constants are optimized in order to reproduce the inelastic scattering effects. Small size of the model and special form of the inelastic self-energy terms in the NEGF formalism make it a powerful tool to study dissipative transport in realistic NW transistors. The utility of the method is demonstrated by computing inelastic transport characteristics in Si NW FETs.     

Benchmarking of GFET devices for amplifier application using multiscale simulation approach

Starting from advanced NEGF physical simulation of a 100 nm gate length Graphene FET, we attempt to use these results as a starting point to evaluate this technology for microwave circuit benchmarking. Using an improved compact model carefully adjusted on NEGF simulation data, in both DC and AC regime, we use this model to design a mmW amplifier at 140 GHz. In the first part of the design procedure, we use the ADS compact model for coplanar waveguide of passive elements. The complete design is then verified using electromagnetic FEM simulation which gives more reliable results at very high frequencies for passive elements and interconnections. This analysis has shown that unlike first GFET generations, impedance matching problems may be naturally solved with transistor performance improvements. Finally, the GFET device and circuit is compared to HEMT technologies and shows promising performances.     

Gate-modulated graphene quantum point contact device for DNA sensing

In this paper, we present a computational model to describe the electrical response of a constricted graphene nanoribbon (GNR) to biomolecules translocating through a nanopore. For this purpose, we use a self-consistent 3D Poisson equation solver coupled with an accurate three-orbital tight-binding model to assess the ability for a gate electrode to modulate both the carrier concentration as well as the conductance in the GNR. We also investigate the role of electrolytic screening on the sensitivity of the conductance to external charges and find that the gate electrode can either suppress or enhance the screening of biomolecular charges in the nanopore depending on the value of its potential. Translocating a double-stranded DNA molecule along the pore axis imparted a large change in the conductance at particular gate voltages, suggesting that such a device can be used to sense translocating biomolecules and can be actively tuned to maximize its sensitivity.     

Performance analysis of multilayer graphene nanoribbon (MLGNR) interconnects

This paper addresses the impact of interlayer resistance due to c-axis resistivity and contact resistance on performance in terms of delay, power dissipation and power delay product (PDP) of Multi-layer graphene nanoribbon (MLGNR) interconnect. The impact of model parameter i.e. Fermi energy \((\hbox {E}_\mathrm{F})\) on performance of MLGNR is also discussed. A similar analysis is performed for copper interconnect and results are compared with MLGNR at 22 nm technology node. The impact of interlayer resistance on equivalent resistance of MLGNR is critically analyzed. Inductive and capacitive coupling between the adjacent layers are included in this analysis. It is found that the MLGNR with interlayer resistance, compared to copper, gives better performance in terms of delay, power dissipation and PDP with higher value of Fermi energy for semi global to global lengths of interconnect (300–1000 \(\upmu \hbox {m})\) whereas reverse is true for local lengths 100–200 \((\upmu \hbox {m})\). In addition, performance gap between MLGNR with and without interlayer resistance decreases with increase in Fermi energy.     

NEGF simulation of the RTD bistability

The simulation of I-V characteristics of Al_0.3Ga_0.7As-GaAs and AlAs-GaAs resonant tunneling diodes (RTD) is presented. The nonequilibrium Green function (NEGF) based 1D quantum transport simulator Wingreen is used in our case. The plateau region on the IV characteristics usually present only by the Wigner function equation (WFE) based simulation appeared now by the NEGF simulation of our AlAs-GaAs RTD and its shape is comparable with our experimental measurements. Analysis of our results from point of view of the scattering and geometrical parameters of the RTD structure is presented.     

New nanoscale band-to-band tunneling junctionless GNRFETs: potential high-performance devices for the ultrascaled regime

High-performance sub-10-nm field-effect transistors (FETs) are considered to be a prerequisite for the development of nanoelectronics and modern integrated circuits. Herein, new band-to-band tunneling (BTBT) junctionless (JL) graphene nanoribbon field-effect transistors (GNRFETs) endowed with sub-10-nm gate length are proposed using a quantum transport simulation. The nonequilibrium Green’s function (NEGF) formalism is used in quantum simulations considering the self-consistent electrostatics and the ballistic transport limit. The computational assessment includes the I_DS–V_GS transfer characteristics, the potential and electron density distributions, the current spectrum, the ambipolar behavior, the leakage current, the subthreshold swing, the current ratio, and the scaling capability. It is found that BTBT JL-GNRFETs can provide subthermionic subthreshold swings and moderate current ratios for sub-10-nm gate lengths. Moreover, a new doping profile, based on the use of lateral lightly n-type-doped pockets, is adopted to boost their performance. The numerical results reveal that BTBT JL-GNRFETs with the proposed doping profile can exhibit improved performance in comparison with uniformly doped BTBT JL-GNRFETs. In addition, the role of the length and n-type doping concentration of the pockets in boosting the device performance is also studied and analyzed while considering the scaling capability of such devices, revealing that low doping concentrations and long pocket lengths are useful for performance improvement. The merits of the BTBT JL-GNRFETs based on the proposed nonuniform doping profile, namely sub-10-nm scale, steep subthermionic subthreshold swing, low leakage current, and improved current ratio and ambipolar behavior, make them promising nanodevices for use in modern nanoelectronics and high-performance integrated circuits.

     

Modeling and simulation of a graphene-based three-terminal junction rectifier

In this paper, we demonstrate the simulation of a graphene-based three-terminal junction using semi-classical drift–diffusion modeling. The DC and AC simulations are carried out separately and characterized at different temperatures and frequencies. The simulated structure is compared with previous results, and the noise spectrum is simulated to explore its behavior using graphene as an active region. At room temperature, the three-terminal junction demonstrates responsivity of up to 594.56 mV/mW, with mobility of 4000 \(\hbox {cm}^{2}/\hbox {Vs}\) and a push–pull input signal of 100 mV at 1 KHz. The corresponding noise-equivalent power is as low as 19.4 \(\hbox {pW}/\hbox {Hz}^{1/2}\). The simulated structure is able to obtain much higher responsivity and lower noise equivalent power by taking advantage of the higher mobility of the graphene. The voltage noise spectrum of the device is analyzed using equivalent two-dimensional geometry. At lower frequencies, flicker noise is found to dominate, due to the variation in charge carrier density.     

First principles modeling of disorder scattering in graphene

It is important to investigate impurity scattering phenomena when modeling graphene nanoscale devices, as impurities are invariably present in any realistic system and can significantly influence graphene carrier transport. We present a short review of quantum transport where density functional theory (DFT) is carried out within the nonequilibrium Green’s function formalism (NEGF), focusing on a recent extension of this framework in the form of nonequilibrium vertex correction (NVC) that captures random graphene impurity scattering in a systematic fashion. Our results show that disorder effects significantly alters the electronic and transport properties of graphene devices. We argue that disorder effects should not be ignored if one were to model graphene nanoscale devices in realistic situations, including arriving at fundamental electronic properties such as Ohm’s law.     

Effect of temperature, electric and magnetic field on spin relaxation in bilayer graphene

In spintronics, spin degree of freedom of an electron is used to store and process information and thus can provide numerous advantages over conventional electronics by providing new functionalities. In this paper, we employ the semiclassical Monte Carlo approach to study the spin polarized transport in bilayer graphene. Due to lower spin orbit interaction (SOI) and higher spin relaxation lengths, graphene is considered as suitable material for spintronics application. Spin relaxation in bilayer graphene is caused by D’yakonov–Perel (DP) relaxation and Elliott–Yafet (EY) relaxation. The effect of temperature, magnetic field and driving electric field on spin relaxation length is studied. We have considered injection polarization along z-direction which is perpendicular to the plane of graphene and the magnitude of ensemble averaged spin variation is studied along the x-direction which is the transport direction.     

Double gate graphene nanoribbon field effect transistor with electrically induced junctions for source and drain regions

In this paper a novel graphene nanoribbon transistor with electrically induced junction for source and drain regions is proposed. An auxiliary junction is used to form electrically induced source and drain regions beside the main regions. Two parts of same metal are implemented at both sides of the main gate region. These metals which act as side gates are connected to each other to form auxiliary junction. A fixed voltage is applied on this junction during voltage variation on other junctions. Side metals have smaller workfunction than the middle one. Tight-binding Hamiltonian and nonequilibrium Green’s function formalism are used to perform atomic scale electronic transport simulation. Due to the difference in metals workfunction, additional gates create two steps in potential profile. These steps increase horizontal distance between conduction and valance bands at gate to drain/source junction and consequently lower band to band tunneling probability. Current ratio and subthreshold swing improved at different channel lengths. Furthermore, device reliability is improved where electric field at drain side of the channel is reduced. This means improvement in leakage current, hot electron effect behavior and breakdown voltage. Application to multi-input logic gates shows higher speed and smaller power delay product in comparison with conventional platform.