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.     

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.     

Effects of phonon scattering on electron transport in double-gate MOSFETs

Current-voltage characteristics of double-gate silicon-on-insulator MOSFETs have been calculated within non-equilibrium Green’s function formalism including g-type, f-type, and acoustic phonon scatterings. Contribution of f-type phonons to the current reduction is smaller than that of g-type phonons. Effects of the phonon scatterings on the drain current at off-states are weaker than those at on-states. At off-states, phonon-assisted tunneling partially compensates a current loss due to scattering for shorter gate lengths, while polaronic current component appears for longer gate lengths.     

Scaling dependence of electron transport in nano-scale Schottky barrier MOSFETs

The scaling dependence of electron transport in the double-gated Schottky barrier MOSFET (DG-SBT) below 10 nm is investigated in the framework of quantum transport theory, using non-equilibrium Green’s function method. Simulation results show that the current-voltage characteristics in ultra-small DG-SBT are characterized by both resonant and direct tunneling effects. The electron potential in the 10-nm-scale DG-SBT surrounded by Schottky barriers acts as a resonant cavity and produce a negative differential resistance due to resonant tunneling effect. While, further scaling shallows the depth of the cavity and makes it difficult to form resonance levels. Hence, at the scaling limit, direct tunneling currents simply dominate the current-voltage characteristics of DG-SBT.     

Study of performance and leakage currents in nanometer-scale bulk,SOI and double-gate MOSFETs

We consider the performance and leakage issues in 80-to-20 nm Ge, Si, and InGaAs bulk, SOI and Double-gate (DG) devices. The performance is studied with DAMOCLES, band-to-band tunneling processes with a nonlocal band-to-band model as a post-processor in DAMOCLES, and gate tunneling by a Green’s function method accounting also for image force effects, so far ignored at ‘internal’ interfaces. The performance is affected by the bottleneck effect in III–Vs, especially for thin channels, but InGaAs and Ge still may be optimized to outperform Si. Zener leakage is high for Ge and tolerable for InGaAs. The effect of image forces led to an order of magnitude increase in gate tunneling currents.     

A study of threshold voltage fluctuations of nanoscale double gate metal-oxide-semiconductor field effect transistors using quantum correction simulation

In this paper, we computationally investigate fluctuations of the threshold voltage introduced by random dopants in nanoscale double gate metal-oxide-semiconductor field effect transistors (DG MOSFETs). To calculate variance of the threshold voltage of nanoscale DG MOSFETs, a quantum correction model is numerically solved with the perturbation and the monotone iterative techniques. Fluctuations of the threshold voltage resulting from the random dopant, the gate oxide thickness, the channel film thickness, the gate channel length, and the device width are calculated. Quantum mechanical and classical results have similar prediction on fluctuations of the threshold voltage with respect to different designing parameters including dimension of device geometry as well as the channel doping. Fluctuation increases when the channel doping, the channel film thickness, and/or the gate oxide thickness increase. On the other hand, it decreases when the channel length and/or the device width increase. Calculations of the quantum correction model are quantitatively higher than that of the classical estimation according to different quantum confinement effects in nanoscale DG MOSFETs. Due to good channel controllability, DG MOSFETs possess relatively lower fluctuation, compared with the fluctuation of single gate MOSFETs (less than a half of the fluctuation[-11pc] of SG MOSFETs). To reduce fluctuations of the threshold voltage, epitaxial layers on both sides of channel with different epitaxial doping are introduced. For a certain thickness of epitaxial layers, the fluctuation of the threshold voltage decreases when epitaxial doping decreases. In contrast to conventional quantum Monte Carlo approach and small signal analysis of the Schrödinger-Poisson equations, this computationally efficient approach shows acceptable accuracy and is ready for industrial technology computer-aided design application.     

Self-consistent quantum transport theory: Applications and assessment of approximate models

We have implemented a fully self-consistent non-equilibrium Green’s function approach for vertical quantum transport in open quantum devices with contacts and study theoretically quantum well heterostructures, resonant tunneling diodes and quantum cascade laser structures in this formalism. We systematically investigate the role and consequences of several widely used approximations such as decoupling the equations for the scattering states and their occupation, neglect of inelastic scattering, and neglect of nonlocal scattering self-energies.     

Wigner Function-Based Simulation of Quantum Transport in Scaled DG-MOSFETs Using a Monte Carlo Method

Source-to-drain tunneling in deca-nanometer double-gate MOSFETs is studied using a Monte Carlo solver for the Wigner transport equation. This approach allows the effect of scattering to be included. The subband structure is calculated by means of post-processing results from the device simulator Minimos-NT, and the contribution of the lowest subband is determined by the quantum transport simulation. By separating the potential profile into a smooth classical component and a rapidly varying quantum component the numerical stability of the Monte Carlo method is improved. The results clearly show an increasing tunneling component of the drain current with decreasing gate length. For longer gate lengths the semi-classical result is approached.     

Modeling gate-all-around Si/SiGe MOSFETs and circuits for digital applications

Apart from excellent electrostatic capability and immunity to short-channel effects, the performance of gate-all-around (GAA) nanowire (NW) metal-oxide-semiconductor field-effect transistors (MOSFETs) can be further enhanced by incorporating strain. Owing to the technological importance of strained GAA (S-GAA) NW MOSFETs in modern electronics, we have proposed an analytical model of the threshold voltage and drain current for S-GAA NW MOSFETs taking into account the appreciable contributions of source (S) and drain (D) series resistances in the nanometer regime, along with quantum mechanical effect. We have focused on the elliptical cross section of the device as is necessary to consider the fabrication imperfections which give rise to such cross section, rather than an ideal circular structure. Incorporating S/D series resistance in the model of drain current demands for algorithms based on multi-iterative technique, which has been proposed in this paper for analyzing the impact of strain, NW width, aspect ratio and so on, on the performance of S-GAA NW devices with emphasis on CMOS digital circuits. Based on our proposed methodology, we have also investigated the scope of using high-k dielectric materials and metal gate in S-GAA NW structures.     

Tunneling CNTFETs

Based on the non-equilibrium Green’s function formalism we numerically studied gate-controlled tunneling carbon nanotube field-effect transistors. The effect of doping concentration on the performance of the device has been investigated. We show that an asymmetric doping profile can improve the I _on/I _off ratio of the device improves.     

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.

     

Mobility Variations in Ultra Small Devices due to Random Discrete Dopants

Scaling of conventional MOSFETs to channel lengths of 20 nm and below will require channel doping in the range of 10¹⁹ cm^?3. At such doping concentrations ionised impurity scattering may start to dominate over interface roughness scattering within the channel. Additionally, discrete doping variations, both in number and position, will become increasingly important in such small devices resulting in mobility variations from device to device. Such mobility variations will be in addition to the random dopant induced fluctuations due to the electrostatics. Here we report results from 3-D Ensemble Monte Carlo simulations that include ab-initio ionised impurity scattering, and has been developed to investigate mobility variations in small volumes comparable to the channel region of nano-scale MOSFETs.     

Analysis of nonequilibrium phenomena on electric characteristics of advanced MOSFETs by using a quantum energy transport model

In this paper, we have investigated nonequilibrium effects for advanced MOSFETs by using a device simulator with quantum energy transport (QET) model. The QET model allows to simulate nonequilibrium carrier transport as well as quantum confinement. The QET model includes the mobility model as a function of carrier temperature in order to consider the nonlocal effects. We have simulated advanced MOSFETs down to 20 nm gate length using the QET model. The QET model is compared with the quantum drift diffusion (QDD) model which includes a mobility model with local assumptions. It is found that the nonlocal mobility model is needed to simulate the advanced MOSFETs with less than 40 nm.     

Comparison of Double-Gate MOSFETs and FinFETs with Monte Carlo Simulation

A full-band Monte Carlo simulator has been used to analyze and compare the performance of n-channel double-gate MOSFETs and FinFETs. Size quantization effects were accounted for by using a quantum correction based on Schrödinger equation. FinFETs are a variation of typical double-gate devices with the gate surrounding the channel on three sides. From our simulations, we observed that the quantization effects in double-gate devices are less significant as compared to bulk MOSFETs. The total sheet charge density drops only slightly as the depletion of charge at the interface is counterbalanced by the increased volume inversion effect. We also observed an appreciable drop in average velocity distribution when quantum corrections were applied. For FinFETs, the fin extension lengths on either side of the gate affect the device performance significantly. These underlap regions have low carrier concentration and behave as large resistors. The current drops non-linearly with increasing fin extension lengths.     

An atomistic quantum transport solver with dephasing for field-effect transistors

Extended Hückel theory (EHT) along with NEGF (Non-equilibrium Green’s function formalism) has been used for modeling coherent transport through molecules. Incorporating dephasing has been proposed to theoretically reproduce experimental characteristics for such devices. These elastic and inelastic dephasing effects are expected to be important in quantum devices with the feature size around 10 nm, and hence an efficient and versatile solver is needed. This model should have flexibility to be applied to a wide range of nano-scale devices, along with 3D electrostatics, for arbitrary shaped contacts and surface roughness. We report one such EHT-NEGF solver with dephasing by self-consistent Born approximation (SCBA). 3D electrostatics is included using a finite-element scheme. The model is applied to a single wall carbon nanotube (CNT) cross-bar structure with a C₆₀ molecule as the active channel. Without dephasing, a negative differential resistance (NDR) peak appears when the C₆₀ lowest unoccupied molecular orbital level crosses a van Hove singularity in the 1D density of states of the metallic CNTs acting as contacts. This NDR diminishes with increasing dephasing in the channel as expected.     

Effective Mass Approach for n-MOSFETs on Arbitrarily Oriented Wafers

The general theory for quantum simulation of cubic semiconductor n-MOSFETs is presented within the effective mass equation approach. The full three-dimensional transport problem is described in terms of coupled transverse subband modes which arise due to quantum confinement along the body thickness direction. Couplings among the subbands are generated for two reasons: due to spatial variations of the confinement potential along the transport direction, and due to non-alignment of the device coordinate system with the principal axes of the constant energy conduction band ellipsoids. The problem simplifies considerably if the electrostatic potential is separable along transport and confinement directions, and further if the potential variations along the transport direction are slow enough to prevent dipolar coupling (Zener tunneling) between subbands. In this limit, the transport problem can be solved by employing two unitary operators to transform an arbitrarily oriented constant energy ellipsoid into a regular ellipsoid with principal axes along the transport, width and confinement directions of the device.     

Phonon exacerbated quantum interference effects in III-V nanowire transistors

In recent years, a great deal of attention has been focused on the development of quantum wire transistors as a means of extending Moore’s Law. Here we present, results of fully three-dimensional, self-consistent quantum mechanical device simulations of InAs tri-gate nanowire transistor (NWT). The effects of inelastic scattering have been included as real-space self-energy terms. We find that the position of dopant atoms in these devices can lead a reduction in the amount of scattering the carriers experience. We find that the combination of deeply buried dopant atoms and the high energy localization of polar optical phonon processes allow devices to recover their ballistic behavior even in the presence of strong inelastic phonon processes. However, we find that dopant atoms close to the source-channel interface cause severe quantum interference effects leading to significant performance reduction.     

Non-equilibrium Green’s function (NEGF) simulation of metallic carbon nanotubes including vacancy defects

The electronic behavior of metallic carbon nanotubes under the influence of externally applied electric fields is investigated using the Non-Equilibrium Green’s function method self consistently coupled with three-dimensional (3D) electrostatics. A nearest neighbor tight binding model based on a single pz orbital for constructing the device Hamiltonian is used. The 3D Poisson equation is solved using the Finite Element Method. Carbon nanotubes exhibit a very weak metallic behavior, and external electric fields can alter the electrostatic potential of the tubes significantly. A single vacancy defect in the channel of a metallic carbon nanotube can decrease its conductance by a factor of two. More than one vacancy can further decrease the conductance.     

Impact of series resistance on Si nanowire MOSFET performance

In gate all around (GAA) nanowire (NW) MOSFETs large series resistance due to narrow width extension regions is an important issue, playing a critical role in determining device and circuit performance. In this paper, we present a series resistance model and analyze its dependence on geometry/process parameters. The series resistance is modelled by dividing it into five resistance components namely spreading resistance, extension resistance, interface resistance, deep source-drain resistance and contact resistance. The model is validated using 3-D device simulations of 22 nm GAA devices with Source/Drain extension (SDE) length of 15 nm to 35 nm, diameter of 8 nm to 16 nm and oxide thickness of 10 A to 40 A for both n-FET and p-FET. It is found that the spreading resistance due to lateral doping gradient contributes significantly to the total series resistance. Further, the dependence of NW device performance on series resistance is quantitatively investigated with change of diameter, SDE length and Source/Drain (S/D) implantation dose. Results show a strong NW device performance dependence on S/D doping profile and extension length defining a design trade-off between Short Channel Effects (SCEs) and series resistance. It is seen that the increase in series resistance due to increase of extension length or decrease of implantation dose beyond a certain limit reduces the device drive current significantly with nearly constant OFF-state leakage current. Hence, optimization of extension length and S/D implant dose is an important device design issue for sub 22 nm technology nodes.