Nonequilibrium Green Function Formalism Research Articles

Simulating graphene-based single-electron transistor: incoherent current effects due to the presence of electron–electron interaction

Carbon-based nanostructures have unparalleled electronic properties. At the same time, using an allotrope of carbon as the contacts can yield better device control and reproducibility. In this work, we simulate a single-electron transistor composed of a segment of a graphene nanoribbon coupled to carbon nanotubes electrodes. Using the non-equilibrium Green's function formalism we atomistically describe the electronic transport properties of the system including electron-electron interactions. Using this methodology we are able to recover experimentally observed phenomena, such as the Coulomb blockade, as well as the corresponding Coulomb diamonds. Furthermore, we separate the different contributions to transport and show that incoherent effects due to the interaction play a crucial role in the transport properties depending on the region of the stability diagram being considered.

Graphene nanoribbon resonant tunneling diode with dual connection between contacts

In this paper, we numerically study the transport properties of a resonant tunneling diode (RTD) based on graphene nanoribbon (GNR) with an H-type antidote between the contacts. The structure may also be thought of as having two parallel (W-shape) parts connecting the contacts, each having a wider channel region sandwiched between two narrower barrier regions. The energy at which quasi-bound states occur in each part depends on the dimensional parameters of the respective portion in the structure. We study how the transmission through quasi-bound states is influenced by the edge states on the contacts and dimensional parameters such as barrier length and also by the ambient temperature. The results are compared with those of an RTD with a single part connecting the contacts. Transmission peaks at different energies are observed for an RTD with asymmetrical lower and upper parts between the contacts. This is then utilized for the creation of two negative differential resistance (NDR) peaks. For numerical computation, the non-equilibrium Green’s function formalism (NEGF) based on the nearest neighbor tight-binding model is employed.

Design of N-doped C60-σ-B-doped C60 photodetector based on resonant tunneling diode using DFT and NEGF method.

Photodetectors utilizing donor/acceptor (D/A) molecules have the capacity to detect light through molecular interactions between a donor and an acceptor molecule. These devices leverage electronic or optical changes within molecules when exposed to light, resulting in observable modifications. The unique properties of photodetectors with D/A molecules make them valuable tools in various fields, including molecular electronics. This paper presents the modeling and simulation of a single-molecule photodetector based on a D/A molecule configuration. The acceptor molecule used is N-doped C60 fullerene, while the donor molecule is B-doped C60 fullerene. Initially, simulations were conducted at zero bias voltage to determine the energy and states of the bipartite molecule. Subsequently, the system's Hamiltonian was computed based on these results. The self-consistent field method (SCF) and optical self-energy coefficients were employed for modeling. Finally, the current-voltage curve of the device was derived for various input light frequencies. The simulation and modeling results demonstrated that the device exhibited negative differential resistances at bias voltages of 0.33 V, 1.58 V, and - 0.93 V, depending on the input light frequency. Furthermore, the designed device demonstrated the ability to detect and absorb waves with different frequencies. The number of current peaks in the current-voltage curve varied with by altering the number of optical modes. The computational work was conducted using the software package of Atomistix ToolKit (ATK-2018.06) and MATLAB code. The calculations were based on the density functional theory (DFT) approach and the self-consistent field method, specifically the non-equilibrium Green function (NEGF). The exchange correlation function was investigated using the generalized gradient approximation (GGA) proposed by Perdew, Burke, and Ernzerhof (PBE). For the calculations, we employed the double-ζ plus polarization (DZP) basis set. Initially, the structures of N doped-C60-σ-B-doped-C60 molecule underwent optimization using the DFT approach implemented in the ATK package. This optimization process allowed us to extract the parameters of the molecule. Subsequently, we utilized the NEGF formalism in MATLAB software to model and simulate photodetector based on the optimized molecule. We calculated important features of the photodetector, such as photocurrent, and compared the performance of the photodetector using photons with energies of 2 and 3 eV.

Ab Initio Phonon Transport Based on Nonequilibrium Green's Function Formalism: A Practical Approach

Herein, a highly practical first‐principles approach for studying phonon transport across various materials, ranging from low‐dimensional systems to three‐dimensional bulk structures, as well as nanostructures, is presented. This method integrates the nonequilibrium Green's function (NEGF) formalism with ab initio calculations of dynamical matrices generated by Quantum Espresso. A detailed technical approach for extracting atomistic force constants and forming dynamical matrices that adhere to the tri‐diagonal technique within the NEGF framework is provided. Additionally, an efficient method for constructing dynamical matrices of conventional cells from those of primary cells is introduced, remarkably reducing the computational costs associated with density‐functional theory calculations. The robustness and applicability of this methodology are validated through several case studies.

Thermal Transport at the AlN-SiC Interface and Grain Boundary of AlN.

AlN is deposited on silicon carbide (SiC) for high-power electronics; in these devices, AlN acts as both a buffer layer for the growth of the active device and a thermal conductor. However, the mechanism of thermal transport through the AlN-SiC interfaces and through grain boundaries of AlN has not been clearly analyzed, even though AlN forms grain boundaries during the deposition process. The thermal properties of the AlN-SiC interface and the inversion domain boundaries (IDBs) of AlN were examined by a phonon transport model based on a nonequilibrium Green function formalism and first-principles calculations. The interface and grain boundary models were designed, and the thermal resistances (TRs) and origins of TR were examined. The TRs of the AlN-SiC interface and the IDB of AlN are much higher than the TRs of AlN and SiC of relevant thickness. Elemental intermixing and vacancy formation were modeled. The formation of charge-balanced defect of VAl + 3ON is thermodynamically favorable compared to other defects, indicating that ON induces formation of VAl. The charge-balanced defect combining VAl and ON increases the TRs of both AlN-SiC interfaces and AlN grain boundaries because vacancy defects induce larger changes in mass than all other defects, and TRs are proportional to changes in mass. In addition, VAl defects are increased by excess ON, resulting in a continuous increase in TR, and then, the calculated thermal boundary resistance (TBR) of the AlN-SiC interface with increased density of VAl by excess ON reaches the experimental TBR. Therefore, it is expected that the large increase in TR by the formation of VAl + ON would be suppressed by controlling the low O density during synthesis.

Enhancing TFET performance through gate length optimization and doping control in phosphorene nanoribbons

In this study, the performance of armchair phosphorene nanoribbons (APNRs) tunnel field-effect transistors (TFETs) is compared to that of conventional Metal-Oxide-Semiconductor Field-Effect Transistors (MOSFETs) based on the self-consistent solution of the Poisson and Schrödinger equation within the non-equilibrium Green's Function formalism and a tight-binding Hamiltonian. As channel length decreases, undesirable consequences such as increased OFF-current and sub-threshold swing can affect MOSFETs' performance. The study thoroughly investigates various aspects of TFET performance, including the impact of channel length, gate length, and doping on parameters like ON-current, OFF-current, the ON-/OFF-current ratio, and sub-threshold swing. An important finding of this research relates to the influence of source and drain doping. We demonstrate that fine-tuning impurity levels directly affects phosphorene nanoribbon TFET (PTFET) performance. The article also investigates the impact of gate length on PTFET performance. New transistor configurations with different gate lengths are proposed in this research. The study shows that optimizing gate length can significantly reduce OFF-current. Furthermore, the combined impact of gate length and doping concentration on PTFET performance is investigated. Through the strategic extension of the gate length towards the drain side and precise adjustments in doping levels, notable improvements in subthreshold swings, ON-current, and the ON-/OFF-current ratio can be realized.

Theoretical prediction of chalcogen-based Janus monolayers for self-powered optoelectronic devices

Exploring potential two-dimensional monolayers with large photogalvanic effect (PGE) has been of great importance for developing self-powered optoelectronic devices. In this paper, we systematically investigate the generation of PGE photocurrent in chalcogen-based Janus XYZ monolayers (X/Y/Z = S, Se, Te; X ≠ Y ≠ Z) based on non-equilibrium Green's function formalism with density functional theory. The optimized Janus SSeTe, SeSTe, and TeSeS monolayers in the rectangular phase are shown stable and, respectively, possess 1.54, 1.49, and 1.74 eV indirect bandgaps. Illuminated by linearly polarized light, the PGE photocurrent without bias voltage can be collected in both armchair and zigzag directions. Unlike common Janus 2D materials with C3v symmetry, the photocurrent peak values of Janus XYZ monolayers do not come up with certain polarization angles, while the relations can be fitted by Iph = α sin(2θ) + β cos(2θ) + γ at each photon energy. Meanwhile, the maximum photoresponses of Janus SSeTe, SeSTe, and TeSeS monolayers are 2.02, 3.33, and 4.42 a20/photon, respectively. The relatively large PGE photocurrents and complicated polarization relations result from the lower symmetry of Janus XYZ monolayers. Moreover, the specific polarization angles for maximum photoresponses at each photon energy and the ratio between two transport directions are demonstrated, reflecting the anisotropy. Our results theoretically predict a potential Janus monolayer family for self-powered optoelectronic applications.

Investigation of Electric Field Tunable Optical and Electrical Characteristics of Zigzag and Armchair Graphene Nanoribbons: An Ab Initio Approach.

Graphene nanoribbons (GNRs), categorized into zigzag and armchair types, hold significant promise in electronics due to their unique properties. In this study, optical properties of zigzag and armchair GNRs are investigated using density functional theory (DFT) in conjunction with Kubo-Greenwood formalism. Our findings reveal that optical characteristics of both GNR types can be extensively modulated through the application of a transverse electric field, e.g., the refractive index of the a zigzag GNR is shown to vary in the range of n = 0.3 and n = 9.9 for the transverse electric field values between 0 V/Å and 10 V/Å. Additionally, electrical transmission spectra and the electrical conductivities of the GNRs are studied using DFT combined with non-equilibrium Green's function formalism, again uncovering a strong dependence on the transverse electric field. For example, the conductance of the armchair GNR is shown to vary in the range of G = 6 μA/V and G = 201 μA/V by the transverse electric field. These results demonstrate the potential of GNRs for use in electronically controlled optoelectronic devices, promising a broad range of applications in advanced electronic systems.

Electroluminescence Rectification and High Harmonic Generation in Molecular Junctions.

The field of molecular electronics has emerged from efforts to understand electron propagation through single molecules and to use them in electronic circuits. Serving as a testbed for advanced theoretical methods, it reveals a significant discrepancy between the operational time scales of experiments (static to GHz frequencies) and theoretical models (femtoseconds). Utilizing a recently developed time-linear nonequilibrium Green function formalism, we model molecular junctions on experimentally accessible time scales. Our study focuses on the quantum pump effect in a benzenedithiol molecule connected to two copper electrodes and coupled with cavity photons. By calculating both electric and photonic current responses to an ac bias voltage, we observe pronounced electroluminescence and high harmonic generation in this setup. The mechanism of the latter effect is more analogous to that from solids than from isolated molecules, with even harmonics being suppressed or enhanced depending on the symmetry of the driving field.

Chirality-Induced Spin Selectivity: Analysis of Density Functional Theory Calculations.

Chirality-induced spin selectivity (CISS), which was demonstrated in several molecular and material systems, has drawn much interest recently. The phenomenon, described in electron transport by the difference in the transport rate of electrons of opposite spins through a chiral system, is however not fully understood. Herein, we employed density functional theory in conjunction with spin-orbit coupling to evaluate the percent spin-polarization in a device setup with finite electrodes at zero bias, using an electron transport program developed in-house. To study the interface effects and the level of theory considered, we investigated a helical oligopeptide chain, an intrinsically chiral gold cluster, and a helicene model system that was previously studied (Zöllner et al. J. Chem. Theory Comput. 2020, 16, 7357-7371). We find that the magnitude of the spin-polarization depends on the chiral system-electrode interface that is modeled by varying the interface boundary between the system's regions, on the method of calculating spin-orbit coupling, and on the exchange-correlation functional, e.g., the amount of exact exchange in the hybrid functionals. In addition, to assess the effects of bias, we employ the nonequilibrium Green's function formalism in the Quantum Atomistix Toolkit program, showing that the spin-flip terms could be important in calculating the CISS effect. Although understanding CISS in comparison to experiment is still not resolved, our study provides intrinsic responses from first-principles calculations.

Jiezi: An open-source Python software for simulating quantum transport based on non-equilibrium Green's function formalism

We present a Python-based open-source library named Jiezi, which provides the means of simulating the electronic transport properties of nanoscaled devices on the atomistic level. The key feature of Jiezi lies in its core algorithm, i.e., self-consistent orchestration between the non-equilibrium Green's function (NEGF) method and a Poisson's equation solver. Beyond the construction of the tight-binding (TB) Hamiltonian with empirical parameters for conventional materials, the package offers a comprehensive framework for constructing the Wannier-based Hamiltonian matrix, enabling the investigation of novel materials and their heterostructures. To expedite the solution of NEGF systems, a methodology based on renormalization theory is proposed for reducing the dimension of the Hamiltonian matrix. Additionally, we adopt a non-linear Poisson equation solver with no analytical approximation in this software. The software facilitates seamless integration with external tools for geometry and mesh generation and post-processing. In this paper, we present the main capabilities and workflow by demonstrating with a simulation for the carbon nanotube field-effect transistor (CNTFET). Program summaryProgram Title: JieziCPC Library link to program files:https://doi.org/10.17632/nk79kbtww4.1Developer's repository link:https://github.com/Jiezi-negf/JieziLicensing provisions: GPLv3Programming language: PythonNature of problem: Simulates the quantum transport property of nano-scaled transistors based on the predefined device structure and the material composition.Solution method: Solves the coupled Schrödinger equation and Poisson equation by NEGF and finite element method.

Numerical simulation of Rashba spin–orbit coupling effect on quantum Hall resistivity within tight-binding approximation

A numerical simulation of the effect of Rashba spin–orbit coupling (RSO) on quantum transport properties of electrons confined to a two-dimensional electron gas (2DEG) in the integer quantum Hall regime is presented. The mechanism of quantization and the dependence of the Hall resistivity (HR) on the system built-in and external parameters are studied using the non-equilibrium Green’s function (NEGF) technique. Relevant Green’s functions are computed numerically using spectral decomposition method in combination with recursive techniques. The tight-binding-like representation of the system Hamiltonian including magnetic field is obtained within the finite difference method, using Dirichlet boundary conditions. Corresponding formula linking the Hall resistivity with the transmission function of the system has been derived analytically within the NEGF formalism in a general form, in the sense that the formula can also be used beyond the linear response limit and for nonzero temperatures. In particular, it was shown explicitly that in the presence of the RSO coupling the even- and odd plateaus emerging in the magnetic-field dependence of the quantum Hall resistivity are related to different physical mechanisms.

Trade-off analysis between gm/ID and fT of GNR-FETs with single-gate and double-gate device structure

This study examines the operational parameters of field-effect transistors (FETs) using single-gate (SG) and double-gate (DG) graphene nanoribbons (GNRs) within the analog/RF domain. A detailed exploration is conducted through an atomistic pz orbital model, derived from the Hamiltonian of graphene nanoribbons, employing the nonequilibrium Green’s function formalism (NEGF) for analysis. The atomic characteristics of the GNRFETs channel are accurately described by utilizing a tight-binding Hamiltonian with an atomistic pz orbital basis set. The primary focus of the analysis revolves around essential analog/RF parameters such as transconductance, transconductance generation factor (TGF), output resistance, early voltage, intrinsic gain, gate capacitance, cut-off frequency, and transit time. Furthermore, the study assesses the gain frequency product (GFP), transfer frequency product (TFP), and gain transfer frequency product (GTFP) to evaluate the balance between transistor efficiency, gain, and cut-off frequency. The research outcomes indicate that double-gate GNRFETs exhibit superior analog/RF performance in comparison to their single-gate counterparts. However, both types of devices demonstrate cut-off frequencies in the gigahertz range. The extensive data presented in this study provides valuable insights into the characteristics of SG and DG GNRFETs, particularly in terms of the figure-of-merit (FoM) for analog/RF performance, offering a comprehensive analysis of the trade-offs in analog applications. In addition, the analysis has been extended be performing a high-performance hybrid 6T static random-access memory (SRAM) to get the impact in their circuit level variation as well as improvement in their circuit performance.

Floquet non-equilibrium Green's function and Floquet quantum master equation for electronic transport: The role of electron-electron interactions and spin current with circular light.

The non-equilibrium Green's function (NEGF) and quantum master equation (QME) are two main classes of approaches for electronic transport. We discuss various Floquet variances of these formalisms for transport properties of a quantum dot driven via interaction with an external periodic field. We first derived two versions of the Floquet NEGF. We also explore an ansatz of the Floquet NEGF formalism for the interacting systems. In addition, we derived two versions of Floquet QME in the weak interaction regime. With each method, we elaborate on the evaluation of the expectation values of the number and current operators. We examined these methods for transport through a two-level system that is subject to periodic driving. The numerical results of all four methods show good agreement for non-interacting systems in the weak regime. Furthermore, we have observed that circular light can introduce spin current. We expect these Floquet quantum transport methods to be useful in studying molecular junctions exposed to light.

Nanotube ferroelectric tunnel junctions with an ultrahigh tunneling electroresistance ratio.

Low-dimensional ferroelectric tunnel junctions are appealing for the realization of nanoscale nonvolatile memory devices due to their inherent advantages of device miniaturization. Those based on current mechanisms have limitations, including low tunneling electroresistance (TER) effects and complex heterostructures. Here, we introduce an entirely new TER mechanism to construct a nanotube ferroelectric tunnel junction with ferroelectric nanotubes as the tunneling region. When rolling a ferroelectric monolayer into a nanotube, due to the coexistence of its intrinsic ferroelectric polarization with the flexoelectric polarization induced by bending, a metal-insulator transition occurs depending on the radiative polarization states. For the pristine monolayer, its out-of-plane polarization is tunable by an in-plane electric field, and the conducting states of the ferroelectric nanotube can thus be tuned between metallic and insulating states via axial electric means. Using α-In2Se3 as an example, our first-principles density functional theory calculations and nonequilibrium Green's function formalism confirm the feasibility of the TER mechanism and indicate an ultrahigh TER ratio that exceeds 9.9 × 1010% of the proposed nanotube ferroelectric tunnel junctions. Our findings provide a promising approach based on simple homogeneous structures for high density ferroelectric microelectric devices with excellent ON/OFF performance.

Enhancing Spin-Transport Characteristics, Spin-Filtering Efficiency, and Negative Differential Resistance in Exchange-Coupled Dinuclear Co(II) Complexes for Molecular Spintronics Applications.

Single-molecule spintronics, where electron transport occurs via a paramagnetic molecule, has gained wide attention due to its potential applications in the area of memory devices to switches. While numerous organic and some inorganic complexes have been employed over the years, there are only a few attempts to employ exchange coupled dinuclear complexes at the interface, and the advantage of fabricating such a molecular spintronics device in the observation of switchable Kondo resonance was demonstrated recently in the dinuclear [Co2(L)(hfac)4] (1) complex (Wagner et al., Nat. Nanotechnol. 2013, 8, 575-579). In this work, employing an array of theoretical tools such as density functional theory (DFT), the ab initio CASSCF/NEVPT2 method, and DFT combined with nonequilibrium Green Function (NEGF) formalism, we studied in detail the role of magnetic coupling, ligand field, and magnetic anisotropy in the transport characteristics of complex 1. Particularly, our calculations not only reproduce the current-voltage (I-V) characteristics observed in experiments but also unequivocally establish that these arise from an exchange-coupled singlet state that arises due to antiferromagnetic coupling between two high-spin Co(II) centers. Further, the estimated spin Hamiltonian parameters such as J, g values, and D and E/D values are only marginally altered for the molecule at the interface. Further, the exchange-coupled state was found to have very similar transport responses, despite possessing significantly different geometries. Our transport calculations unveil a new feature of the negative differential resistance (NDR) effect on 1 at the bias voltage of 0.9 V, which agrees with the experimental I-V characteristics reported. The spin-filtering efficiency (SFE) computed for the spin-coupled states was found to be only marginal (∼25%); however, if the ligand field is fine-tuned to obtain a low-spin Co(II) center, a substantial SFE of 44% was noted. This spin-coupled state also yields a very strong NDR with a peak-to-valley ratio (PVR) of ∼56 - a record number that has not been witnessed so far in this class of compounds. Additionally, we have established further magnetostructural-transport correlations, providing valuable insights into how microscopic spin Hamiltonian parameters can be associated with SFE. Several design clues to improve the spin-transport characteristics, SFE and NDR in this class of molecule, are offered.

Full statistics of nonequilibrium heat and work for many-body quantum Otto engines and universal bounds: A nonequilibrium Green's function approach.

We consider a generic four-stroke quantum Otto engine consisting of two unitary and two thermalization strokes with an arbitrary many-body working medium. Using the Schwinger-Keldysh nonequilibrium Green's function formalism, we provide an analytical expression for the cumulant generating function corresponding to the joint probability distribution of nonequilibrium work and heat. The obtained result is valid up to the second order of the external driving amplitude. We then focus on the linear response limit and obtained Onsager's transport coefficients for the generic Otto cycle and show that the traditional fluctuation-dissipation relation for the total work is violated in the quantum domain, whereas for heat it is preserved. This leads to remarkable consequences in obtaining universal constraints on heat and work fluctuations for engine and refrigerator regimes of the Otto cycle and further allows us to make connections to the thermodynamic uncertainty relations. These findings are illustrated using a paradigmatic model that can be feasibly implemented in experiments.

Automatic differentiable nonequilibrium Green's function formalism: An end-to-end differentiable quantum transport simulator

Automatic differentiable nonequilibrium Green's function formalism: An end-to-end differentiable quantum transport simulator

Tunnel-magneto resistance of double-barrier tunnel junctions in the presence of spin-orbit coupling within spin-filter barriers

The tunnel magneto-resistance ratio is investigated for double-barrier tunnel junctions with spin-filter (magnetic insulators) barriers. The transmission probability is calculated in the tight-binding model by the non-equilibrium Green's function formalism considering spin-orbit coupling within barriers. The formation of resonant states inside a non-magnetic spacer gives rise to an enhancement in tunnel magneto-resistance ratio. Double spin-filter tunnel junctions have also shown a higher tunnel magneto-resistance ratio compared to that in double-barrier magnetic tunnel junctions. These findings will be valuable to improve the performance of spintronics devices.

Influence of a static electric field on magnetic materials monitored by X-ray magnetic circular dichroism

The magnetic circular X-ray dichroism (XMCD) in X-ray absorption spectroscopy (XAS) is extensively used to monitor the response of a magnetic system to an external perturbation. Application of a static external electric field to control its magnetic properties may just lead to a charge rearrangement or to a steady electric current dependent on the geometry. As it is demonstrated, the first situation can be handled with minor modifications of the standard well established schemes to calculate XAS and XMCD spectra. For the second case, however, more advanced schemes have to be used that account for the steady-state out-of-equilibrium situation. It is shown, that this can indeed be achieved by making use of the Keldysh non-equilibrium Green function formalism that allows in particular to express the X-ray absorption coefficient in terms of the corresponding greater Green function G>(E). As an alternative approach, a bi-linear response formalism is presented that can be used to calculate the modification of the XMCD spectra due to the electric field directly.