Nonequilibrium Green Function Research Articles

Combined resonant tunneling and rate equation modeling of terahertz quantum cascade lasers

Terahertz (THz) quantum cascade lasers (QCLs) are technologically important laser sources for the THz range but are complex to model. An efficient extended rate equation model is developed here by incorporating the resonant tunneling mechanism from the density matrix formalism, which permits to simulate THz QCLs with thick carrier injection barriers within the semi-classical formalism. A self-consistent solution is obtained by iteratively solving the Schrödinger–Poisson equation with this transport model. Carrier–light coupling is also included to simulate the current behavior arising from stimulated emission. As a quasi-ab initio model, intermediate parameters, such as pure dephasing time and optical linewidth, are dynamically calculated in the convergence process, and the only fitting parameters are the interface roughness correlation length and height. Good agreement has been achieved by comparing the simulation results of various designs with experiments, and other models such as density matrix Monte Carlo and non-equilibrium Green's function method that, unlike here, require important computational resources. The accuracy, compatibility, and computational efficiency of our model enable many application scenarios, such as design optimization and quantitative insights into THz QCLs. Finally, the source code of the model is also provided in the supplementary material of this article for readers to repeat the results presented here, investigate, and optimize new designs.

Analyzing the effect of doping concentration in split-well resonant-phonon terahertz quantum cascade lasers.

The effect of doping concentration on the temperature performance of the novel split-well resonant-phonon (SWRP) terahertz quantum-cascade laser (THz QCL) scheme supporting a clean 4-level system design was analyzed using non-equilibrium Green's functions (NEGF) calculations. Experimental research showed that increasing the doping concentration in these designs led to better results compared to the split-well direct-phonon (SWDP) design, which has a larger overlap between its active laser states and the doping profile. However, further improvement in the temperature performance was expected, which led us to assume there was an increased gain and line broadening when increasing the doping concentration despite the reduced overlap between the doped region and the active laser states. Through simulations based on NEGF calculations we were able to study the contribution of the different scattering mechanisms on the performance of these devices. We concluded that the main mechanism affecting the lasers' temperature performance is electron-electron (e-e) scattering, which largely contributes to gain and line broadening. Interestingly, this scattering mechanism is independent of the doping location, making efforts to reduce overlap between the doped region and the active laser states less effective. Optimization of the e-e scattering thus could be reached only by fine tuning of the doping density in the devices. By uncovering the subtle relationship between doping density and e-e scattering strength, our study not only provides a comprehensive understanding of the underlying physics but also offers a strategic pathway for overcoming current limitations. This work is significant not only for its implications on specific devices but also for its potential to drive advancements in the entire THz QCL field, demonstrating the crucial role of e-e scattering in limiting temperature performance and providing essential knowledge for pushing THz QCLs to new temperature heights.

High sensitivity of s-triazine based g-C3N4 surface to pollutant gases

Rapid detection of harmful airborne substances caused by daily activities and industrial activity is vital. In the current study, the applicability of s-triazine based g-C3N4 nanosheet as a potential sensor for environmentally dangerous gases, NO, N2O, NO2, SO, SO2, and SO3, was investigated using the density functional theory and non-equilibrium Green's function (NEGF) method. Sulfur-containing gases exhibited stronger interactions with the surface. The obtained adsorption energies are in the range of −0.21 to −1.13 eV, which is associated with charge transfer in the range of −0.09 to −0.29 e. The molecules' overall structures are preserved during the adsorption process. The sensitivity of the surface to the adsorbed molecules was confirmed by analyzing the work function changes and calculating the transmission coefficients using the NEGF approach. All adsorbate species, except SO3, have short recovery times of up to 3.9 s at room temperature, proving the efficiency of this surface as a viable sensor material. Furthermore, by analyzing the humidity impact, the g-C3N4 ability as a sensor in more realistic conditions was also validated. The results indicate that the g-C3N4 surface can be an excellent candidate for toxic gas detection with high selectivity and sensitivity.

Significant effects of magnetic electrodes on rhenium phthalocyanine molecules

The investigation focused on examining the spin polarization and thermal spin polarization transport characteristics of dual rhenium phthalocyanine (Re2PC2) molecular junctions. This analysis was conducted using first-principles density-functional theory and the non-equilibrium Green's function approach. Calculations were performed on molecular junctions in two configurations: one at a non-magnetic electrode (Au) and the other at a magnetic electrode (Ni). A comparison of the spin transport properties of the two electrodes shows significant differences. The magnetic electrode has a notable effect on the spin-polarization and thermal spin-polarization transport properties of the devices. In contrast, the nickel electrode bis-phthalocyanine rhenium molecular device exhibits perfect spin/thermal spin-filtering efficiencies in a parallel structure. The properties of the dual phthalocyanine rhenium molecular devices were significantly affected by the nature of the electrodes. This makes dual rhenium phthalocyanine molecular junctions have great potential for the development of high-performance multifunctional spintronic and spin caloritronic devices.

A computational study of rectification behavior of doped α-graphyne nanotubes

α-graphyne is a carbon nanosheet with sp and sp2 hybridization. This sheet is a hexagonal semi-metal like graphene. In this paper, we roll α-graphyne sheet and build zigzag nanotubes with three different size (n = 5, 6, 7). We used density functional tight binding (DFTB) to compute the band structures of nanotubes. The results show that the gap energies for n = 5, 6, 7 are about 0.648, 0.115, 0.309 eV, respectively. We add impurity atoms such as boron (B) and nitrogen (N) to nanotube. We found that the band gap energy of these doped nanotubes decrease. In addition, the structures that carbon atoms with sp2 hybridization replaced by impurity atoms are more stable. For the first time, we build two doped nanotube diodes at low (M1 model) and high (M2 model) concentration and compute current-voltage (I–V) curves with non-equilibrium Green's functions (NEGF). The I–V curves of doped nanotubes show non-linear asymmetric behavior. Form I–V curves, we compute rectification ratio and negative differential resistance (NDR). The low doped zigzag nanotube with n = 5 (M1 model) shows the highest rectification ratio (about 12.236 × 104) at 0.3 V. In addition, the rectification ratio of this diode at high concentration (M2) is about 3.67 × 103 at 0.6 V. The I–V curve of M2 model illustrations a notably negative differential resistance (NDR) at reverse bias. The ratio of current at peak to current at valley is about 26.83. To describe the I–V curves, we used transmission spectrum, the band structures of electrodes and the density of states (DOS) of central scattering region. In general, transition occurs when the energy levels of three regions (left electrode, scattering and right electrode) overlap.

Ballistic Performance of Quasi-One-Dimensional Hafnium Disulfide Field-Effect Transistors

Hafnium disulfide (HfS2) monolayer is one of the most promising two-dimensional (2D) materials for future nanoscale electronic devices, and patterning it into quasi-one-dimensional HfS2 nanoribbons (HfS2NRs) enables multi-channel architectures for field-effect transistors (FETs). Electronic, transport and ballistic device characteristics are studied for sub-7 nm-wide and ~15 nm-long zigzag HfS2NR FETs using non-equilibrium Green’s functions (NEGF) formalism with density functional theory (DFT) and maximally localized Wannier functions (MLWFs). We provide an in-depth analysis of quantum confinement effects on ON-state performance. We show that bandgap and hole transport mass are immune to downscaling effects, while the ON-state performance is boosted by up to 53% but only in n-type devices. Finally, we demonstrate that HfS2NR FETs can fulfill the industry requirements for future technology nodes, which makes them a promising solution for FET architectures based on multiple nanosheets or nanowires.

Comparison of SiGeC/SiGe/SiC–Si heterojunction based vertical nanowire FET using non equilibrium Green's function

Advancement in FET technology has forced researchers to seek alternate semiconductor devices and materials. TFETs, junctionless FETs, and nanowires are a few examples of modern FETs, whereas Si alloys, graphene, and TMDC are a few materials that have shown promising behaviour to replace Si in the future. In this work, SiGeC/SiGe/SiC–Si based vertical heterostructure nanowires have been investigated. Due to the nanoscale dimensions of the FET and to incorporate the quantum effects along with Schrodinger-Poisson equations, non-equilibrium Green's function has been used as a principle simulator. For simulation, Ge/Carbon mole concentration of 0.25 and 0.01, respectively is used. To thoroughly investigate the effect of variation in doping profile and temperature range, simulated heterojunction nanowire showed that SiGeC-based nanowire result in a better ION/IOFF ratio as compared to SiGe and SiC-based heterojunction nanowire.

Radical and quantum interference-enhanced thermoelectric performance of the junctions based on porphyrin dimer molecules

Manipulating the π-electron magnetism of single-molecule junctions is an effective means to improve the electronic and spin-polarized thermoelectric transport properties. Here, using the density functional theory combined with the nonequilibrium Green's function method, we demonstrate that the electronic conductance (σ) of molecular junctions (MJs) can be significantly enhanced by organic radicals due to the shifting of resonant states. Moreover, we find that the spin-dependent quantum interference (SDQI) effects can be largely influenced by organic radicals. The SDQI effects result in nearly 100% spin filtering efficiency in open-shell molecules and greatly enhance the Seebeck coefficients. As a result, the thermoelectric performances of open-shell MJs at room temperature are greatly improved through the combined effects of radicals and SDQI. In particular, the maximum ZTsp in the four radical junctions reaches up to 36.5. Our results show great potential for improving thermoelectric performance through the utilization of quantum interference and organic radical.

Electronic and transport properties of boron and nitrogen passivated zigzag graphene nanoribbons

A systematic study is conducted on 8ZGNR by edge terminations with boron and nitrogen at I and II termination sites by replacing hydrogen atoms in a single layer and in two probe systems. Electronic properties were observed in the DFT framework. Non-equilibrium green’s function (NEGF) tool was used to study the transport properties. Analysis of band structure, total energy, formation energy, and projected density of states (PDOS) suggest that despite Boron and Nitrogen passivation at all the termination sites, the electronic behavior of the system remains metallic. The analysis of Transmission spectra also confirms its metallic behavior in all these cases. This study reveals that B and N passivated graphene nanoribbons are sensitive to electronic transmission. This fact makes it potentially useful for application in sensors, memory devices and many other nano-electronic devices.

Effective Descriptor for Screening Single-Molecule Conductance Switches.

The adsorption-type molecular switch exhibits bistable states with an equivalently long lifetime at the organic/inorganic interface, promising reliable switching behavior and superior assembly ability in the electronic circuits at the molecular scale. However, the number of reported adsorption-type molecular switches is currently less than 10, and exploring these molecular switches poses a formidable challenge due to the intricate interplay occurring at the interface. To address this challenge, we have developed a model enabling the identification of diverse molecular switches on metal surfaces based on easily accessible physical characteristics. These characteristics primarily include the metal valency electron concentration, the work function of metal surfaces, and the electronegativity difference of molecules. Using this model, we identified 56 new molecular switches. Employing the gradient descent algorithm and statistical linear discriminant analysis, we constructed an explicit descriptor that establishes a relationship between the interfacial structure and chemical environment and the stability of molecular switches. The model's accuracy was validated through density functional theory calculations, achieving a 90% accuracy for aromatic molecular switches. The conductive switching behaviors were further confirmed by nonequilibrium Green's function transport calculations.

Influence of varying carbon oxides concentrations on the selectivity of an electrical sensor utilizing graphene nanoribbons

We have considered a graphene nano ribbon-based two probe-device working on the principle of alteration of current-voltage (I–V) characteristic, upon interactions of its channel material with the adsorbed gas molecules. The analysis of sensing parameters alongside the electron transport mechanism was carried out by using density functional theory (DFT) formulated on the Hohenberg-Kohen paradigm in conjunction with the non-equilibrium green functions (NEGF) method. Electronic transport through similar work reported earlier reveals that the combination of these two techniques coordinates extremely well and yields convincing electronic results. The nanoribbon-based sensing device was employed to evaluate its capability to detect Carbon dioxide (CO2) and Carbon monoxide (CO) molecules. Analysis of the computed result reveals significant modifications in the electronic property of the device upon adsorption of carbon dioxide and carbon monoxide entities on the channel surface. One such significant and dramatic change in the characteristic that we observed is the nature of the channel that transforms from metallic to semi-metallic. Another observed change is the signal amplification capability relative to the pristine device. The signal gets amplified on increasing number of molecular entities from one to six.The transformation in sensor performance is additionally supported by examining variations in multiple parameters, including adsorption energy, charge transfer, differential resistance, and the figure of merit, also known as the peak-to-valley ratio (PVR). The investigation unveiled that the currently designed zigzag graphene nanoribbon (ZGNR) model exhibits high sensitivity to both CO2 and CO gases. This phenomenon is substantiated by the elevated adsorption energy, increased charge transfer, elevated peak-to-valley ratio (PVR), and heightened sensor response. The substantial sensor response, registering at a magnitude of 8.3, underscores the efficacy of the current system in detecting both low and high concentrations of CO and CO2 molecules. The current study emphasizes the notion that understanding the electronic and transport behaviour of zigzag graphene nanoribbons (ZGNR) and analogous materials could offer valuable insights for addressing the threat of environmental pollution.

Adsorption of cadmium selenide clusters: A novel approach to enhance solar energy conversion using armchair graphene nanoribbons

Tailoring the electronic, optical, and transport properties of low-dimensional semiconductor materials is essential to improve the light-conversion efficiency of thin-film solar cell materials. Here, using first-principles calculations and non-equilibrium Green functions, we investigate the enhancement of optoelectronic and transport properties of armchair graphene nanoribbons (AGNRs) upon adsorption of cadmium selenide clusters. Upon adsorption of a CdSe diatomic molecule on an AGNR, the most energetically favorable configuration is the cadmium end sitting on top of a carbon atom. The corresponding electronic bandgap reduces ∼5 times with respect to that of the pristine system, thanks to the formation of a polaron state formed by the p-orbital of the selenide atom. Upon adsorption of CdSe cyclohexane molecules, the bandgap of this system slightly shrinks by 0.121 eV with respect to the pristine system. The charge accumulation induced by these clusters significantly enhances the absorption coefficient of the adsorbed systems, resulting in a red shift of the optical spectra toward the infrared region. More interestingly, by solving the Bethe–Salpeter equations with the Tamm–Dancoff approximation, we provide a direct link between the first-principles optical prediction and experimental observations. In addition, the electron transfer from these molecules to the hosted systems increases the transmission spectra in the vicinity of the Fermi level, leading to a remarkable electronic current passing through these scattering regions. These results highlight the role of cadmium selenide clusters in enhancing the light-to-energy conversion efficiency of next-generation solar cell devices.

Strain-Modulated Electronic Transport Properties in Two-Dimensional Green Phosphorene with Different Edge Morphologies

Based on two-dimensional green phosphorene, we designed two molecular electronic devices with zigzag (Type 1) and whisker-like (Type 2) configurations. By combining density functional theory (DFT) and non-equilibrium Green’s function (NEGF), we investigated the electronic properties of Types 1 and 2. Type 1 exhibits an interesting negative differential resistance (NDR), while the current characteristics of Type 2 show linear growth in the current–voltage curve. We studied the electronic transport properties of Type 1 under uniaxial strain modulation and find that strained devices also exhibit a NDR effect, and the peak-to-valley ratio of device could be controlled by varying the strain intensity. These results show that the transport properties of green phosphorene with different edge configuration are different, and the zigzag edge have adjustable negative differential resistance properties.

Temperature-dependent electronic, optical, and solar cell device properties of AlAs and AlSb semiconductors and their p-n homojunctions

AlSb and AlAs have attracted renewed interest in recent years as promising photovoltaic (PV) materials due to significant light absorption, eco-friendliness, and low cost. Here, density functional theory (DFT) in combination with the non-equilibrium Green's function method (NEGF) has been used to compute the temperature-dependent PV parameters of nanoscale AlSb and AlAs p-n junction solar cell devices. In particular, the influence of electron-phonon coupling (EPC) and spin-orbit coupling (SOC) on the PV properties of these devices is investigated. Our results highlight the importance of inclusion of EPC in evaluating the ab initio PV properties of p-n junctions at finite temperatures. At non-zero temperatures, the PV parameters can differ significantly compared to those at zero temperature due to phonon-assisted tunnelling of charge carriers across the p-n junction. In particular, the mobility of low-effective-mass carriers at the p-n junction is found to be enhanced by phonon scattering, which in turn results in improved PV transport properties. The short-circuit current (Jsc) at 300 K proved to be 21.7% (16.2%) higher for AlSb (AlAs) than that at 0 K. On the other hand, the open-circuit voltage (Voc) at 300 K proved to be 19.1% (16.7%) lower for AlSb (AlAs) than that at 0 K. Jsc is higher in AlSb than in AlAs due to higher phonon-influenced mobility of low-effective-mass carriers. Overall, our study strongly suggests the importance of inclusion of EPC and hence phonon scattering in the first-principles quantitative determination of PV parameters of solar cells. The estimates obtained in this study may be utilized as input ab initio parameters in continuum-model-based multi-scale simulations of AlSb and AlAs p-n homo-junction solar cells.

Theoretical Study of Electronic and Thermoelectric Properties of Ultra-Thin Silicene and Germanene

In this study, we used the Non-Equilibrium Green Function (NEGF) and Density Functional Theory (DFT) to analyze the nanoscale electronic properties of silicene and germanene structures, the band structure and Density of State (DOS) for the unit cell of silicene and germanene are found that the energy gap is (0 eV) in both. A comparison was made between silicene and germanene in terms of electrical and thermal properties, by calculating the transmission coefficient T(E) for silicene patterns (Si1, Si2, Si3, and Si4) and germanene patterns (Ge1, Ge2, Ge3, and Ge4). The results show that T(E) decreases with increasing etching depth, which also leads to a decrease in electronic conductivity. Moreover, the value of the Seebeck coefficient (S) increases with increasing drilling depth, and also the sign of S varies from a positive value for (Si1, Si4, Ge1, Ge2, Ge4) to a negative value for (Si2, Si3, Ge3) at Fermi level (Ef) equal to (0 eV). The highest value of the figure of merit is about (1.8) for the Ge4 structure.

Unveiling the temperature-dependent thermoelectric properties of the undoped and Na-doped monolayer SnSe allotropes: a comparative study

Motivated by the excellent thermoelectric (TE) performance of bulk SnSe, extensive attention has been drawn to the TE properties of the monolayer SnSe. To uncover the fundamental mechanism of manipulating the TE performance of the SnSe monolayer, we perform a systematic study on the TE properties of five monolayer SnSe allotropes such as α-, β-, γ-, δ-, and ε-SnSe based on the density functional theory and the non-equilibrium Green’s functions. By comparing the TE properties of the Na-doped SnSe allotropes with the undoped ones, the influences of the Na doping and the temperature on the TE properties are deeply investigated. It is shown that the figure of merit ZT will increase as the temperature increases, which is the same for almost all the Na-doped and undoped cases. The Na doping can enhance or suppress the ZT in different SnSe allotropes at different temperatures, implying the presence of the anomalous suppression of the ZT. The Na doping induced ZT suppression may be caused basically by the sharp decrease of the power factor and the weak decrease of the electronic thermal conductance, rather than by the decrease of the phononic thermal conductance. We hope this work will be able to enrich the understanding of the manipulation of TE properties by means of dimensions, structurization, doping, and temperature.

Influence of temperature on bandgap shifts, optical properties and photovoltaic parameters of GaAs/AlAs and GaAs/AlSb p–n heterojunctions: insights from ab-initio DFT + NEGF studies

The III–V group semiconductors are highly promising absorbers for heterojunctions based solar cell devices due to their high conversion efficiency. In this work, we explore the solar cell properties and the role of electron–phonon coupling (EPC) on the solar cell parameters of GaAs/AlSb and GaAs/AlAs p–n heterojunctions using non-equilibrium Green function method (NEGF) in combination of ab-initio density functional theory (DFT). In addition, the band offsets at the heterointerfaces, optical absorption and bandgap shifts (BGSs) due to temperature are estimated using DFT + NEGF approach. The interface band gaps in heterostructures are found to be lower than bulk band gaps leading to a shift in optical absorption coefficient towards lower energy side that results in stronger photocurrent. The temperature dependent electronic BGS is significantly influenced by the phonon density and phonon energy via EPC. The phonon influenced BGS is found to change the optical absorption, photocurrent density and open-circuit voltage. In case of GaAs/AlSb junction, the interface phonons are found to have significantly higher energies as compared to the bulk phonons and thereby may have important implications for photovoltaic (PV) properties. Overall, the present study reveals the influence of EPC on the optical absorption and PV properties of GaAs/AlSb and GaAs/AlSb p–n heterojunctions. Furthermore, the study shows that the DFT + NEGF method can be successfully used to obtain the reasonable quantitative estimates of temperature dependent BGSs, optical absorption and PV properties of p–n heterojunctions.

Performance analysis of carbon nanotube and graphene nanoribbon based biochemical sensors at atomic scale

Advancements in fabrication technologies have led to the possibility of synthesizing atomic-scale graphene nanoribbon (GNR) and carbon nanotube (CNT) based nanodevices. The purpose of this study was to model the electronic properties and electrical characteristics of these devices by atomistic modeling using density functional theory and the non-equilibrium Green’s function and compare the effects of molecular functionalization and sensing. The potential profile of the device was computed using the three-dimensional Poisson equation for smaller applied bias within one voltage range. Simulations showed a bandgap of 1 eV for armchair GNRs (AGNRs), which were insensitive to functionalized amine molecules, resulting in fewer alterations in the density of states (DoS), transmission spectra and the device current (ΔI). The bandgap further increased to 2 eV upon rolling the GNR into a armchair CNT (ACNT), which further decreased sensitivity. However, changing the configuration of the AGNR to a zigzag GNR (ZGNR) led to remarkable changes in the DoS and transmission spectra and a significant improvement in sensitivity. This improvement increased by 1.5–2 times upon rolling the ZGNR into a zigzag CNT (ZCNT). Thus, at lower dimensions in atomic scale, we found an alteration in device current of the carbon structures that was directly proportional to sensitivity in the following order: ΔI ACNT < ΔI AGNR < ΔI ZGNR < ΔI ZCNT. However, the same was found to fall for ZGNR and ZCNT with an increase in width to length (W/L) ratio. This highlights the importance of smaller atomic structures and this work provides a guideline for effective utilization of these structures for biochemical sensing.

Nonequilibrium Dynamics of the Hubbard Dimer

Electron dynamics in a two‐sites Hubbard model is studied using the nonequilibrium Green's function approach. The study is motivated by the empirical observation that a full solution of the integro‐differential Kadanoff–Baym equation (KBE) is more stable and often accompanied by artificial damping [Marc Puig von Friesen, C. Verdozzi, and C.‐O. Almbladh (2009)] than its time‐linear reformulations relying on the generalized Kadanoff–Baym ansatz (GKBA). Additionally, for conserving theories, numerical simulations suggest that KBE produces natural occupations bounded by one and zero in agreement with the Pauli exclusion principle, whereas, in some regimes, GKBA‐based theories violate this principle. As the first step for understanding these issues, the electron dynamics arising in the adiabatic switching scenario is studied. Many‐body approximations are classified according to the channel of the Bethe–Salpeter equation in which electronic correlations are explicitly treated. They give rise to the so‐called second Born, T‐matrix, and GW approximations. In each of these cases, the model is reduced to a system of ordinary differential equations, which resemble equations of motion for a driven harmonic oscillator with time‐dependent frequencies. A more complete treatment of electronic correlations is achieved by combining different correlation channels, with parquet theory serving as a starting point.

Proposal for All-Electrical Skyrmion Detection in van der Waals Tunnel Junctions.

A major challenge for magnetic skyrmions in atomically thin van der Waals (vdW) materials is reliable skyrmion detection. Here, based on rigorous first-principles calculations, we show that all-electrical skyrmion detection is feasible in two-dimensional vdW magnets via scanning tunneling microscopy (STM) and in planar tunnel junctions. We use the nonequilibrium Green's function method for quantum transport in planar junctions, including self-energy due to electrodes and working conditions, going beyond the standard Tersoff-Hamann approximation. We obtain a very large tunneling anisotropic magnetoresistance (TAMR) around the Fermi energy for a graphite/Fe3GeTe2/germanene/graphite vdW tunnel junction. For atomic-scale skyrmions, the noncollinear magnetoresistance (NCMR) reaches giant values. We trace the origin of the NCMR to spin mixing between spin-up and -down states of pz and dz2 character at the surface atoms. Both TAMR and NCMR are drastically enhanced in tunnel junctions with respect to STM geometry due to orbital symmetry matching at the interface.