Nonequilibrium Green Function Calculations Research Articles

Assessing electron conduction mechanisms in highly organized surface water on a model neuronal lipid using quantum chemical methods

A comprehensive characterization of key mechanisms underlying signal transmission within the human brain remains an unsolved problem. The neuronal surface, composed principally of phosphatidylcholine (POPC), has a known ordering effect on water. This produces highly organized water layers (OWLs) at the neuron–water interface—the neurochemical implications of which are not currently understood. The human brain is 75% water by volume, with folds and grooves to maximize surface area, suggesting that characterization of neuronal OWLs may contribute to an understanding of neuronal signal transmission. Previous experimental work has measured enhanced conductivity of POPC OWLs relative to bulk water. The mechanism underlying this conductivity is still debated. Using quantum chemical methods on a POPC–water interface model system, we present data characterizing OWL conductance. Non-equilibrium Green's function calculation results demonstrate that there is negligible electron transfer-based conductivity through the OWL at biological temperatures. This is consistent with existing studies suggesting the Grotthuss mechanism as the most likely explanation for experimentally observed enhanced conductivity at the POPC–water interface. The broader implications of enhanced proton conductivity at the neuron–water interface are discussed.

Sensing of sulfur containing toxic gases with double transition metal carbide MXenes

Sensing of sulfur containing gases, such as hydrogen sulfide (H2S) and sulfur dioxide (SO2), on double transition metal carbide MXenes has been studied by means of density functional theory calculations. It is found that both H2S and SO2 strongly physisorbed on M2TiC2Tx (M = Mo, Cr; Tx = O, S, OH) monolayers. The adsorption of H2S is stronger in the case of oxygen termination, (Mo2TiC2O2, Cr2TiC2O2), whereas SO2 has stronger adsorption on sulfur terminated (Mo2TiC2S2, Cr2TiC2S2) monolayers. Binding characteristics of H2S and SO2 are further confirmed with Bader charge transfer, density of states, and charge density differences. Using a statistical thermodynamic analysis, the sensing mechanism of H2S and SO2 is studied under varied pressures and temperature conditions. By means of non-equilibrium Green's function calculations, the sensitivities of H2S and SO2 on the Mo2TiC2S2 monolayer are found to be 16.3%, 10.3%, respectively, which showed promising sensing characteristics. Our results reveal that double transition metal carbide MXenes can be a potential candidate for the sensing of sulfur containing gases.

Spintronic action of Cn-C6H6-Fe-C6H6-C13-n; n = 6: How crucial are d electrons?

The pi stacked complex C6C6H6-Fe-C6H6C7, while sandwiched amongst two Fe (100) electrodes display molecular spintronic characteristics with spin filtration and spin rectification under applied bias. Spintronic feature of C6C6H6-Fe-C6H6C7 has been validated by performing best in class nonequilibrium Green's function calculations and an examination of density of states of iron and carbon. Our study also reports spin filtration, spin rectification and measurement of pure spin current corresponding to n = 6. Entire explanation has been provided through a prognosis of projected device density of states and transmission pathways of our chosen system. These observations, certainly provides a new dimension in the design of pi stacked transition metal complex exhibiting spintronic feature and opens up another prospective area of spintronic research. Our study reveals that final transmission behaviour is decided by dominant carbon 2p electrons along with small contribution of 3d electrons of iron.

Parallel-Self-Assembling Stack, Center-Capture Effect, and Reactivity-Enhancing Effect of N-Layer (N = 1, 2, 3) Cyclo[18]carbon.

Cyclo[18]carbon (C18) is an captivating allotrope of carbon synthesized recently, which has drawn the attention among scientists. There are still few studies on the dynamic behaviors of C18. To gain knowledge in this area, we systematically explored the stacking behaviors and the oxidation kinetics of C18, as well the electronic transport behaviors of C18 oxides, by density functional theory and nonequilibrium Green's function calculations combined with reactive force field molecular dynamics simulations. The parallel-self-assembling behaviors were observed in the stack of two- or three-layer C18. During the oxidation process of C18, we found an evident center-capture effect in which the hollow rings would preferentially attract an O2 molecule into their centers. Moreover, the adsorption of O2 on the O2-doped rings was dramatically enhanced by the O2 at the center of the ring, showing the reactivity-enhancing effect. The excellent electron transport property of central-O2-doped C18 among 13 types of C18 oxides demonstrates the potential of C18 oxides as promising molecular devices for various applications. This study reveals the dynamic behaviors of C18 and provides theoretical guidance for use of C18 and C18 oxides in molecular devices.

THz intersubband electroluminescence from n-type Ge/SiGe quantum cascade structures

We report electroluminescence originating from L-valley transitions in n-type Ge/Si0.15Ge0.85 quantum cascade structures centered at 3.4 and 4.9 THz with a line broadening of Δf/f≈0.2. Three strain-compensated heterostructures, grown on a Si substrate by ultrahigh vacuum chemical vapor deposition, have been investigated. The design is based on a single quantum well active region employing a vertical optical transition, and the observed spectral features are well described by non-equilibrium Green's function calculations. The presence of two peaks highlights a suboptimal injection in the upper state of the radiative transition. Comparison of the electroluminescence spectra with a similar GaAs/AlGaAs structure yields one order of magnitude lower emission efficiency.

A model for dynamical solvent control of molecular junction electronic properties

Experimental measurements of electron transport properties of molecular junctions are often performed in solvents. Solvent-molecule coupling and physical properties of the solvent can be used as the external stimulus to control the electric current through a molecule. In this paper, we propose a model that includes dynamical effects of solvent-molecule interaction in non-equilibrium Green's function calculations of the electric current. The solvent is considered as a macroscopic dipole moment that reorients stochastically and interacts with the electrons tunneling through the molecular junction. The Keldysh-Kadanoff-Baym equations for electronic Green's functions are solved in the time domain with subsequent averaging over random realizations of rotational variables using the Furutsu-Novikov method for the exact closure of infinite hierarchy of stochastic correlation functions. The developed theory requires the use of wideband approximation as well as classical treatment of solvent degrees of freedom. The theory is applied to a model molecular junction. It is demonstrated that not only electrostatic interaction between molecular junction and solvent but also solvent viscosity can be used to control electrical properties of the junction. Alignment of the rotating dipole moment breaks the particle-hole symmetry of the transmission favoring either hole or electron transport channels depending upon the aligning potential.

Spin-orbit-proximitized ferromagnetic metal by monolayer transition metal dichalcogenide: Atlas of spectral functions, spin textures, and spin-orbit torques in Co/MoSe2, Co/WSe2 , and Co/TaSe2 heterostructures

The bilayer heterostructures composed of an ultrathin ferromagnetic metal (FM) and a material hosting strong spin-orbit (SO) coupling are principal resource for SO torque and spin-to-charge conversion nonequilibrium effects in spintronics. We demonstrate how hybridization of wavefunctions of Co layer and a monolayer of transition metal dichalcogenides (TMDs)---such as semiconducting MoSe$_2$ and WSe$_2$ or metallic TaSe$_2$---can lead to dramatic transmutation of electronic and spin structure of Co within some distance away from its interface with TMD, when compared to the bulk of Co or its surface in contact with vacuum. This is due to proximity induced SO splitting of Co bands encoded in the spectral functions and spin textures on its monolayers, which we obtain using noncollinear density functional theory (ncDFT) combined with equilibrium Green function (GF) calculations. In fact, SO splitting is present due to structural inversion asymmetry of the bilayer even if SO coupling within TMD monolayer is artificially switched off in ncDFT calculations, but switching it on makes the effects associated with proximity SO coupling within Co layer about five times larger. Injecting spin-unpolarized charge current through SO-proximitized monolayers of Co generates nonequilibrium spin density over them, so that its cross product with the magnetization of Co determines SO torque. The SO torque computed via first-principles quantum transport methodology, which combines ncDFT with nonequilibrium GF calculations, can be used as the screening parameter to identify optimal combination of materials and their interfaces for applications in spintronics. In particular, we identify heterostructure two-monolayer-Co/monolayer-WSe$_2$ as the most optimal.

Stochastic simulation of nonequilibrium heat conduction in extended molecular junctions.

Understanding phononic heat transport processes in molecular junctions is a central issue in the developing field of nanoscale heat conduction. Here, we present a Langevin dynamics simulation framework to investigate heat transport processes in molecular junctions at and beyond the linear response regime and apply it to saturated and unsaturated linear hydrocarbon chains connecting two gold substrates. Thermal boundary conditions represented by Markovian noise and damping are filtered through several (up to four) gold layers to provide a realistic and controllable bath spectral density. Classical simulations using the full universal force field are compared with quantum calculations that use only the harmonic part of this field. The close agreement found at about room temperature between these very different calculations suggests that heat transport at such temperatures is dominated by lower frequency vibrations whose dynamics is described well by classical mechanics. The results obtained for alkanedithiol molecules connecting gold substrates agree with previous quantum calculations based on the Landauer formula and match recent experimental measurements [e.g., thermal conductance around 20 pW/K for alkanedithiols in single-molecule junctions (SMJs)]. Heat conductance simulations on polyynes of different lengths illuminate the effects of molecular conjugation on thermal transport. The difference between alkanes and polyynes is not large but correlates with the larger rigidity and stronger mode localization that characterize the polyyne structure. This computational approach has been recently used [R. Chen, I. Sharony, and A. Nitzan, J. Phys. Chem. Lett. 11, 4261-4268 (2020)] to unveil local atomic heat currents and phononic interference effect in aromatic-ring based SMJs.

Speed Up Quantum Transport Device Simulation on Ferroelectric Tunnel Junction With Machine Learning Methods

As the device size scales down to the nanometer regime, quantum effects play an important role in device characteristics and performance. Quantum transport device simulation based on the nonequilibrium Green's function (NEGF) has been extensively applied to simulate the nanoscale devices. The NEGF simulations, however, can be computationally expensive, especially in the presence of scattering. In this study, a machine learning (ML)-based framework is developed, targeting on replacing the computationally intensive NEGF simulations. This framework first learns a sparse representation of a quantum transport property of interest and then trains a model to describe the quantitative mapping relation between the device parameters and properties. Also, the accuracy is further improved with the application of feature engineering. As an example, a graphene-ferroelectric-metal (GFM) ferroelectric tunnel junction (FTJ) is simulated. The results show that the ML-based framework allows circumventing the NEGF calculation and simultaneously maintaining high accuracy in quantum transmissions and tunneling I-V characteristics. This ML-based framework can be applied to speed up the quantum transport device simulations and enable efficient tunneling device design.

First-principles study of the electronic structure and transport properties of armchair graphene nanoribbons with adsorbed super-halogen LiF2 and super-alkali Li3 clusters

The electronic structure and quantum transport properties of pristine armchair graphene nanoribbons (AGNRs) and AGNRs adsorbing super-halogen LiF2 and super-alkaline Li3 clusters (Li3/AGNRs/LiF2) were investigated using density functional theory and non-equilibrium Green's function calculations. It was found that LiF2 and Li3 clusters are stably adsorbed on the AGNRs, and the adsorption of Li3 and LiF2 endows AGNRs with the characteristics of n-type and p-type semiconductors, respectively. The Li3/AGNRs/LiF2 structure reduces the band gap and the turn-on voltage, and improves the transmission coefficient of the ANGRs device. This structure also exhibit the rectification characteristics of a pn junction with the forward bias current greater than the reverse bias current. This shows that adsorption of super-alkali and super-halogen clusters in different regions of AGNRs is a feasible approach for obtaining AGNRs with pn junction characteristics.

Quasi-Fermi level splitting in nanoscale junctions from ab initio

The splitting of quasi-Fermi levels (QFLs) represents a key concept utilized to describe finite-bias operations of semiconductor devices, but its atomic-scale characterization remains a significant challenge. Herein, the nonequilibrium QFL or electrochemical potential profiles within single-molecule junctions obtained from the first-principles multispace constrained-search density-functional formalism are presented. Benchmarking the standard nonequilibrium Green's function calculation results, it is first established that algorithmically the notion of separate electrode-originated nonlocal QFLs should be maintained within the channel region during self-consistent finite-bias electronic structure calculations. For the insulating hexandithiolate junction, the QFL profiles exhibit discontinuities at the left and right electrode interfaces and across the molecule the accompanying electrostatic potential drops linearly and Landauer residual-resistivity dipoles are uniformly distributed. For the conducting hexatrienedithiolate junction, on the other hand, the electrode QFLs penetrate into the channel region and produce split QFLs. With the highest occupied molecular orbital entering the bias window and becoming a good transport channel, the split QFLs are accompanied by the nonlinear electrostatic potential drop and asymmetric Landauer residual-resistivity dipole formation. Our findings underscore the importance of the first-principles extraction of QFLs in nanoscale junctions and point to a future direction for the computational design of next-generation semiconductor devices.

Surface Strain-Induced Collective Switching of Ensembles of Molecules on Metal Surfaces.

A central difficulty in the design of molecular electronics is poor control of the contact state between the molecule and metal electrode, which may induce instability and noise in logic and memory devices and even destroy the intrinsic functionality of the device. Here, we theoretically propose a simple and effective strategy for realizing full control of the contact state of organic molecules coated on the metal surface by applying homogeneous surface strain. As exemplified by pyrazine molecules on Cu(111), application of compressive (tensile) strain causes the molecules to uniformly adopt the physisorbed (chemisorbed) state. Within the framework of non-equilibrium Green's function calculations, we show that the two distinct contact states yield simultaneous rectification and switching behaviors. Because the contact states of all surface-bound molecules are transformed uniformly via surface strain perturbations, fully controlled collective switching and rectification effects can be simultaneously achieved in this contact system.

Removing all periodic boundary conditions: Efficient nonequilibrium Green's function calculations

We describe a method and its implementation for calculating electronic structure and electron transport without approximating the structure using periodic super-cells. This effectively removes spurious periodic images and interference effects. Our method is based on already established methods readily available in the non-equilibrium Green function formalism and allows for non-equilibrium transport. We present examples of a N defect in graphene, finite voltage bias transport in a point-contact to graphene, and a graphene-nanoribbon junction. This method is less costly, in terms of CPU-hours, than the super-cell approximation.

Competitive conductive mechanism of interstitial Ag and oxygen vacancies in Ag/Ta2O5/Pt stack

The transport properties of Ag/Ta2O5/Pt with coexisting interstitial Ag and oxygen vacancies are examined by density-functional theory and nonequilibrium Green's function calculation. The results show that the coexistence of interstitial Ag and oxygen vacancies results in a reduced transmission coefficient, implying an antagonistic interaction between Ag and oxygen vacancies. Interstitial Ag atoms may take the position of oxygen vacancies and block the oxygen vacancy channel. Alternatively, oxygen vacancies attract electrons from nearby Ag channels thereby reducing the conductance. By comparing the different dual-component channels, it is found that Ag and oxygen vacancies tend to form a complete oxygen vacancy channel with a few Ag atoms giving rise to higher conductance. Our calculation reveals a competitive conductive mechanism of interstitial Ag and oxygen vacancies and a promising strategy to investigate multicomponent channels and improve the design of future synaptic devices.

Decomposition of Ferrocene on Pt(111) and Its Effect on Molecular Electronic Junctions

From dilute vapor, ferrocene encountering Pt(111) decomposes, producing bound cyclopentadienyl rings, in contrast to its legendary stability in solution electrochemistry. We propose that decomposition occurs through initial chemisorption, making a Pt−C bond to a ferrocenium hydride, followed by step-edge catalyzed decomposition leading to migration of the Fe atom inside the Pt bulk. These conclusions are based on results from density functional theory (DFT) calculations. When Pt(111) approaches ferrocene tethered to a self-assembled monolayer, only the first, spontaneous but mechanically reversible chemisorption is predicted. Nonequilibrium Green's function calculations utilizing DFT predict that chemisorption increases molecular junction conductivities by a factor of 2−5. This could contribute to the extremely high conductivities observed in junctions supporting rectification up to unprecedented high-frequency cutoffs of ∼520 GHz, though squashed junctions at half monolayer coverage are predicted to conduct 104 times better.

Study of an application of non-parabolic complex band structures to the design for mid-infrared quantum cascade lasers

We have investigated the influence of nonparabolicity both of an imaginary band located in a bandgap and of a conduction band to improve the accuracy of energy levels for the design of GaInAs/AlInAs mid-infrared quantum cascade lasers (QCLs). The lasing wavelength of the QCL obtained experimentally was compared to that of the calculated optical gain peak by utilizing the single-band non-equilibrium Green's function (NEGF) method. We calculated the energy-dependent effective mass of electrons used in the NEGF calculation from the complex band structure of each bulk material forming the QCL. In a widely lasing wavelength range of 5–10 μm, the calculated gain peaks of the QCLs each agreed very well with the lasing wavelengths obtained experimentally. We have confirmed that in designing the QCL structures, energy dependency of the energy effective mass in the complex bands is significant.

Sub-thermal switching of ultra-narrow graphene nanoribbon tunnel field effect transistors

In this paper, we study the device performance of the graphene nanoribbon tunnel field effect transistors in the sub 0.5V bias voltage range by non-equilibrium Green's function calculation. The ON/OFF ratio is found to increases with decreasing bias voltage, as the improved current suppression in the OFF state at low bias is more effective than the reduction of carriers in the ON state. Abrupt increase of the subthreshold slope (SS) from sub-thermal ∼30 mV/dec to 60 mV/dec below VBias of 0.1 V is observed. SS relates to the occupancy of carriers at the threshold energy of band-to-band tunneling. We furthermore discuss the constant potential barrier scaling of the graphene channel width and length.

Control over Near-Ballistic Electron Transport through Formation of Parallel Pathways in a Single-Molecule Wire.

This paper reports highly efficient coherent tunneling in single-molecule wires of oligo-ferrocenes with one to three Fc units. The Fc units were directly coupled to the electrodes, i.e., without chemical anchoring groups between the Fc units and the terminal electrodes. We found that a single Fc unit readily interacts with the metal electrodes of an STM break junction (STM = scanning tunneling microscope) and that the zero-voltage bias conductance of an individual Fc molecular junction increased 5-fold, up to 80% of the conductance quantum G0 (77.4 μS), when the length of the molecular wire was increased from one to three connected Fc units. Our compendium of experimental evidence combined with nonequilibrium Green function calculations contemplate a plausible scenario to explain the exceedingly high measured conductance based on the electrode/molecule contact via multiple Fc units. The oligo-Fc backbone is initially connected through all Fc units, and, as one of the junction electrodes is pulled away, each Fc unit is sequentially disconnected from one of the junction terminals, resulting in several distinct conductance features proportional to the number of Fc units in the backbone. The conductance values are independent of the applied temperature (-10 to 85 °C), which indicates that the mechanism of charge transport is coherent tunneling for all measured configurations. These measurements show the direct Fc-electrode coupling provides highly efficient molecular conduits with very low barrier for electron tunneling and whose conductivity can be modulated near the ballistic regime through the number of Fc units able to bridge and the energy position of the frontier molecular orbital.

Microcanonical RT-TDDFT simulations of realistically extended devices.

In this paper, real-time time-dependent density functional theory (RT-TDDFT) calculations of realistically sized nanodevices are presented. These microcanonical simulations rely on a closed boundary approach based on recent advances in the software package CP2K. The obtained results are compared to those derived from the open-boundary Non-equilibrium Green's Function (NEGF) formalism. A good agreement between the "current vs. voltage" characteristics produced by both methods is demonstrated for three representative device structures, a carbon nanotube field-effect transistor, a GeSe selector for crossbar arrays, and a conductive bridging random-access memory cell. Different approaches to extract the electrostatic contribution from the RT-TDDFT Hamiltonian and to incorporate the result into the NEGF calculations are presented.

Modified MXene: promising electrode materials for constructing Ohmic contacts with MoS2 for electronic device applications.

The development of MoS2-based electronic devices is dependent on finding electrode materials suitable for forming Ohmic contacts with MoS2. For this purpose, we carried out density functional theory and nonequilibrium Green's function calculations to investigate the possibility of using pristine and modified MXene (Ta2C/Ta2CF2/Ta2C(OH)2) monolayers as the electrode materials in such devices. These calculations indicated the formation of chemical bonds at the MoS2/Ta2C interface, and resulting strong orbital hybridization between the MoS2 and Ta2C components, but relatively weak interactions for MoS2/Ta2CF2 and MoS2/Ta2C(OH)2. Ohmic contacts were observed in all three cases. Transport properties were further simulated by modeling two-probe field effect transistors (FETs) with Ta2C/Ta2CF2/Ta2C(OH)2 as electrodes. Interestingly, these simulations indicated the formation of Ohmic contacts between Ta2CF2/Ta2C(OH)2 electrodes and the channel, but an n-type Schottky barrier for the Ta2C electrode. Furthermore, we found the resistance of the FET based on MoS2/Ta2C(OH)2 to be half of that based on MoS2/Ta2CF2. The results of our study not only revealed promising electrode materials for forming full Ohmic contacts with MoS2 monolayers in FET devices, but also validated the effective role of a small-molecule fragment as a buffer layer in realizing Ohmic contacts between metal and semiconductor.