Nonequilibrium Green Function Approach Research Articles

Nonequilibrium Green's-Function Approach to the Suppression of Rectification at Metal–Mott-Insulator Interfaces

The suppression of rectification at metal-Mott-insulator interfaces, which was previously shown by numerical solutions to the time-dependent Schrodinger equation and experiments on real devices, is reinvestigated theoretically using nonequilibrium Green's functions. The one-dimensional Hubbard model is used for a Mott insulator. The effects of attached metallic electrodes are incorporated into the self-energy. A scalar potential originating from work-function differences and satisfying the Poisson equation is added to the model. For electron density, we decompose it into three parts. One is obtained by integrating the local density of states over energy to the midpoint of the electrodes' chemical potentials. The others, obtained by integrating lesser Green's functions, are due to couplings with the electrodes and correspond to an inflow and an outflow of electrons. In Mott insulators, incoming electrons and holes are extended over the whole system, avoiding further accumulation of charges relative to that in the case without bias. This induces collective charge transport and results in the suppression of rectification.

Vibrational Nonequilibrium Effects in the Conductance of Single Molecules with Multiple Electronic States

Vibrational nonequilibrium effects in charge transport through single-molecule junctions are investigated. Focusing on molecular bridges with multiple electronic states, it is shown that electronic-vibrational coupling triggers a variety of vibronic emission and absorption processes, which influence the conductance properties and mechanical stability of single-molecule junctions profoundly. Employing a master equation and a nonequilibrium Green's function approach, these processes are analyzed in detail for a generic model of a molecular junction and for benzenedibutanethiolate bound to gold electrodes.

Spin and charge pumping in magnetic tunnel junctions with precessing magnetization: A nonequilibrium Green function approach

We study spin and charge currents pumped by precessing magnetization of a single ferromagnetic layer within $F|I|N$ or $F|I|F$ ($F$-ferromagnet; $I$-insulator; $N$-normal metal) multilayers of nanoscale thickness attached to two normal-metal electrodes with no applied bias voltage between them. Both simple one-dimensional model, consisting of a single precessing spin and a potential barrier as the ``sample,'' and realistic three-dimensional devices are investigated. In the rotating reference frame, where the magnetization appears to be static, these junctions are mapped onto a four-terminal dc circuit whose effectively half-metallic ferromagnetic electrodes are biased by the frequency $\ensuremath{\hbar}\ensuremath{\omega}/e$ of microwave radiation driving magnetization precession at the ferromagnetic resonance (FMR) conditions. We show that pumped spin current in $F|I|F$ junctions, diminished behind the tunnel barrier and increased in the opposite direction, is filtered into charge current by the second $F$ layer to generate dc pumping voltage of the order of $\ensuremath{\sim}1\text{ }\ensuremath{\mu}\text{V}$ (at FMR frequency $\ensuremath{\sim}10\text{ }\text{GHz}$) in an open circuit. In $F|I|N$ devices, several orders of magnitude smaller charge current and the corresponding dc voltage appear concomitantly with the pumped spin current due to barrier induced asymmetry in the transmission coefficients connecting the four electrodes in the rotating-frame picture of pumping.

Electron–electron interaction effects in quantum point contacts

We consider electron–electron interaction effects in quantum point contacts on the first quantization plateau, taking into account all scattering processes. We compute the low-temperature linear and nonlinear conductance, shot noise and thermopower, by perturbation theory and a self-consistent nonperturbative method. On the conductance plateau, the low-temperature corrections are solely due to momentum-nonconserving processes that change the relative number of left- and right-moving electrons. This leads to a suppression of the conductance for increasing temperature or voltage. The size of the suppression is estimated for a realistic saddle-point potential, and is largest in the beginning of the conductance plateau. For large magnetic field, interaction effects are strongly suppressed by the Pauli principle, and hence the first spin-split conductance plateau has a much weaker interaction correction. For the nonperturbative calculations, we use a self-consistent nonequilibrium Green's function approach, which suggests that the conductance saturates at elevated temperatures. These results are consistent with many experimental observations related to the so-called 0.7 anomaly.

Performance and Design Considerations of a Novel Dual-Material Gate Carbon Nanotube Field-Effect Transistors: Nonequilibrium Green's Function Approach

The concept of dual-material gate (DMG) is applied to the carbon nanotube field-effect transistor (CNTFET) with doped source and drain extensions, and the features exhibited by the resulting new structure, i.e., the DMG-CNTFET structure, have been examined for the first time by developing a two-dimensional (2D) full quantum simulation. The simulations have been done by the self-consistent solution of 2D Poisson–Schrödinger equations, within the nonequilibrium Green's function (NEGF) formalism. The results show DMG-CNTFET decreases significantly leakage current and drain conductance and increases on-off current ratio and voltage gain as compared to the single material gate counterparts CNTFET. It is seen that short channel effects in this structure are suppressed because of the perceivable step in the surface potential profile, which screens the drain potential. Moreover, these unique features can be controlled by engineering the workfunction and length of the gate metals. Therefore, this work provides an incentive for further experimental exploration.

ATOMISTIC SIMULATION OF GATE EFFECT ON NANOSCALE INTRINSIC Si FIELD-EFFECT TRANSISTORS

We study the electrostatic and quantum transport properties of nanoscale double-gated Si -based field effect transistors within the framework of density functional theory combined with nonequilibrium Green's function approach. In our model device system, a Si slab is sandwiched between two insulator slabs and connected to two semi-infinite Si electrodes at its left and right ends. The effect of the double gates is taken into account by applying proper electrostatic boundary conditions and solving the Poisson equation self-consistently in the system. In the representation of localized SIESTA linear combination of atomic orbitals, the study is carried out with the help of Atomistix ToolKit (ATK) package together with an efficient multigrid Poisson solver. We find that the surface potential versus gate voltage curve shows similar characteristics as in conventional MOSFETs even for devices of 1 nm size, though the shape of the curve varies with the shrink of the system. In different working regimes of the devices, the electrostatic potential and the transmission spectrum are analyzed for an atomistic understanding of the device behavior.

Tunnel magnetoresistance for coherent spin-flip processes on an interacting quantumdot

Spin-polarized electronic tunneling through a quantum dot coupled to ferromagneticelectrodes is investigated within a nonequilibrium Green function approach. Aninterplay between coherent intradot spin-flip transitions, tunneling processes andCoulomb correlations on the dot is studied for current–voltage characteristicsof the tunneling junction in parallel and antiparallel magnetic configurationsof the leads. It is found that due to the spin-flip processes electric current inthe antiparallel configuration tends to the current characteristics in the parallelconfiguration, thus giving rise to suppression of the tunnel magnetoresistance (TMR)between the threshold bias voltages at which the dot energy level becomes active intunneling. Also, the effect of a negative differential conductance in symmetricaljunctions, splitting of the conductance peaks, significant modulation of TMRpeaks around the threshold bias voltages as well as suppression of the diode-likebehavior in asymmetrical junctions is discussed in the context of coherent intradotspin-flip transitions. It is also shown that TMR may be inverted at selected gatevoltages, which qualitatively reproduces the TMR behavior predicted recentlyfor temperatures in the Kondo regime, and observed experimentally beyond theKondo regime for a semiconductor InAs quantum dot coupled to nickel electrodes.

Spin Current Characteristics in a Quantum Dot-Ferromagnetic Contacts Sandwich Structure

We present an accurate theoretical treatment of spin current transport in a ferromagnetic-quantum dot-ferromagnetic (FM-QD-FM) system. The current flowing through the system is spin-polarized due to the spin asymmetric density of states (DOS) in the FM region. In the FM contacts, the spin current is modeled by the conventional macroscopic analysis-spin-drift-diffusion (SDD) model based on the Boltzmann equations. However, in the QD region, the current needs to be treated under mesoscopic regime to account for the electron correlation and the dot-leads coupling. We use the Keldysh non-equilibrium Green function (NEGF) approach based on equation of motion technique to model the current transport in the dot region and integrate the macroscopic treatment in the FM leads and microscopic treatment in the QD in a self-consistent manner. The multi-scale approach we introduced here presents a realistic and simplified way for calculating spin current in such a FM-QD-FM system.

Kinetics of spin coherence of electrons inn-type InAs quantum wells under intense terahertz laser fields

Spin kinetics in $n$-type InAs quantum wells under intense terahertz laser fields is investigated by developing fully microscopic kinetic spin Bloch equations via the Floquet-Markov theory and the nonequilibrium Green's function approach, with all the relevant scattering, such as the electron-impurity, electron-phonon, and electron-electron Coulomb scattering explicitly included. We find that a finite steady-state terahertz spin polarization induced by the terahertz laser field, first predicted by Cheng and Wu [Appl. Phys. Lett. 86, 032107 (2005)] in the absence of dissipation, exists even in the presence of all the scattering. We further discuss the effects of the terahertz laser fields on the spin relaxation and the steady-state spin polarization. It is found that the terahertz laser fields can strongly affect the spin relaxation via hot-electron effect and the terahertz-field-induced effective magnetic field in the presence of spin-orbit coupling. The two effects compete with each other, giving rise to nonmonotonic dependence of the spin-relaxation time as well as the amplitude of the steady-state spin polarization on the terahertz field strength and frequency. The terahertz field dependences of these quantities are investigated for various impurity densities, lattice temperatures, and strengths of the spin-orbit coupling. Finally, the importance of the electron-electron Coulomb scattering on spin kinetics is also addressed.

Modeling of Nanoscale Devices

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> We aim to provide engineers with an introduction to the nonequilibrium Green's function (NEGF) approach, which is a powerful conceptual tool and a practical analysis method to treat nanoscale electronic devices with quantum mechanical and atomistic effects. We first review the basis for the traditional, semiclassical description of carriers that has served device engineers for more than 50 years. We then describe why this traditional approach loses validity at the nanoscale. Next, we describe semiclassical ballistic transport and the Landauer–Buttiker approach to phase-coherent quantum transport. Realistic devices include interactions that break quantum mechanical phase and also cause energy relaxation. As a result, transport in nanodevices is between diffusive and phase coherent. We introduce the NEGF approach, which can be used to model devices all the way from ballistic to diffusive limits. This is followed by a summary of equations that are used to model a large class of structures such as nanotransistors, carbon nanotubes, and nanowires. Applications of the NEGF method in the ballistic and scattering limits to silicon nanotransistors are discussed. </para>

Multimode vibrational effects in single-molecule conductance: A nonequilibrium Green’s function approach

The role of multimode vibrational dynamics in electron transport through single molecule junctions is investigated. The study is based on a generic model, which describes charge transport through a single molecule that is attached to metal leads. To address vibrationally-coupled electron transport, we employ a nonequilibrium Green's function approach that extends a method recently proposed by Galperin et al. [Phys. Rev. B 73, 045314 (2006)] to multiple vibrational modes. The methodology is applied to two systems: a generic model with two vibrational degrees of freedom and benzenedibutanethiolate covalently bound to gold electrodes. The results show that the coupling to multiple vibrational modes can have a significant effect on the conductance of a molecular junction. In particular, we demonstrate the effect of electronically induced coupling between different vibrational modes and study nonequilibrium vibrational effects by calculating the current-induced excitation of vibrational modes.

Non-Equilibrium Green's Function Approach to Three-Dimensional Carbon Nanotube Field Effect Transistor Simulations

Non-Equilibrium Green's Function Approach to Three-Dimensional Carbon Nanotube Field Effect Transistor Simulations

Impact of strain on scaling of Double Gate nanoMOSFETs using NEGF approach

AbstractThe effect of biaxial strain on double gate (DG) nanoscaled MOSFET with channel lengths in the nanometre range is investigated using Non‐Equilibrium Green's Functions (NEGF) simulations. The NEGF simulations are fully 2D in order to accurately evaluate the effects of strain in strongly confined channels. Starting with a 14 nm gate length DG MOSFET with a corresponding body thickness of 9 nm we scale the transistors to gate lengths of 10, 6 and 4 nm and body thicknesses of 6.1, 2.6 and 1.3 nm, respectively. The simulated ID‐VG characteristics show 11% improvement in the oncurrent for the 14 nm gate length transistor due to the Δ valley splitting. This improvement in the on‐current is due to separate contributions from the 2 fold and 4 fold valleys to the carrier transport. However, in the device with an extreme body thickness of 1.3 nm the strain has no impact on its performance because the strong confinement itself produces a large valley splitting. (© 2008 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Quantum Modeling of Thermoelectric Properties of Si/Ge/Si Superlattices

Using a nonequilibrium Green's function approach, quantum simulations are performed to assess the device characteristics for cross-plane transport in Si/Ge/Si-superlattice thin films. The effect of quantum confinement on the Seebeck coefficient and electrical transport and its impact on the power factor of superlattices are studied. In this case, decreasing well width leads to an increased subband spacing causing the Seebeck coefficient of the superlattice to decrease. Electron confinement also causes a drastic reduction in the overall available density of states. Results show that confinement effects in the silicon barrier are responsible for a 40% decrease in the electrical conductivity of superlattices where barrier films are thinner by a factor of 1.5. In the same two devices, there is a negligible change in the Seebeck coefficient, which results in a decrease in the power factor corresponding to the decrease in conductivity. This decrease in the electrical performance for superlattices with thinner layers may offset the previously hypothesized gains of highly scaled superlattice structures resulting from reduced thermal conductivity. Simulations of the present superlattice structure at varying doping levels show a decrease in power factor with a decrease in device size parameters.

Corrected Article: “ac response of a carbon chain under a finite frequency bias” [J. Chem. Phys. 127, 104701 (2007)

Based on nonequilibrium Green's function approach and density functional theory, we report first principles investigation on ac transport of four carbon atomic chain connected by two semi-infinite aluminum leads, Al-C(4)-Al. For small alternating external bias voltage, we expanded nonequilibrium Green's function to the first order in the external voltage and calculated the dynamical conductance. The suppression of the dynamic conductance was obtained near the resonant level, while far away from the resonance, the large enhancement of the dynamic conductance was observed. These behaviors can be understood well under the wide-band limit. By changing the coupling distance between the carbon atom and the aluminum leads, the system could change its transport response between capacitivelike and inductivelike.

Ac response of a carbon chain under a finite frequency bias

Based on nonequilibrium Green's function approach and density functional theory, we report first principles investigation on ac transport of four carbon atom chain connected by two semi-infinite aluminum leads Al-C(4)-Al. For small alternating external bias voltage, we expanded nonequilibrium Green's function to the first order in the external voltage and calculated the dynamical conductance. The suppression of the dynamic conductance was obtained near the resonant level while far away from the resonance the giant enhancement of the dynamic conductance was also observed. These behaviors can be well understood under the wide-band limit. By changing the coupling distance between the carbon atom and aluminum leads, the system could change its transport response between capacitivelike and inductivelike.

Quantum electronic transport: Linear and nonlinear conductance from the Keldysh approach

This is a review of the derivation of the Landauer conductance using the Keldysh non-equilibrium Green's function (NEGF) formalism and the equations-of-motion (EOM) method. We consider the elastic quantum electronic transport through a multi-lead device and treat the conductor in the mean-field approximation. This is suitable for open quantum dots as well as for several molecular systems where charging effects are negligible. The focus of the presentation is to unveil the technical issues involved in the formalism. We show how the Landauer conductance emerges as a linear term in the current–voltage I – V characteristics and indicate how to go beyond this regime. We address the connection of the NEGF approach to recent developments in molecular transport and discuss the problems that arise when one tries to include interaction effects beyond the mean field.

The Impact of Random Dopant Aggregation in Source and Drain on the Performance of Ballistic DG Nano-MOSFETs: A NEGF Study

We have studied the effect of deviations from doping uniformity in source and drain on the performance of sub-20 nm silicon double-gate MOSFET devices. The study is motivated by recent direct observation of such inhomogeneities in small MOSFET devices. The model assumes a continuous charge distribution with randomly located regions of high doping. Individual dopants are not resolved. Impurity scattering in the source and drain regions is neglected. The current-voltage characteristics are computed for devices that differ only in the microscopic arrangement of the randomly distributed high doping regions. We have also studied devices that differ in the number of these clusters. An ensemble of devices with fluctuating numbers of clusters has been constructed based on a Gaussian distribution centered on the mean cluster number derived from the average doping concentration in the source/drain. The impact of high doping clusters, particularly on charge injection, has been studied in detail for the first time using full quantum simulation based on the 2D nonequilibrium Green function approach coupled self-consistently to Poisson's equation. We have assumed an average lateral symmetry for the double-gate MOSFET. Therefore, we only consider inhomogeneities in doping in the plane of the simulation. The devices studied have 12 nm channel lengths which allows the approximation of ballistic quantum transport through the self-consistent electrostatic potential landscape of the device. The computed current-voltage characteristics are monotonic and they are most strongly affected by the fluctuations in the total number of high doping regions. Fluctuations in the spatial configuration of clusters have a lesser effect. Threshold voltages shifts around 100 mV and on-current fluctuations around 50% are obtained from the simulations. However, the subthreshold slope remains almost independent of the microscopic cluster distribution. The on-current variations are considerably larger than those predicted from classical modeling.

Electronic and transport properties of silicon nanowires

The electronic, structural and transport properties of silicon nanowires have been investigated with different approaches. The Empirical Tight-Binding model (ETB) and Linear Combination of Bulk Bands (LCBB) method are used to calculate effect of quantum confinement on electronic energies, bandgap and effective masses in silicon nanowires in function of Si cell size. Both hydrogenated and SiO2 terminated silicon surfaces are studied. Transport properties of nanowires are obtained by applying the Non-Equilibrium Green Function (NEGF) method. NEGF approach has been used to describe nanoMOSFET devices based on Silicon nanowires.

Spin-dependent inelastic transport through single-molecule junctions with ferromagnetic electrodes

Using the nonequilibrium Green's function approach and taking into account contributions of both electron and hole, we investigate the spin-dependent carrier transport in a magnetic tunnel junction consisting of a molecular quantum dot coupled to two ferromagnetic leads and to a local vibrational mode. The calculated results show a remarkable influence of electron-phonon interaction and electron-electron interaction on spin-dependent density of states, charge current, and tunneling magnetoresistance (TMR). The oscillating TMR is attributed to the phonon-assisted resonant tunneling rather than the well-known charging effect. The behavior of the zero-bias TMR dip or peak depends to a great degree on whether the quantum dot is in the Kondo or non-Kondo regime.