Nonequilibrium Green Function Research Articles

Electron Transport Properties of Graphene/WS2 Van Der Waals Heterojunctions.

Van der Waals heterojunctions of two-dimensional atomic crystals are widely used to build functional devices due to their excellent optoelectronic properties, which are attracting more and more attention, and various methods have been developed to study their structure and properties. Here, density functional theory combined with the nonequilibrium Green's function technique has been used to calculate the transport properties of graphene/WS2 heterojunctions. It is observed that the formation of heterojunctions does not lead to the opening of the Dirac point of graphene. Instead, the respective band structures of both graphene and WS2 are preserved. Therefore, the heterojunction follows a unique Ohm's law at low bias voltages, despite the presence of a certain rotation angle between the two surfaces within the heterojunction. The transmission spectra, the density of states, and the transmission eigenstate are used to investigate the origin and mechanism of unique linear I-V characteristics. This study provides a theoretical framework for designing mixed-dimensional heterojunction nanoelectronic devices.

Rate equations description of the asymmetric double barrier electronic cooler

Recent experimental results showed that an electron gas in an asymmetrical double barrier heterostructure can be effectively cooled down under resonant tunneling condition, thus leading to the realization of an electronic cooler. The cooling process is a multi-parameters phenomenon and it is desirable to handle this problem through a reasonably simple approach, in order to understand the role of each parameter. To this end, we present a rate equation modeling of the electron cooling. We model the resonant tunnel injection of the electrons in the well and their thermionic emission assisted by Longitudinal Optical (LO) phonons absorption and emission. The influence of several parameters on the electronic temperature is discussed. This simple model compares rather well to the predictions of non-equilibrium Green function approach and to the experiments.

Excellent spin filtering and significant magnetoresistance of rhenium phthalocyanine molecular junctions on Au(100)

Spin transport properties of single rhenium phthalocyanine (RePc) and double-rhenium phthalocyanine (Re2Pc2) molecular devices with gold electrodes have been investigated by combining Density Functional theory and nonequilibrium Green’s functions. It was found that the RePc molecular devices exhibited good spin filtration efficiency in the small bias range even in the absence of magnetic electrodes. The Re2Pc2 molecular device exhibited a large magnetoresistance and excellent spin-filtering properties at a finite bias, which can only be achieved by altering the magnetization orientation of the rhenium atom at the center of the phthalocyanine molecule. These conclusions of the rhenium phthalocyanine molecule may have potential application in magnetoresistive devices and spin filters.

C-doped zigzag blue phosphorene nanoribbons for GMR, rectification behaviour and NDR based devices

ABSTRACT Based on density functional theory (DFT) and nonequilibrium Green's function (NEGF) framework, to study the monolayer (ML) blue phosphorene (BlueP) doped with C along zigzag direction, such as the structural stability, and electronic and transport properties. Interestingly, we found that doping engineering strategies can effectively transform monolayer ML ZBlueP doped with C into a spintronic nanodevice with a few unique transport properties. Firstly, our model showed a magnificently giant magnetoresistance (GMR) up to 10 4 under low bias. Secondly, a rectifier with a large rectification ratio (RR) of 10 5 was observed. Lastly, negative differential resistance with a peak-to-valley current ratio (PVCR) of 10 4 was observed. Our research shows a promising route towards the development of high-performance ML ZBlueP spintronics technology by doping with C atom. Our results indicate that our models have immense potential for application in nanoscale spintronic devices.

SnSe Monolayer-Based heavy metal sensors with high Sensitivity, Selectivity, and Reusability: Insights from first principle calculation

Heavy metal pollution has a negative impact on both human health and the environment. The monitoring of heavy metal is therefore very important from a practical standpoint. In this study, the adsorption energy, charge transfer, band, densities of states, and sensitivity of SnSe monolayers toward heavy metals (As, Cd, Cr, Hg, Ni, Pb) were investigated using density functional theory combined with the non-equilibrium Green's function approach. The calculations show that SnSe monolayers have excellent sensitivities exceeding the limit of quantitation (LOQ) towards As, Cd, Hg, and Pb, which are as high as 384467%, 1462%, 1791%, and 26160%, respectively. Moreover, analyzing response peaks at various bias voltages can identify the composition of heavy metals from diverse sources, providing valuable insights for selective heavy metal monitoring. SnSe monolayers exhibit wide bias voltage windows that enhance sensor sensitivity by reaching the detection threshold, while also simplifying sensor encapsulation, resulting in higher reliability. The SnSe monolayer exhibits rapid recovery times for As, Hg, and Cd at room temperature, while for Pb, heating to 498 K is required for rapid recovery. These findings show that SnSe monolayers have a strong potential for constructing extremely sensitive and selective heavy metal sensors that are also reusable, implying that SnSe monolayers might serve as a possible online sensor for environmental monitoring.

Enhanced in-plane thermoelectric properties achieved through the vertical van der Waals stacking of black phosphorus and Ti2C

Vertical van der Waals heterostructures (vdWHs) exhibit considerable freedom in integrating two-dimensional layered materials for achieving excellent performance. In this study, we construct a double-layer Ti2C/BP vdWH by stacking pristine monolayer black phosphorus (BP) and Ti2C vertically. The in-plane thermoelectric properties of BP, Ti2C and Ti2C/BP vdWHs at different temperatures are investigated using density functional theory combined with the non-equilibrium Green's function method. Results showed that the thermoelectric figure of merit (ZT) of Ti2C/BP vdWHs at room temperature (300 K) was approximately 103 and 104 times that of Ti2C and BP, respectively. Because of the mutual compensation of the electronic energy bands and interfacial phonon scattering, Ti2C/BP vdWHs have higher electron conductance and lower phonon conductance than both BP and Ti2C, which significantly enhances the ZT value of these structures. More importantly, the prominent thermoelectric properties of Ti2C/BP vdWHs maintain greater stability as the temperature rises (300–900 K), which leads to a high thermoelectric power factor and ZT value without relying on high temperatures. These results provide a new idea for designing two-dimensional functionalised nanoscale devices with excellent thermoelectric performance.

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.

First-Principles Investigation of Nucleobase Detection by Tetranitrogen Coordinated Transition Metal Doped Graphene Nanoribbons.

Detection of nucleobases is of great significance in DNA sequencing, which is one of the main goals of the Human Genome Project. By employing the nonequilibrium Green function method combined with density functional theory, we proposed a biosensor based on the TMN4 (TM = Ni, Cu) embedded graphene nanoribbons for nucleobase detection. The adsorption energy calculations show that all five nucleobases are physisorbed on the TMN4-doped graphene nanoribbons. Utilizing the distinction of current, the bases T, C, and U can be gradually detected at the biases of 0.4, 0.6, and 0.8 V by NiN4-doped graphene nanoribbons, respectively. The bases A and G can be finally distinguished by CuN4-doped graphene nanoribbons under an external bias of not less than 0.8 V. The identification of individual nucleobases at specific biases could provide a novel mechanism for the further development of biosensors in rapid genome sequencing applications.

Layer engineering piezotronic effect in two-dimensional homojunction transistors

The semiconductor junctions based on piezoelectric materials are of great importance for the realization of functionality and versatility in sensing devices. Two-dimensional (2D) stacked materials provide a promising route to design novel semiconductor junctions due to their layer-dependent electronic and optical properties. However, the combination of layer-dependent band structure and piezoelectricity in device designs is rarely explored to date. In this work, we propose piezotronic transistors designed by layer engineering 2D homojunction. A 2D Poisson equation including the piezoelectric polarization is derived and then combined self-consistently with the non-equilibrium Green function to explore the carrier transport. We find a peculiar symmetrical modulation mechanism of piezotronic effect on carrier transport, i.e., flipping the sign of externally applied strain can drive symmetrical transport process regarding bias polarity. Additionally, the results show that the transport is a mixing of thermionic and tunneling current, which are comparable at low bias but predominated by the quantum tunneling effect at high bias. Although our 2D homojunction transistor is similar to Schottky diodes, the on/off ratio and gauge factors are higher than most of metal-semiconductor contact piezotronic devices. Moreover, for the device with symmetrical stacking configurations, increasing layer number in 2D homojunction can decrease the output current but enhance the gauge factors. By contrast, the device performance in asymmetrical stacking systems is insensitive to the variation of layer number. Our demonstration of layer engineering 2D homojunction transistor not only enriches the fundamental physics of piezotronics, but also open an avenue for designing highly sensitive strain sensors based on diverse 2D layered junctions.

(Invited) Advanced Modeling of Nanoscale Devices

Moore’s scaling law has survived during more than 50 years because the transistor fabrication recipes have been continuously adapted and technology boosters have been gradually introduced, e.g. strain, high- dielectrics, or 3-D FinFETs. The driving force behind these innovations has always been the intuition of clever researchers who benefited from classical technology computer aided design (TCAD) tools. The latter have been used in the semiconductor industry since the end of the 1970’s, when the first 2-D simulations of CMOS devices became feasible on a supercomputer [1]. Over the last 40 years, transistors have undergone tremendous evolutions, their dimensions being reduced by several orders of magnitude, while the physical models at the core of commercially available device simulators have remained the same: electron transport is still described by classical drift-diffusion (DD) equations, which have been modified to capture parts of the quantum mechanical effects affecting nano-transistors, e.g. geometrical confinement tunnelling leakages, or energy quantization [2].A new generation of advanced TCAD tools that go beyond the DD equations and rely on atomistic quantum mechanical concepts is needed to reproduce the characteristics of today’s nanostructures and to predict the performance of not-yet-fabricated components. Such tools should combine different modelling approaches to be able to treat various device types, from state-of-the-art nano-transistors to photo-detectors based on two-dimensional materials or resistive switching random access memories. For example, to shed light on the behaviour of valence change memory (VCM) cells, which consist of metal-insulator-metal stacks, molecular dynamics (MD), kinetic Monte Carlo (KMC), density functional theory (DFT), and quantum transport (QT) should be allied, as illustrated in the accompanying figure. By doing so, the growth of nano-filaments through realistic oxides embedded between two metallic electrodes can be accurately simulated and the electrical current flowing through computed with, e.g., the Non-equilibrium Green’s Function (NEGF) formalism [3]. In this presentation the multi-method simulation environment shown the accompanying Figure will be briefly reviewed. The main focus will be set on the discussion of few applications, among them transistors and memory cells.

The understanding of the impact of efficiently optimized underlap length on analog/RF performance parameters of GNR-FETs

The aim of this study is to examine the analog/RF performance characteristics of graphene nanoribbon (GNR) field-effect transistors (FETs) using a novel technique called underlap engineering. The study employs self-consistent atomistic simulations and the non-equilibrium Green's function (NEGF) formalism. Initially, the optimal underlap length for the GNR-FET by device has been determined evaluating the ON-current (ION) to OFF-current (IOFF) ratio, which is a critical parameter for digital applications. Subsequently, the impact of underlap engineering on analog/RF performance metrics has been analyzed and conducting a comprehensive trade-off analysis considering parameters such as intrinsic-gain, transistor efficiency, and device cut-off frequency. The results demonstrate that the device incorporating the underlap mechanism exhibits superior performance in terms of the ION/IOFF ratio, transconductance generation factor (TGF), output resistance (r0), intrinsic gain (gmr0), gain frequency product (GFP), and gain transfer frequency product (GTFP). However, the device without the underlap effect demonstrates the highest transconductance (gm) and cut-off frequency (fT). Finally, a linearity analysis has been conducted to compare the optimized GNR-FET device with the conventional GNR-FET device without the underlap effect.

Electronic-, Optical-, and Temperature-Dependent Carrier Mobility Simulations of Perovskite-Type Liganded PbS Quantum Dot Array

Recent experimental results suggest that higher mobility of perovskite-type ligand passivated PbS quantum dots (QDs) could be useful for efficient solar cell applications. However, theoretical understanding of the mechanism through first principal modeling is still lacking. In this study, electronic-, optical-, and temperature-dependent carrier mobility for perovskite ligand passivated PbS QD array is calculated by using the first-principles density functional theory (DFT) combined with the nonequilibrium Green’s function (NEGF) technique and a molecular dynamics (MD)-Landauer approach. It is found that formamidinium (FA)-liganded QDs have higher mobility and enhanced optical absorption comparing to that of Cl-liganded QDs. The difference could be understood through the intermediate band featured electronic structure.

High-harmonic generation in spin and charge current pumping at ferromagnetic or antiferromagnetic resonance in the presence of spin–orbit coupling

One of the cornerstone effects in spintronics is spin pumping by dynamical magnetization that is steadily precessing (around, for example, the z-axis) with frequency ω 0 due to absorption of low-power microwaves of frequency ω 0 under the resonance conditions and in the absence of any applied bias voltage. The two-decades-old ‘standard model’ of this effect, based on the scattering theory of adiabatic quantum pumping, predicts that component of spin current vector is time-independent while and oscillate harmonically in time with a single frequency ω 0 whereas pumped charge current is zero in the same adiabatic limit. Here we employ more general approaches than the ‘standard model’, namely the time-dependent nonequilibrium Green’s function (NEGF) and the Floquet NEGF, to predict unforeseen features of spin pumping: namely precessing localized magnetic moments within a ferromagnetic metal (FM) or antiferromagnetic metal (AFM), whose conduction electrons are exposed to spin–orbit coupling (SOC) of either intrinsic or proximity origin, will pump both spin and charge I(t) currents. All four of these functions harmonically oscillate in time at both even and odd integer multiples of the driving frequency ω 0. The cutoff order of such high harmonics increases with SOC strength, reaching in the one-dimensional FM or AFM models chosen for demonstration. A higher cutoff can be achieved in realistic two-dimensional (2D) FM models defined on a honeycomb lattice, and we provide a prescription of how to realize them using 2D magnets and their heterostructures.

A Comparative Study of the Electronic Transport and Gas-Sensitive Properties of Graphene+, T-graphene, Net-graphene, and Biphenylene-Based Two-Dimensional Devices.

The electronic transport properties of the four carbon isomers: graphene+, T-graphene, net-graphene, and biphenylene, as well as the gas-sensing properties to the nitrogen-based gas molecules including NO2, NO, and NH3 molecules, are systematically studied and comparatively analyzed by combining the density functional theory with the nonequilibrium Green's function. The four carbon isomers are metallic, especially with graphene+ being a Dirac metal due to the two Dirac cones present at the Fermi energy level. The two-dimensional devices based on these four carbon isomers exhibit good conduction properties in the order of biphenylene > T-graphene > graphene+ > net-graphene. More interestingly, net-graphene-based and biphenylene-based devices demonstrate significant anisotropic transport properties. The gas sensors based on the above four structures all have good selectivity and sensitivity to the NO2 molecule, among which T-graphene-based gas sensors are the most prominent with a maximum ΔI value of 39.98 μA, being only three-fifths of the original. In addition, graphene+-based and biphenylene-based gas sensors are also sensitive to the NO molecule with maximum ΔI values of 29.42 and 25.63 μA, respectively. However, the four gas sensors are all physically adsorbed for the NH3 molecule. By the adsorption energy, charge transfer, electron localization functions, and molecular projection of self-consistent Hamiltonian states, the mechanisms behind all properties can be clearly explained. This work shows the potential of graphene+, T-graphene, net-graphene, and biphenylene for the detection of toxic molecules of NO and NO2.

Linear photogalvanic effects in monolayer ternary metallic compound Na2MgSn.

The linear photogalvanic effect (LPGE) is investigated by using the non-equilibrium Green's function (NEGF) technique combined with density functional theory (DFT) in monolayer Na2MgSn. We consider the cases of three different central regions, which are pure Na2MgSn, Na-vacancy, and Pb-substituted. It is found that both pure and defective Na2MgSn monolayers induce photoresponse under linearly polarized light. The photoresponse varies periodically as a form of either sinusoidal or cosinoidal function of the polarization angle. In the near-infrared and visible ranges, the photoresponse is more sensitive to the long wave range of visible light. In the case of single-atom defects, the photoresponse with Na-vacancy is larger than that of pb-substitution defects. Compared with the other two central regions, the maximum extinction ratio (ER) of Na-vacancy is larger, so it has higher polarization sensitivity. When the location of Na-vacancy is adjusted, the photoresponse changes obviously, and the Na 1*- vacancy has the largest photoresponse. With the increase of the Na-vacancy concentration, the photoresponse changes nonlinearly but is smaller than that of a single vacancy. A small bias voltage can greatly improve the photoresponse. Our results suggest an effective method to enhance the photoresponse and show the promise of Na2MgSn monolayers in optical detection.

Transport Property of Wrinkled Graphene Nanoribbon Tuned by Spin-Polarized Gate Made of Vanadium-Benzene Nanowire.

A series of four-terminal V7(Bz)8-WGNR devices were established with wrinkled graphene nanoribbon (WGNR) and vanadium-benzene nanowire (V7(Bz)8). The spin-polarized V7(Bz)8 as the gate channel was placed crossing the plane, the concave (endo-positioned) and the convex (endo-positioned) surface of WGNR with different curvatures via Van der Waals interaction. The density functional theory (DFT) and nonequilibrium Green's function (NEGF) methods were adopted to calculate the transport properties of these devices at various bias voltages (VS) and gate voltages (VG), such as the conductance, spin-polarized currents, transmission spectra (TS), local density of states (LDOS), and scattering states. The results indicate that the position of V7(Bz)8 and the bending curvature of WGNR play important roles in tuning the transport properties of these four-terminal devices. A spin-polarized transport property is induced for these four-terminal devices by the spin-polarized nature of V7(Bz)8. Particularly, the down-spin channel disturbs strongly on the source-to-drain conductance of WGNR when V7(Bz)8 is endo-positioned crossing the WGNR. Our findings on the novel property of four-terminal V7(Bz)8-WGNR devices provide useful guidelines for achieving flexible graphene-based electronic nanodevices by attaching other similar multidecker metal-arene nanowires.

Electron transport properties of van der Waals heterostructures composed by one-dimensional carbon nanotubes and two-dimensional germanium selenide

Based on density functional theory (DFT) and non-equilibrium Green's function (NEGF) method, we studied the electron transport properties of van der Waals heterostructures (vdWHs) composed by (n,0) single-walled carbon nanotubes (SWCNTs) (n = 5–11) and two-dimensional germanium selenide (2D GeSe). The (n,0)SWCNT/GeSe vdWHs (n = 5–11) display distinct electron transport properties which can be tuned by the variation of diameter in SWCNTs. The results of the I-V characteristic curves show that the conductances of the (n,0)SWCNT/GeSe vdWHs (n = 7–9,11) are improved after the integration of (n,0)SWCNT (n = 7–9,11) with 2D GeSe. The current in (9,0)SWCNT/GeSe vdWH shows a quite high conductance, which can reach 100 μA under 1.5 V bias. The obtained transmission spectra under bias reveals the tendency of electrons and holes in participating the transport of (n,0)SWCNT/GeSe vdWHs (n = 5–11).

Manipulation of quantum spin transport of TM (Mn, Fe, Co, and Ni) (II) phthalocyanines coupled to carbon nanotube leads applicable in spintronic devices

We conducted a theoretical scrutiny on the quantum spin transport characteristics of a class of open-shell 3d-transition metal (TM = Mn, Fe, Co, and Ni) (II) phthalocyanines (TMPcs) molecules sandwiched between two semi-infinite armchair single-walled carbon nanotube probes. Herein, the spin density functional formalism is utilized in conjunction with state-of-the-art non-equilibrium Green's function technique. Molecular junctions composed of MnPc and FePc have higher local magnetic spin moments than CoPc and NiPc because of the strong exchange spin-splitting between the 3d-states of the Mn or Fe cation atoms and the p-states of the N anion atom. This indicates that TMPc molecules (TM = Mn, and Fe) bridged between two single-walled carbon nanotube (SWCNT) electrodes with a π-type geometry demonstrate a pronounced transmission near the Fermi level. Furthermore, the sign and robustness of spin filter efficiency are tailored by manipulating the central atom of 3d-transition metal and the contact SWCNT electrodes. Subsequently, FePc and MnPc molecular junctions have the advantage of operating practically as ideal spin filter devices compared to CoPc and NiPc molecular structures. Moreover, the tunneling magnetoresistance (TMR) of these molecular devices is assessed. For MnPc and FePc molecular junctions, the estimated total conductance exhibited a robust trend at zero bias voltage, whereas the magnitudes of spin-up and spin-dn quantum conductances increased significantly in CoPc and NiPc molecular configurations with bias voltages range between ±0.45 and ±0.95 Volt. Spin-down carriers essentially govern the quantum conductance of TMPc (Mn, Fe, Co, and Ni) molecular junctions at bias voltage around ±0.75 Volt. By examining their I-V characteristics, it has been established that MnPc, and FePc molecular junctions exhibit metal-like behavior, whereas CoPc and NiPc molecular devices are subject to negative differential resistance. As a result of our theoretical findings, it is found that TMPcs (TM = Fe, Mn) coupled to SWCNT probes yield a robust spin filter efficiency that may be of interest for prospective technological realizations in organic-inorganic molecular spintronic devices.

Atomistic Simulation of Nanoscale Devices

Device simulation is nowa­days fully integrated into the production tool chain of transistors. The geometry of the latter can be carefully optimized, possible design pitfalls can be identified early on, and the obtained experimental data can be analyzed in detail thanks to state-of-the-art technology computer aided design tools. However, on the one hand, the dimensions of transistors are reaching the atomic scale. On the other hand, novel functionalities (e.g., light emission/detection) and materials, for example III-V semiconductors, are being added to silicon-based chips. To cope with these challenges it is crucial that device simulators go beyond classical theories, pure electronic transport, and continuum models. The inclusion of quantum mechanical phenomena, electro-thermal effects, and light-matter interactions in systems made of thousands of atoms and of various materials has become critical. In this paper, we review one approach that satisfies all these requirements, the Non-equilibrium Green’s Function (NEGF) formalism, focusing on its combination with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ab initio</i> bandstructure models. The NEGF method allows to treat electrical, thermal, and optical transport at the quantum mechanical level in multi-material, multi-functional devices, without any empirical parameters. Besides advanced logic switches, it can be used to simulate e.g., photo-detectors, thermoelectric generators, or memory cells composed of almost any materials, in the ballistic limit of transport and in the presence of scattering. The key features of NEGF are summarized first, then selected applications are presented, finally challenges and opportunities are discussed.

Adsorption of DNA nucleobases on single-layer Ti3C2 MXene and graphene: vdW-corrected DFT and NEGF studies.

We investigated the interaction of DNA nucleobases [adenine (A), guanine (G), thymine (T), and cytosine (C)] with single-layer Ti3C2 MXene using Van der Waals (vdW)-corrected density functional theory and non-equilibrium Green's function methods. All calculations were benchmarked against graphene. We showed that depending on the initial vertical height of a nucleobase above the Ti3C2 surface, two interaction mechanisms are possible, namely, physisorption and chemisorption. For graphene, DNA nucleobases always physisorbed onto the graphene surface irrespective of the initial vertical height of the nucleobase above the graphene sheet. The PBE+vdW binding energies for graphene are high (0.55-0.74eV) and follow the order G > A > T > C, with adsorption heights in the range of 3.16-3.22 Å, indicating strong physisorption. For Ti3C2, the PBE+vdW binding energies are relatively weaker (0.16-0.20eV) and follow the order A > G = T > C, with adsorption heights in the range of 5.51-5.60 Å, indicating weak physisorption. The binding energies for chemisorption follow the order G > A > T > C, which is the same order for physisorption. The binding energy values (5.3-7.5eV) indicate very strong chemisorption (∼40 times larger than the physisorption binding energies). Furthermore, our band structure and electronic transport analysis showed that for physisorption, there is neither significant variation in the band structure nor modulation in the transmission function and device density of states. The relatively weak physisorption and strong chemisorption show that Ti3C2 might not be capable of identifying DNA nucleobases using the physisorption method.