Semi-empirical Tight-binding Model Research Articles

Molecular relaxation by reverse diffusion with time step prediction

Abstract Molecular relaxation, finding the equilibrium state of a non-equilibrium structure, is an essential component of computational chemistry to understand reactivity. Classical force field (FF) methods often rely on insufficient local energy minimization, while neural network FF models require large labeled datasets encompassing both equilibrium and non-equilibrium structures. As a remedy, we propose MoreRed, molecular relaxation by reverse diffusion, a conceptually novel and purely statistical approach where non-equilibrium structures are treated as noisy instances of their corresponding equilibrium states. To enable the denoising of arbitrarily noisy inputs via a generative diffusion model, we further introduce a novel diffusion time step predictor. Notably, MoreRed learns a simpler pseudo potential energy surface (PES) instead of the complex physical PES. It is trained on a significantly smaller, and thus computationally cheaper, dataset consisting of solely unlabeled equilibrium structures, avoiding the computation of non-equilibrium structures altogether. We compare MoreRed to classical FFs, equivariant neural network FFs trained on a large dataset of equilibrium and non-equilibrium data, as well as a semi-empirical tight-binding model. To assess this quantitatively, we evaluate the root-mean-square deviation between the found equilibrium structures and the reference equilibrium structures as well as their energies.

Significant k-point selection scheme for computationally efficient band structure based UTB device simulations

The accurate calculation of channel electrostatics parameters in ultra-thin body devices requires self-consistent solution of the Poisson’s equation and the full-band structure of the thin channel. For silicon channel, the full-band structure is obtained using the semi-empirical tight-binding model. To make this approach computationally tractable for a wide range of channel thicknesses, in terms of time and resource, only significant k-points in the irreducible Brillouin zone need to be considered. In this work, we present a scheme for precisely identifying the significant k-points based on Fermi–Dirac probability and show that the band-structure approach using those significant k-points can be applied over a wide range of channel thicknesses, oxide thicknesses, device temperatures and different channel orientations. The benchmarking of the obtained channel electrostatics parameters is performed with the results from accurate full-band structure simulations showing excellent agreement (maximum error within ) along with significant reduction in computational time.

NanoNET: An extendable Python framework for semi-empirical tight-binding models

We present a novel open-source Python framework called NanoNET (Nanoscale Non-equilibrium Electron Transport) for modeling electronic structure and transport. Our method is based on the tight-binding method and non-equilibrium Green’s function theory. The core functionality of the framework is providing facilities for efficient construction of tight-binding Hamiltonian matrices from a list of atomic coordinates and a lookup table of the two-center integrals in dense, sparse, or block-tridiagonal forms. The framework implements a method based on kd-tree nearest-neighbor search and is applicable to isolated atomic clusters and periodic structures. A set of subroutines for detecting the block-tridiagonal structure of a Hamiltonian matrix and splitting it into series of diagonal and off-diagonal blocks is based on a new greedy algorithm with recursion. Additionally the developed software is equipped with a set of programs for computing complex band structure, self-energies of elastic scattering processes, and Green’s functions. Examples of usage and capabilities of the computational framework are illustrated by computing the band structure and transport properties of a silicon nanowire as well as the band structure of bulk bismuth. Program summaryProgram Title:NanoNETCPC Library link to program files:https://doi.org/10.17632/b9p7kyzdj9.1Developer’s repository link:https://github.com/freude/NanoNetLicensing provisions: MITProgramming language: PythonNature of problem: The framework NanoNET solves a problem which is, having a set of atomic coordinates and tight-binding parameters, to construct Hamiltonian matrices in one of several desired forms. In particular, some applications require those matrices to have a reduced bandwidth and/or to possess a block-tridiagonal structure.Solution method: The problem is solved using a combination of kd-tree-based fast nearest-neighbor search and atomic coordinate sorting. Furthermore, a new greedy recursive algorithm is proposed for detecting block-tridiagonal structure of a matrix in a non-optimal way. Additionally, we propose an algorithm of a polynomial time for optimizing block sizes.Additional features: Although the resulting matrices can be processed by many existing software packages, the framework also has built-in standard tools for diagonalizing Hamiltonian matrices and computing Green’s functions that make it an independent tool for solving electronic structure and transport problems.

Fast and automatic estimation of transition state structures using tight binding quantum chemical calculations

We present a method for the automatic determination of transition states (TSs) that is based on Grimme’s RMSD-PP semiempirical tight binding reaction path method (J. Chem. Theory Comput. 2019, 15, 2847–2862), where the maximum energy structure along the path serves as an initial guess for DFT TS searches. The method is tested on 100 elementary reactions and located a total of 89 TSs correctly. Of the 11 remaining reactions, nine are shown not to be elementary reactions after all and for one of the two true failures the problem is shown to be the semiempirical tight binding model itself. Furthermore, we show that the GFN2-xTB RMSD-PP barrier is a good approximation for the corresponding DFT barrier for reactions with DFT barrier heights up to about 30 kcal/mol. Thus, GFN2-xTB RMSD-PP barrier heights, which can be estimated at the cost of a single energy minimisation, can be used to quickly identify reactions with low barriers, although it will also produce some false positives.

Analysis of electronical properties of Bismuth and Silicene antidot in the presence of strain using the four-orbital tight-binding method

We have performed a tight-binding calculation of the band structure of Bi/Si sheets on which hexagonal holes are embedded. We named this kind of structure as Bismuth/Silicene antidot lattice (BAL/SAL). We have considered the semi-empirical sp3 tight-binding model on which the nearest and next-nearest neighbors of atoms have been taken into account. Our numerical results show that the size of holes in the two-dimensional sheets as the antidot lattice points are effective on the band structures and also transport properties of the system. Also, we have observed that BALs are almost conductors with very small band gaps for the large radius of circles, but about SALs for the large radius of holes, we obtain a considerable band gap, and conductivity is reduced. Besides, we have seen that, for the different radius of holes in the monolayer of Silicene, the presence of spin-orbit coupling in our band gaps obtained by tight-binding is not very important. On the contrary to Silicene antidot lattice, SOC interaction has a considerable effect on the band gap for Bismuth antidot lattice for the various radiuses of holes in their monolayer. Also, we have investigated the effects of the distance between holes on BAL/SAL band gaps and their band structures. Finally, we have obtained the band gap of Bismuth/Silicene antidot under strain, and we have compared results of sheet and antidot in the presence of strain.

Terahertz-Driven Stark Spectroscopy of CdSe and CdSe-CdS Core-Shell Quantum Dots.

The effects of large external fields on semiconductor nanostructures could reveal much about field-induced shifting of electronic states and their dynamical responses and could enable electro-optic device applications that require large and rapid changes in optical properties. Studies of quasi-dc electric field modulation of quantum dot (QD) properties have been limited by electrostatic breakdown processes observed under high externally applied field levels. To circumvent this, here we apply ultrafast terahertz (THz) electric fields with switching times on the order of 1 ps. We show that a pulsed THz electric field, enhanced by a microslit field enhancement structure (FES), can strongly manipulate the optical absorption properties of a thin film of CdSe and CdSe-CdS core-shell QDs on the subpicosecond time scale with spectral shifts that span the visible to near-IR range. Numerical simulations using a semiempirical tight binding model show that the band gap of the QD film can be shifted by as much a 79 meV during these time scales. The results allow a basic understanding of the field-induced shifting of electronic levels and suggest electro-optic device applications.

Probing Charge Carrier Movement in Organic Semiconductor Thin Films via Nanowire Conductance Spectroscopy

Understanding the movement of charge within organic semiconducting films is crucial for applications in photo-voltaics and flexible electronics. We study the sensitivity of the electrical conductance of a silicon nanowire to changes of charge states within an organic semiconductor physisorbed on the surface of the nanowire. Elastic scattering caused by motion of charge carriers near the nanowire modifies the mean-free path for backscattering of electrons propagating within it, which we have mathematically expressed in terms of the causal Green's functions. The scattering potential has been computed using a combination of the polarizable continuum model and density functional theory with the range-separated exchange-correlation functional for organic molecules and the semi-empirical tight-binding model for silicon. As an example, the sensitivity to charge state changes in tetracene is computed as a function of operating temperature and geometrical parameters of a nanowire. For a single molecule, ultra-thin silicon nanowires with characteristic sizes of the cross-section below 2 nm produce a detectable conductance change at room temperature. For larger nanowires the sensitivity is reduced, however the conductance change grows with the number of charged molecules: with sub-4 nm nanowires being sensitive enough to detect several tens of charge carriers. We propose using noise spectroscopy to access the temporal evolution of the charge states. Information regarding the spatial distribution of charge carries in organic thin films can be obtained using a grid of nanowire resistors and electric impedance tomography.

Transient hot electron dynamics in single-layer TaS2

Using time- and angle-resolved photoemission spectroscopy, we study the response of metallic single layer TaS$_2$ in the 1H structural modification to the generation of excited carriers by a femtosecond laser pulse. A complex interplay of band structure modifications and electronic temperature increase is observed and analyzed by direct fits of model spectral functions to the two-dimensional (energy and $k$-dependent) photoemission data. Upon excitation, the partially occupied valence band is found to shift to higher binding energies by up to 150 meV, accompanied by electronic temperatures exceeding 3000~K. These observations are explained by a combination of temperature-induced shifts of the chemical potential, as well as temperature-induced changes in static screening. Both contributions are evaluated in a semi-empirical tight-binding model. The shift resulting from a change in the chemical potential is found to be dominant.

Current induced forces in graphene nanoribbons

Current induced forces at atomic scale have proven to limit the stability and performance of nanoscale devices. In this work, we employed a semiempirical tight-binding model along with a generalized Hellmann–Feynman theorem to calculate “wind-forces” due to the flow of electric current. The developed model is applied to calculate these forces for pristine and defected armchair and zigzag graphene nanoribbons under different magnetic states. Special profile, dependence on the ribbon’s width, and the effect of defects on the current induced forces are discussed. Transport calculations are followed by molecular dynamics simulations for evaluating atomic displacement and mechanical strains due to current induced forces. The results indicate the importance of including current induced forces for a careful analysis of two-dimensional based devices.

Calculating the band structure of 3C-SiC using sp3d5s*\u2009+\u2009\u2206 model

We report on a semiempirical tight-binding model for 3C-SiC including the effect of sp3d5s* orbitals and spin–orbit coupling (∆). In this work, we illustrate in detail the method to develop such a model for semiconductors with zincblende structure, based on Slater–Koster integrals, and we explain the optimization method used to fit the experimental results with such a model. This method shows high accuracy for the evaluation of 3C-SiC band diagram in terms of both the experimental energy levels at high symmetry points and the effective masses.

GFN2-xTB-An Accurate and Broadly Parametrized Self-Consistent Tight-Binding Quantum Chemical Method with Multipole Electrostatics and Density-Dependent Dispersion Contributions.

An extended semiempirical tight-binding model is presented, which is primarily designed for the fast calculation of structures and noncovalent interaction energies for molecular systems with roughly 1000 atoms. The essential novelty in this so-called GFN2-xTB method is the inclusion of anisotropic second order density fluctuation effects via short-range damped interactions of cumulative atomic multipole moments. Without noticeable increase in the computational demands, this results in a less empirical and overall more physically sound method, which does not require any classical halogen or hydrogen bonding corrections and which relies solely on global and element-specific parameters (available up to radon, Z = 86). Moreover, the atomic partial charge dependent D4 London dispersion model is incorporated self-consistently, which can be naturally obtained in a tight-binding picture from second order density fluctuations. Fully analytical and numerically precise gradients (nuclear forces) are implemented. The accuracy of the method is benchmarked for a wide variety of systems and compared with other semiempirical methods. Along with excellent performance for the "target" properties, we also find lower errors for "off-target" properties such as barrier heights and molecular dipole moments. High computational efficiency along with the improved physics compared to its precursor GFN-xTB makes this method well-suited to explore the conformational space of molecular systems. Significant improvements are furthermore observed for various benchmark sets, which are prototypical for biomolecular systems in aqueous solution.

High thermoelectric and electronic performance in graphene nanoribbons by isotope and vacancy engineering

We study the effects of isotope doping and vacancies on the electronic, phononic and thermoelectric properties of graphene nano-ribbons by means of atomistic simulation based on semi-empirical Tight Binding and Force Constant models combined with the Non-Equilibrium Green’s Function formalism of transport. We demonstrate that from the phononic perspective, the impact of isotope doping on transmission is very dependent on the phonon frequency and particularly strong at high frequency, while vacancies wield their influence on the whole frequency range. From the electronic point of view, if placed at dimer line positions m = 3i + 1, 3i + 2, vacancies induce a strong reduction of the electrical conductance while vacancies at positions m = 3i act as isotopes, i.e. they are transparent to electrons and do not affect the electronic properties. The thermoelectric study is conducted by combining both electronic and phononic properties. It demonstrates the possibility of a remarkable enhancement of figure of merit ZT. In the presence of both types of defects, ZT can be enhanced significantly from 0.26 in pristine ribbons to values larger than 2.5 for ribbons of width M = 5.

Optical and Electronic Propreties of GeSn and GeSiSn Heterostructures and Nanowires

Sn-containing group-IV semiconductor binary and ternary alloys (GeSn, SiSn, and GeSiSn) provide a wealth of opportunities to independently manipulate band gap and lattice parameter. This opens up the possibility to create an entirely new family of electronic and optoelectronic devices. Towards this end, it is of paramount importance to develop a deep understanding of the electronic and optical properties of these group-IV alloys-based heterostructures, nanoscale structures, and devices. In this perspective, this work reports detailed studies of the influence of both strain and composition on the band structure of GeSiSn ternary alloys. First, we developed a simple yet rigorous semi-empirical second nearest neighbors tight binding1 sp3s*method that incorporates the effect of substitutional disorder. We have found that the composition of α-Sn at the direct to indirect crossover of the ternary alloy decreases from 11% in a fully relaxed alloy to 7% in tensile strained alloy (for a strain value of 0.71%). In the latter case, we have considered a thin GeSiSn layer is epitaxialy grown on a thin Ge substrate.Furthermore, we also studied the properties of electronic confinement and optical responses in variety of systems. This includes Ge/GeSn, Ge/GeSiSn and GeSn/GeSiSn heterostructures, where the strain effect is incorporated using the second nearest neighbors sp3s* semi-empirical tight binding model.1 - 2 The second set of the investigated systems consists of superlattices3 (,), where n and m are the number of monolayer considered. The compositions of Si and Sn in the ternary alloy vary in the range of 0-40% and 0-20%, respectively. The effect of growth orientations are also treated by focusing on three crystallographic growth orientations; mainly [001], [110] and [111]. The strain effect was also considered in these cases. Moreover, the effect of spatial charges separation on the intersubband and interband transitions in the superlattice, is treated in order to quantify optical properties of theses superlattices.The last section of this work addresses the behavior of GeSn and GeSiSn semiconductor nanowires. Herein, we have solved the effective mass Hamiltonian in cylindrical coordinates using a finite difference technique4 for the core-shell nanowires where the core and the shell are made of different alloys. In figure I. (b), a schematic representation of one of the investigated nanowire heterostructures consisting of a radial Type I junction of a compressively strained GeSn core and tensile strained GeSiSn shell. Moreover, in order to quantify the effect of doping concentration and the radius of the core on the spatial localization of electrons and holes densities inside the nanowire, we present in Figure I. (a) the calculated effect of the doping concentration on the electronic confinement for a Ge0.90Sn0.10/Ge core-shell nanowire for different core radiuses in the 10-40 nm range. In the case of relaxed nanowire heterostructures, we show that for an indirect band gap Ge0.9Sn0.1 binary alloy localized at L symmetry point, above a doping concentration of 5×1016 cm-3and below a core radius of 20 nm, the electron density is localized in the Ge shell. Above this concentration, electrons are confined in the core. This change in localization of electron in core/shell nanowire, corresponds to a transition where the electron gas in the middle of the core becomes strongly localized in the heterojunction core/shell interface or beyond. Based on these calculations, we will present and discuss a variety of novel electronic and optoelectronic devices.

Semi-empirical tight binding method for calculating energy levels of hydrogenated silicon nanoclusters as a function of size

A semi-empirical tight binding model is used for calculating energy levels of spherical hydrogenated silicon nanoclusters in the form of SimHn and two independent bases. The first basis is the nearest neighbor approximation of sp3s⁎ orthogonal basis and the second basis is the third nearest neighbor approximation of sp3 nonorthogonal basis. Also, bulk properties of silicon crystal are used in the calculations. As we expected, obtained results show that the change in the size of nanoclusters has a great influence on their energy levels. So optical properties of these nanoclusters can be controlled externally. A comparative study on the calculated results and experimental results also reveals a good agreement between the two approaches.

The semi-empirical tight-binding model for carbon allotropes “between diamond and graphite”

The new carbon allotropes “between diamond and graphite” have come under intensive examination during the last decade due to their numerous technical applications. The modification of energy gap in thin films of these allotropes was studied experimentally using optical methods. The proposed simple model of carbon clusters with variable lengths of chemical bonds allows us to imitate the transfer from diamond and diamond-like to graphite-like structures, as well as the corresponding modification of hybridization sp3/sp2 for diamond-like and spz for graphite-like phases. This enables us to estimate various allotropes parameters, like the gap Eg, energies of valence Ev, and conduction Ec band edges, and the value of electronic affinity, i.e., optical work function X, which are all of practical importance. The obtained estimations correspond to the experimental data.

An environment-dependent semi-empirical tight binding model suitable for electron transport in bulk metals, metal alloys, metallic interfaces, and metallic nanostructures. II. Application—Effect of quantum confinement and homogeneous strain on Cu conductance

The Semi-Empirical tight binding model developed in Part I Hegde et al. [J. Appl. Phys. 115, 123703 (2014)] is applied to metal transport problems of current relevance in Part II. A systematic study of the effect of quantum confinement, transport orientation, and homogeneous strain on electronic transport properties of Cu is carried out. It is found that quantum confinement from bulk to nanowire boundary conditions leads to significant anisotropy in conductance of Cu along different transport orientations. Compressive homogeneous strain is found to reduce resistivity by increasing the density of conducting modes in Cu. The [110] transport orientation in Cu nanowires is found to be the most favorable for mitigating conductivity degradation since it shows least reduction in conductance with confinement and responds most favorably to compressive strain.

An environment-dependent semi-empirical tight binding model suitable for electron transport in bulk metals, metal alloys, metallic interfaces, and metallic nanostructures. I. Model and validation

Semi-empirical Tight Binding (TB) is known to be a scalable and accurate atomistic representation for electron transport for realistically extended nano-scaled semiconductor devices that might contain millions of atoms. In this paper, an environment-aware and transferable TB model suitable for electronic structure and transport simulations in technologically relevant metals, metallic alloys, metal nanostructures, and metallic interface systems are described. Part I of this paper describes the development and validation of the new TB model. The new model incorporates intra-atomic diagonal and off-diagonal elements for implicit self-consistency and greater transferability across bonding environments. The dependence of the on-site energies on strain has been obtained by appealing to the Moments Theorem that links closed electron paths in the system to energy moments of angular momentum resolved local density of states obtained ab initio. The model matches self-consistent density functional theory electronic structure results for bulk face centered cubic metals with and without strain, metallic alloys, metallic interfaces, and metallic nanostructures with high accuracy and can be used in predictive electronic structure and transport problems in metallic systems at realistically extended length scales.

Combined effect of strain and defects on the conductance of graphene nanoribbons

We investigate the combined influence of structural defects and uniaxial longitudinal strain on the electronic transport properties of armchair graphene nanoribbons using the numerical approach based on the semiempirical tight-binding model, the Landauer formalism, and the recursion method for Green functions. We calculate the conductance of graphene nanoribbons in the quantum coherent regime with different types and concentrations of defects. Further, we apply uniform planar tension to the nonideal graphene ribbons with randomly distributed and oriented single and double vacancies and Stone-Wales defects. Since transport characteristics of graphene nanoribbons are found to be very sensitive to edge termination and aspect ratio, and it has been shown that energy gaps can emerge under critical strain; the interplay of both effects needs to be studied. We show that band gap engineering using strain is still possible for nonideal armchair ribbons with a small defect concentration, as the oscillatory behavior of the gap is preserved.

Ab Initio Prediction of Boron Compounds Arising from Borozene: Structural and Electronic Properties

Structure and electronic properties of two unusual boron clusters obtained by fusion of borozene rings have been studied by means of first principles calculations based on the generalized-gradient approximation of the density functional theory. Moreover, a semiempirical tight-binding model has been appropriately calibrated for transport calculations on these clusters. Results show that the pure boron clusters are topologically planar and characterized by (3c–2e) bonds, which can explain, together with the aromaticity (estimated by means of NICS), the remarkable cohesive energy values obtained. Such feature makes these systems competitive with the most stable boron clusters to date. The energy gap values indicate that these clusters possess a semiconducting character, while when the larger system is considered, zero-values of the density of states are found exclusively within the HOMO–LUMO gap. Electron transport calculations within the Landauer formalism confirm these indications, showing semiconductor-like low bias differential conductance for these structures. Differences and similarities with carbon clusters are highlighted in the discussion.

Curvature and Hybridization Effects on the Persistent Current of a Carbon Nanotorus

To accurately describe the persistent current for various toroidal carbon nanotubes (TCNs), a semiempirical sp3 tight-binding model is presented, in which the intrinsic curvature and hybridization have been fully taken into account. The calculations show that the curvature and hybridization can induce dramatic changes in the energy spectra of TCNs such as the Fermi energy EF shifting up, an energy gap opening at EF, and the energy spectrum symmetry about EF destroyed, which leads to a decrease of persistent current and changes in the shape of the flux-dependent current. In the presence of curvature and hybridization, the persistent current in non-armchair TCNs is nearly an order of magnitude lower than that obtained by using the Brillouin-zone folding approach, while it is of the same order of magnitude in armchair TCNs.