Pseudopotentials, tight-binding models, and $k\cdot p$ theory have stood for many years as the standard techniques for computing electronic states in crystalline solids. Here we present the first new method in decades, which we call atomistic $k\cdot p$ theory. In its usual formulation, $k\cdot p$ theory has the advantage of depending on parameters that are directly related to experimentally measured quantities, however it is insensitive to the locations of individual atoms. We construct an atomistic $k\cdot p$ theory by defining envelope functions on a grid matching the crystal lattice. The model parameters are matrix elements which are obtained from experimental results or {\it ab initio} wave functions in a simple way. This is in contrast to the other atomistic approaches in which parameters are fit to reproduce a desired dispersion and are not expressible in terms of fundamental quantities. This fitting is often very difficult. We illustrate our method by constructing a four-band atomistic model for a diamond/zincblende crystal and show that it is equivalent to the $sp^3$ tight-binding model. We can thus directly derive the parameters in the $sp^3$ tight-binding model from experimental data. We then take the atomistic limit of the widely used eight-band Kane model and compute the band structures for all III-V semiconductors not containing nitrogen or boron using parameters fit to experimental data. Our new approach extends $k\cdot p$ theory to problems in which atomistic precision is required, such as impurities, alloys, polytypes, and interfaces. It also provides a new approach to multiscale modeling by allowing continuum and atomistic $k\cdot p$ models to be combined in the same system.
Low dimensional materials provide the possibility of improved thermoelectric performance due to the additional length scale degree of freedom for engineering their electronic and thermal properties. As a result of suppressed phonon conduction, large improvements on the thermoelectric figure of merit, ZT, have been recently reported in nanostructures, compared to the raw materials' ZT values. In addition, low dimensionality can improve a device's power factor, offering an additional enhancement in ZT. In this work the atomistic sp3d5s*-spin-orbit-coupled tight-binding model is used to calculate…
We present a tight-binding potential for transition metals, carbon, and transition metal carbides, which has been optimized through a systematic fitting procedure. A minimal basis, including the s, p electrons of carbon and the d electrons of the transition metal, is used to obtain a transferable tight-binding model of the carbon-carbon, metal-metal and metal-carbon interactions applicable to binary systems. The Ni-C system is more specifically discussed. The successful validation of the potential for different atomic configurations indicates a good transferability of the model and makes it a …
We present two approaches for coarse-graining interplanar potentials and determining the corresponding macroscopic cohesive laws based on energy relaxation and the renormalization group. We analyze the cohesive behavior of a large---but finite---number of interatomic planes and find that the macroscopic cohesive law adopts a universal asymptotic form. The universal form of the macroscopic cohesive law is an attractive fixed point of a suitably-defined renormalization-group transformation.
Large-supercell tight-binding calculations are presented for GaBi$_{x}$As$_{1-x}$/GaAs single quantum wells (QWs) with Bi fractions $x$ of 3.125% and 12.5%. Our results highlight significant distortion of the valence band states due to the alloy disorder. A large full-width-half-maximum (FWHM) is estimated in the ground state interband transition energy ($\approx$ 33 meV) at 3.125% Bi, consistent with recent photovoltage measurements for similar Bi compositions. Additionally, the alloy disorder effects are predicted to become more pronounced as the QW width is increased. However, they are less…
Recently, there has been tremendous research interest in novel bismide semiconductor materials (such as GaBi$_x$As$_{1-x}$) for wavelength-engineered, low-loss optoelectronic devices. We report a first study of the quantum confined Stark effect (QCSE) computed for GaBi$_x$As$_{1-x}$/GaAs quantum well (QW) structures based on large-scale atomistic tight-binding calculations. A comprehensive investigation of the QCSE as a function of the applied electric field orientations and the QW Bi fractions reveals unconventional character of the Stark shift at low Bi compositions ($x$=3.125\%). This atypi…
The ballistic performance of electron transport in nanowire transistors is examined using a 10 orbital sp3d5s* atomistic tight-binding model for the description of the electronic structure, and the top-of-the-barrier semiclassical ballistic model for calculation of the transport properties of the transistors. The dispersion is self consistently computed with a 2D Poisson solution for the electrostatic potential in the cross section of the wire. The effective mass of the nanowire changes significantly from the bulk value under strong quantization, and effects such as valley splitting strongly l…
The wave function and binding energy for shallow donors in GaAs are calculated within the tight binding (TB) approach, for supercells containing up to two million atoms. The resulting solutions, coupled with a scaling law, allow extrapolation to the bulk limit. A sharp shallow-deep transition is obtained as the impurity perturbation increases. The model allows investigating the quantitative consistency between the effective mass theory and the TB formalism. Although the calculated binding energies are in excellent agreement, anisotropies and the overall decay obtained in the TB envelope functi…
Orientation effects on the resistivity of copper grain boundaries are studied systematically with two different atomistic tight binding methods. A methodology is developed to model the resistivity of grain boundaries using the Embedded Atom Model, tight binding methods and non-equilibrum Green's functions (NEGF). The methodology is validated against first principles calculations for small, ultra-thin body grain boundaries (<5nm) with 6.4% deviation in the resistivity. A statistical ensemble of 600 large, random structures with grains is studied. For structures with three grains, it is found th…
We present a density functional theory parametrized hybrid k$\cdot$p tight binding model for electronic properties of atomically thin films of transition-metal dichalcogenides, 2H-$MX_2$ ($M$=Mo, W; $X$=S, Se). We use this model to analyze intersubband transitions in $p$- and $n$-doped $2{\rm H}-MX_2$ films and predict the line shapes of the intersubband excitations, determined by the subband-dependent two-dimensional electron and hole masses, as well as excitation lifetimes due to emission and absorption of optical phonons. We find that the intersubband spectra of atomically thin films of the…
In the present work, we have investigated the quantum transport in n Si junction less nanowire field effect transistors using 3 D, full band atomistic sp3d5s spin orbital coupled tight binding method. We have investigated the IDS VGS transfer characteristics, IDS VDS output characteristics, ON current, OFF current leakage, subthreshold swing and energy position resolved electron density spectrum Gn x, E in n Si junction less nanowire field effect transistors. We also study IDS VGS transfer characteristics with variation of High K gate materials. Quantum mechanical simulation is performed on th…
In the present work, we have investigated the performances of L shaped Vertical broken bandgapheterostructureInSb InAsn-channel tunnel field effect transistors TFETs of 4 nm thin channel structures with the gate lengths of 20nm. We have used a 3D full band, quantum mechanical simulator based on atomistic sp3d5s spin-orbital coupled tight binding method.In this L shaped nonlinear geometry the gate electric field and tunnel junction internal field are oriented in same direction. A broken narrow bandgap BG structure has another advantage that transport is by mixture of electrons holes. TFETs are …
We present an atomistic investigation of the influence of strain on the electronic properties of quantum dots (QD's) within the empirical $s p^{3} s^{*}$ tight-binding (ETB) model with interactions up to 2nd nearest neighbors and spin-orbit coupling. Results for the model system of capped pyramid-shaped InAs QD's in GaAs, with supercells containing $10^{5}$ atoms are presented and compared with previous empirical pseudopotential results. The good agreement shows that ETB is a reliable alternative for an atomistic treatment. The strain is incorporated through the atomistic valence force field m…
We propose a simple and effective approach to construct the empirical tight-binding parameters of ternary alloys in the virtual crystal approximation. This combines a new, compact formulation of the strain parameters and a linear interpolation of the hamiltonians of binary materials strained to the alloy equilibrium lattice parameter. We show that it is possible to obtain a perfect description of the bandgap bowing of ternary alloys in the InGaAsSb family of materials. Furthermore, this approach is in a good agreement with supercell calculations using the same set of parameters. This scheme op…
First-principles calculations were performed to investigate the electronic structure of two-dimensional (2-D) Ge, Sn, and Pb without and with the presence of an external electric field in combination with spin-orbit coupling. Tight-binding calculations based on four orbitals per atom and an effective single orbital are presented to match with the results obtained from first-principles calculations. In particular, the electronic band structure and the band splitting are investigated with both models. Moreover, the simple $k\cdot p$ model is also considered in order to understand the band splitt…
Atomistically detailed computational studies of nanocrystals, such as those derived from the promising lead-halide perovskites, are challenging due to the large number of atoms and lack of symmetries to exploit. Here, focusing on methylammonium lead iodide nanocrystals, we combine a real-space tight binding model with the GW approximation to the self-energy and obtain exciton wavefunctions and absorption spectra via solutions of the associated Bethe-Salpeter equation. We find that the size dependence of carrier confinement, dielectric contrast, electron-hole exchange, and exciton binding energ…
Molybdenum disulfide (MoS2) is a layered semiconductor which has become very important recently as an emerging electronic device material. Being an intrinsic semiconductor the two-dimensional MoS2 has major advantages as the channel material in field-effect transistors. In this work we determine the electronic structure of MoS2 with the highly accurate screened hybrid functional within the density functional theory (DFT) including the spin-orbit coupling. Using the DFT electronic structures as target, we have developed a single generic tight-binding (TB) model that accurately produces the elec…
A series of III-V ternary and quarternary digital alloy avalanche photodiodes (APDs) have recently been seen to exhibit very low excess noise. Using band inversion of an environment-dependent atomistic tight binding description of short period superlattices, we argue that a combination of increased effective mass, minigaps and band split-off are primarily responsible for the observed superior performance. These properties significantly limit the ionization rate of one carrier type, either holes or electrons, making the avalanche multiplication process unipolar in nature. The unipolar behavior …
A dynamics of the precession of coupled atomic moments in the tight-binding (TB) approximation is presented. By implementing an angular penalty functional in the energy that captures the magnetic effective fields self-consistently, the motion of the orientation of the local magnetic moments is observed faster than the variation of their magnitudes. This allows the computation of the effective atomic magnetic fields that are found consistent with the Heisenberg's exchange interaction, by comparison with classical atomistic spin dynamics on Fe, Co and Ni magnetic clusters.
An application of the tight binding approximation is presented for the description of electronic structure and interatomic force in magnetic iron, both pure and containing hydrogen impurities. We assess the simple canonical d-band description in comparison to a non orthogonal model including s and d bands. The transferability of our models is tested against known properties including the segregation energies of hydrogen to vacancies and to surfaces of iron. In many cases agreement is remarkably good, opening up the way to quantum mechanical atomistic simulation of the effects of hydrogen on me…
We use atomistic tight-binding theory with a configuration interaction description of Coulomb and exchange effects to describe excitons in symmetric quantum dots in a vertical electric field. We show that field-induced manipulation of exciton orientation and phase produces a drastic reduction of fine structure splitting, an anticrossing, and a 90 degree rotation of polarization, similar to experiment. An atomistic analysis is needed to explain how exciton reorientation modifies anisotropic exchange and fine structure splitting without significantly altering other splittings.
In this work we theoretically explore the effect of dimensionality on the thermoelectric power factor of InAs nanowires by coupling atomistic tight-binding calculations to the Linearized Boltzmann transport formalism. We consider nanowires with diameters from 40nm (bulk-like) down to 3nm (1D), which allows for the proper exploration of the power factor within a unified large-scale atomistic description across a large diameter range. We find that as the diameter of the nanowires is reduced below d < 10 nm, the Seebeck coefficient increases substantially, a consequence of strong subband quantiza…
Using an $sp^{3}s^{*}$ tight-binding model we demonstrate how the observed strong bowing of the band gap and spin-orbit-splitting with increasing Bi composition in the dilute bismide alloy GaBi$_{x}$As$_{1-x}$ can be described in terms of a band-anticrossing interaction between the extended states of the GaAs valence band edge and highly localised Bi-related resonant states lying below the GaAs valence band edge. We derive a 12-band $\textbf{k}\cdot\textbf{p}$ Hamiltonian to describe the band structure of GaBi$_{x}$As$_{1-x}$ and show that this model is in excellent agreement with full tight-b…
In this work we present a comparison of multiband k.p-models, the effective bond-orbital approach, and an empirical tight-binding model to calculate the electronic structure for the example of a truncated pyramidal GaN/AlN self-assembled quantum dot with a zincblende structure. For the system under consideration, we find a very good agreement between the results of the microscopic models and the 8-band k.p-formalism, in contrast to a 6+2-band k.p-model, where conduction band and valence band are assumed to be decoupled. This indicates a surprisingly strong coupling between conduction and valen…
This work reports the measurement of electron $g$ factor anisotropy ($| Δg |$ = $| g_{001} - g_{1 \bar 1 0} |$) for phosphorous donor qubits in strained silicon (sSi = Si/Si$_{1-x}$Ge$_x$) environments. Multi-million-atom tight-binding simulations are performed to understand the measured decrease in $| Δg |$ as a function of $x$, which is attributed to a reduction in the interface-related anisotropy. For $x <$7\%, the variation in $| Δg |$ is linear and can be described by $η_x x$, where $η_x \approx$1.62$\times$ 10$^{-3}$. At $x$=20\%, the measured $| Δg |$ is 1.2 $\pm$ 0.04 $\times$ 10$^{-3}…
Incorporation of bismuth (Bi) in dilute quantities in (In)GaAs has been shown to lead to unique electronic properties that can in principle be exploited for the design of high efficiency telecomm lasers. This motivates the development of simple models of the electronic structure of these dilute bismide alloys, which can be used to evaluate their potential as a candidate material system for optical applications. Here, we begin by using detailed calculations based on an $sp^{3}s^{*}$ tight-binding model of (In)GaBi$_{x}$As$_{1-x}$ to verify the presence of a valence band-anticrossing interaction…
Empirical Tight Binding (TB) methods are widely used in atomistic device simulations. Existing TB methods to passivate dangling bonds fall into two categories: 1) Method that explicitly includes passivation atoms is limited to passivation with atoms and small molecules only. 2) Method that implicitly incorporates passivation does not distinguish passivation atom types. This work introduces an implicit passivation method that is applicable to any passivation scenario with appropriate parameters. This method is applied to a Si quantum well and a Si ultra-thin body transistor oxidized with SiO2 i…
Monolayer transition metal dichalcogenides $MX_2$ ($M$ = Mo,W and $X$ = Te, Se, S) in 1T' structure were predicted to be quantum spin Hall insulators based on first-principles calculations, which were quickly confirmed by multiple experimental groups. For a better understanding of their properties, in particular their responses to external fields, we construct a realistic four-band tight-binding (TB) model by combining the symmetry analysis and first-principles calculations. Our TB model respects all the symmetries and can accurately reproduce the band structure in a large energy window from -…
The Empirical Tight Binding(ETB) method is widely used in atomistic device simulations. The reliability of such simulations depends very strongly on the choice of basis sets and the ETB parameters. The traditional way of obtaining the ETB parameters is by fitting to experiment data, or critical theoretical bandedges and symmetries rather than a foundational mapping. A further shortcoming of traditional ETB is the lack of an explicit basis. In this work, a DFT mapping process which constructs TB parameters and explicit basis from DFT calculations is developed. The method is applied to two mater…
Atomic scale simulations at finite temperature are an ideal approach to study the thermodynamic properties of magnetic transition metals. However, the development of interatomic potentials explicitly taking into account magnetic variables is a delicate task. In this context, we present a tight-binding model for magnetic transition metals in the Stoner approximation. This potential is integrated into a Monte Carlo structural relaxations code where trials of atomic displacements as well as fluctuations of local magnetic moments are performed to determine the thermodynamic equilibrium state of th…
Empirical tight binding(ETB) methods are widely used in atomistic device simulations. Traditional ways of generating the ETB parameters rely on direct fitting to bulk experiments or theoretical electronic bands. However, ETB calculations based on existing parameters lead to unphysical results in ultra small structures like the As terminated GaAs ultra thin bodies(UTBs). In this work, it is shown that more reliable parameterizations can be obtained by a process of mapping ab-initio bands and wave functions to tight binding models. This process enables the calibration of not only the ETB energy …
Recent density functional theory (DFT) calculations by Foerst et al. have predicted that vacancies in both low and high carbon steels have a carbon dimer bound to them. This is likely to change the thinking of metallurgists in the kinetics of the development of microstructures. While the notion of a C2 molecule bound to a vacancy in Fe will potentially assume a central importance in the atomistic modeling of steels, neither a recent tight binding (TB) model nor existing classical interatomic potentials can account for it. Here we present a new TB model for C in Fe, based on our earlier work fo…
We present an atomistic study of the strain field, the one-particle electronic spectrum and the oscillator strength of the fundamental optical transition in chemically disordered In$_{x}$Ga$_{1-x}$As pyramidal quantum dots (QDs). Interdiffusion across the interfaces of an originally ``pure'' InAs dot buried in a GaAs matrix is simulated through a simple model, leading to atomic configurations where the abrupt hetero-interfaces are replaced by a spatially inhomogeneous composition profile $x$. Structural relaxation and the strain field calculations are performed through the Keating valence forc…
Bridging the gap between first principles methods and empirical schemes, the density functional based tight-binding method (DFTB) has become a versatile tool in predictive atomistic simulations over the past years. One of the major restrictions of this method is the limitation to local or gradient corrected exchange-correlation functionals. This excludes the important class of hybrid or long-range corrected functionals, which are advantageous in thermochemistry, as well as in the computation of vibrational, photoelectron and optical spectra. The present work provides a detailed account of the …
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 is 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-…
We present an effective mass theory for SiGe/Si/SiGe quantum wells, with an emphasis on calculating the valley splitting. The theory introduces a valley coupling parameter, $v_v$, which encapsulates the physics of the quantum well interface. The new effective mass parameter is computed by means of a tight binding theory. The resulting formalism provides rather simple analytical results for several geometries of interest, including a finite square well, a quantum well in an electric field, and a modulation doped two-dimensional electron gas. Of particular importance is the problem of a quantum …
The $\mathbf{k \cdot p}$ method is a successful approach to obtain band structure, optical and transport properties of semiconductors, and it depends on external parameters that are obtained either from experiments, tight binding or ab initio calculations. Despite the widespread use of the $\mathbf{k \cdot p}$ method, a systematic analysis of the stability and the accuracy of its parameters is not usual in the literature. In this work, we report a theoretical framework to determine the $\mathbf{k \cdot p}$ parameters from state-of-the-art hybrid density functional theory including spin-orbit c…
In recent years, metal halide perovskites (MHPs) for optoelectronic applications have attracted the attention of the scientific community due to their outstanding performance. The fundamental understanding of their physicochemical features is essential for improving their efficiency and stability. Atomistic and molecular simulations have played an essential role in the description of the optoelectronic properties and dynamical behaviour of MHPs, respectively. However, the complex interplay of the dynamical and optoelectronic properties in MHPs requires the simultaneous modelling of electrons a…
We develop an atomistic, nearest-neighbor sp3s* tight-binding Hamiltonian to investigate the electronic structure of dilute bismide alloys of GaP and GaAs. Using this model we calculate that the incorporation of dilute concentrations of Bi in GaP introduces Bi-related defect states in the band gap, which interact with the host matrix valence band edge via a Bi composition dependent band anti-crossing (BAC) interaction. By extending this analysis to GaBiAs we demonstrate that the observed strong variation of the band gap Eg and spin-orbit-splitting (SO) energy with Bi composition can be well ex…
