Empirical Tight-binding Model Research Articles

Improving strong scalability of electronic structure simulations with reduced overhead of communications

Physically realizable semiconductor electronic devices easily include more than several million atoms even though they are in nanoscale, so electronic structure simulations of huge atomic systems are the key to predict performance characteristics of such devices. The empirical tight-binding (TB) model, which uses a finite set of localized bases for descriptions of a single atom with assumption of nearest-neighbor coupling, has been extensively adopted to solve electronic structures of large-scale atomic systems, and the size-capability of TB simulations has been continuously improved with aids of parallel computing. Recently, we have demonstrated a strong scalability of TB simulations up to 2,500 computing nodes for a model problem consisting of 400 million atoms, where the scalability is limited due to the overhead of collective communications that the core numerical method must involve to get a partial eigenspectrum of the sparse Hamiltonian system matrix. To reduce the cost of Message Passing Interface (MPI) communications and its effect on the end-to-end simulation time, here we design an equivalent transformation of the sparse matrix eigensolver, and employ a core dedicated to MPI communications with dynamic scheduling of threads. Through rigorous benchmark tests against model problems of various sizes, it is confirmed that our method improves the strong scalability of TB simulations by more than 10% in a huge computing environment, by reducing the time-cost of both core computations and collective communications.

Impact of random alloy fluctuations on the electronic and optical properties of (Al,Ga)N quantum wells: Insights from tight-binding calculations.

Light emitters based on the semiconductor alloy aluminum gallium nitride [(Al,Ga)N] have gained significant attention in recent years due to their potential for a wide range of applications in the ultraviolet (UV) spectral window. However, current state-of-the-art (Al,Ga)N light emitters exhibit very low internal quantum efficiencies (IQEs). Therefore, understanding the fundamental electronic and optical properties of (Al,Ga)N-based quantum wells is key to improving the IQE. Here, we target the electronic and optical properties of c-plane AlxGa1-xN/AlN quantum wells by means of an empirical atomistic tight-binding model. Special attention is paid to the impact of random alloy fluctuations on the results as well as the Al content x in the well. We find that across the studied Al content range (from 10% to 75% Al), strong hole wave function localization effects are observed. Additionally, with increasing Al content, electron wave functions may also start to exhibit carrier localization features. Overall, our investigations on the electronic structure of c-plane AlxGa1-xN/AlN quantum wells reveal that already random alloy fluctuations are sufficient to lead to (strong) carrier localization effects. Furthermore, our results indicate that random alloy fluctuations impact the degree of optical polarization in c-plane AlxGa1-xN quantum wells. We find that the switching from transverse electric to transverse magnetic light polarization occurs at higher Al contents in the atomistic calculation, which accounts for random alloy fluctuations, compared to the widely used virtual crystal approximation approach. This observation is important for light extraction efficiencies in (Al,Ga)N-based light emitting diodes operating in the deep UV.

Tight-binding description of inorganic lead halide perovskites in cubic phase

Band structure of inorganic lead halide perovskites is substantially different from the band structure of group IV, III–V and II–VI semiconductors. However, the standard empirical tight-binding model with sp3d5s∗ basis gives nearly perfect fit of band structure calculated in the density functional theory. The tight-binding calculations of ultrathin CsPbI3 layer show good agreement with the corresponding DFT calculations. The parameters corrected for the experimental data allow for the numerically cheap atomistic calculations of inorganic perovskite nanostructures.

Electronic dispersions of a stable twisted bilayer phosphorene in 2O-tαP phase

It is reported for the electronic properties of an in-plane twisted bilayer phosphorene, known as the 2O-tαP phase, and the only dynamically stable phase beyond the AB stacking. This was achieved using first-principles calculations, a generalized empirical tight-binding model inclusive of electric field effects, and a two-parameter low energy effective model, the latter two providing an efficient scheme for nanoelectronics related applications. The tight-binding model reproduces a global fit to the first-principles dispersion, and the low energy model provides more accurate near-gap bands. Both are orders-of-magnitude faster and less memory-intensive than performing first-principles calculations. The twisted 2O-tαP structure possesses a direct bandgap of 1.27 eV, larger than that of the shifted AB structure (1.03 eV). The hole and electron polar effective mass anisotropy ratios are 27.34 and 1.95, respectively. An important observation is that the layer twisting results in the removal of Dirac cones as a reflection of a different band topology compared to the AB one, while the twofold degeneracy at the Brillouin zone boundary and the symmetry of the energy surface are both broken by an external vertical electric field. With an increasing electric field strength, a decreasing bandgap and an increasing energy difference between the valence band maximum and the twisted band point are both predicted by the tight-binding model and the low energy model.

Simulating random alloy effects in III-nitride light emitting diodes

Statistical fluctuations in the alloy composition on the atomic scale can have important effects on electronic and optical properties of bulk materials and devices. In particular, carrier localization induced by alloy disorder has been a much discussed topic during the last decade with regard to III-nitride light emitting diodes (LEDs). Much experimental and theoretical work has been dedicated to the study of the effects of alloy disorder on carrier localization and finally on the efficiency and transport properties in such devices. Modeling approaches range from empirical analytical models down to atomistic ab initio ones, each with its advantages and disadvantages. In this tutorial, we discuss the simulation of alloy fluctuations in nitride quantum well LEDs by combining continuum device models and an atomistic empirical tight binding model, which provides a suitable compromise between atomic precision and computational effort.

The importance of relativistic effects on two-photon absorption spectra in metal halide perovskites

Despite intense research into the optoelectronic properties of metal halide perovskites (MHPs), sub-bandgap absorption in MHPs remains largely unexplored. Here we recorded two-photon absorption spectra of MHPs using the time-resolved microwave conductivity technique. A two-step upward trend is observed in the two-photon absorption spectrum for methylammonium lead iodide, and some analogues, which implies that the commonly used scaling law is not applicable to MHPs. This aspect is further confirmed by temperature-dependent conductivity measurements. Using an empirical multiband tight binding model, spectra for methylammonium lead iodide were calculated by integration over the entire Brillouin zone, showing compelling similarity with experimental results. We conclude that the second upward trend in the two-photon absorption spectrum originates from additional optical transitions to the heavy and light electron bands formed by the strong spin-orbit coupling. Hence, valuable insight can be obtained in the opto-electronic properties of MHPs by sub-bandgap spectroscopy, complemented by modelling.

Carrier Transport Mechanism via a High-k HfO₂ Thin Layer Between GaAs Layers.

Carrier transport mechanisms via a high-k gate dielectric material of hafnium dioxide (HfO2) between III-V GaAs were investigated by using a non-equilibrium Green's function (NEGF). The full band structure for the HfO2 layer was determined by using a sp3d5s* closest neighbor empirical tight-binding model. The band structure of the GaAs bulk was determined by using an empirical tight-binding model. The tunneling currents dependent on the thickness of the HfO2 layer with a GaAs layer were obtained by solving the NEGF in an open boundary condition. The applied voltage to obtain the tunneling currents through the HfO2 layer between the GaAs layers was higher than that for the Si/HfO2/Si structure. This was due to the much smaller energy difference between the conduction band edge (Ec) and the Fermi level (Ef) of the Si layer than that of the GaAs layer. The GaAs/HfO2/GaAs structure showed an increase in the leakage current in comparison with the Si/HfO2/Si structure.

Role of Valley Anisotropy in Optical Absorption of Monodisperse PbS Nanocrystals

We study light absorption by nearly monodisperse PbS nanocrystals grown in a glass matrix. The absorption spectra demonstrate a well-resolved structure at energies above the first absorption peak. The absorption cross sections are calculated with an empirical tight-binding model accounting for the quantum confinement, the band anisotropy, and valley splittings. Absorption spectra measured at 4K quantitatively agree with the atomistic calculations. This allows us to unambiguously ascribe the much-debated second absorption peak to the p-p optical transition and directly measure the splitting of excited p-states.

Symmetry-Based Tight Binding Modeling of Halide Perovskite Semiconductors.

On the basis of a general symmetry analysis, this paper presents an empirical tight-binding (TB) model for the reference Pm-3m perovskite cubic phase of halide perovskites of general formula ABX3. The TB electronic band diagram, with and without spin orbit coupling effect of MAPbI3 has been determined based on state of the art density functional theory results including many body corrections (DFT+GW). It affords access to various properties, including distorted structures, at a significantly reduced computational cost. This is illustrated with the calculation of the band-to-band absorption spectrum, the variation of the band gap under volumetric strain, as well as the Rashba effect for a uniaxial symmetry breaking. Compared to DFT approaches, this empirical model will help to tackle larger issues, such as the electronic band structure of large nanostructures, including many-body effects, or heterostructures relevant to perovskite device modeling suited to the description of atomic-scale features.

Interacting quasi-band theory for electronic states in compound semiconductor alloys: Wurtzite structure

This paper reports on the electronic states of compound semiconductor alloys of wurtzite structure calculated by the recently proposed interacting quasi-band (IQB) theory combined with empirical sp3 tight-binding models. Solving derived quasi-Hamiltonian 24 × 24 matrix that is characterized by the crystal parameters of the constituents facilitates the calculation of the conduction and valence bands of wurtzite alloys for arbitrary concentrations under a unified scheme. The theory is applied to III–V and II–VI wurtzite alloys: cation-substituted Al1−xGaxN and Ga1−xInxN and anion-substituted CdS1−xSex and ZnO1−xSx. The obtained results agree well with the experimental data, and are discussed in terms of mutual mixing between the quasi-localized states (QLS) and quasi-average bands (QAB): the latter bands are approximately given by the virtual crystal approximation (VCA). The changes in the valence and conduction bands, and the origin of the band gap bowing are discussed on the basis of mixing character.

The Electron-Hole Interactions in Si Hydrogenate Nanocrystals: Tight-Binding Theory

Theory of electronic and optical properties of excitonic states confining in Si nanocrystals is presented. The electron and hole states are numerically computed using the atomistic empirical tight-binding Hamiltonian including the spin-orbit coupling together with the first nearest-neighboring interaction. We theoretically study the electron-hole interactions in spherical silicon hydrogenated nanocrystals by incorporating coulomb and exchange interaction into the empirical tight-binding model. The comparisons of coulomb and exchange energies with empirical pseudopotential method (EPM), tight-binding method (TB), effective-mass approximation (EMA) and ab initio calculations are quantitatively realized. Finally the energies of the excitonic ground states obtained from diagonalizing the tight-binding configuration-interaction scheme are in a good agreement with other theoretical and experimental data.

Room temperature observation of quantum confinement in single InAs nanowires.

Quantized conductance in nanowires can be observed at low temperature in transport measurements; however, the observation of sub-bands at room temperature is challenging due to temperature broadening. So far, conduction band splitting at room temperature has not been observed in III-V nanowires mainly due to the small energetic separations between the sub-bands. We report on the measurement of conduction sub-bands at room temperature, in single InAs nanowires, using Kelvin probe force microscopy. This method does not rely on charge transport but rather on measurement of the nanowire Fermi level position as carriers are injected into a single nanowire transistor. As there is no charge transport, electron scattering is no longer an issue, allowing the observation of the sub-bands at room temperature. We measure the energy of the sub-bands in nanowires with two different diameters, and obtain excellent agreement with theoretical calculations based on an empirical tight-binding model.

Variation in the structural and optical properties of CdSe/ZnS core/shell nanocrystals with ratios between core and shell radius

The structural and optical properties of CdSe/ZnS core/shell nanocrystals are studied using a combination of valence force field and sp3s⁎ empirical tight-binding model with the aim of studying the relative impacts of ratios (σ) between core and shell radius in the fixed volume. The control and tunability of the strain distribution, single-particle spectra, density of states, overlaps, oscillation strengths, excitonic states and radiative lifetimes by properly engineering structural ratios (σ) are mainly elucidated and quantified. The calculations highlight that the sensitivity of these physical properties with the aspect ratios (σ) is mainly presented. An excellent agreement with literature experiments is achieved from this model. The theoretical results shed light on to the electronic configuration of CdSe/ZnS core/shell nanocrystals and can enable the use of CdSe/ZnS core/shell nanocrystals for further feasible applications.

Accelerating atomistic calculations of quantum energy eigenstates on graphic cards

Electronic properties of nanoscale materials require the calculation of eigenvalues and eigenvectors of large matrices. This bottleneck can be overcome by parallel computing techniques or the introduction of faster algorithms. In this paper we report a custom implementation of the Lanczos algorithm with simple restart, optimized for graphical processing units (GPUs). The whole algorithm has been developed using CUDA and runs entirely on the GPU, with a specialized implementation that spares memory and reduces at most machine-to-device data transfers. Furthermore parallel distribution over several GPUs has been attained using the standard message passing interface (MPI). Benchmark calculations performed on a GaN/AlGaN wurtzite quantum dot with up to 600,000 atoms are presented. The empirical tight-binding (ETB) model with an sp3d5s∗+spin–orbit parametrization has been used to build the system Hamiltonian (H).

Phonon decay in silicon nanocrystals: Fast phonon recycling

We present a theory of electron-phonon interaction and phonon decay in Si nanocrystals based on $s{p}^{3}{d}^{5}{s}^{*}$ empirical tight-binding model and anharmonic Keating model. We demonstrate that the time of optical phonon emission by hot carriers in Si nanocrystal lies in the subpicosecond time range. However, due to the fast phonon recycling, the energy relaxation rate is determined not by the phonon emission but by the phonon decay rate. The decay rate of the optical phonon into two phonons of smaller energy is found to be in the 1--10 ps range. It is this anharmonic phonon decay process that may control the energy relaxation rate of excited carriers in Si nanocrystals.

Electronic properties ofδ-doped Si:P and Ge:P layers in the high-density limit using a Thomas-Fermi method

The Thomas-Fermi-Dirac (TFD) approximation and an sp3d5s* tight binding method were used to calculate the electronic properties of a delta-doped phosphorus layer in silicon. This self-consistent model improves on the computational efficiency of "more rigorous" empirical tight binding and ab initio density functional theory models without sacrificing the accuracy of these methods. The computational efficiency of the TFD model provides improved scalability for large multi-atom simulations, such as of nanoelectronic devices that have experimental interest. We also present the first theoretically calculated electronic properties of a delta-doped phosphorus layer in germanium as an application of this TFD model.

Interplay between Coulomb interaction and quantum-confined Stark-effect in polar and nonpolar wurtzite InN/GaN quantum dots

In this paper we systematically analyze the electronic structures of polar and nonpolar wurtzite-InN/GaN quantum dots and their modification due to the quantum-confined Stark effect caused by intrinsic fields. This is achieved by combining continuum elasticity theory with an empirical tight binding model to describe the elastic and single-particle electronic properties in these nitride systems. Based on these results, a many-body treatment is used to determine optical absorption spectra. The efficiency of optical transitions depends on the interplay between the Coulomb interaction and the quantum-confined Stark effect. We introduce an effective confinement potential which represents the electronic structure under the influence of the intrinsic polarization fields and calculate the needed strength of Coulomb interaction to diminish the separation of electrons and holes.

Electron transport in nano-scaled piezoelectronic devices

The Piezoelectronic Transistor (PET) has been proposed as a post-CMOS device for fast, low-power switching. In this device, the piezoresistive channel is metalized via the expansion of a relaxor piezoelectric element to turn the device on. The mixed-valence compound SmSe is a good choice of PET channel material because of its isostructural pressure-induced continuous metal insulator transition, which is well characterized in bulk single crystals. Prediction and optimization of the performance of a realistic, nano-scaled PET based on SmSe requires the understanding of quantum confinement, tunneling, and the effect of metal interface. In this work, a computationally efficient empirical tight binding (ETB) model is developed for SmSe to study quantum transport in these systems and the scaling limit of PET channel lengths. Modulation of the SmSe band gap under pressure is successfully captured by ETB, and ballistic conductance shows orders of magnitude change under hydrostatic strain, supporting operability of the PET device at nanoscale.

Complete fabrication study of InAs/GaSb superlattices for long-wavelength infrared detection

We report a complete fabrication process of InAs/GaSb type-II superlattice long-wavelength infrared photodiodes with band structure modelling, materials growth and device fabrication. The optoelectronic property of InAs/GaSb type-II superlattices is simulated by the modified empirical tight binding model for interface stoichiometry. We chose target superlattices from the simulation results. To obtain good lattice matched and high interface quality material, a two-step strain balance method of migration-enhanced epitaxy is applied in the growth of superlattices. The property of superlattices is matched well with the simulation results. Finally, photodiodes with 50% cutoff wavelength of 8.72 µm and peak detectivity of 8.1 × 1010 cm Hz1/2 W−1 at 77 K are demonstrated.

Theory of band gap bowing of disordered substitutional II–VI and III–V semiconductor alloys

For a wide class of technologically relevant compound III-V and II-VI semiconductor materials AC and BC mixed crystals (alloys) of the type A(x)B(1-x)C can be realized. As the electronic properties like the bulk band gap vary continuously with x, any band gap in between that of the pure AC and BC systems can be obtained by choosing the appropriate concentration x, granted that the respective ratio is miscible and thermodynamically stable. In most cases the band gap does not vary linearly with x, but a pronounced bowing behavior as a function of the concentration is observed. In this paper we show that the electronic properties of such A(x)B(1-x)C semiconductors and, in particular, the band gap bowing can well be described and understood starting from empirical tight binding models for the pure AC and BC systems. The electronic properties of the A(x)B(1-x)C system can be described by choosing the tight-binding parameters of the AC or BC system with probabilities x and 1-x, respectively. We demonstrate this by exact diagonalization of finite but large supercells and by means of calculations within the established coherent potential approximation (CPA). We apply this treatment to the II-VI system Cd(x)Zn(1-x)Se, to the III-V system In(x)Ga(1-x)As and to the III-nitride system Ga(x)Al(1-x)N.