Empirical Tight-binding Model Research Articles

Multiband and multidimensional quantum transport

We give an overview of a numerically stable and efficient method for computing transmission coefficients in semiconductor heterostructures using multiband band structure models. The multiband quantum transmitting boundary method (MQTBM) has been successfully implemented for the empirical tight-binding model, the effective bond orbital, the k·p model, and the pseudopotential method. It has been used extensively in the investigation of band structure effects such as valley mixing and band mixing. We use a GaAs/AlAs double barrier heterostructure and an InAs/GaSb/AlSb interband tunnel device to illustrate the applications of this method to the phenomena of X-point tunneling, hole tunneling, and interband magneto-tunneling. We then review a closely related method, the open-boundary planar supercell stack method (OPSSM), as a means for treating 3D quantum transport in mesoscopic tunnel structures. The flexibility of the method allows us to examine a variety of physical phenomena relevant to quantum transport, including alloy disorder, interface roughness, defect impurities, and 0D, 1D, and 2D quantum confinement, in device geometries ranging from double barrier heterostructures to quantum wire electron waveguides. As examples, we examine double barrier structures with interface roughness, resonant tunneling through self-organized InAs quantum dots, and MOS tunnel structures with non-uniform ultra-thin oxide layers.

Structure of high temperature fluid selenium

Monte Carlo simulations based on a semi empirical tight binding model including dispersion forces were performed to study liquid selenium at temperatures between 600 and 2000 K. The atomic structures obtained are in agreement with the X-ray scattering and extended X-ray absorption fine structure (EXAFS) data in a range of temperatures and densities. A correlation between the conductivity of high temperature fluid selenium and the degree of branching and breaking of the selenium chains is observed.

Simulations of GaN using an environment-dependent empirical tight-binding model

We have developed an empirical, total-energy tight-binding model for gallium nitride which we have used in molecular-dynamics simulations of the bulk material as well as several native point defects. The Ga-N and N-N interactions are treated using the standard two-center approximation whereas the Ga-Ga interactions contain three-body effects that make these interactions sensitive to the local environment of the Ga atoms, thus making the model more transferrable than a strictly two-center model. The parameters of this model provide a good fit to experimental data and ab initio calculations.

Theory of electronic and optical properties of 3C-SiC

We study the electronic and optical properties of cubic (3C) SiC, using a combination of first-principles and tight-binding electronic structure calculations. We employ pseudopotential density functional theory calculations, with appropriate corrections to the energy of conduction bands, to investigate the band structure of this material and obtain band gaps that are in agreement with experimental results. The optical properties are then studied within the framework of the empirical tight-binding model, which is fitted to reproduce the first-principles calculations. This approach allows for a thorough investigation of the dielectric functions, the reflectivity, and the refractive index. Critical points are identified and connected to the appropriate transitions in the band structure. The results are in good agreement with available experimental data. In addition, we investigate spin splitting effects.

Piezooptical Properties of GaAs and InP

An empirical tight-binding model with an orthogonal sp 3 set of orbitals, interactions up to second neighbor and spin-orbit coupling, is used to describe the electronic and optical properties of bulk as well as strained GaAs and InP. The band structure and the dielectric functions of bulk GaAs and InP are calculated and found to be in good agreement with experimental results. The deformation potentials for the E 1 and E 1 + Δ 1 transitions, for uniaxial strain along the [001] and [111] directions, are evaluated. Also the piezooptical tensor components P 11 , P 12 , P 44 , as well as the differential reflectivity were calculated. Finally the refractive index as a function of energy is calculated for hydrostatic pressures in the range of 0 to 8 GPa. The theoretically obtained results are in good agreement with existing experimental data.

Theory of Piezo-Optical Properties for Group IV Elements and III-V Compounds

An empirical tight-binding model with an orthogonal sp3 set of orbitals is used to describe the optical properties of strained Si, Ge, GaAs and InP. The piezo-optical tensor components Pij are calculated. The dielectric constant as a function of pressure is evaluated for hydrostatic pressures in the range of 0 to 8 GPa. The theoretically obtained results are in good agreement with existing experimental data.

Ordering of conduction band states in thin-layer superlattices

The electronic structures of thin-layer superlattices (SLs) are investigated versus the SL layer thicknesses (m, n) and the band offsets. The calculations are based on the empirical tight-binding model, which includes only nearest-neighbour interactions. Particular attention is given to the effect of the interface parametrization on the SL electronic properties. This is done, mainly, by varying the band offsets over a sufficiently broad range. The results show that the existence of type-II behaviour in the ultrathin-layer SLs necessitates a large valence band offset and small conduction band offset . Providing that these offset values are achieved, it is found that the highest state of the valence band is always confined to the GaAs slabs whereas the bottom state of the conduction band shows different behaviours as it is sensitive to band-mixing effects. It is due to these mixing effects that most of the ultrathin-layer SLs (with ) behave as type-II heterostructures, where the electrons are localized in the AlAs valley. The rest of the ultrathin-layer SLs behave as type-I heterostructures with a direct bandgap at the point, whenever the GaAs slabs are thick enough to make the electron confinement energy small in the GaAs wells. For thick-layer SLs, our results suggest the existence of a critical barrier thickness, beyond which the GaAs wells become completely decoupled and the SL behaves as a type I heterostructure. The estimated critical layer thickness, for the crossover from type-I to type-II behaviour, is for the SLs with m = n when using VBO = 0.56 eV. This -value is consistent with the photoreflectance experiments. The relevance of our work to photonic device applications is discussed further.

Tight-binding design of intersubband transitions in InGaAs/AlAs quantum heterostructures grown pseudomorphically on InP

Intersubband optical properties of InGaAs/AlAs quantum heterostructures grown on InP are analysed. Our calculations based on a recently developed empirical tight-binding model show that the system is ideally suited for the tailoring of optical properties in a wide range. In particular, structures matching the frequency requirements of ultra-fast fibre optics communications are presented and discussed.

Electronic structure of (001) AlAs–InAs–GaAs multilayer structures

The electronic structure of different (001) (AlAs) m (InAs) 1(GaAs) n multilayer structures is studied. We have thus seen the influence of the relative thicknesses of the constituent materials and of the positions of the InAs principal layers in the multilayer structures on the energy eigenstates and on their spatial localization. The calculations are based on an sp 3s * empirical tight-binding model and on the surface Green function matching method.

Effective masses of wurtzite GaN calculated from an empirical tight binding model

The energy band structure of wurtzite GaN is calculated using an sp 3d 5 - sp 3 empirical tight-binding method (ETBM) that includes the spin-orbit interaction. The model incorporates all nearest-neighbor and some second-nearest neighbor interactions within the two-center approximation. The second-nearest neighbor interactions excluded are the cation-cation interactions involving the Ga 3 d orbital. The effective masses of the conduction and A, B, and C valence bands have been calculated and found to be in good agreement with published experimental data.

Multiband quantum transport with Γ– X valley-mixing via evanescent states

Calculations of quantum transport of electrons through heterostructures are presented based on an empirical tight-binding model where an evanescent-wave matching at a heterointerface as well as the Γ– X valley-mixing effects are duly taken into account. Our results show, in particular, that current–voltage ( I– V) characteristics of a GaAs/AlAs/GaAs single barrier diode have extra structures associated with the X valley tunneling, which can illustrate the experimental results. It should also be noted that the matching of evanescent electron modes is essentially necessary to include the valley-mixing effects for GaAs/AlAs heterostructures, since a lattice-translational symmetry is lacking in the growth direction in such structures.

Piezooptical Properties of Si

The deformation potentials and the piezooptical properties of Si, for strain along the [001] and [111] directions, are investigated with the use of a realistic empirical tight-binding model. The values, as well as their sign, of the deformation potential constants D 1 1 , D 1 5 , D 3 3 , and D 3 5 for the variation of the critical energy E 1 are evaluated for uniaxial and biaxial strain. The sign is found to be negative for D 1 1 , D 3 3 , and D 3 5 , and positive for D 1 5 . The dielectric function of Si under pressure, as well as the reflectivity and the linear piezooptical tensor components P 11 (ω), P 12 (ω) and P 44 (ω) are also evaluated. The main structures in P ij are located around the critical points E 1 and E 2 .

Piezooptical Properties of Si

The deformation potentials and the piezooptical properties of Si, for strain along the [001] and [111] directions, are investigated with the use of a realistic empirical tight-binding model. The values, as well as their sign, of the deformation potential constants D11, D51, D33, and D53 for the variation of the critical energy E1 are evaluated for uniaxial and biaxial strain. The sign is found to be negative for D11, D33, and D53, and positive for D51. The dielectric function of Si under pressure, as well as the reflectivity and the linear piezooptical tensor components P11(ω), P12(ω) and P44(ω) are also evaluated. The main structures in Pij are located around the critical points E1 and E2.

Transition behavior from coupled to uncoupled GaAs/InAs double quantum wells

The electronic structures of the InAs single and double quantum wells buried in bulk GaAs (001) are presented based on the sp3s* empirical tight-binding model. Both electrons and holes are found to be confined in the c-axis direction around the inserted InAs monomolecular plane with a localization length of the order of 110 Å. The inserted InAs monolayer is, therefore, playing the role of a quantum well for all charge carriers and, as a consequence, the formed heterojunction is of type I. The system, composed of two InAs monolayers buried in GaAs and separated by N monolayers of GaAs, is studied versus the barrier thickness (N). Our results of the variation of band gap energy as a function of barrier thickness (N) are in excellent agreement with the available photoluminescence data when a small valence band offset (of order 80 meV including the spin-orbit effects) is employed. A critical barrier thickness of about 220 Å is suggested to decouple the InAs quantum wells.

Effect of hydrostatic strain on the band gap of wurtzite GaN

The effect of hydrostatic strain on wurtzite GaN is studied theoretically using an sp 3d 5-sp 3 empirical tight-binding model (ETBM). The model incorporates all nearest-neighbor and some second-nearest neighbor interactions within the two-center approximation. The second-nearest neighbor interactions excluded are the cation-cation interactions involving the Ga 3d orbital. Strain is included by scaling the two-center integrals appropriately. The strain is, therefore, modeled without invoking deformation potential theory, eliminating the need for additional strain parameters. The effective band gap has been calculated for various hydrostatic strains and the results compared with published experimental data. The theory reproduces the sublinear dependence of the band gap with pressure, and the calculated pressure dependence of the band gap and the hydrostatic deformation potential are found to agree well with experiment and with previously published results calculated via ab initio techniques, showing the validity of the present approach.

Piezo-optical properties of Ge

The piezo-optical properties of Ge, for pressure along the [001] and [111] directions, are calculated with the use of a realistic empirical tight-binding model. The real and imaginary part of components ${P}_{11}(\ensuremath{\omega})$, ${P}_{12}(\ensuremath{\omega})$, and ${P}_{44}(\ensuremath{\omega})$ of the linear piezo-optical tensor for Ge are evaluated. The main structures in ${P}_{\mathrm{ij}}$ are located around the ${E}_{1}$ and ${E}_{2}$ critical points. Deformation potential constants ${D}_{1}^{1}$, ${D}_{1}^{5}$, ${D}_{3}^{3}$, and ${D}_{3}^{5}$, for the ${E}_{1}\ensuremath{-}{(E}_{1}+{\ensuremath{\Delta}}_{1})$ transitions are also evaluated. The theoretically obtained results are in good agreement with existing experimental values.

Electronic states in diffused quantum wells

In the present study we calculate the energy values and the spatial distributions of the bound electronic states in some diffused quantum wells. The calculations are performed within the virtual crystal approximation, sp3s* spin dependent empirical tight-binding model and the surface Green function matching method. A good agreement is found between our results and experimental data obtained for AlGaAs/GaAs quantum wells with thermally induced changes in the profile at the interfaces. Our calculations show that for diffusion lengths LD=0−20 Å the optical transition between the ground electron and hole states is less sensitive to the LD changes than the optical transitions between the excited electron and hole states. For diffusion lengths LD=20−100 Å, the optical transition between the second excited states is not sensitive to the diffusion length, but the other optical transitions display large “blue shifts” as LD increases. The observed dependence is explained in terms of the bound states spatial distributions.

Simulation of Vacancy Pairs in GaN Using Tight-Binding Molecular Dynamics

AbstractThe electronic structure, geometry and energetics of Ga vacancy pairs and N vacancy pairs in both wurtzite and zincblende GaN are investigated via molecular dynamics (MD) simulations using an empirical tight-binding (TB) model with total energy capabilities and supercells containing up to 216 atoms. Our calculations suggest that, by pairing, N vacancies, which in isolation act as shallow donors, can lower their collective formation energy by about 5 eV. In doing so, however, these N vacancies lose their shallow-donor character as the lattice relaxes in response to this aggregation. Contrasting with the N vacancies, the Ga vacancies are found to retain their isolated shallow acceptor behavior and do not gain significant energy upon aggregation. The possible implications for larger aggregate defects are discussed.

Electronic structure of (001) superlattices

The electronic structure of (001) superlattices is studied for many combinations of values of k,l,m and n. We have charted the regions of indirect gap and direct gap respectively by studying energy eigenvalues, especially band-edge levels, and also the spatial dependence of the local amplitude of some representative states, in order to obtain information on the confinement problems. The calculations are based on an empirical tight-binding model and on the surface Green-function-matching method.

Electronic states of (211) [formula omitted] quantum wells

The electronic states of (211) AlAs GaAs quantum wells at the k = (0,0) point are studied for different well thicknesses in the range 0 < d ≤ 60 A ̊ . The calculations are performed by using a sp 3s∗ empirical tight-binding model together with the surface Green's-function matching method. The evolution of the energy for the different bound states versus the variation of d and the orbital character of the bound states are studied, and a comparison is made with the (001) and (311) quantum wells.