Empirical Tight-binding Model Research Articles

Band structure of hydrogenated Si nanosheets and nanotubes

The band structures of fully hydrogenated Si nanosheets and nanotubes are elucidated bythe use of an empirical tight-binding model. The hydrogenated Si sheet is a semiconductorwith an indirect band gap of about 2.2 eV. The symmetries of the wavefunctions allow us toexplain the origin of the gap. We predict that, for certain chiralities, hydrogenated Sinanotubes represent a new type of semiconductor, one with coexisting directand indirect gaps of exactly the same magnitude. This behavior is different fromthat governed by the Hamada rule established for non-hydrogenated carbon andsilicon nanotubes. A comparison to the results of an ab initio calculation is made.

Multiband tight-binding theory of disordered A x B1- x C semiconductor quantum dots

Zero-dimensional nanocrystals, as obtained by chemical synthesis, offer a broad range of applications, as their spectrum and thus their excitation gap can be tailored by variation of their size. Additionally, nanocrystals of the type ABC can be realized by alloying of two pure compound semiconductor materials AC and BC, which allows for a continuous tuning of their absorption and emission spectrum with the concentration x. We use the single-particle energies and wave functions calculated from a multiband sp^3 empirical tight-binding model in combination with the configuration interaction scheme to calculate the optical properties of CdZnSe nanocrystals with a spherical shape. In contrast to common mean-field approaches like the virtual crystal approximation (VCA), we treat the disorder on a microscopic level by taking into account a finite number of realizations for each size and concentration. We then compare the results for the optical properties with recent experimental data and calculate the optical bowing coefficient for further sizes.

Simulation of AlGaN/GaN high-electron-mobility transistor gauge factor based on two-dimensional electron gas density and electron mobility

The gauge factor of AlGaN/GaN high-electron-mobility transistor was determined theoretically, considering the effect of stress on the two-dimensional electron gas (2DEG) sheet carrier density and electron mobility. Differences in the spontaneous and piezoelectric polarization between the AlGaN and GaN layers, with and without external mechanical stress, were investigated to calculate the stress-altered 2DEG density. Strain was incorporated into a sp3d5–sp3 empirical tight-binding model to obtain the change in electron effective masses under biaxial and uniaxial stress. The simulated longitudinal gauge factor (−7.9±5.2) is consistent with experimental results (−2.4±0.5) obtained from measurements eliminating parasitic charge trapping effects through continuous subbandgap optical excitation.

Accurate and computationally efficient third-nearest-neighbor tight-binding model for large graphene fragments

Owing to the large sizes involved, most calculations of the electronic properties of graphene and its fragments involve empirical tight-binding models restricted to nearest-neighbor interactions only. Such approaches fail to predict key electronic and magnetic properties, however, and rely on assumed geometries. While alternative approaches based on density-functional theory are much more successful in predicting properties, they are often computationally prohibitive to apply. We introduce a simple third-nearest-neighbor $\ensuremath{\pi}$-only tight-binding approach that maintains the computational efficiency of the empirical method while achieving the accuracy of the density-functional methods to which it is parametrized. It yields both nuclear geometries and electronic structures of graphene fragments, providing an efficient and accurate replacement for traditional tight-binding models of graphene.

Ab initio calculation of band edges modified by (001) biaxial strain in group IIIA–VA and group IIB–VIA semiconductors: Application to quasiparticle energy levels of strained InAs/InP quantum dot

Results of first-principles full potential calculations of absolute position of valence and conduction energy bands as a function of (001) biaxial strain are reported for group IIIA–VA (InAs, GaAs, InP) and group IIB–VIA (CdTe, ZnTe) semiconductors. Our computational procedure is based on the Kohn–Sham form of density functional theory (KS DFT), local spin density approximation (LSDA), variational treatment of spin-orbital coupling, and augmented plane wave plus local orbitals method (APW+lo). The band energies are evaluated at lattice constants obtained from KS DFT total energy as well as from elastic free energy. The conduction band energies are corrected with a rigid shift to account for the LSDA band gap error. The dependence of band energies on strain is fitted to polynomial of third degree and results are available for parameterization of biaxial strain coupling in empirical tight-binding models of IIIA–VA and IIB–VIA self-assembled quantum dots (SAQDs). The strain effects on the quasiparticle energy levels of InAs/InP SAQD are illustrated with empirical atomistic tight-binding calculations.

Environment-dependent Empirical Tight-binding Molecular Dynamics Study of Amorphous Silicon

A 216-atom computer model of amorphous silicon is generated by rapid quenching from the silicon melt using an environment-dependent empirical tight-binding (EDETB) potential model. The pair correlation function, the bond angle distribution, and the electronic density of states are in good agreement with available experimental data and ab-initio molecular dynamics results. The quenching rate appears to play an important role in the structures of the computer model. If possible, a quenching rate that approaches the experimental value should be used to build a more structurally reliable computer model.

Multiband effective bond-orbital model for nitride semiconductors with wurtzite structure

A multiband empirical tight-binding model for group-III-nitride semiconductors with a wurtzite structure has been developed and applied to both bulk systems and embedded quantum dots. As a minimal basis set we assume one s-orbital and three p-orbitals, localized in the unit cell of the hexagonal Bravais lattice, from which one conduction band and three valence bands are formed. Non-vanishing matrix elements up to second nearest neighbors are taken into account. These matrix elements are determined so that the resulting tight-binding band structure reproduces the known Gamma-point parameters, which are also used in recent kp-treatments. Furthermore, the tight-binding band structure can also be fitted to the band energies at other special symmetry points of the Brillouin zone boundary, known from experiment or from first-principle calculations. In this paper, we describe details of the parametrization and present the resulting tight-binding band structures of bulk GaN, AlN, and InN with a wurtzite structure. As a first application to nanostructures, we present results for the single-particle electronic properties of lens-shaped InN quantum dots embedded in a GaN matrix.

Multiband description of the optical properties of zincblende nitride quantum dots

We use the single-particle energies and wave functions calculated from an effective bond-orbital model and a microscopic empirical tight-binding model in combination with the configuration-interaction scheme to calculate the optical properties of cubic GaN/AlN quantum dots. Special attention is paid to the possible influence of the weak spin-orbit coupling on the optical spectra. The results are compared to recent experimental data. In agreement with the experiments, we find a strong polarization anisotropy of the excitonic transitions in the microscopic empirical tight-binding model, while the effective bond-orbital model misses this anisotropy in the absence of a piezoelectric field and an atomistic strain field. This missing anisotropy can be attributed to the artificially increased symmetry of the combined system of quantum dot geometry and underlying lattice structure.

Comparison of atomistic and continuum theoretical approaches to determine electronic properties of GaN/AlN quantum dots

In this work we present a comparison of multiband $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ 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 zinc-blende structure. For the system under consideration, we find very good agreement between the results of the microscopic models and the eight-band $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ formalism, in contrast to a $6+2$-band $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ model, where conduction band and valence band are assumed to be decoupled. This indicates a surprisingly strong coupling between conduction- and valence-band states for the wide-band-gap materials GaN and AlN. Special attention is paid to the possible influence of the weak spin-orbit coupling on the localized single-particle wave functions of the investigated structure.

Ab-initiocalculations of spin tunneling through an indirect barrier

We use a fully relativistic layer Green's functions approach to investigate spin-dependent tunneling through a symmetric indirect band gap barrier like GaAs/AlAs/GaAs heterostructure along [100] direction. The method is based on Linear Muffin Tin Orbitals and it is within the Density Functional Theory (DFT) in the Local Density Approximation (LDA). We find that the results of our {\it ab-initio} calculations are in good agreement with the predictions of our previous empirical tight binding model [Phys. Rev. {\bf B}, 075313 (2006)]. In addition we show the $k_{||}$-dependence of the spin polarization which we did not previously include in the model. The {\it ab-initio} calculations indicate a strong $k_{||}$-dependence of the transmission and the spin polarization due to band non-parabolicity. A large window of 25-50 % spin polarization was found for a barrier of 8 AlAs monolayers at $k_{||}$ = 0.03 $2\pi/a$. Our calculations show clearly that the appearance of energy windows with significant spin polarization depends mostly on the location of transmission resonances and their corresponding zeros and not on the magnitude of the spin splitting in the barrier.

Interplay between Tamm-like and Shockley-like surface states in photonic crystals

The goal of this paper is to demonstrate that surface states in a defect chain embedded in a host photonic crystal can be viewed as an interplay between the Tamm-like and Shockley-like states. The defect chain with alternating strong and weak bonds is analyzed using an empirical tight-binding model and the finite difference time domain technique. We investigate how the spectrum of the structures changes with different termination of the chain. It is shown that under certain conditions the Tamm and Shockley states can coexist or can transform from one to the other. These important features allow for controlling the surface states in photonic crystals in frequency, location, and strength.

Existence and control of Shockley surface states of a one-dimensional defect chain in a photonic crystal

We present detailed results of analytical and numerical investigation of the Shockley surface states in photonic crystals doped with a chain of alternating s- and p-type defects. Conditions for the existence and control of such surface states are studied using the empirical tight-binding model and verified by the finite-difference time-domain technique. We show for the first time, to our knowledge, that, in contrast to the case of solids, the Shockley states in photonic crystals with complete unit cells of defects do not appear simultaneously with the opening of the inverted bandgap between s and p bands. Rather, the width of the inverted bandgap must reach a critical value equal to the separation between the discrete levels. This results in a system size effect of the Shockley states in photonic crystals. We show how such system size effect can be used to control the surface states. We also demonstrate the control of the Shockley states by controlling the overlap of s and p bands, achieved through change in either the radius of one of the defects or the refractive index via electro-optical effects.

Electronic and transport properties of silicon nanowires

The electronic, structural and transport properties of silicon nanowires have been investigated with different approaches. The Empirical Tight-Binding model (ETB) and Linear Combination of Bulk Bands (LCBB) method are used to calculate effect of quantum confinement on electronic energies, bandgap and effective masses in silicon nanowires in function of Si cell size. Both hydrogenated and SiO2 terminated silicon surfaces are studied. Transport properties of nanowires are obtained by applying the Non-Equilibrium Green Function (NEGF) method. NEGF approach has been used to describe nanoMOSFET devices based on Silicon nanowires.

Tight-binding theory ofZnS∕CdSnanoscale heterostructures: Role of strain anddorbitals

The electronic and optical properties of colloidal multishell $\mathrm{Zn}\mathrm{S}∕\mathrm{Cd}\mathrm{S}$ nanoscale heterostructures have been studied in the framework of empirical tight-binding models. Our approach takes into account the effects of the strain caused by the large lattice mismatch at the interface between the two materials. We show that the inclusion of $d$ orbitals into a minimal basis set is necessary to provide a correct description of the ZnS and CdS clads that are only a few monolayers (MLs) thick. The role of strain is also important. Strain shifts of the electron energy levels are highly dependent on the thickness of the core and shell materials. The effects of strain in the valence band are more complex. In $\mathrm{Cd}\mathrm{S}∕\mathrm{Zn}\mathrm{S}$ structures, strain can change the symmetry of the ground hole state. In $\mathrm{Zn}\mathrm{S}∕\mathrm{Cd}\mathrm{S}$ systems, strain lowers the energy of the ground hole state of $P$ symmetry with respect to the first $S$ symmetry state. Lattice relaxation also redistributes the charge densities of electron and hole states. The predicted absorption onsets resulting from our model are in good agreement with the experimental data and in better agreement with data than previous theories without strain and $d$ orbitals.

Empirical tight-binding model for titanium phase transformations

For a previously published study of the titanium hexagonal close packed $(\ensuremath{\alpha})$ to omega $(\ensuremath{\omega})$ transformation, a tight-binding model was developed for titanium that accurately reproduces the structural energies and electron eigenvalues from all-electron density-functional calculations. We use a fitting method that matches the correctly symmetrized wave functions of the tight-binding model to those of the density-functional calculations at high symmetry points. The structural energies, elastic constants, phonon spectra, and point-defect energies predicted by our tight-binding model agree with density-functional calculations and experiment. In addition, a modification to the functional form is implemented to overcome the ``collapse problem'' of tight binding, necessary for phase transformation studies and molecular dynamics simulations. The accuracy, transferability, and efficiency of the model makes it particularly well suited to understanding structural transformations in titanium.

Excitation and chirality dependence of the exciton-phonon coupling in carbon nanotubes

Based on the empirical nearest-neighbor tight-binding model, we predict that the dependence of the cross section of the resonance Raman scattering from the radial breathing mode of a carbon nanotube multiplied by the fourth power of the nanotube radius is a quadratic function of a newly introduced parameter characterizing nanotube chirality. This dependence reflects the dependence of the exciton-phonon coupling matrix element on the nanotube radius and chiral angle. We perform Raman scattering measurements on nanotubes in solution and confirm the predicted parabolic dependence assuming a close-to-uniform distribution of chiral angles in nanotube samples. The deviation of the experimental points from the parabola provides information about chirality distribution of nanotubes in a sample, which opens new horizons in characterization of samples containing nanotubes of different chiralities.

Voltage-controlled spin injection in a(Ga,Mn)As∕(Al,Ga)AsZener diode

The spin polarization of the electron current in a p-(Ga,Mn)As-n-(Al,Ga)As-Zener tunnel diode, which is embedded in a light-emitting diode, has been studied theoretically. A series of self-consistent simulations determines the charge distribution, the band bending, and the current-voltage characteristics for the entire structure. An empirical tight-binding model, together with the Landauer- Buttiker theory of coherent transport has been developed to study the current spin polarization. This dual approach allows to explain the experimentally observed high magnitude and strong bias dependence of the current spin polarization.

Optical matrix elements in tight-binding models with overlap

We investigate the effect of orbital overlap on optical matrix elements in empirical tight-binding models. Empirical tight-binding models assume an orthogonal basis of (atomiclike) states and a diagonal coordinate operator which neglects the intra-atomic part. It is shown that, starting with an atomic basis which is not orthogonal, the orthogonalization process induces intra-atomic matrix elements of the coordinate operator and extends the range of the effective Hamiltonian. We analyze simple tight-binding models and show that nonorthogonality plays an important role in optical matrix elements. In addition, the procedure gives formal justification to the nearest-neighbor spin-orbit interaction introduced by Boykin [Phys. Rev. B 57, 1620 (1998)] in order to describe the Dresselhaus term which is neglected in empirical tight-binding models.

Electronic states in silicon quantum dot devices

Electronic states in Si quantum dots are theoretically examined, taking account of a multivalley structure of conduction band. Using the effective mass approximation, we find that one-electron levels in different valleys are degenerate when the confinement potential is smooth. The exchange interaction between different valleys is negligibly small, which results in the degeneracy of different spin states. In the presence of intervalley scattering, caused by e.g. impurities within the dot, sharp edge of the confinement potential, the degenerate one-electron levels are split and the lowest spin state is realized. To confirm the validity of the effective mass approximation, we calculate the electronic states in an empirical tight-binding model, considering the atomic structure in Si quantum dots. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Effect of wetting layers on the strain and electronic structure of InAs self-assembled quantum dots

The effect of wetting layers on the strain and electronic structure of InAs self-assembled quantum dots grown on GaAs is investigated with an atomistic valence-force-field model and an empirical tight-binding model. By comparing a dot with and without a wetting layer, we find that the inclusion of the wetting layer weakens the strain inside the dot by only 1% relative change, while it reduces the energy gap between a confined electron and hole level by as much as 10%. The small change in the strain distribution indicates that strain relaxes only little through the thin wetting layer. The large reduction of the energy gap is attributed to the increase of the confining-potential width rather than the change of the potential height. First-order perturbation calculations or, alternatively, the addition of an InAs disk below the quantum dot confirm this conclusion. The effect of the wetting layer on the wave function is qualitatively different for the weakly confined electron state and the strongly confined hole state. The electron wave function shifts from the buffer to the wetting layer, while the hole shifts from the dot to the wetting layer.